diff --git a/manuscript/BrJG_submit.cls b/manuscript/BrJG_submit.cls new file mode 100755 index 0000000..6314a55 --- /dev/null +++ b/manuscript/BrJG_submit.cls @@ -0,0 +1,325 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% +%% RBGf Class for LaTeX files +%% August 2021 +%% +%% This file is for the exclusive use of the editorial board of the Brazilian Journal of Geophysics +%% +%% Initial Class Provide by: +%% +%% Thiago R Almeida +%% +%% Modified by: Cicero Regis +%% +%% Revised by: +%% +%% Versions: +%% +%% v.02 in August, 2021 +%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% ------------------------------------------------------------------- +%% +%% ------------------------------------------------------------------- +\NeedsTeXFormat{LaTeX2e} +\ProvidesClass{BrJG_submit} +\DeclareOption{P}{\newcommand\tipo{P}} +\DeclareOption{M}{\newcommand\tipo{M}} + +% USAR AS CONFIGURACOES DA CLASSE article % +\DeclareOption*{\PassOptionsToClass{\CurrentOption}{article}} +\ProcessOptions\relax +\LoadClass[twoside,a4paper,twocolumn,11pt]{article} + +%% Page style +\setlength{\textheight}{25cm} +\setlength{\textwidth}{17cm} +\setlength{\oddsidemargin}{-0.5cm} +\setlength{\evensidemargin}{-0.5cm} +\setlength{\topmargin}{-1.5cm} +\setlength{\headheight}{0.5cm} +\setlength{\headsep}{1cm} +%\setlength{\columnsep}{0.75cm} + +%\linespread{1} + +%% ------------------------------------------------------------------- +%% Text configuration: +%% ------------------------------------------------------------------- +\RequirePackage{ifthen} +\RequirePackage{etoolbox} + +\RequirePackage[english]{babel} +\RequirePackage[utf8]{inputenc} +\RequirePackage[T1]{fontenc} + +\hyphenpenalty1 + +%% ------------------------------------------------------------------- +%% Main document font: +%% ------------------------------------------------------------------- +\RequirePackage[scaled]{helvet} +\renewcommand{\familydefault}{\sfdefault} + +%% ------------------------------------------------------------------- +%% Math, units and science packages: +%% ------------------------------------------------------------------- +\RequirePackage{amsmath,amsfonts,dsfont,amssymb} +\RequirePackage{mathtools} + +%% ------------------------------------------------------------------- +%% To control the floating elements position (graphics, tables, figures, etc): +%% ------------------------------------------------------------------- +\RequirePackage{graphicx} +\RequirePackage[labelsep=period]{caption} +\RequirePackage{subcaption} +\RequirePackage{float} +\RequirePackage{setspace} +\RequirePackage{array} + \renewcommand{\arraystretch}{1.5} + +%% ------------------------------------------------------------------- +%% To merge rows and columns into tables: +%% ------------------------------------------------------------------- +\RequirePackage{multirow} +\RequirePackage{multicol} +\setlength{\columnsep}{0.75cm} + +%%------------------------------------------------------------------- +%% Configuration of hyperlinks: +%% ------------------------------------------------------------------- +\RequirePackage[colorlinks=true,linkcolor=black,urlcolor=blue,citecolor=blue]{hyperref} +%% To have the possibility to change the urlcolor +\newcommand{\changeurlcolor}[1]{\hypersetup{urlcolor=#1}} + +\RequirePackage{cleveref} + + +%% ------------------------------------------------------------------- +%% Article numbers: +%% ------------------------------------------------------------------- + +\makeatletter + +\DeclareRobustCommand{\ano}[1]{\newcommand{\yr}{#1}} +\DeclareRobustCommand{\correspondent}[1]{\newcommand{\correspond}{#1}} + +%%------------------------------------------------------------------- +%% Commands for title and authors. +%% ------------------------------------------------------------------- +\DeclareRobustCommand{\shorttitle}[1]{\newcommand{\titulocurto}{#1}} +\DeclareRobustCommand{\shortauthors}[1]{\newcommand{\autorescurto}{#1}} + +%%------------------------------------------------------------------- +%% First page layout: +%% ------------------------------------------------------------------- + +%% ------------------------------------------------------------------- +%% Set the start pages numbering: +%% ------------------------------------------------------------------ +%\usepackage{lastpage} +%\newcommand{\@lastpg}{\pageref{LastPage}} + +%%------------------------------------------------------------------- +%% Document header and footer (except first page): +%% ------------------------------------------------------------------- +\RequirePackage{fancyhdr} +\pagestyle{fancy} + \fancyhead[EL]{ {\Large \thepage} \hspace{1mm} {\small \MakeUppercase{\text{\titulocurto}}} } + \fancyhead[ER]{} + \ifthenelse{\equal{\tipo}{P}}{ + \fancyhead[OR]{ {\small \text{\autorescurto}} \hspace{1mm} {\Large \thepage} } }{ + \fancyhead[OR]{ {\Large \thepage} } + } + \fancyhead[OL]{} + \fancyfoot[ER,OL]{\small Braz. 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Geophys., \yr} + \cfoot{} + +\DeclareRobustCommand\blfootnote[1]{% + \begingroup + \renewcommand\thefootnote{}\footnote{#1}% + \addtocounter{footnote}{-1}% + \endgroup +} +%\newcounter{filiacao} +%\DeclareRobustCommand{\affiliation}[1]{\stepcounter{filiacao} \blfootnote{$^{\arabic{filiacao}}$#1} } + +\DeclareRobustCommand{\affiliation}[2]{ \ifthenelse{\equal{\tipo}{P}}{ \blfootnote{$^{#1}$#2} }{\relax} } +\DeclareRobustCommand{\affil}[1]{ $^{#1}$ } + +%\forcsvlist{\listadd\filiacao}{\@affil} + +%\forcsvlist{\listadd\mylist}{item1, item2, item3} + +%\renewcommand*{\do}[1]{\footnote{#1}} + + +%%------------------------------------------------------------------- +%% Section and subsection configuration: +%% ------------------------------------------------------------------- + +\setcounter{secnumdepth}{4} +% Section titles: Uppercase, boldface. +\renewcommand{\section}{\@startsection + {section}% % the name + {1}% % the level + {0mm}% % the indent {-10\p@} + {-\baselineskip}% % the before 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\vspace{1cm}\\ + \setstretch{1.5} + \begin{center} + \begin{minipage}{0.9\textwidth} + \centering + {\Large\bfseries\MakeUppercase \@title}\\ + \ifthenelse{\equal{\tipo}{P}}{ + \vspace{0.5cm} + {\large \@author} + \vspace{1cm} }{ + \vspace{1cm} } + \end{minipage} + \end{center} + } + +%%------------------------------------------------------------------- +%% Abstract configuration: +%% ------------------------------------------------------------------- +%\makeatletter +\DeclareRobustCommand{\keywords}[1]{\newcommand{\@keys}{#1}} +\renewenvironment{abstract} + { + \thispagestyle{empty} + \noindent\setstretch{1} + \begin{minipage}{\textwidth} + \textbf{ABSTRACT.} + } + { + \ifthenelse{ \isundefined{\@keys} }{}{\vskip 10\p@ \noindent{\bf Keywords:} \ \@keys } + \end{minipage} + \vspace{1cm} + } + +\DeclareRobustCommand{\chaves}[1]{\newcommand{\@chaves}{#1}} +\newenvironment{resumo} + { + \thispagestyle{empty} + \noindent\setstretch{1} + \begin{minipage}{\textwidth} + \textbf{RESUMO.} + } + { + \ifthenelse{ \isundefined{\@chaves} }{}{\vskip 10\p@ \noindent{\bf Palavras-chave:} \ \@chaves } + \end{minipage} + \ifthenelse{\equal{\tipo}{P}}{ + \vfill + {\footnotesize Corresponding author: \correspond} }{\relax} + \newpage +% \vskip 20\p@ + \ifthenelse{\equal{\tipo}{P}}{\twocolumn}{\onecolumn} + } + +%\makeatother + +%\makeatletter +%\DeclareRobustCommand{\keywords}[1]{\newcommand{\@keys}{#1}} +%{ +% \newsavebox{\@abstr} +% \setlength{\fboxsep}{10pt} +% \renewenvironment{abstract}{ +%% \onecolumn +% \begin{lrbox}{\@abstr}\begin{minipage}{0.95\columnwidth}% +% \noindent\setstretch{1}\textbf{ABSTRACT.}\medskip}{% +% \medskip\end{minipage}\end{lrbox}% +% \noindent\fbox{\usebox{\@abstr}} +% \ifthenelse{ \isundefined{\@keys} }{}{\vskip 10\p@ \noindent{\bf Keywords:} \ \@keys } } +% \twocolumn +%} +%\makeatother + +%%------------------------------------------------------------------- +%% References configuration: +%% ------------------------------------------------------------------- +\RequirePackage[round]{natbib} % Para fazer bibliografia no estilo autor-ano. +\setlength{\bibsep}{0cm} +% + + +\AtBeginDocument{ + \onecolumn + \cover + \ifthenelse{\equal{\tipo}{P}}{\setstretch{1}}{\setstretch{2}} + } + +%\AtEndDocument{ +% {\scriptsize +% \vspace{1.5cm} +% \noindent +% Recebido em \recebido. / Aceito em \aceito.\\ +% Received on \received / Accepted em \accepted. +% } +%} + +\makeatother + diff --git a/manuscript/Copernicus_LaTeX_Package.zip b/manuscript/Copernicus_LaTeX_Package.zip deleted file mode 100644 index 52dca8a..0000000 Binary files a/manuscript/Copernicus_LaTeX_Package.zip and /dev/null differ diff --git a/manuscript/Fig/Figure_Pressure_complex_reservoir.png b/manuscript/Fig/Figure_Pressure_complex_reservoir.png deleted file mode 100644 index ff02be0..0000000 Binary files a/manuscript/Fig/Figure_Pressure_complex_reservoir.png and /dev/null differ diff --git a/manuscript/Logo_BrJG.png b/manuscript/Logo_BrJG.png new file mode 100755 index 0000000..df7f0fa Binary files /dev/null and b/manuscript/Logo_BrJG.png differ diff --git a/manuscript/README_copernicus_package_6_0.txt b/manuscript/README_copernicus_package_6_0.txt deleted file mode 100644 index 88aac55..0000000 --- a/manuscript/README_copernicus_package_6_0.txt +++ /dev/null @@ -1,23 +0,0 @@ -File: README_copernicus_package_6_0.txt -------------------------------------------------------------------------- -This is a README file for the Copernicus Publications LaTeX Macro Package -copernicus_package.zip in the version 6.0, 25 June 2020 -------------------------------------------------------------------------- -It consists of several files, each with its separate copyright. -This specific archive is collected for journals published by -Copernicus Publications (Copernicus GmbH). - -Copyright (C) 2020 Copernicus GmbH - -E-mail: publications@copernicus.org -URL: https://publications.copernicus.org - - - -Content: -- copernicus.cls: The LaTeX2e class file designed for Copernicus Publications journals. Current Version 9.11, 24 June 2020 -- copernicus.cfg: The configuration file containing journal-specific information used by the class file. Last update 25 June 2020 -- copernicus.bst: The bibliographic style file for BibTeX. Current Version 1.2, September 2017 -- natbib.sty -- pdfscreencop.sty / pdfscreen.sty -- template.tex: A LaTeX template in journal style. \ No newline at end of file diff --git a/manuscript/copernicus.bst b/manuscript/copernicus.bst deleted file mode 100644 index 026d575..0000000 --- a/manuscript/copernicus.bst +++ /dev/null @@ -1,1680 +0,0 @@ -%% -%% This is file `copernicus.bst', version 1.2 (September 2017), -%% generated with the docstrip utility. -%% -%% The original source files were: -%% -%% merlin.mbs (with options: `head,ay,nat,seq-key,nm-rev,ed-rev,keyxyr,blkyear,dt-end,note-yr,atit-u,jttl-rm,vnum-x,volp-com,pgsep-s,num-xser,btit-rm,bt-rm,agu-doi,doi,edby,blk-com,au-col,in-col,pp,ed,abr,xedn,jabr,url,url-nt,{}') -%% physjour.mbs (with options: `ay,nat,seq-key,nm-rev,ed-rev,keyxyr,blkyear,dt-end,note-yr,atit-u,jttl-rm,vnum-x,volp-com,pgsep-s,num-xser,btit-rm,bt-rm,agu-doi,doi,edby,blk-com,au-col,in-col,pp,ed,abr,xedn,jabr,url,url-nt,{}') -%% geojour.mbs (with options: `ay,nat,seq-key,nm-rev,ed-rev,keyxyr,blkyear,dt-end,note-yr,atit-u,jttl-rm,vnum-x,volp-com,pgsep-s,num-xser,btit-rm,bt-rm,agu-doi,doi,edby,blk-com,au-col,in-col,pp,ed,abr,xedn,jabr,url,url-nt,{}') -%% merlin.mbs (with options: `tail,ay,nat,seq-key,nm-rev,ed-rev,keyxyr,blkyear,dt-end,note-yr,atit-u,jttl-rm,vnum-x,volp-com,pgsep-s,num-xser,btit-rm,bt-rm,agu-doi,doi,edby,blk-com,au-col,in-col,pp,ed,abr,xedn,jabr,url,url-nt,{}') -%% ---------------------------------------- -%% *** For journals of Copernicus Publications *** -%% -%% Copyright 1994-2006 Patrick W Daly - % =============================================================== - % IMPORTANT NOTICE: - % This bibliographic style (bst) file has been generated from one or - % more master bibliographic style (mbs) files, listed above. - % - % This generated file can be redistributed and/or modified under the terms - % of the LaTeX Project Public License Distributed from CTAN - % archives in directory macros/latex/base/lppl.txt; either - % version 1 of the License, or any later version. - % =============================================================== - % Name and version information of the main mbs file: - % \ProvidesFile{merlin.mbs}[2006/02/15 4.16 (PWD, AO, DPC)] - % For use with BibTeX version 0.99a or later - %------------------------------------------------------------------- - % This bibliography style file is intended for texts in ENGLISH - % This is an author-year citation style bibliography. As such, it is - % non-standard LaTeX, and requires a special package file to function properly. - % Such a package is natbib.sty by Patrick W. Daly - % The form of the \bibitem entries is - % \bibitem[Jones et al.(1990)]{key}... - % \bibitem[Jones et al.(1990)Jones, Baker, and Smith]{key}... - % The essential feature is that the label (the part in brackets) consists - % of the author names, as they should appear in the citation, with the year - % in parentheses following. There must be no space before the opening - % parenthesis! - % With natbib v5.3, a full list of authors may also follow the year. - % In natbib.sty, it is possible to define the type of enclosures that is - % really wanted (brackets or parentheses), but in either case, there must - % be parentheses in the label. - % The \cite command functions as follows: - % \citet{key} ==>> Jones et al. (1990) - % \citet*{key} ==>> Jones, Baker, and Smith (1990) - % \citep{key} ==>> (Jones et al., 1990) - % \citep*{key} ==>> (Jones, Baker, and Smith, 1990) - % \citep[chap. 2]{key} ==>> (Jones et al., 1990, chap. 2) - % \citep[e.g.][]{key} ==>> (e.g. Jones et al., 1990) - % \citep[e.g.][p. 32]{key} ==>> (e.g. Jones et al., p. 32) - % \citeauthor{key} ==>> Jones et al. - % \citeauthor*{key} ==>> Jones, Baker, and Smith - % \citeyear{key} ==>> 1990 - %--------------------------------------------------------------------- - - -ENTRY - { address - author - booktitle - chapter - doi - edition - editor - eid - howpublished - institution - journal - key - month - note - number - organization - pages - publisher - school - series - title - type - url - volume - year - } - {} - { label extra.label sort.label short.list } -INTEGERS { output.state before.all mid.sentence after.sentence after.block } -FUNCTION {init.state.consts} -{ #0 'before.all := - #1 'mid.sentence := - #2 'after.sentence := - #3 'after.block := -} -STRINGS { s t} -FUNCTION {output.nonnull} -{ 's := - output.state mid.sentence = - { ", " * write$ } - { output.state after.block = - { add.period$ write$ - newline$ - "\newblock " write$ - } - { output.state before.all = - 'write$ - { add.period$ " " * write$ } - if$ - } - if$ - mid.sentence 'output.state := - } - if$ - s -} -FUNCTION {output} -{ duplicate$ empty$ - 'pop$ - 'output.nonnull - if$ -} -FUNCTION {output.check} -{ 't := - duplicate$ empty$ - { pop$ "empty " t * " in " * cite$ * warning$ } - 'output.nonnull - if$ -} -FUNCTION {fin.entry} -{ add.period$ - write$ - newline$ -} - -FUNCTION {new.block} -{ output.state before.all = - 'skip$ - { after.block 'output.state := } - if$ -} -FUNCTION {new.sentence} -{ output.state after.block = - 'skip$ - { output.state before.all = - 'skip$ - { after.sentence 'output.state := } - if$ - } - if$ -} -FUNCTION {add.blank} -{ " " * before.all 'output.state := -} - -FUNCTION {add.colon} -{ duplicate$ empty$ - 'skip$ - { ":" * add.blank } - if$ -} - -FUNCTION {date.block} -{ - skip$ -} - -FUNCTION {not} -{ { #0 } - { #1 } - if$ -} -FUNCTION {and} -{ 'skip$ - { pop$ #0 } - if$ -} -FUNCTION {or} -{ { pop$ #1 } - 'skip$ - if$ -} -FUNCTION {new.block.checkb} -{ empty$ - swap$ empty$ - and - 'skip$ - 'new.block - if$ -} -FUNCTION {field.or.null} -{ duplicate$ empty$ - { pop$ "" } - 'skip$ - if$ -} -FUNCTION {emphasize} -{ duplicate$ empty$ - { pop$ "" } - { "{\em " swap$ * "\/}" * } - if$ -} -FUNCTION {tie.or.space.prefix} -{ duplicate$ text.length$ #3 < - { "~" } - { " " } - if$ - swap$ -} - -FUNCTION {capitalize} -{ "u" change.case$ "t" change.case$ } - -FUNCTION {space.word} -{ " " swap$ * " " * } - % Here are the language-specific definitions for explicit words. - % Each function has a name bbl.xxx where xxx is the English word. - % The language selected here is ENGLISH -FUNCTION {bbl.and} -{ "and"} - -FUNCTION {bbl.etal} -{ "et~al." } - -FUNCTION {bbl.editors} -{ "eds." } - -FUNCTION {bbl.editor} -{ "ed." } - -FUNCTION {bbl.edby} -{ "edited by" } - -FUNCTION {bbl.edition} -{ "edn." } - -FUNCTION {bbl.volume} -{ "vol." } - -FUNCTION {bbl.of} -{ "of" } - -FUNCTION {bbl.number} -{ "no." } - -FUNCTION {bbl.nr} -{ "no." } - -FUNCTION {bbl.in} -{ "in" } - -FUNCTION {bbl.pages} -{ "pp." } - -FUNCTION {bbl.page} -{ "p." } - -FUNCTION {bbl.chapter} -{ "chap." } - -FUNCTION {bbl.techrep} -{ "Tech. 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Lett."} -MACRO {pla} {"Phys. Lett. A"} -MACRO {plb} {"Phys. Lett. B"} -MACRO {prep} {"Phys. Rep."} -MACRO {pnas} {"Proc. Nat. Acad. Sci. USA"} -MACRO {pp} {"Phys. Plasmas"} -MACRO {ppcf} {"Plasma Phys. \& Controlled Fusion"} -MACRO {phitrsl} {"Philos. Trans. Roy. Soc. London"} -MACRO {prl} {"Phys. Rev. Lett."} -MACRO {pr} {"Phys. Rev."} -MACRO {physrev} {"Phys. Rev."} -MACRO {pra} {"Phys. Rev. A"} -MACRO {prb} {"Phys. Rev. B"} -MACRO {prc} {"Phys. Rev. C"} -MACRO {prd} {"Phys. Rev. D"} -MACRO {pre} {"Phys. Rev. E"} -MACRO {ps} {"Phys. Scripta"} -MACRO {procrsl} {"Proc. Roy. Soc. London"} -MACRO {rmp} {"Rev. Mod. Phys."} -MACRO {rsi} {"Rev. Sci. Inst."} -MACRO {science} {"Science"} -MACRO {sciam} {"Sci. Am."} -MACRO {sam} {"Stud. Appl. Math."} -MACRO {sjpp} {"Sov. J. Plasma Phys."} -MACRO {spd} {"Sov. Phys.--Doklady"} -MACRO {sptp} {"Sov. Phys.--Tech. Phys."} -MACRO {spu} {"Sov. Phys.--Uspeki"} -MACRO {st} {"Sky and Telesc."} - % End module: physjour.mbs - %------------------------------------------------------------------- - % Begin module: - % \ProvidesFile{geojour.mbs}[2002/07/10 2.0h (PWD)] -MACRO {aisr} {"Adv. Space Res."} -MACRO {ag} {"Ann. Geophys."} -MACRO {anigeo} {"Ann. Geofis."} -MACRO {angl} {"Ann. Glaciol."} -MACRO {andmet} {"Ann. d. Meteor."} -MACRO {andgeo} {"Ann. d. Geophys."} -MACRO {andphy} {"Ann. Phys.-Paris"} -MACRO {afmgb} {"Arch. Meteor. Geophys. Bioklimatol."} -MACRO {atph} {"Atm\'osphera"} -MACRO {aao} {"Atmos. Ocean"} -MACRO {ass}{"Astrophys. Space Sci."} -MACRO {atenv} {"Atmos. Environ."} -MACRO {aujag} {"Aust. J. Agr. Res."} -MACRO {aumet} {"Aust. Meteorol. Mag."} -MACRO {blmet} {"Bound.-Lay. Meteorol."} -MACRO {bams} {"Bull. Amer. Meteorol. Soc."} -MACRO {cch} {"Clim. Change"} -MACRO {cdyn} {"Clim. Dynam."} -MACRO {cbul} {"Climatol. Bull."} -MACRO {cap} {"Contrib. Atmos. Phys."} -MACRO {dsr} {"Deep-Sea Res."} -MACRO {dhz} {"Dtsch. Hydrogr. Z."} -MACRO {dao} {"Dynam. Atmos. Oceans"} -MACRO {eco} {"Ecology"} -MACRO {empl}{"Earth, Moon and Planets"} -MACRO {envres} {"Environ. Res."} -MACRO {envst} {"Environ. Sci. Technol."} -MACRO {ecms} {"Estuarine Coastal Mar. Sci."} -MACRO {expa}{"Exper. Astron."} -MACRO {geoint} {"Geofis. Int."} -MACRO {geopub} {"Geofys. Publ."} -MACRO {geogeo} {"Geol. Geofiz."} -MACRO {gafd} {"Geophys. Astrophys. Fluid Dyn."} -MACRO {gfd} {"Geophys. Fluid Dyn."} -MACRO {geomag} {"Geophys. Mag."} -MACRO {georl} {"Geophys. Res. Lett."} -MACRO {grl} {"Geophys. Res. Lett."} -MACRO {ga} {"Geophysica"} -MACRO {gs} {"Geophysics"} -MACRO {ieeetap} {"IEEE Trans. Antenn. Propag."} -MACRO {ijawp} {"Int. J. Air Water Pollut."} -MACRO {ijc} {"Int. J. Climatol."} -MACRO {ijrs} {"Int. J. Remote Sens."} -MACRO {jam} {"J. Appl. Meteorol."} -MACRO {jaot} {"J. Atmos. Ocean. Technol."} -MACRO {jatp} {"J. Atmos. Terr. Phys."} -MACRO {jastp} {"J. Atmos. Solar-Terr. Phys."} -MACRO {jce} {"J. Climate"} -MACRO {jcam} {"J. Climate Appl. Meteor."} -MACRO {jcm} {"J. Climate Meteor."} -MACRO {jcy} {"J. Climatol."} -MACRO {jgr} {"J. Geophys. Res."} -MACRO {jga} {"J. Glaciol."} -MACRO {jh} {"J. Hydrol."} -MACRO {jmr} {"J. Mar. Res."} -MACRO {jmrj} {"J. Meteor. Res. Japan"} -MACRO {jm} {"J. Meteor."} -MACRO {jpo} {"J. Phys. Oceanogr."} -MACRO {jra} {"J. Rech. Atmos."} -MACRO {jaes} {"J. Aeronaut. Sci."} -MACRO {japca} {"J. Air Pollut. Control Assoc."} -MACRO {jas} {"J. Atmos. Sci."} -MACRO {jmts} {"J. Mar. Technol. Soc."} -MACRO {jmsj} {"J. Meteorol. Soc. Japan"} -MACRO {josj} {"J. Oceanogr. Soc. Japan"} -MACRO {jwm} {"J. Wea. Mod."} -MACRO {lao} {"Limnol. Oceanogr."} -MACRO {mwl} {"Mar. Wea. Log"} -MACRO {mau} {"Mausam"} -MACRO {meteor} {"``Meteor'' Forschungsergeb."} -MACRO {map} {"Meteorol. Atmos. Phys."} -MACRO {metmag} {"Meteor. Mag."} -MACRO {metmon} {"Meteor. Monogr."} -MACRO {metrun} {"Meteor. Rundsch."} -MACRO {metzeit} {"Meteor. Z."} -MACRO {metgid} {"Meteor. Gidrol."} -MACRO {mwr} {"Mon. Weather Rev."} -MACRO {nwd} {"Natl. Weather Dig."} -MACRO {nzjmfr} {"New Zeal. J. Mar. Freshwater Res."} -MACRO {npg} {"Nonlin. Proc. Geophys."} -MACRO {om} {"Oceanogr. Meteorol."} -MACRO {ocac} {"Oceanol. Acta"} -MACRO {oceanus} {"Oceanus"} -MACRO {paleoc} {"Paleoceanography"} -MACRO {pce} {"Phys. Chem. Earth"} -MACRO {pmg} {"Pap. Meteor. Geophys."} -MACRO {ppom} {"Pap. Phys. Oceanogr. Meteor."} -MACRO {physzeit} {"Phys. Z."} -MACRO {pps} {"Planet. Space Sci."} -MACRO {pss} {"Planet. Space Sci."} -MACRO {pag} {"Pure Appl. Geophys."} -MACRO {qjrms} {"Quart. J. Roy. Meteorol. Soc."} -MACRO {quatres} {"Quat. Res."} -MACRO {rsci} {"Radio Sci."} -MACRO {rse} {"Remote Sens. Environ."} -MACRO {rgeo} {"Rev. Geophys."} -MACRO {rgsp} {"Rev. Geophys. Space Phys."} -MACRO {rdgeo} {"Rev. Geofis."} -MACRO {revmeta} {"Rev. Meteorol."} -MACRO {sgp}{"Surveys in Geophys."} -MACRO {sp} {"Solar Phys."} -MACRO {ssr} {"Space Sci. Rev."} -MACRO {tellus} {"Tellus"} -MACRO {tac} {"Theor. Appl. Climatol."} -MACRO {tagu} {"Trans. Am. Geophys. Union (EOS)"} -MACRO {wrr} {"Water Resour. Res."} -MACRO {weather} {"Weather"} -MACRO {wafc} {"Weather Forecast."} -MACRO {ww} {"Weatherwise"} -MACRO {wmob} {"WMO Bull."} -MACRO {zeitmet} {"Z. Meteorol."} - % End module: geojour.mbs -%% Copyright 1994-2006 Patrick W Daly -MACRO {acmcs} {"ACM Comput. Surv."} - -MACRO {acta} {"Acta Inf."} - -MACRO {cacm} {"Commun. ACM"} - -MACRO {ibmjrd} {"IBM J. Res. Dev."} - -MACRO {ibmsj} {"IBM Syst.~J."} - -MACRO {ieeese} {"IEEE Trans. Software Eng."} - -MACRO {ieeetc} {"IEEE Trans. Comput."} - -MACRO {ieeetcad} - {"IEEE Trans. Comput. Aid. Des."} - -MACRO {ipl} {"Inf. Process. Lett."} - -MACRO {jacm} {"J.~ACM"} - -MACRO {jcss} {"J.~Comput. Syst. Sci."} - -MACRO {scp} {"Sci. Comput. Program."} - -MACRO {sicomp} {"SIAM J. Comput."} - -MACRO {tocs} {"ACM Trans. Comput. Syst."} - -MACRO {tods} {"ACM Trans. Database Syst."} - -MACRO {tog} {"ACM Trans. Graphic."} - -MACRO {toms} {"ACM Trans. Math. Software"} - -MACRO {toois} {"ACM Trans. Office Inf. Syst."} - -MACRO {toplas} {"ACM Trans. Progr. Lang. Syst."} - -MACRO {tcs} {"Theor. Comput. Sci."} - -FUNCTION {bibinfo.check} -{ swap$ - duplicate$ missing$ - { - pop$ pop$ - "" - } - { duplicate$ empty$ - { - swap$ pop$ - } - { swap$ - pop$ - } - if$ - } - if$ -} -FUNCTION {bibinfo.warn} -{ swap$ - duplicate$ missing$ - { - swap$ "missing " swap$ * " in " * cite$ * warning$ pop$ - "" - } - { duplicate$ empty$ - { - swap$ "empty " swap$ * " in " * cite$ * warning$ - } - { swap$ - pop$ - } - if$ - } - if$ -} -INTEGERS { nameptr namesleft numnames } - - -STRINGS { bibinfo} - -FUNCTION {format.names} -{ 'bibinfo := - duplicate$ empty$ 'skip$ { - 's := - "" 't := - #1 'nameptr := - s num.names$ 'numnames := - numnames 'namesleft := - { namesleft #0 > } - { s nameptr - "{vv~}{ll}{, jj}{, f.}" - format.name$ - bibinfo bibinfo.check - 't := - nameptr #1 > - { - namesleft #1 > - { ", " * t * } - { - s nameptr "{ll}" format.name$ duplicate$ "others" = - { 't := } - { pop$ } - if$ - numnames #2 > - { "," * } - 'skip$ - if$ - t "others" = - { - " " * bbl.etal * - } - { - bbl.and - space.word * t * - } - if$ - } - if$ - } - 't - if$ - nameptr #1 + 'nameptr := - namesleft #1 - 'namesleft := - } - while$ - } if$ -} -FUNCTION {format.names.ed} -{ - format.names -} -FUNCTION {format.key} -{ empty$ - { key field.or.null } - { "" } - if$ -} - -FUNCTION {format.authors} -{ author "author" format.names -} -FUNCTION {get.bbl.editor} -{ editor num.names$ #1 > 'bbl.editors 'bbl.editor if$ } - -FUNCTION {format.editors} -{ editor "editor" format.names duplicate$ empty$ 'skip$ - { - "," * - " " * - get.bbl.editor - * - } - if$ -} -FUNCTION {format.doi} -{ doi "doi" bibinfo.check - duplicate$ empty$ 'skip$ - { - "\doi{" swap$ * "}" * - } - if$ -} -FUNCTION {format.note} -{ - url empty$ - 'skip$ - { "\urlprefix\url{" url * "}" * output } - if$ - note empty$ - { "" } - { note #1 #1 substring$ - duplicate$ "{" = - 'skip$ - { output.state mid.sentence = - { "l" } - { "u" } - if$ - change.case$ - } - if$ - note #2 global.max$ substring$ * "note" bibinfo.check - } - if$ -} - -FUNCTION {format.title} -{ title - "title" bibinfo.check -} -FUNCTION {format.full.names} -{'s := - "" 't := - #1 'nameptr := - s num.names$ 'numnames := - numnames 'namesleft := - { namesleft #0 > } - { s nameptr - "{vv~}{ll}" format.name$ - 't := - nameptr #1 > - { - namesleft #1 > - { ", " * t * } - { - s nameptr "{ll}" format.name$ duplicate$ "others" = - { 't := } - { pop$ } - if$ - t "others" = - { - " " * bbl.etal * - } - { - numnames #2 > - { "," * } - 'skip$ - if$ - bbl.and - space.word * t * - } - if$ - } - if$ - } - 't - if$ - nameptr #1 + 'nameptr := - namesleft #1 - 'namesleft := - } - while$ -} - -FUNCTION {author.editor.key.full} -{ author empty$ - { editor empty$ - { key empty$ - { cite$ #1 #3 substring$ } - 'key - if$ - } - { editor format.full.names } - if$ - } - { author format.full.names } - if$ -} - -FUNCTION {author.key.full} -{ author empty$ - { key empty$ - { cite$ #1 #3 substring$ } - 'key - if$ - } - { author format.full.names } - if$ -} - -FUNCTION {editor.key.full} -{ editor empty$ - { key empty$ - { cite$ #1 #3 substring$ } - 'key - if$ - } - { editor format.full.names } - if$ -} - -FUNCTION {make.full.names} -{ type$ "book" = - type$ "inbook" = - or - 'author.editor.key.full - { type$ "proceedings" = - 'editor.key.full - 'author.key.full - if$ - } - if$ -} - -FUNCTION {output.bibitem} -{ newline$ - "\bibitem[{" write$ - label write$ - ")" make.full.names duplicate$ short.list = - { pop$ } - { * } - if$ - "}]{" * write$ - cite$ write$ - "}" write$ - newline$ - "" - before.all 'output.state := -} - -FUNCTION {if.digit} -{ duplicate$ "0" = - swap$ duplicate$ "1" = - swap$ duplicate$ "2" = - swap$ duplicate$ "3" = - swap$ duplicate$ "4" = - swap$ duplicate$ "5" = - swap$ duplicate$ "6" = - swap$ duplicate$ "7" = - swap$ duplicate$ "8" = - swap$ "9" = or or or or or or or or or -} -FUNCTION {n.separate} -{ 't := - "" - #0 'numnames := - { t empty$ not } - { t #-1 #1 substring$ if.digit - { numnames #1 + 'numnames := } - { #0 'numnames := } - if$ - t #-1 #1 substring$ swap$ * - t #-2 global.max$ substring$ 't := - numnames #5 = - { duplicate$ #1 #2 substring$ swap$ - #3 global.max$ substring$ - "\," swap$ * * - } - 'skip$ - if$ - } - while$ -} -FUNCTION {n.dashify} -{ - n.separate - 't := - "" - { t empty$ not } - { t #1 #1 substring$ "-" = - { t #1 #2 substring$ "--" = not - { "--" * - t #2 global.max$ substring$ 't := - } - { { t #1 #1 substring$ "-" = } - { "-" * - t #2 global.max$ substring$ 't := - } - while$ - } - if$ - } - { t #1 #1 substring$ * - t #2 global.max$ substring$ 't := - } - if$ - } - while$ -} - -FUNCTION {word.in} -{ bbl.in - ":" * - " " * } - -FUNCTION {format.date} -{ year "year" bibinfo.check duplicate$ empty$ - { - } - 'skip$ - if$ - extra.label * -} -FUNCTION {format.btitle} -{ title "title" bibinfo.check - duplicate$ empty$ 'skip$ - { - } - if$ -} -FUNCTION {either.or.check} -{ empty$ - 'pop$ - { "can't use both " swap$ * " fields in " * cite$ * warning$ } - if$ -} -FUNCTION {format.bvolume} -{ volume empty$ - { "" } - { bbl.volume volume tie.or.space.prefix - "volume" bibinfo.check * * - series "series" bibinfo.check - duplicate$ empty$ 'pop$ - { swap$ bbl.of space.word * swap$ - emphasize * } - if$ - "volume and number" number either.or.check - } - if$ -} -FUNCTION {format.number.series} -{ volume empty$ - { number empty$ - { series field.or.null } - { series empty$ - { number "number" bibinfo.check } - { output.state mid.sentence = - { bbl.number } - { bbl.number capitalize } - if$ - number tie.or.space.prefix "number" bibinfo.check * * - bbl.in space.word * - series "series" bibinfo.check * - } - if$ - } - if$ - } - { "" } - if$ -} - -FUNCTION {format.edition} -{ edition duplicate$ empty$ 'skip$ - { - output.state mid.sentence = - { "l" } - { "t" } - if$ change.case$ - "edition" bibinfo.check - " " * bbl.edition * - } - if$ -} -INTEGERS { multiresult } -FUNCTION {multi.page.check} -{ 't := - #0 'multiresult := - { multiresult not - t empty$ not - and - } - { t #1 #1 substring$ - duplicate$ "-" = - swap$ duplicate$ "," = - swap$ "+" = - or or - { #1 'multiresult := } - { t #2 global.max$ substring$ 't := } - if$ - } - while$ - multiresult -} -FUNCTION {format.pages} -{ pages duplicate$ empty$ 'skip$ - { duplicate$ multi.page.check - { - bbl.pages swap$ - n.dashify - } - { - bbl.page swap$ - } - if$ - tie.or.space.prefix - "pages" bibinfo.check - * * - } - if$ -} -FUNCTION {format.journal.pages} -{ pages duplicate$ empty$ 'pop$ - { swap$ duplicate$ empty$ - { pop$ pop$ format.pages } - { - ", " * - swap$ - n.dashify - "pages" bibinfo.check - * - } - if$ - } - if$ -} -FUNCTION {format.journal.eid} -{ eid "eid" bibinfo.check - duplicate$ empty$ 'pop$ - { swap$ duplicate$ empty$ 'skip$ - { - ", " * - } - if$ - swap$ * - } - if$ -} -FUNCTION {format.vol.num.pages} -{ volume field.or.null - duplicate$ empty$ 'skip$ - { - "volume" bibinfo.check - } - if$ - eid empty$ - { format.journal.pages } - { format.journal.eid } - if$ -} - -FUNCTION {format.chapter.pages} -{ chapter empty$ - 'format.pages - { type empty$ - { bbl.chapter } - { type "l" change.case$ - "type" bibinfo.check - } - if$ - chapter tie.or.space.prefix - "chapter" bibinfo.check - * * - pages empty$ - 'skip$ - { ", " * format.pages * } - if$ - } - if$ -} - -FUNCTION {format.booktitle} -{ - booktitle "booktitle" bibinfo.check -} -FUNCTION {format.in.ed.booktitle} -{ format.booktitle duplicate$ empty$ 'skip$ - { - editor "editor" format.names.ed duplicate$ empty$ 'pop$ - { - bbl.edby - " " * swap$ * - swap$ - "," * - " " * swap$ - * } - if$ - word.in swap$ * - } - if$ -} -FUNCTION {format.thesis.type} -{ type duplicate$ empty$ - 'pop$ - { swap$ pop$ - "t" change.case$ "type" bibinfo.check - } - if$ -} -FUNCTION {format.tr.number} -{ number "number" bibinfo.check - type duplicate$ empty$ - { pop$ bbl.techrep } - 'skip$ - if$ - "type" bibinfo.check - swap$ duplicate$ empty$ - { pop$ "t" change.case$ } - { tie.or.space.prefix * * } - if$ -} -FUNCTION {format.article.crossref} -{ - word.in - " \cite{" * crossref * "}" * -} -FUNCTION {format.book.crossref} -{ volume duplicate$ empty$ - { "empty volume in " cite$ * "'s crossref of " * crossref * warning$ - pop$ word.in - } - { bbl.volume - swap$ tie.or.space.prefix "volume" bibinfo.check * * bbl.of space.word * - } - if$ - " \cite{" * crossref * "}" * -} -FUNCTION {format.incoll.inproc.crossref} -{ - word.in - " \cite{" * crossref * "}" * -} -FUNCTION {format.org.or.pub} -{ 't := - "" - address empty$ t empty$ and - 'skip$ - { - t empty$ - { address "address" bibinfo.check * - } - { t * - address empty$ - 'skip$ - { ", " * address "address" bibinfo.check * } - if$ - } - if$ - } - if$ -} -FUNCTION {format.publisher.address} -{ publisher "publisher" bibinfo.warn format.org.or.pub -} - -FUNCTION {format.organization.address} -{ organization "organization" bibinfo.check format.org.or.pub -} - -FUNCTION {article} -{ output.bibitem - format.authors "author" output.check - author format.key output - add.colon - format.title "title" output.check - crossref missing$ - { - journal - "journal" bibinfo.check - "journal" output.check - format.vol.num.pages output - format.doi output - } - { format.article.crossref output.nonnull - format.pages output - } - if$ - format.note output - format.date "year" output.check - fin.entry -} -FUNCTION {book} -{ output.bibitem - author empty$ - { format.editors "author and editor" output.check - editor format.key output - add.colon - } - { format.authors output.nonnull - add.colon - crossref missing$ - { "author and editor" editor either.or.check } - 'skip$ - if$ - } - if$ - format.btitle "title" output.check - crossref missing$ - { format.bvolume output - format.number.series output - format.publisher.address output - } - { - format.book.crossref output.nonnull - } - if$ - format.edition output - format.doi output - format.note output - format.date "year" output.check - fin.entry -} -FUNCTION {booklet} -{ output.bibitem - format.authors output - author format.key output - add.colon - format.title "title" output.check - howpublished "howpublished" bibinfo.check output - address "address" bibinfo.check output - format.doi output - format.note output - format.date "year" output.check - fin.entry -} - -FUNCTION {inbook} -{ output.bibitem - author empty$ - { format.editors "author and editor" output.check - editor format.key output - add.colon - } - { format.authors output.nonnull - add.colon - crossref missing$ - { "author and editor" editor either.or.check } - 'skip$ - if$ - } - if$ - format.btitle "title" output.check - crossref missing$ - { - format.bvolume output - format.chapter.pages "chapter and pages" output.check - format.number.series output - format.publisher.address output - } - { - format.chapter.pages "chapter and pages" output.check - format.book.crossref output.nonnull - } - if$ - format.edition output - format.doi output - format.note output - format.date "year" output.check - fin.entry -} - -FUNCTION {incollection} -{ output.bibitem - format.authors "author" output.check - author format.key output - add.colon - format.title "title" output.check - crossref missing$ - { format.in.ed.booktitle "booktitle" output.check - format.bvolume output - format.number.series output - format.chapter.pages output - format.publisher.address output - format.edition output - } - { format.incoll.inproc.crossref output.nonnull - format.chapter.pages output - } - if$ - format.doi output - format.note output - format.date "year" output.check - fin.entry -} -FUNCTION {inproceedings} -{ output.bibitem - format.authors "author" output.check - author format.key output - add.colon - format.title "title" output.check - crossref missing$ - { format.in.ed.booktitle "booktitle" output.check - format.bvolume output - format.number.series output - format.pages output - publisher empty$ - { format.organization.address output } - { organization "organization" bibinfo.check output - format.publisher.address output - } - if$ - } - { format.incoll.inproc.crossref output.nonnull - format.pages output - } - if$ - format.doi output - format.note output - format.date "year" output.check - fin.entry -} -FUNCTION {conference} { inproceedings } -FUNCTION {manual} -{ output.bibitem - format.authors output - author format.key output - add.colon - format.btitle "title" output.check - organization "organization" bibinfo.check output - address "address" bibinfo.check output - format.edition output - format.doi output - format.note output - format.date "year" output.check - fin.entry -} - -FUNCTION {mastersthesis} -{ output.bibitem - format.authors "author" output.check - author format.key output - add.colon - format.btitle - "title" output.check - bbl.mthesis format.thesis.type output.nonnull - school "school" bibinfo.warn output - address "address" bibinfo.check output - format.doi output - format.note output - format.date "year" output.check - fin.entry -} - -FUNCTION {misc} -{ output.bibitem - format.authors output - author format.key output - add.colon - format.title output - howpublished "howpublished" bibinfo.check output - format.doi output - format.note output - format.date "year" output.check - fin.entry -} -FUNCTION {phdthesis} -{ output.bibitem - format.authors "author" output.check - author format.key output - add.colon - format.btitle - "title" output.check - bbl.phdthesis format.thesis.type output.nonnull - school "school" bibinfo.warn output - address "address" bibinfo.check output - format.doi output - format.note output - format.date "year" output.check - fin.entry -} - -FUNCTION {proceedings} -{ output.bibitem - format.editors output - editor format.key output - add.colon - format.btitle "title" output.check - format.bvolume output - format.number.series output - publisher empty$ - { format.organization.address output } - { organization "organization" bibinfo.check output - format.publisher.address output - } - if$ - format.doi output - format.note output - format.date "year" output.check - fin.entry -} - -FUNCTION {techreport} -{ output.bibitem - format.authors "author" output.check - author format.key output - add.colon - format.title - "title" output.check - format.tr.number output.nonnull - institution "institution" bibinfo.warn output - address "address" bibinfo.check output - format.doi output - format.note output - format.date "year" output.check - fin.entry -} - -FUNCTION {unpublished} -{ output.bibitem - format.authors "author" output.check - author format.key output - add.colon - format.title "title" output.check - format.doi output - format.note "note" output.check - format.date output - fin.entry -} - -FUNCTION {default.type} { misc } -READ -FUNCTION {sortify} -{ purify$ - "l" change.case$ -} -INTEGERS { len } -FUNCTION {chop.word} -{ 's := - 'len := - s #1 len substring$ = - { s len #1 + global.max$ substring$ } - 's - if$ -} -FUNCTION {format.lab.names} -{ 's := - "" 't := - s #1 "{vv~}{ll}" format.name$ - s num.names$ duplicate$ - #2 > - { pop$ - " " * bbl.etal * - } - { #2 < - 'skip$ - { s #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" = - { - " " * bbl.etal * - } - { bbl.and space.word * s #2 "{vv~}{ll}" format.name$ - * } - if$ - } - if$ - } - if$ -} - -FUNCTION {author.key.label} -{ author empty$ - { key empty$ - { cite$ #1 #3 substring$ } - 'key - if$ - } - { author format.lab.names } - if$ -} - -FUNCTION {author.editor.key.label} -{ author empty$ - { editor empty$ - { key empty$ - { cite$ #1 #3 substring$ } - 'key - if$ - } - { editor format.lab.names } - if$ - } - { author format.lab.names } - if$ -} - -FUNCTION {editor.key.label} -{ editor empty$ - { key empty$ - { cite$ #1 #3 substring$ } - 'key - if$ - } - { editor format.lab.names } - if$ -} - -FUNCTION {calc.short.authors} -{ type$ "book" = - type$ "inbook" = - or - 'author.editor.key.label - { type$ "proceedings" = - 'editor.key.label - 'author.key.label - if$ - } - if$ - 'short.list := -} - -FUNCTION {calc.label} -{ calc.short.authors - short.list - "(" - * - year duplicate$ empty$ - short.list key field.or.null = or - { pop$ "" } - 'skip$ - if$ - * - 'label := -} - -FUNCTION {sort.format.names} -{ 's := - #1 'nameptr := - "" - s num.names$ 'numnames := - numnames 'namesleft := - { namesleft #0 > } - { s nameptr - "{vv{ } }{ll{ }}{ f{ }}{ jj{ }}" - format.name$ 't := - nameptr #1 > - { - " " * - namesleft #1 = t "others" = and - { "zzzzz" * } - { numnames #2 > nameptr #2 = and - { "zz" * year field.or.null * " " * } - 'skip$ - if$ - t sortify * - } - if$ - } - { t sortify * } - if$ - nameptr #1 + 'nameptr := - namesleft #1 - 'namesleft := - } - while$ -} - -FUNCTION {sort.format.title} -{ 't := - "A " #2 - "An " #3 - "The " #4 t chop.word - chop.word - chop.word - sortify - #1 global.max$ substring$ -} -FUNCTION {author.sort} -{ author empty$ - { key empty$ - { "to sort, need author or key in " cite$ * warning$ - "" - } - { key sortify } - if$ - } - { author sort.format.names } - if$ -} -FUNCTION {author.editor.sort} -{ author empty$ - { editor empty$ - { key empty$ - { "to sort, need author, editor, or key in " cite$ * warning$ - "" - } - { key sortify } - if$ - } - { editor sort.format.names } - if$ - } - { author sort.format.names } - if$ -} -FUNCTION {editor.sort} -{ editor empty$ - { key empty$ - { "to sort, need editor or key in " cite$ * warning$ - "" - } - { key sortify } - if$ - } - { editor sort.format.names } - if$ -} -FUNCTION {presort} -{ calc.label - label sortify - " " - * - type$ "book" = - type$ "inbook" = - or - 'author.editor.sort - { type$ "proceedings" = - 'editor.sort - 'author.sort - if$ - } - if$ - #1 entry.max$ substring$ - 'sort.label := - sort.label - * - " " - * - cite$ - * - #1 entry.max$ substring$ - 'sort.key$ := -} - -ITERATE {presort} -SORT -STRINGS { last.label next.extra } -INTEGERS { last.extra.num number.label } -FUNCTION {initialize.extra.label.stuff} -{ #0 int.to.chr$ 'last.label := - "" 'next.extra := - #0 'last.extra.num := - #0 'number.label := -} -FUNCTION {forward.pass} -{ last.label label = - { last.extra.num #1 + 'last.extra.num := - last.extra.num int.to.chr$ 'extra.label := - } - { "a" chr.to.int$ 'last.extra.num := - "" 'extra.label := - label 'last.label := - } - if$ - number.label #1 + 'number.label := -} -FUNCTION {reverse.pass} -{ next.extra "b" = - { "a" 'extra.label := } - 'skip$ - if$ - extra.label 'next.extra := - extra.label - duplicate$ empty$ - 'skip$ - { "{\natexlab{" swap$ * "}}" * } - if$ - 'extra.label := - label extra.label * 'label := -} -EXECUTE {initialize.extra.label.stuff} -ITERATE {forward.pass} -REVERSE {reverse.pass} -FUNCTION {bib.sort.order} -{ sort.label - " " - * - year field.or.null sortify - * - " " - * - cite$ - * - #1 entry.max$ substring$ - 'sort.key$ := -} -ITERATE {bib.sort.order} -SORT -FUNCTION {begin.bib} -{ preamble$ empty$ - 'skip$ - { preamble$ write$ newline$ } - if$ - "\begin{thebibliography}{" number.label int.to.str$ * "}" * - write$ newline$ - "\providecommand{\natexlab}[1]{#1}" - write$ newline$ - "\providecommand{\url}[1]{{\tt #1}}" - write$ newline$ - "\providecommand{\urlprefix}{URL }" - write$ newline$ - "\expandafter\ifx\csname urlstyle\endcsname\relax" - write$ newline$ - " \providecommand{\doi}[1]{https://doi.org/\discretionary{}{}{}#1}\else" - write$ newline$ - " \providecommand{\doi}{https://doi.org/\discretionary{}{}{}\begingroup \urlstyle{rm}\Url}\fi" - write$ newline$ -} -EXECUTE {begin.bib} -EXECUTE {init.state.consts} -ITERATE {call.type$} -FUNCTION {end.bib} -{ newline$ - "\end{thebibliography}" write$ newline$ -} -EXECUTE {end.bib} -%% End of customized bst file -%% -%% End of file `copernicus.bst'. diff --git a/manuscript/copernicus.cfg b/manuscript/copernicus.cfg deleted file mode 100644 index f6768d7..0000000 --- a/manuscript/copernicus.cfg +++ /dev/null @@ -1,1038 +0,0 @@ -\newif\ifprp \DeclareOption{prp} {\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue \@bartrue \prptrue} -\newif\ifgtes \DeclareOption{gtes} {\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue \@bartrue \gtestrue} -\newif\ifcopyediting \DeclareOption{copyediting}{\copyeditingtrue\@noreftrue} -\newif\ifjbji \DeclareOption{jbji}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\jbjitrue} -\newif\ifmr \DeclareOption{mr}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\@twostagejnltrue\mrtrue} - \DeclareOption{mrd}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\@stage@finalfalse\mrtrue} -\newif\ifejm \DeclareOption{ejm}{\@abstractcenteredtrue\@bartrue\ejmtrue} -\newif\ifwcd \DeclareOption{wcd}{\@twostagejnltrue\wcdtrue} - \DeclareOption{wcdd}{\@stage@finalfalse\wcdtrue} -\newif\ifgchron \DeclareOption{gchron}{\@sansseriffacetrue\@sansserifheadertrue\@twostagejnltrue\gchrontrue} - \DeclareOption{gchrond}{\@sansseriffacetrue\@sansserifheadertrue\@stage@finalfalse\gchrontrue} -\newif\ifdeuquasp \DeclareOption{deuquasp}{\@sansseriffacetrue\@sansserifheadertrue\@abstractindentedtrue\@bartrue\@seclinetrue\deuquasptrue} -\newif\ifgc \DeclareOption{gc}{\@sansseriffacetrue\@sansserifheadertrue\@bartrue\@twostagejnltrue\gctrue} - \DeclareOption{gcd}{\@sansseriffacetrue\@sansserifheadertrue\@bartrue\@stage@finalfalse\gctrue} -\newif\ifegqsj \DeclareOption{egqsj}{\@sansseriffacetrue\@sansserifheadertrue\@abstractindentedtrue\@bartrue\@seclinetrue\egqsjtrue} -\newif\ifjm \DeclareOption{jm}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\jmtrue} -\newif\ifwes \DeclareOption{wes}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\@twostagejnltrue\westrue} - \DeclareOption{wesd}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\@stage@finalfalse\westrue} -\newif\ifaab \DeclareOption{aab}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\aabtrue} -\newif\ifpiahs \DeclareOption{piahs}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\piahstrue} -\newif\ifascmo \DeclareOption{ascmo}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\@corrigendumtrue\@editorialnotetwoctrue\ascmotrue} -\newif\ifpb \DeclareOption{pb}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\pbtrue} -\newif\ifap \DeclareOption{ap}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\aptrue} -\newif\ifsoil \DeclareOption{soil}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\@twostagejnltrue\soiltrue} - \DeclareOption{soild}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\@stage@finalfalse\soiltrue} -\newif\ifangeocom \DeclareOption{angeocom}{\@bartrue\@twostagejnltrue\angeocomtrue} - \DeclareOption{angeocomd}{\@bartrue\@stage@finalfalse\angeocomtrue} -\newif\ifwe \DeclareOption{we}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\wetrue} -\newif\ifsdpd \DeclareOption{sdpd}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\sdpdtrue} -\newif\ifsdwr \DeclareOption{sdwr}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\sdwrtrue} -\newif\ifsdtd \DeclareOption{sdtd}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\sdtdtrue} -\newif\ifsdpr \DeclareOption{sdpr}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\sdprtrue} -\newif\ifsdsr \DeclareOption{sdsr}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\sdsrtrue} -\newif\ifasr \DeclareOption{asr}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\asrtrue} -\newif\ifms \DeclareOption{ms}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\mstrue} -\newif\ifjsss \DeclareOption{jsss}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\jssstrue} -\newif\ifhgss \DeclareOption{hgss}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\hgsstrue} -\newif\ifgh \DeclareOption{gh}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\ghtrue} -\newif\ifesurf \DeclareOption{esurf}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\@twostagejnltrue\esurftrue} - \DeclareOption{esurfd}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\@stage@finalfalse\esurftrue} -\newif\ifessd \DeclareOption{essd}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@twostagejnltrue\essdtrue} - \DeclareOption{essdd}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@stage@finalfalse\essdtrue} -\newif\ifdwes \DeclareOption{dwes}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@twostagejnltrue\dwestrue} - \DeclareOption{dwesd}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@stage@finalfalse\dwestrue} -\newif\iftc \DeclareOption{tc}{\@twostagejnltrue\tctrue} - \DeclareOption{tcd}{\@stage@finalfalse\tctrue} -\newif\ifsmsps \DeclareOption{smsps}{\smspstrue} -\newif\ifse \DeclareOption{se}{\@bartrue\@twostagejnltrue\setrue} - \DeclareOption{sed}{\@bartrue\@stage@finalfalse\setrue} -\newif\ifos \DeclareOption{os}{\@twostagejnltrue\ostrue} - \DeclareOption{osd}{\@stage@finalfalse\ostrue} -\newif\ifnpg \DeclareOption{npg}{\@editorialnotedtrue\@twostagejnltrue\npgtrue} - \DeclareOption{npgd}{\@stage@finalfalse\npgtrue} -\newif\ifnhess \DeclareOption{nhess}{\@editorialnotedtrue\@twostagejnltrue\nhesstrue} - \DeclareOption{nhessd}{\@stage@finalfalse\nhesstrue} -\newif\ifhess \DeclareOption{hess}{\@twostagejnltrue\hesstrue} - \DeclareOption{hessd}{\@stage@finalfalse\hesstrue} -\newif\ifgmd \DeclareOption{gmd}{\@twostagejnltrue\gmdtrue} - \DeclareOption{gmdd}{\@stage@finalfalse\gmdtrue} -\newif\ifgi \DeclareOption{gi}{\@corrigendumtrue\@editorialnotetwoctrue\@editorialnotedtrue\@twostagejnltrue\gitrue} - \DeclareOption{gid}{\@stage@finalfalse\gitrue} -\newif\ifesd \DeclareOption{esd}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\@twostagejnltrue\esdtrue} - \DeclareOption{esdd}{\@sansseriffacetrue\@sansserifheadertrue\@abstractcenteredtrue\@bartrue\@stage@finalfalse\esdtrue} -\newif\ifcp \DeclareOption{cp}{\@sansseriffacetrue\@sansserifheadertrue\@twostagejnltrue\cptrue} - \DeclareOption{cpd}{\@sansseriffacetrue\@sansserifheadertrue\@stage@finalfalse\cptrue} -\newif\ifastra \DeclareOption{astra}{\astratrue} -\newif\ifars \DeclareOption{ars}{\arstrue} -\newif\ifangeo \DeclareOption{angeo}{\@twostagejnltrue\angeotrue} - \DeclareOption{angeod}{\@stage@finalfalse\angeotrue} -\newif\ifamt \DeclareOption{amt}{\@twostagejnltrue\amttrue} - \DeclareOption{amtd}{\@stage@finalfalse\amttrue} -\newif\ifadgeo \DeclareOption{adgeo}{\adgeotrue} -\newif\iffr \DeclareOption{fr}{\frtrue} -\newif\ifbg \DeclareOption{bg}{\@twostagejnltrue\bgtrue} - \DeclareOption{bgd}{\@stage@finalfalse\bgtrue} -\newif\ifacp \DeclareOption{acp}{\@twostagejnltrue\acptrue} - \DeclareOption{acpd}{\@stage@finalfalse\acptrue} - - - -\def\@addjournalconfig{% - - -\ifcopyediting% Definition of layout used for copy-editing track changes document - \def\@journalurl{} - \def\@sentence{\textcolor[rgb]{1,0.58,0.25}{% - Copy-Editing track changes document -- Do not use for proof-reading}} - \let\@journalnameabbreviation\@sentence - \if@sansserifface - \definecolor{textcol}{rgb}{0,0,0} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{barcol}{gray}{0.8} - \definecolor{rulecol}{gray}{0.8} - \fi -\fi - -\ifacp%classical - \def\@journalname{Atmospheric Chemistry and Physics} - \def\@journalnameabbreviation{Atmos. Chem. Phys.} - \def\@journalnameshort{ACP} - \def\@journalnameshortlower{acp} - \def\@journalstartyear{2001} - \def\@sentence{Published by Copernicus Publications on behalf of the European Geosciences Union.} - \if@stage@final - \def\@journalurl{www.atmos-chem-phys.net} - \def\@journallogo{\includegraphics{ACP_Logo.pdf}} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} - \else - \def\@journalurl{www.atmos-chem-phys-discuss.net} - \def\@journallogo{\includegraphics{ACPD_Logo.pdf}} - \def\@sentenceDiscussion{This discussion paper is/has been under review for the journal Atmospheric Chemistry\\ and Physics (ACP). Please refer to the corresponding final paper in ACP if available.} - \if@cop@home - \definecolor{journalname}{rgb}{0.0,0.58,0.91} - \definecolor{buttonbackground}{rgb}{0.0,0.58,0.91} - \definecolor{paneltext}{rgb}{0.0,0.58,0.91} - \definecolor{buttontext}{rgb}{1.0,1.0,1.0} - \fi - \fi -\fi -\ifbg%classical - \def\@journalname{Biogeosciences} - \def\@journalnameabbreviation{Biogeosciences} - \def\@journalnameshort{BG} - \def\@journalnameshortlower{bg} - \def\@journalstartyear{2004} - \def\@sentence{Published by Copernicus Publications on behalf of the European Geosciences Union.} - \if@stage@final - \def\@journalurl{www.biogeosciences.net} - \def\@journallogo{\includegraphics{BG_Logo.pdf}} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} - \else - \def\@journalurl{www.biogeosciences-discuss.net} - \def\@journallogo{\includegraphics{BGD_Logo.pdf}} - \def\@sentenceDiscussion{This discussion paper is/has been under review for the journal Biogeosciences (BG).\\ Please refer to the corresponding final paper in BG if available.} - \if@cop@home - \definecolor{journalname}{rgb}{0.612,0.698,0.145} - \definecolor{buttonbackground}{rgb}{0.612,0.698,0.145} - \definecolor{paneltext}{rgb}{0.612,0.698,0.145} - \definecolor{buttontext}{rgb}{0.612,0.0,0.055} - \fi - \fi -\fi -\iffr%classical - \def\@journalname{Fossil Record} - \def\@journalnameabbreviation{Foss. Rec.} - \def\@journalnameshort{FR} - \def\@journalnameshortlower{fr} - \def\@journalstartyear{1998} - \def\@sentence{Published by Copernicus Publications on behalf of the Museum f{\"u}r Naturkunde Berlin.} - \def\@journalurl{www.foss-rec.net} - \def\@journallogo{\includegraphics{FR_Logo.pdf}} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} -\fi -\ifadgeo%classical - \def\@journalname{Advances in Geosciences} - \def\@journalnameabbreviation{Adv. Geosci.} - \def\@journalnameshort{ADGEO} - \def\@journalnameshortlower{adgeo} - \def\@journalstartyear{2013} - \def\@sentence{Published by Copernicus Publications on behalf of the European Geosciences Union.} - \def\@journalurl{www.adv-geosci.net} - \def\@journallogo{\includegraphics{ADGEO_Logo.pdf}} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} -\fi -\ifamt%classical - \def\@journalname{Atmospheric Measurement Techniques} - \def\@journalnameabbreviation{Atmos. Meas. Tech.} - \def\@journalnameshort{AMT} - \def\@journalnameshortlower{amt} - \def\@journalstartyear{2008} - \def\@sentence{Published by Copernicus Publications on behalf of the European Geosciences Union.} - \if@stage@final - \def\@journalurl{www.atmos-meas-tech.net} - \def\@journallogo{\includegraphics{AMT_Logo.pdf}} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} - \else - \def\@journalurl{www.atmos-meas-tech-discuss.net} - \def\@journallogo{\includegraphics{AMTD_Logo.pdf}} - \def\@sentenceDiscussion{This discussion paper is/has been under review for the journal Atmospheric Measurement\\ Techniques (AMT). Please refer to the corresponding final paper in AMT if available.} - \if@cop@home - \definecolor{journalname}{rgb}{0.0,0.259,0.475} - \definecolor{buttonbackground}{rgb}{0.0,0.259,0.475} - \definecolor{paneltext}{rgb}{0.0,0.259,0.475} - \definecolor{buttontext}{rgb}{1.0,1.0,1.0} - \fi - \fi -\fi -\ifangeo%classical - \def\@journalname{Annales Geophysicae} - \def\@journalnameabbreviation{Ann. Geophys.} - \def\@journalnameshort{ANGEO} - \def\@journalnameshortlower{angeo} - \def\@journalstartyear{1983} - \def\@sentence{Published by Copernicus Publications on behalf of the European Geosciences Union.} - \if@stage@final - \def\@journalurl{www.ann-geophys.net} - \def\@journallogo{\includegraphics{ANGEO_Logo.pdf}} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} - \else - \def\@journalurl{} - \def\@journallogo{} - \def\@sentenceDiscussion{} - \if@cop@home - \definecolor{journalname}{rgb}{1.0,1.0,1.0} - \definecolor{buttonbackground}{rgb}{1.0,1.0,1.0} - \definecolor{paneltext}{rgb}{1.0,1.0,1.0} - \definecolor{buttontext}{rgb}{1.0,1.0,1.0} - \fi - \fi -\fi -\ifars%classical - \def\@journalname{Advances in Radio Sciences} - \def\@journalnameabbreviation{Adv. Radio Sci.} - \def\@journalnameshort{ARS} - \def\@journalnameshortlower{ars} - \def\@journalstartyear{2003} - \def\@sentence{Published by Copernicus Publications on behalf of the URSI Landesausschuss in der Bundesrepublik Deutschland e.V.} - \def\@journalurl{www.adv-radio-sci.net} - \def\@journallogo{\includegraphics{ARS_Logo.pdf}} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} -\fi -\ifastra%classical - \def\@journalname{Astrophysics and Space Sciences Transactions} - \def\@journalnameabbreviation{Astrophys. Space Sci. Trans.} - \def\@journalnameshort{ASTRA} - \def\@journalnameshortlower{astra} - \def\@journalstartyear{2004} - \def\@sentence{Published by Copernicus Publications on behalf of the Arbeitsgemeinschaft Extraterrestrische Forschung e.V.} - \def\@journalurl{www.astrophys-space-sci-trans.net} - \def\@journallogo{} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} -\fi -\ifcp%classical - \def\@journalname{Climate of the Past} - \def\@journalnameabbreviation{Clim. Past} - \def\@journalnameshort{CP} - \def\@journalnameshortlower{cp} - \def\@journalstartyear{2005} - \def\@sentence{Published by Copernicus Publications on behalf of the European Geosciences Union.} - \if@stage@final - \def\@journalurl{www.clim-past.net} - \def\@journallogo{\includegraphics{CP_Logo.pdf}} - \definecolor{textcol}{rgb}{0.357,0.039,0.475} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} - \else - \def\@journalurl{www.clim-past-discuss.net} - \def\@journallogo{\includegraphics{CPD_Logo.pdf}} - \def\@sentenceDiscussion{This discussion paper is/has been under review for the journal Climate of the Past (CP).\\ Please refer to the corresponding final paper in CP if available.} - \if@cop@home - \definecolor{journalname}{rgb}{0.357,0.039,0.475} - \definecolor{buttonbackground}{rgb}{0.357,0.039,0.475} - \definecolor{paneltext}{rgb}{0.357,0.039,0.475} - \definecolor{buttontext}{rgb}{1.0,0.796,0.02} - \fi - \fi -\fi -\ifesd%classical - \def\@journalname{Earth System Dynamics} - \def\@journalnameabbreviation{Earth Syst. Dynam.} - \def\@journalnameshort{ESD} - \def\@journalnameshortlower{esd} - \def\@journalstartyear{2010} - \def\@sentence{Published by Copernicus Publications on behalf of the European Geosciences Union.} - \if@stage@final - \def\@journalurl{www.earth-syst-dynam.net} - \def\@journallogo{\includegraphics{ESD_Logo.pdf}} - \definecolor{textcol}{rgb}{0.0,0.224,0.455} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{barcol}{rgb}{1.0,1.0,1.0} - \definecolor{rulecol}{rgb}{0.0,0.224,0.455} - \else - \def\@journalurl{www.earth-syst-dynam-discuss.net} - \def\@journallogo{\includegraphics{ESDD_Logo.pdf}} - \def\@sentenceDiscussion{This discussion paper is/has been under review for the journal Earth System\\ Dynamics (ESD). Please refer to the corresponding final paper in ESD if available.} - \if@cop@home - \definecolor{journalname}{rgb}{0.0,0.224,0.455} - \definecolor{buttonbackground}{rgb}{0.0,0.224,0.455} - \definecolor{paneltext}{rgb}{0.0,0.224,0.455} - \definecolor{buttontext}{rgb}{1.0,1.0,1.0} - \fi - \fi -\fi -\ifgi%classical - \def\@journalname{Geoscientific Instrumentation, Methods and Data Systems} - \def\@journalnameabbreviation{Geosci. Instrum. Method. Data Syst.} - \def\@journalnameshort{GI} - \def\@journalnameshortlower{gi} - \def\@journalstartyear{2012} - \def\@sentence{Published by Copernicus Publications on behalf of the European Geosciences Union.} - \if@stage@final - \def\@journalurl{www.geosci-instrum-method-data-syst.net} - \def\@journallogo{\includegraphics{GI_Logo.pdf}} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} - \else - \def\@journalurl{www.geosci-instrum-method-data-syst-discuss.net} - \def\@journallogo{\includegraphics{GID_Logo.pdf}} - \def\@sentenceDiscussion{This discussion paper is/has been under review for the journal Geoscientific Instrumentation,\\ Methods and Data Systems (GI). Please refer to the corresponding final paper in GI if available.} - \if@cop@home - \definecolor{journalname}{rgb}{0.012,0.306,0.635} - \definecolor{buttonbackground}{rgb}{0.635,0.635,0.635} - \definecolor{paneltext}{rgb}{0.012,0.306,0.635} - \definecolor{buttontext}{rgb}{0.012,0.306,0.635} - \fi - \fi -\fi -\ifgmd%classical - \def\@journalname{Geoscientific Model Development} - \def\@journalnameabbreviation{Geosci. Model Dev.} - \def\@journalnameshort{GMD} - \def\@journalnameshortlower{gmd} - \def\@journalstartyear{2008} - \def\@sentence{Published by Copernicus Publications on behalf of the European Geosciences Union.} - \if@stage@final - \def\@journalurl{www.geosci-model-dev.net} - \def\@journallogo{\includegraphics{GMD_Logo.pdf}} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} - \else - \def\@journalurl{www.geosci-model-dev-discuss.net} - \def\@journallogo{\includegraphics{GMDD_Logo.pdf}} - \def\@sentenceDiscussion{This discussion paper is/has been under review for the journal Geoscientific Model\\ Development (GMD). Please refer to the corresponding final paper in GMD if available.} - \if@cop@home - \definecolor{journalname}{rgb}{0.973,0.584,0.055} - \definecolor{buttonbackground}{rgb}{0.973,0.584,0.055} - \definecolor{paneltext}{rgb}{0.973,0.584,0.055} - \definecolor{buttontext}{rgb}{0.769,0.086,0.11} - \fi - \fi -\fi -\ifhess%classical - \def\@journalname{Hydrology and Earth System Sciences} - \def\@journalnameabbreviation{Hydrol. Earth Syst. Sci.} - \def\@journalnameshort{HESS} - \def\@journalnameshortlower{hess} - \def\@journalstartyear{1997} - \def\@sentence{Published by Copernicus Publications on behalf of the European Geosciences Union.} - \if@stage@final - \def\@journalurl{www.hydrol-earth-syst-sci.net} - \def\@journallogo{\includegraphics{HESS_Logo.pdf}} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} - \else - \def\@journalurl{www.hydrol-earth-syst-sci-discuss.net} - \def\@journallogo{\includegraphics{HESSD_Logo.pdf}} - \def\@sentenceDiscussion{This discussion paper is/has been under review for the journal Hydrology and Earth System\\ Sciences (HESS). Please refer to the corresponding final paper in HESS if available.} - \if@cop@home - \definecolor{journalname}{rgb}{0.38,0.643,0.161} - \definecolor{buttonbackground}{rgb}{0.38,0.643,0.161} - \definecolor{paneltext}{rgb}{0.38,0.643,0.161} - \definecolor{buttontext}{rgb}{0.122,0.153,0.498} - \fi - \fi -\fi -\ifnhess%classical - \def\@journalname{Natural Hazards and Earth System Sciences} - \def\@journalnameabbreviation{Nat. Hazards Earth Syst. Sci.} - \def\@journalnameshort{NHESS} - \def\@journalnameshortlower{nhess} - \def\@journalstartyear{2001} - \def\@sentence{Published by Copernicus Publications on behalf of the European Geosciences Union.} - \if@stage@final - \def\@journalurl{www.nat-hazards-earth-syst-sci.net} - \def\@journallogo{\includegraphics{NHESS_Logo.pdf}} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} - \else - \def\@journalurl{www.nat-hazards-earth-syst-sci-discuss.net} - \def\@journallogo{\includegraphics{NHESSD_Logo.pdf}} - \def\@sentenceDiscussion{This discussion paper is/has been under review for the journal Natural Hazards and Earth\\ System Sciences (NHESS). Please refer to the corresponding final paper in NHESS if available.} - \if@cop@home - \definecolor{journalname}{rgb}{0.263,0.416,0.702} - \definecolor{buttonbackground}{rgb}{0.69,0.639,0.576} - \definecolor{paneltext}{rgb}{0.263,0.416,0.702} - \definecolor{buttontext}{rgb}{0.263,0.416,0.702} - \fi - \fi -\fi -\ifnpg%classical - \def\@journalname{Nonlinear Processes in Geophysics} - \def\@journalnameabbreviation{Nonlin. Processes Geophys.} - \def\@journalnameshort{NPG} - \def\@journalnameshortlower{npg} - \def\@journalstartyear{1994} - \def\@sentence{Published by Copernicus Publications on behalf of the European Geosciences Union \& the American Geophysical Union.} - \if@stage@final - \def\@journalurl{www.nonlin-processes-geophys.net} - \def\@journallogo{\includegraphics{NPG_Logo.pdf}} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} - \else - \def\@journalurl{www.nonlin-processes-geophys-discuss.net} - \def\@journallogo{\includegraphics{NPGD_Logo.pdf}} - \def\@sentenceDiscussion{This discussion paper is/has been under review for the journal Nonlinear Processes\\ in Geophysics (NPG). Please refer to the corresponding final paper in NPG if available.} - \if@cop@home - \definecolor{journalname}{rgb}{0.102,0.278,0.6} - \definecolor{buttonbackground}{rgb}{0.996,0.749,0.004} - \definecolor{paneltext}{rgb}{0.102,0.278,0.6} - \definecolor{buttontext}{rgb}{0.102,0.278,0.6} - \fi - \fi -\fi -\ifos%classical - \def\@journalname{Ocean Science} - \def\@journalnameabbreviation{Ocean Sci.} - \def\@journalnameshort{OS} - \def\@journalnameshortlower{os} - \def\@journalstartyear{2005} - \def\@sentence{Published by Copernicus Publications on behalf of the European Geosciences Union.} - \if@stage@final - \def\@journalurl{www.ocean-sci.net} - \def\@journallogo{\includegraphics{OS_Logo.pdf}} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} - \else - \def\@journalurl{www.ocean-sci-discuss.net} - \def\@journallogo{\includegraphics{OSD_Logo.pdf}} - \def\@sentenceDiscussion{This discussion paper is/has been under review for the journal Ocean Science (OS).\\ Please refer to the corresponding final paper in OS if available.} - \if@cop@home - \definecolor{journalname}{rgb}{0.039,0.282,0.494} - \definecolor{buttonbackground}{rgb}{0.039,0.282,0.494} - \definecolor{paneltext}{rgb}{0.039,0.282,0.494} - \definecolor{buttontext}{rgb}{1.0,1.0,1.0} - \fi - \fi -\fi -\ifse%classical - \def\@journalname{Solid Earth} - \def\@journalnameabbreviation{Solid Earth} - \def\@journalnameshort{SE} - \def\@journalnameshortlower{se} - \def\@journalstartyear{2010} - \def\@sentence{Published by Copernicus Publications on behalf of the European Geosciences Union.} - \if@stage@final - \def\@journalurl{www.solid-earth.net} - \def\@journallogo{\includegraphics{SE_Logo.pdf}} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} - \else - \def\@journalurl{www.solid-earth-discuss.net} - \def\@journallogo{\includegraphics{SED_Logo.pdf}} - \def\@sentenceDiscussion{This discussion paper is/has been under review for the journal Solid Earth (SE).\\ Please refer to the corresponding final paper in SE if available.} - \if@cop@home - \definecolor{journalname}{rgb}{0.482,0.349,0.259} - \definecolor{buttonbackground}{rgb}{0.482,0.349,0.259} - \definecolor{paneltext}{rgb}{0.482,0.349,0.259} - \definecolor{buttontext}{rgb}{0.98,0.922,0.835} - \fi - \fi -\fi -\ifsmsps%classical - \def\@journalname{Stephan Mueller Special Publication Series} - \def\@journalnameabbreviation{Stephan Mueller Spec. Publ. Ser.} - \def\@journalnameshort{SMSPS} - \def\@journalnameshortlower{smsps} - \def\@journalstartyear{2002} - \def\@sentence{Published by Copernicus Publications on behalf of the European Geosciences Union.} - \def\@journalurl{www.stephan-mueller-spec-publ-ser.net} - \def\@journallogo{\includegraphics{SMSPS_Logo.pdf}} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} -\fi -\iftc%classical - \def\@journalname{The Cryosphere} - \def\@journalnameabbreviation{The Cryosphere} - \def\@journalnameshort{TC} - \def\@journalnameshortlower{tc} - \def\@journalstartyear{2007} - \def\@sentence{Published by Copernicus Publications on behalf of the European Geosciences Union.} - \if@stage@final - \def\@journalurl{www.the-cryosphere.net} - \def\@journallogo{\includegraphics{TC_Logo.pdf}} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} - \else - \def\@journalurl{www.the-cryosphere-discuss.net} - \def\@journallogo{\includegraphics{TCD_Logo.pdf}} - \def\@sentenceDiscussion{This discussion paper is/has been under review for the journal The Cryosphere (TC).\\ Please refer to the corresponding final paper in TC if available.} - \if@cop@home - \definecolor{journalname}{rgb}{0.341,0.596,0.824} - \definecolor{buttonbackground}{rgb}{0.341,0.596,0.824} - \definecolor{paneltext}{rgb}{0.341,0.596,0.824} - \definecolor{buttontext}{rgb}{1.0,1.0,1.0} - \fi - \fi -\fi -\ifdwes%classical - \def\@journalname{Drinking Water Engineering and Science Discussions} - \def\@journalnameabbreviation{Drink. Water Eng. Sci.} - \def\@journalnameshort{DWES} - \def\@journalnameshortlower{dwes} - \def\@journalstartyear{2008} - \def\@sentence{Published by Copernicus Publications on behalf of the Delft University of Technology.} - \if@stage@final - \def\@journalurl{www.drink-water-eng-sci.net} - \def\@journallogo{\includegraphics{DWES_Logo.pdf}} - \definecolor{textcol}{rgb}{0.0,0.0,0.0} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{barcol}{rgb}{0.0,0.0,0.0} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} - \else - \def\@journalurl{www.drink-water-eng-sci-discuss.net} - \def\@journallogo{\includegraphics{DWESD_Logo.pdf}} - \def\@sentenceDiscussion{This discussion paper is/has been under review for the journal Drinking Water Engineering and\\ Science (DWES). Please refer to the corresponding final paper in DWES if available.} - \if@cop@home - \definecolor{journalname}{rgb}{0.0,0.49,0.761} - \definecolor{buttonbackground}{rgb}{0.0,0.49,0.761} - \definecolor{paneltext}{rgb}{0.0,0.49,0.761} - \definecolor{buttontext}{rgb}{0.682,0.824,0.31} - \fi - \fi -\fi -\ifessd%classical - \def\@journalname{Earth System Science Data} - \def\@journalnameabbreviation{Earth Syst. Sci. Data} - \def\@journalnameshort{ESSD} - \def\@journalnameshortlower{essd} - \def\@journalstartyear{2009} - \def\@sentence{Published by Copernicus Publications.} - \if@stage@final - \def\@journalurl{www.earth-syst-sci-data.net} - \def\@journallogo{\includegraphics{ESSD_Logo.pdf}} - \definecolor{textcol}{rgb}{0.102,0.4,0.573} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{barcol}{rgb}{1.0,1.0,1.0} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} - \else - \def\@journalurl{www.earth-syst-sci-data-discuss.net} - \def\@journallogo{\includegraphics{ESSDD_Logo.pdf}} - \def\@sentenceDiscussion{This discussion paper is/has been under review for the journal Earth System Science\\ Data (ESSD). Please refer to the corresponding final paper in ESSD if available.} - \if@cop@home - \definecolor{journalname}{rgb}{0.102,0.4,0.573} - \definecolor{buttonbackground}{rgb}{0.102,0.4,0.573} - \definecolor{paneltext}{rgb}{0.102,0.4,0.573} - \definecolor{buttontext}{rgb}{1.0,1.0,1.0} - \fi - \fi -\fi -\ifesurf%classical - \def\@journalname{Earth Surface Dynamics} - \def\@journalnameabbreviation{Earth Surf. Dynam.} - \def\@journalnameshort{ESURF} - \def\@journalnameshortlower{esurf} - \def\@journalstartyear{2013} - \def\@sentence{Published by Copernicus Publications on behalf of the European Geosciences Union.} - \if@stage@final - \def\@journalurl{www.earth-surf-dynam.net} - \def\@journallogo{\includegraphics{ESURF_Logo.pdf}} - \definecolor{textcol}{rgb}{0.541,0.549,0.557} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{barcol}{rgb}{1.0,1.0,1.0} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} - \else - \def\@journalurl{www.earth-surf-dynam-discuss.net} - \def\@journallogo{\includegraphics{ESURFD_Logo.pdf}} - \def\@sentenceDiscussion{This discussion paper is/has been under review for the journal Earth Surface Dynamics (ESurfD).\\ Please refer to the corresponding final paper in ESurf if available.} - \if@cop@home - \definecolor{journalname}{rgb}{0.0,0.0,0.0} - \definecolor{buttonbackground}{rgb}{0.541,0.549,0.557} - \definecolor{paneltext}{rgb}{0.0,0.0,0.0} - \definecolor{buttontext}{rgb}{1.0,1.0,1.0} - \fi - \fi -\fi -\ifgh%classical - \def\@journalname{Geographica Helvetica} - \def\@journalnameabbreviation{Geogr. Helv.} - \def\@journalnameshort{GH} - \def\@journalnameshortlower{gh} - \def\@journalstartyear{1946} - \def\@sentence{\small Published by Copernicus Publications for the Geographisch-Ethnographische Gesellschaft Z\"urich \& Association Suisse de G\'eographie.} - \def\@journalurl{www.geogr-helv.net} - \def\@journallogo{\includegraphics{GH_Logo.pdf}} - \definecolor{textcol}{rgb}{0.569,0.58,0.588} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{barcol}{rgb}{1.0,1.0,1.0} - \definecolor{rulecol}{rgb}{0.569,0.58,0.588} -\fi -\ifhgss%classical - \def\@journalname{History of Geo- and Space Sciences} - \def\@journalnameabbreviation{Hist. Geo Space Sci.} - \def\@journalnameshort{HGSS} - \def\@journalnameshortlower{hgss} - \def\@journalstartyear{2010} - \def\@sentence{Published by Copernicus Publications.} - \def\@journalurl{www.hist-geo-space-sci.net} - \def\@journallogo{\includegraphics{HGSS_Logo.pdf}} - \definecolor{textcol}{rgb}{0.0,0.443,0.706} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{barcol}{rgb}{1.0,1.0,1.0} - \definecolor{rulecol}{rgb}{0.0,0.443,0.706} -\fi -\ifjsss%classical - \def\@journalname{Journal of Sensors and Sensor Systems} - \def\@journalnameabbreviation{J. Sens. Sens. Syst.} - \def\@journalnameshort{JSSS} - \def\@journalnameshortlower{jsss} - \def\@journalstartyear{2012} - \def\@sentence{Published by Copernicus Publications on behalf of the AMA Association for Sensor Technology.} - \def\@journalurl{www.j-sens-sens-syst.net} - \def\@journallogo{\includegraphics{JSSS_Logo.pdf}} - \definecolor{textcol}{rgb}{0.051,0.298,0.561} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{barcol}{rgb}{1.0,1.0,1.0} - \definecolor{rulecol}{rgb}{0.051,0.298,0.561} -\fi -\ifms%classical - \def\@journalname{Mechanical Sciences} - \def\@journalnameabbreviation{Mech. Sci.} - \def\@journalnameshort{MS} - \def\@journalnameshortlower{ms} - \def\@journalstartyear{2010} - \def\@sentence{Published by Copernicus Publications.} - \def\@journalurl{www.mech-sci.net} - \def\@journallogo{\includegraphics{MS_Logo.pdf}} - \definecolor{textcol}{rgb}{0.471,0.655,0.808} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{barcol}{rgb}{0.0,0.0,0.0} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} -\fi -\ifasr%classical - \def\@journalname{Advances in Science and Research} - \def\@journalnameabbreviation{Adv. Sci. Res.} - \def\@journalnameshort{ASR} - \def\@journalnameshortlower{asr} - \def\@journalstartyear{2007} - \def\@sentence{Published by Copernicus Publications.} - \def\@journalurl{www.adv-sci-res.net} - \def\@journallogo{\includegraphics{ASR_Logo.pdf}} - \definecolor{textcol}{rgb}{0.004,0.302,0.545} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{barcol}{rgb}{1.0,1.0,1.0} - \definecolor{rulecol}{rgb}{0.004,0.302,0.545} -\fi -\ifsdsr%classical - \def\@journalname{Scientific Drilling - Science Reports} - \def\@journalnameabbreviation{Sci. Dril.} - \def\@journalnameshort{SD} - \def\@journalnameshortlower{sd} - \def\@journalstartyear{2013} - \def\@sentence{Published by Copernicus Publications on behalf of the IODP and the ICDP.} - \def\@journalurl{www.sci-dril.net} - \def\@journallogo{\includegraphics{SD_Logo.pdf}} - \definecolor{textcol}{rgb}{0.075,0.239,0.553} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{barcol}{rgb}{1.0,1.0,1.0} - \definecolor{rulecol}{rgb}{0.075,0.239,0.553} -\fi -\ifsdpr%classical - \def\@journalname{Scientific Drilling - Progress Reports} - \def\@journalnameabbreviation{Sci. Dril.} - \def\@journalnameshort{SD} - \def\@journalnameshortlower{sd} - \def\@journalstartyear{2013} - \def\@sentence{Published by Copernicus Publications on behalf of the IODP and the ICDP.} - \def\@journalurl{www.sci-dril.net} - \def\@journallogo{\includegraphics{SD_Logo.pdf}} - \definecolor{textcol}{rgb}{0.906,0.651,0.278} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{barcol}{rgb}{1.0,1.0,1.0} - \definecolor{rulecol}{rgb}{0.906,0.651,0.278} -\fi -\ifsdtd%classical - \def\@journalname{Scientific Drilling - Technical Developments} - \def\@journalnameabbreviation{Sci. Dril.} - \def\@journalnameshort{SD} - \def\@journalnameshortlower{sd} - \def\@journalstartyear{2013} - \def\@sentence{Published by Copernicus Publications on behalf of the IODP and the ICDP.} - \def\@journalurl{www.sci-dril.net} - \def\@journallogo{\includegraphics{SD_Logo.pdf}} - \definecolor{textcol}{rgb}{0.722,0.094,0.141} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{0.722,0.094,0.141} -\fi -\ifsdwr%classical - \def\@journalname{Scientific Drilling - Workshop Reports} - \def\@journalnameabbreviation{Sci. Dril.} - \def\@journalnameshort{SD} - \def\@journalnameshortlower{sd} - \def\@journalstartyear{2013} - \def\@sentence{Published by Copernicus Publications on behalf of the IODP and the ICDP.} - \def\@journalurl{www.sci-dril.net} - \def\@journallogo{\includegraphics{SD_Logo.pdf}} - \definecolor{textcol}{rgb}{0.486,0.298,0.216} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{barcol}{rgb}{1.0,1.0,1.0} - \definecolor{rulecol}{rgb}{0.486,0.298,0.216} -\fi -\ifsdpd%classical - \def\@journalname{Scientific Drilling - Program Developments} - \def\@journalnameabbreviation{Sci. Dril.} - \def\@journalnameshort{SD} - \def\@journalnameshortlower{sd} - \def\@journalstartyear{2013} - \def\@sentence{Published by Copernicus Publications on behalf of the IODP and the ICDP.} - \def\@journalurl{www.sci-dril.net} - \def\@journallogo{\includegraphics{SD_Logo.pdf}} - \definecolor{textcol}{rgb}{0.027,0.498,0.325} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{barcol}{rgb}{1.0,1.0,1.0} - \definecolor{rulecol}{rgb}{0.027,0.498,0.325} -\fi -\ifwe%classical - \def\@journalname{Web Ecology} - \def\@journalnameabbreviation{Web Ecol.} - \def\@journalnameshort{WE} - \def\@journalnameshortlower{we} - \def\@journalstartyear{2001} - \def\@sentence{Published by Copernicus Publications on behalf of the European Ecological Federation (EEF).} - \def\@journalurl{www.web-ecol.net} - \def\@journallogo{\includegraphics{WE_Logo.pdf}} - \definecolor{textcol}{rgb}{0.2,0.6,0.2} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{barcol}{rgb}{1.0,1.0,1.0} - \definecolor{rulecol}{rgb}{0.2,0.6,0.2} -\fi -\ifangeocom%classical - \def\@journalname{AnGeo Communicates} - \def\@journalnameabbreviation{Ann. Geophys.} - \def\@journalnameshort{ANGEOCOM} - \def\@journalnameshortlower{angeo} - \def\@journalstartyear{1983} - \def\@sentence{Published by Copernicus Publications on behalf of the European Geosciences Union.} - \if@stage@final - \def\@journalurl{www.ann-geophys.net} - \def\@journallogo{\includegraphics{ANGEO_Logo.pdf}} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{barcol}{rgb}{0.851,0.851,0.851} - \definecolor{rulecol}{rgb}{0.0,0.0,0.0} - \else - \def\@journalurl{} - \def\@journallogo{} - \def\@sentenceDiscussion{} - \if@cop@home - \definecolor{journalname}{rgb}{1.0,1.0,1.0} - \definecolor{buttonbackground}{rgb}{1.0,1.0,1.0} - \definecolor{paneltext}{rgb}{1.0,1.0,1.0} - \definecolor{buttontext}{rgb}{1.0,1.0,1.0} - \fi - \fi -\fi -\ifsoil%classical - \def\@journalname{SOIL} - \def\@journalnameabbreviation{SOIL} - \def\@journalnameshort{SOIL} - \def\@journalnameshortlower{soil} - \def\@journalstartyear{2015} - \def\@sentence{Published by Copernicus Publications on behalf of the European Geosciences Union.} - \if@stage@final - \def\@journalurl{www.soil-journal.net} - \def\@journallogo{\includegraphics{SOIL_Logo.pdf}} - \definecolor{textcol}{rgb}{0.29,0.267,0.165} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{barcol}{rgb}{1.0,1.0,1.0} - \definecolor{rulecol}{rgb}{0.29,0.267,0.165} - \else - \def\@journalurl{www.soil-discuss.net} - \def\@journallogo{\includegraphics{SOILD_Logo.pdf}} - \def\@sentenceDiscussion{This discussion paper is/has been under review for the journal SOIL. Please refer to the\\ corresponding final paper in SOIL if available.} - \if@cop@home - \definecolor{journalname}{rgb}{0.29,0.267,0.165} - \definecolor{buttonbackground}{rgb}{0.29,0.267,0.165} - \definecolor{paneltext}{rgb}{0.29,0.267,0.165} - \definecolor{buttontext}{rgb}{1.0,1.0,1.0} - \fi - \fi -\fi -\ifap%classical - \def\@journalname{ASTRA Proceedings} - \def\@journalnameabbreviation{ASTRA Proc.} - \def\@journalnameshort{AP} - \def\@journalnameshortlower{ap} - \def\@journalstartyear{2014} - \def\@sentence{Published by Copernicus Publications.} - \def\@journalurl{www.astra-proceedings.net} - \def\@journallogo{\includegraphics{AP_Logo.pdf}} - \definecolor{textcol}{rgb}{0.094,0.259,0.647} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{barcol}{rgb}{1.0,1.0,1.0} - \definecolor{rulecol}{rgb}{0.094,0.259,0.647} -\fi -\ifpb%classical - \def\@journalname{Primate Biology} - \def\@journalnameabbreviation{Primate Biol.} - \def\@journalnameshort{PB} - \def\@journalnameshortlower{pb} - \def\@journalstartyear{2014} - \def\@sentence{Published by Copernicus Publications on behalf of the Deutsches Primatenzentrum GmbH (DPZ).} - \def\@journalurl{www.primate-biol.net} - \def\@journallogo{\includegraphics{PB_Logo.pdf}} - \definecolor{textcol}{rgb}{0.0,0.0,0.0} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{0.0,0.0,0.0} -\fi -\ifascmo%classical - \def\@journalname{Advances in Statistical Climatology, Meteorology and Oceanography} - \def\@journalnameabbreviation{Adv. Stat. Clim. Meteorol. Oceanogr.} - \def\@journalnameshort{ASCMO} - \def\@journalnameshortlower{ascmo} - \def\@journalstartyear{2015} - \def\@sentence{Published by Copernicus Publications.} - \def\@journalurl{www.adv-stat-clim-meteorol-oceanogr.net} - \def\@journallogo{\includegraphics{ASCMO_Logo.pdf}} - \definecolor{textcol}{rgb}{0.392,0.039,0.039} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{barcol}{rgb}{1.0,1.0,1.0} - \definecolor{rulecol}{rgb}{0.392,0.039,0.039} -\fi -\ifpiahs%classical - \def\@journalname{Proceedings of the International Association of Hydrological Sciences} - \def\@journalnameabbreviation{Proc. IAHS} - \def\@journalnameshort{PIAHS} - \def\@journalnameshortlower{piahs} - \def\@journalstartyear{1924} - \def\@sentence{Published by Copernicus Publications on behalf of the International Association of Hydrological Sciences.} - \def\@journalurl{proc-iahs.net} - \def\@journallogo{\includegraphics{PIAHS_Logo.pdf}} - \definecolor{textcol}{rgb}{0.553,0.035,0.035} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{barcol}{rgb}{1.0,1.0,1.0} - \definecolor{rulecol}{rgb}{0.553,0.035,0.035} -\fi -\ifaab%classical - \def\@journalname{Archives Animal Breeding} - \def\@journalnameabbreviation{Arch. Anim. Breed.} - \def\@journalnameshort{AAB} - \def\@journalnameshortlower{aab} - \def\@journalstartyear{2015} - \def\@sentence{Published by Copernicus Publications on behalf of the Leibniz Institute for Farm Animal Biology (FBN).} - \def\@journalurl{www.arch-anim-breed.net} - \def\@journallogo{\includegraphics{AAB_Logo.pdf}} - \definecolor{textcol}{rgb}{0.6,0.0,0.0} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} -\fi -\ifwes%classical - \def\@journalname{Wind Energy Science} - \def\@journalnameabbreviation{Wind Energ. Sci.} - \def\@journalnameshort{WES} - \def\@journalnameshortlower{wes} - \def\@journalstartyear{2016} - \def\@sentence{Published by Copernicus Publications on behalf of the European Academy of Wind Energy e.V.} - \if@stage@final - \def\@journalurl{www.wind-energ-sci.net} - \def\@journallogo{\includegraphics{WES_Logo.pdf}} - \definecolor{textcol}{rgb}{0.075,0.263,0.565} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{barcol}{rgb}{1.0,1.0,1.0} - \definecolor{rulecol}{rgb}{0.075,0.263,0.565} - \else - \def\@journalurl{www.wind-energ-sci-discuss.net} - \def\@journallogo{\includegraphics{WESD_Logo.pdf}} - \def\@sentenceDiscussion{This discussion paper is/has been under review for the journal Wind Energy Science (WES).\\ Please refer to the corresponding final paper in WES if available.} - \if@cop@home - \definecolor{journalname}{rgb}{0.075,0.263,0.565} - \definecolor{buttonbackground}{rgb}{0.075,0.263,0.565} - \definecolor{paneltext}{rgb}{0.075,0.263,0.565} - \definecolor{buttontext}{rgb}{0.584,0.761,0.239} - \fi - \fi -\fi -\ifjm%classical - \def\@journalname{Journal of Micropalaeontology} - \def\@journalnameabbreviation{J. Micropalaeontology} - \def\@journalnameshort{JM} - \def\@journalnameshortlower{jm} - \def\@journalstartyear{1982} - \def\@sentence{Published by Copernicus Publications on behalf of The Micropalaeontological Society.} - \def\@journalurl{www.j-micropalaeontol.net/} - \def\@journallogo{\includegraphics{JM_Logo.pdf}} - \definecolor{textcol}{rgb}{0.047,0.306,0.427} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{0.047,0.306,0.427} -\fi -\ifegqsj%classical - \def\@journalname{E&G Quaternary Science Journal} - \def\@journalnameabbreviation{E\&G Quaternary Sci. J.} - \def\@journalnameshort{EGQSJ} - \def\@journalnameshortlower{egqsj} - \def\@journalstartyear{1951} - \def\@sentence{Published by Copernicus Publications on behalf of the Deutsche Quart\"arvereinigung (DEUQUA) e.V.} - \def\@journalurl{www.eg-quaternary-sci-j.net} - \def\@journallogo{\includegraphics{EGQSJ_Logo.pdf}} - \definecolor{textcol}{rgb}{0.0,0.459,0.722} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} -\fi -\ifgc%classical - \def\@journalname{Geoscience Communication} - \def\@journalnameabbreviation{Geosci. Commun.} - \def\@journalnameshort{GC} - \def\@journalnameshortlower{gc} - \def\@journalstartyear{2018} - \def\@sentence{Published by Copernicus Publications on behalf of the European Geosciences Union.} - \if@stage@final - \def\@journalurl{www.geosci-commun.net} - \def\@journallogo{\includegraphics{GC_Logo.pdf}} - \definecolor{textcol}{rgb}{0.067,0.494,1.0} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{0.067,0.494,1.0} - \else - \def\@journalurl{www.geosci-commun-discuss.net} - \def\@journallogo{\includegraphics{GCD_Logo.pdf}} - \def\@sentenceDiscussion{} - \if@cop@home - \definecolor{journalname}{rgb}{1.0,1.0,1.0} - \definecolor{buttonbackground}{rgb}{1.0,1.0,1.0} - \definecolor{paneltext}{rgb}{1.0,1.0,1.0} - \definecolor{buttontext}{rgb}{1.0,1.0,1.0} - \fi - \fi -\fi -\ifdeuquasp%classical - \def\@journalname{DEUQUA Special Publications} - \def\@journalnameabbreviation{DEUQUA Spec. Pub.} - \def\@journalnameshort{DEUQUASP} - \def\@journalnameshortlower{deuquasp} - \def\@journalstartyear{2018} - \def\@sentence{Published by Copernicus Publications on behalf of the Deutsche Quart\"arvereinigung (DEUQUA) e.V.} - \def\@journalurl{www.deuqua-spec-pub.net} - \def\@journallogo{\includegraphics{DEUQUASP_Logo.pdf}} - \definecolor{textcol}{rgb}{0.529,0.533,0.541} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} -\fi -\ifgchron%classical - \def\@journalname{Geochronology} - \def\@journalnameabbreviation{Geochronology} - \def\@journalnameshort{GCHRON} - \def\@journalnameshortlower{gchron} - \def\@journalstartyear{2019} - \def\@sentence{Published by Copernicus Publications on behalf of the European Geosciences Union.} - \if@stage@final - \def\@journalurl{www.geochronology.net} - \def\@journallogo{\includegraphics{GCHRON_Logo.pdf}} - \definecolor{textcol}{rgb}{0.447,0.247,0.329} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} - \else - \def\@journalurl{www.geochronology-discuss.net} - \def\@journallogo{\includegraphics{GCHROND_Logo.pdf}} - \def\@sentenceDiscussion{This discussion paper is/has been under review for the journal Geochronology (GChron).\\ Please refer to the corresponding final paper in GChron if available.} - \if@cop@home - \definecolor{journalname}{rgb}{1.0,1.0,1.0} - \definecolor{buttonbackground}{rgb}{1.0,1.0,1.0} - \definecolor{paneltext}{rgb}{1.0,1.0,1.0} - \definecolor{buttontext}{rgb}{1.0,1.0,1.0} - \fi - \fi -\fi -\ifwcd%classical - \def\@journalname{Weather and Climate Dynamics} - \def\@journalnameabbreviation{Weather Clim. Dynam.} - \def\@journalnameshort{WCD} - \def\@journalnameshortlower{wcd} - \def\@journalstartyear{2019} - \def\@sentence{Published by Copernicus Publications on behalf of the European Geosciences Union.} - \if@stage@final - \def\@journalurl{www.weather-clim-dynam.net} - \def\@journallogo{\includegraphics{WCD_Logo.pdf}} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} - \else - \def\@journalurl{www.weather-clim-dynam-discuss.net} - \def\@journallogo{\includegraphics{WCDD_Logo.pdf}} - \def\@sentenceDiscussion{} - \if@cop@home - \definecolor{journalname}{rgb}{1.0,1.0,1.0} - \definecolor{buttonbackground}{rgb}{1.0,1.0,1.0} - \definecolor{paneltext}{rgb}{1.0,1.0,1.0} - \definecolor{buttontext}{rgb}{1.0,1.0,1.0} - \fi - \fi -\fi -\ifejm%classical - \def\@journalname{European Journal of Mineralogy} - \def\@journalnameabbreviation{Eur. J. Mineral.} - \def\@journalnameshort{EJM} - \def\@journalnameshortlower{ejm} - \def\@journalstartyear{1989} - \def\@sentence{Published by Copernicus Publications on behalf of the European mineralogical societies DMG, SEM, SIMP \& SFMC.} - \def\@journalurl{www.eur-j-mineral.net} - \def\@journallogo{\includegraphics{EJM_Logo.pdf}} - \definecolor{textcol}{rgb}{0.0,0.0,0.0} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} -\fi -\ifmr%classical - \def\@journalname{Magnetic Resonance} - \def\@journalnameabbreviation{Magn. Reson.} - \def\@journalnameshort{MR} - \def\@journalnameshortlower{mr} - \def\@journalstartyear{2020} - \def\@sentence{Published by Copernicus Publications on behalf of the Groupement AMPERE.} - \if@stage@final - \def\@journalurl{www.magn-reson.net} - \def\@journallogo{\includegraphics{MR_Logo.pdf}} - \definecolor{textcol}{rgb}{0.627,0.098,0.086} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{rulecol}{rgb}{1.0,1.0,1.0} - \else - \def\@journalurl{} - \def\@journallogo{\includegraphics{MRD_Logo.pdf}} - \def\@sentenceDiscussion{} - \if@cop@home - \definecolor{journalname}{rgb}{1.0,1.0,1.0} - \definecolor{buttonbackground}{rgb}{1.0,1.0,1.0} - \definecolor{paneltext}{rgb}{1.0,1.0,1.0} - \definecolor{buttontext}{rgb}{1.0,1.0,1.0} - \fi - \fi -\fi -\ifjbji%classical - \def\@journalname{Journal of Bone and Joint Infection} - \def\@journalnameabbreviation{J. Bone Joint Infect.} - \def\@journalnameshort{JBJI} - \def\@journalnameshortlower{jbji} - \def\@journalstartyear{2016} - \def\@sentence{Published by Copernicus Publications on behalf of the European Bone and Joint Infection Society.} - \def\@journalurl{https://jbji.copernicus.org/} - \def\@journallogo{\includegraphics{JBJI_Logo.pdf}} - \definecolor{textcol}{rgb}{0.161,0.337,0.361} - \definecolor{bgcol}{rgb}{1,1,1} - \definecolor{barcol}{rgb}{1.0,1.0,1.0} - \definecolor{rulecol}{rgb}{0.161,0.337,0.361} -\fi - -} \ No newline at end of file diff --git a/manuscript/copernicus.cls b/manuscript/copernicus.cls deleted file mode 100644 index 7483c08..0000000 --- a/manuscript/copernicus.cls +++ /dev/null @@ -1,2629 +0,0 @@ -%% -%% This is file `copernicus.cls', -%% generated with the docstrip utility. -%% -%% The original source files were: -%% -%% copernicus.dtx (with options: `class') -%% -%% ----------------------------------------------------------------- -%% Author: copernicus.org and le-tex publishing services -%% -%% This file is part of the copernicus package for papers -%% published by Copernicus Publications (Copernicus GmbH). -%% -%% Copyright (C) 2020 by Copernicus Publications -%% ----------------------------------------------------------------- -\NeedsTeXFormat{LaTeX2e}[1995/12/01] -\ProvidesClass{copernicus} - 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\fi -\else%discussions - \paperheight159mm - \paperwidth166mm -\fi -\parskip0pt% plus 1pt -\def\topfraction{1}%standard is .7 -\def\textfraction{0}%standard is .2 -\def\floatpagefraction{.7}%standard is .5 -\def\dbltopfraction{1}%standard is .7 -\def\dblfloatpagefraction{.7}%standard is .5 -\if@stage@final - \def\@ddsidemarginbar{% - \rlap{% - \@tempdima-6.5mm\kern-\@tempdima - \@tempdima\dimexpr\@tempdima+\paperwidth-\textwidth-\oddsidemargin+\bleed\relax - \@tempdimb\dimexpr\headheight+\topmargin\relax - \@tempdimc\dimexpr\paperheight-\@tempdimb\relax - \advance\@tempdimb\bleed - \advance\@tempdimc\bleed - \smash{\vrule\@width\@tempdima\@height\@tempdimb\@depth\@tempdimc}}} - \def\@vensidemarginbar{% - \llap{% - \@tempdima\dimexpr1in+\evensidemargin+\bleed\relax - \@tempdimb\dimexpr\headheight+\topmargin\relax - \@tempdimc\dimexpr\paperheight-\@tempdimb\relax - \advance\@tempdimb\bleed - \advance\@tempdimc\bleed - \smash{\vrule\@width\@tempdima\@height\@tempdimb\@depth\@tempdimc}% - \kern6.5mm}} - \def\@ddsidemarginrule{% - \rlap{% - \@tempdima0.8\p@ - \kern6.5mm\kern-0.5\@tempdima - \@tempdimb\dimexpr\headheight+\topmargin\relax - \@tempdimc\dimexpr\paperheight-\@tempdimb\relax - \advance\@tempdimb\bleed - \advance\@tempdimc\bleed - \smash{\vrule\@width\@tempdima\@height\@tempdimb\@depth\@tempdimc}}} - \def\@vensidemarginrule{% - \llap{% - \@tempdima0.8\p@ - \@tempdimb\dimexpr\headheight+\topmargin\relax - \@tempdimc\dimexpr\paperheight-\@tempdimb\relax - \advance\@tempdimb\bleed - \advance\@tempdimc\bleed - \smash{\vrule\@width\@tempdima\@height\@tempdimb\@depth\@tempdimc}% - \kern6.5mm\kern-0.5\@tempdima}} -\fi -\def\check@journalnameabbreviation#1 Discuss.#2\@nil{#2} -\def\@journalInfo{% - \ifx\specialp@perstring\@undefined\else - {\specialp@perstring} to\space - %check for configured line breaks: - \def\1{Corrigendum}\ifx\specialp@perstring\1\if@corrigendum\hfil\break\fi\else - \def\1{Editorial note}\ifx\specialp@perstring\1 - \edef\1{\expandafter\expandafter\expandafter\check@journalnameabbreviation\expandafter\@journalnameabbreviation\space Discuss.\@nil}% - \ifx\1\@empty\if@editorialnotetwoc\hfil\break\fi\else - \if@editorialnoted\hfil\break\fi\fi\fi - \fi - \fi - \@journalnameabbreviation - \ifcopyediting\else\if@noref,\space\@msnumber\else,\space\@pvol, \@fpage\if@nolastpage\else{--\@lpage}\fi\fi, \@pyear\fi} -\def\@journalurlInfo{% - %% URL raus, DOI rein; 2020-05-15 - \if@preface - %\@journalurl\ifcopyediting\else/\preface@abbrev.pdf\fi - https://doi.org/10.5194/\preface@abbrev.pdf - \else - https://doi.org/10.5194/\if@noref\@msnumber\else\@journalnameshortlower-\@pvol-\@fpage-\@pyear\fi - %\@journalurl\ifcopyediting\else/\if@noref\@msnumber\else\@pvol/\@fpage/\@pyear\fi/\fi - \fi} -\def\runningheaderfont{% - \if@stage@final%spec. obsolete ? - \if@sansserifheader - \reset@font\sffamily\mathversion{sans}\normalsize\color{textcol}% - \else - \bfseries - \fi - \fi} -\def\prefacetype#1{% - \if@preface - \def\@argi{#1}% - \def\1{volume}\ifx\@argi\1 - \ifx\v@num\@undefined\CopernicusError{\string\prefacetype{} is "volume", but no {\string\vnumber} was given!}{\string\prefacetype{} is "volume", but no {\string\vnumber} was given!}\fi - \gdef\preface@abbrev{\@journalnameshortlower-volume\v@num-preface}% - \else - \def\1{issue}\ifx\@argi\1 - \ifx\i@num\@undefined\CopernicusError{\string\prefacetype{} is "issue", but no {\string\inumber} was given!}{\string\prefacetype{} is "isue", but no {\string\inumber} was given!}\fi - \ifx\v@num\@undefined\CopernicusError{\string\prefacetype{} is "issue", but no {\string\vnumber} was given!}{\string\prefacetype{} is "issue", but no {\string\vnumber} was given!}\fi - \gdef\preface@abbrev{\@journalnameshortlower-volume\v@num-issue\i@num-preface}% - \else - \def\1{SI}\ifx\@argi\1 - \ifx\SI@num\@undefined\CopernicusError{\string\prefacetype{} is "SI", but no {\string\sinumber} was given!}{\string\prefacetype{} is "issue", but no {\string\sinumber} was given!}\fi - \gdef\preface@abbrev{\@journalnameshortlower-special\_issue\SI@num-preface}% - \else - \CopernicusError{Empty \string\prefacetype{} not allowed!} - {\string\prefacetype{} must be on of: "volume", "issue", or "SI"} - \fi - \fi - \fi - \else - \CopernicusError{Found \string\prefacetype{#1} in an article without the preface class option!}{Please do not use \string\prefacetype\space unless you chose preface^^Jas class option to \string\documentclass{copernicus}}% - \fi -}% -\def\vnumber#1{\if@preface\gdef\v@num{#1}\else\CopernicusError{\string\vnumber\space is only available in preface papers!}{Omit \string\vnumber\space and use \string\publvol\space or \string\origpublvol\space instread.}\fi} -\def\sinumber#1{\if@preface\gdef\SI@num{#1}\else\CopernicusError{\string\sinumber\space is only available in preface papers!}{Omit \string\sinumber\space when articly type is not preface.}\fi} -\def\inumber#1{\if@preface\gdef\i@num{#1}\else\CopernicusError{\string\inumber\space is only available in preface papers!}{Omit \string\inumber\space and use \string\articlenumber\space instread.}\fi} -\def\@manuscriptInfo{% - % Manuscript prepared for \@journalnameabbreviation\\ - % with version \csname ver@\@classfilename.cls\endcsname\ % - % of the \LaTeX\ class \@classfilename.cls.\\ - % Date: \number\day~\ifcase\month\or January\or February\or - % March\or April\or May\or June\or July\or August\or September\or - % October\or November\or December\fi~\number\year - %~\\[12pt] - } -\if@stage@final - \def\ps@plain{%only used for manuscript - \let\@mkboth\@gobbletwo - \let\@oddhead\@empty - \let\@evenhead\@empty - \def\@oddfoot{\reset@font\bfseries\hfil\thepage\hfil}% - \let\@evenfoot\@oddfoot} - \def\ps@headings{% - \def\@oddhead{% - \runningheaderfont - \@runhd\hfil\llap{\thepage}% - \if@cop@home\if@bar - \textcolor{barcol}{\@ddsidemarginbar}% - %\textcolor{textcol}{\@ddsidemarginrule}% - \textcolor{rulecol}{\@ddsidemarginrule}% - \fi\fi} - \def\@evenhead{% - \if@cop@home\if@bar - \textcolor{barcol}{\@vensidemarginbar}% - %\textcolor{textcol}{\@vensidemarginrule}% - \textcolor{rulecol}{\@vensidemarginrule}% - \fi\fi - \runningheaderfont - \rlap{\thepage}\hfil\@runhd} - \if@cop@home - \def\@oddfoot{\edit@rnotereminder\runningheaderfont\if@preface \@journalurlInfo\hfil Preface\else\@journalurlInfo\hfil\ifx\specialp@perstring\@undefined\@journalInfo\else\specialp@perstring\fi\fi} - \def\@evenfoot{\edit@rnotereminder\runningheaderfont\if@preface Preface\hfil\@journalurlInfo\else\ifx\specialp@perstring\@undefined\@journalInfo\else\specialp@perstring\fi\hfil\@journalurlInfo\fi} - \else - \let\@oddfoot\@empty - \let\@evenfoot\@empty - \fi - \let\@mkboth\@gobbletwo} -\else%discussions - \def\ps@headings{% - \def\@oddhead{% - \hfil - \rlap{% - \kern5mm - \@tempdimb\dimexpr\headheight+\topmargin+1in\relax - \@tempdimc\dimexpr\paperheight-\@tempdimb\relax - \advance\@tempdimb\bleed - \advance\@tempdimc\bleed - \color{discussion_bartext_background}\smash{\vrule\@width5mm\@height\@tempdimb\@depth\@tempdimc}}% - \rlap{% - \kern5.7mm - \rotatebox{-90}{% - \fontsize{10}{10}\usefont{T1}{ma1}{m}{n}% - \textcolor{discussion_bartext}{\kern-0.5mm% - Discussion Paper \quad | \quad Discussion Paper \quad | \quad Discussion Paper \quad | \quad Discussion Paper \quad |}}}} - \let\@evenhead\@oddhead - \def\@oddfoot{\if@cop@home\edit@rnotereminder\fi\hfil\thepage\hfil} - \let\@evenfoot\@oddfoot} -\fi -\if@stage@final - \if@bar - \def\@titlebar{% - \textcolor{barcol}{\@ddsidemarginbar}% - %\textcolor{textcol}{\@ddsidemarginrule}% - \textcolor{rulecol}{\@ddsidemarginrule}% - \rlap{\kern7.5mm\smash{% - \raise3mm\hbox{\rotatebox[origin=Bl]{-90}{\reset@font\sffamily\Large\textcolor{textcol}{\@btext\strut}}}}}} - \fi - \def\ps@titlepage{% - \if@cop@home - \ifcopyediting - \def\@oddhead{% - \parbox[t] - {\textwidth} - {{\runningheaderfont\@sentence}\\ - \color[gray]{0.55}\put(0.7,0){\rule[1mm]{\textwidth}{0.1mm}}\\ - \textcolor[gray]{0.55}{Your manuscript was typeset and received English language copy-editing.\\ - The resulting file is available for proof-reading in the final journal style.\\ - The present document is only to review the language changes.}}% - \if@bar\@titlebar\fi} - \else - \def\@oddhead{% - \parbox[t] - {0.6\textwidth} - {\if@sansserifheader\leavevmode\runningheaderfont\fi - \if@preface - doi:10.5194/\preface@abbrev% - \else - \@journalInfo\\ - %\@journalurlInfo\\ %raus laut Ticket 4529 - https://doi.org/10.5194/% - \if@noref - \@msnumber - \else - \@journalnameshortlower - -\@pvol-\@fpage-\@pyear - \fi - \fi - \ifx\specialp@perstring\@undefined\else-\def\1{Corrigendum}\ifx\specialp@perstring\1corrigendum\else editorial-note\fi\fi - \\ - \@journalcopyright\\[1mm] - \includegraphics[width=1.5cm]{CreativeCommons_Attribution_License.png}}% - \hfill - \setbox\z@\hbox{\@journallogo}% - \@tempdima\ht\z@\advance\@tempdima-8\p@\lower\@tempdima\box\z@\\ - \ifangeocom - \textcolor{barcol}{\@ddsidemarginbar}% - %\textcolor{textcol}{\@ddsidemarginrule}% - \textcolor{rulecol}{\@ddsidemarginrule}% - \rlap{\kern9mm\smash{% - \@tempdimc\headsep\advance\@tempdimc\textheight\advance\@tempdimc\footskip - \lower\@tempdimc\hbox{\rotatebox[origin=lB]{90}{\fontsize{15}{15}\usefont{T1}{ma1}{m}{n}AnGeo Communicates}}}}% - \else - \if@bar\@titlebar\fi - \fi} - \fi - \def\@oddfoot{\edit@rnotereminder\runningheaderfont\@sentence\hfil} - \else - \def\@oddhead{\parbox[t]{0.6\textwidth}{\@manuscriptInfo}} - \let\@oddfoot\@empty - \fi - \let\@mkboth\@gobbletwo} -\fi -\AtEndDocument{% - \clearpage - \addtocounter{page}{-1}% - \immediate\write\@auxout{\string\newlabel{LastPage}{{}{\thepage}{}{}{}}}% - \addtocounter{page}{1}} -\if@stage@final - \def\@lpage{\hypersetup{linkcolor=textcol}\pageref{LastPage}} -\else - \def\@lpage{\pageref*{LastPage}} -\fi -\newcommand\sw@and{% - \end{minipage}\\[1em]% - \begin{minipage}[t]{\hsize}% - \flushleft\baselineskip12pt} -\def\@runtest{% - \if@noauthor\else\if!\@runauth!\UndefinedError{\string\runningauthor}\fi\fi - \if!\@runtit!\UndefinedError{\string\runningtitle}\fi} -\def\maketitle{% - \gdef\supplement##1{% - \href{https://doi.org/10.5194/\@journalnameshortlower-\@pvol-\@fpage-\@pyear-supplement}% - {https://doi.org/10.5194/\@journalnameshortlower-\@pvol-\@fpage-\@pyear-supplement}}% - \ifnum\@fpage<0 - \CopernicusError{No article number given but citation by article number required} - {Please provide \string\articlenumber.} - \fi - \ifx\citati@nbyarticlenumber\@undefined - \ifodd\@fpage\else - \CopernicusError - {Starting page must be odd!}{change the firstpage command}% - \fi - \ifx\specialp@perstring\@undefined - \setcounter{page}{\@fpage}% - \fi - \fi - \setcounter{footnote}{0}% - \if@stage@final\if@manuscript\else\thispagestyle{titlepage}\fi\fi - \begingroup - \parindent=\z@ - \@maketitle - \endgroup - \global\let\thanks\relax - \global\let\maketitle\relax - \global\let\@thanks\@empty - \global\let\@author\@empty - \global\let\@title\@empty - \if@stage@final - \if@manuscript\gdef\baselinestretch{1.4}\reset@font\normalsize\fi - \fi - \@runtest} -\if@stage@final - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - %% This is taken from `long2.sty'. - %% Author: Tomas "tohecz" Hejda - %% Licenced under LaTeX-Project Public License version 1.3 or newer. - \newlength\longtwo@top - \newlength\longtwo@bottom - \newsavebox\longtwo@box - \def\longtwo@repeat{% - \longtwo@column[{\@twocolumnfalse - \ifdim\ht\longtwo@box>1.00\textheight%1 - \begingroup - \vbadness10000 - \setbox0\vsplit\longtwo@box to 1.00\textheight%1 - \setbox1\vbox{\unvbox\longtwo@box} - \global\setbox\longtwo@box\vbox{\unvbox1}% - \setbox2\vbox to \textheight{\unvbox0}% - \ht2=0.9\textheight - \box2 - \endgroup - \else - \ifdim\ht\longtwo@box>0.84\textheight - \global\let\longtwo@repeat\clearpage - \else - \global\let\longtwo@repeat\relax - \fi - \unvbox\longtwo@box - \vspace{15pt plus 15pt}% - \fi - }]% - \longtwo@repeat} - \long\def\longtwo@[#1]{% - \begingroup - \let\longtwo@column\twocolumn - \let\longtwo@mkttl\maketitle - \def\maketitle{% - \begingroup - \let\newpage\relax - \longtwo@mkttl - \endgroup} - \longtwo@column[{\@twocolumnfalse - \global\setbox\longtwo@box\vbox{#1}% - \ifdim\ht\longtwo@box>\textheight - \begingroup - \vbadness10000 - \setbox0\vsplit\longtwo@box to 1.00\textheight%1 - \setbox1\vbox{\unvbox\longtwo@box}% - \global\setbox\longtwo@box\vbox{\unvbox1}% - \setbox2\vbox to \textheight{\unvbox0}% - \ht2=0.9\textheight - \box2 - \endgroup - \else - \ifdim\ht\longtwo@box>0.87\textheight - \global\let\longtwo@repeat\clearpage - \else - \global\let\longtwo@repeat\relax - \fi - \unvbox\longtwo@box - \fi - }]% - \longtwo@repeat - \endgroup} - \def\longtwocolumn{\@ifnextchar[\longtwo@\twocolumn} - %% End of file `long2.sty'. - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - \def\@maketitle{% - \if@manuscript%layout for first page in one-column mode - \@@maketitlemanuscript - \else%layout for first page in two-column mode - \if@twocolumn - \longtwocolumn[\@@maketitlefinal]% - \else%allows output of heads larger than one page - \@@maketitlefinal - \fi - \fi} - \def\@@maketitlemanuscript{% - \global\@topnum\z@ - \begin{nolinenumbers}% - \parbox[t]{\textwidth}{\@manuscriptInfo}\par - \vskip\baselineskip - \raggedright - \let\footnotesize\normalsize - \let\footnoterule\relax - \def\thefootnote{\fnsymbol{footnote}}% - \def\@mpfn{footnote}% - \let\thempfn=\thefootnote - \renewcommand\@makefntext[1]{\parindent1em\noindent\@makefnmark##1}% - {\LARGE\bfseries\if@sansserifface\mathversion{sansbold}\else\mathversion{bold}\fi\@title\par}% - \if@noauthor - \else - {\large - \renewcommand\Authfont{\normalfont}% - \renewcommand\Affilfont{\normalsize\normalfont}% - \setlength\affilsep{4pt}% - \let\and=\sw@and - \flushleft - \@author\\[4pt] - \ifx\@corresp\@empty\else\textbf{{\if@sansserifface\sffamily\fi\upshape\noindent\color{textcol} Correspondence:}} \@corresp\ifx\@howtocite\@empty\else\\[4pt]\fi\fi - \ifx\@howtocite\@empty\else\textbf{{\if@sansserifface\sffamily\fi\upshape\noindent\color{textcol} How to cite:}} \@howtocite\fi - \par}% - \fi - \@thanks - \vspace{\baselineskip}% - \end{nolinenumbers}} - \def\@maketitle@setup{% - \let\footnotesize\normalsize - \let\footnoterule\relax - \def\thefootnote{\fnsymbol{footnote}}% - \def\@mpfn{footnote}% - \let\thempfn=\thefootnote - \renewcommand\@makefntext[1]{\parindent1em\noindent\@makefnmark##1}} - \if@abstractcentered%modern - \def\@@maketitlefinal{% - \vspace*{31mm}% - {\list{}{\leftmargin10mm\rightmargin\leftmargin}% - \item\relax - \hsize\linewidth - \@maketitle@setup - \centering - \center{\LARGE\bfseries\if@sansserifface\sffamily\mathversion{sansbold}\else\mathversion{bold}\fi\color{textcol}% - \ifx\specialp@perstring\@undefined\else\textit{{\specialp@perstring} to}\break``\fi - \@title - \ifx\specialp@perstring\@undefined - \else - ''\if@noref,\else\space published in\fi\space - \@journalnameabbreviation , - \if@noref\@msnumber \else \@pvol, \@fpage\if@nolastpage\else{--\@lpage}\fi\fi, \@pyear - \fi - \par}% - \vspace{10pt}% - \if@noauthor - \else - {\normalsize - \renewcommand\Authfont{\bfseries}% - \renewcommand\Affilfont{\reset@font}% - \setlength\affilsep{4pt}% - \let\and=\sw@and - \@author\par}% - \vskip-0.5\baselineskip - \fi - \ifx\@corresp\@empty\else\vskip\topsep\centering\textbf{{\if@sansserifface\sffamily\fi\upshape\noindent\color{textcol} Correspondence:}}\space\@corresp\fi - \ifx\@howtocite\@empty\else\vskip.5\topsep\centering\textbf{{\if@sansserifface\sffamily\fi\upshape\noindent\color{textcol} How to cite:}}\space\@howtocite\fi - \par\vskip0.33\baselineskip - {\small - \ifx\specialp@perstring\@undefined - \if!\@recvd! - \else - Received: \@recvd - \def\datesep{ -- }% - \if@twostagejnl\ifx\@pubdiscuss\@empty\else - \datesep Discussion started:\nobreakspace\@pubdiscuss\def\datesep{\break\def\datesep{ -- }}% - \fi\fi - \if!\@revsd!\else\datesep Revised:\nobreakspace\@revsd\fi - \if!\@accptd!\else\datesep Accepted:\nobreakspace\@accptd\fi - \ifx\@published\@undefined\else\datesep\fi - \fi - \fi - \ifx\@published\@undefined\else Published:\nobreakspace\@published\fi - }% - \ifx\abstractexists\@undefined - \else - \par\vskip0.5\baselineskip - \bgroup - \advance\hsize-2\fboxsep\advance\hsize-2\fboxrule - \parskip\z@ - \trivlist\item\relax - \textcolor{textcol}{\reset@font\normalsize\if@sansserifface\sffamily\fi\bfseries\abstractname.}% - \enspace\ignorespaces\@abstr - \ifx\second@bstract\@undefined\else\par\vspace{1.7mm}\noindent - \second@bstract - \fi - \if!\@keyw!\else - \par\vspace{1.7mm}\noindent - \textcolor{textcol}{\reset@font\normalsize\if@sansserifface\sffamily\fi\bfseries Keywords.}% - \enspace\ignorespaces\@keyw - \fi - \endtrivlist - \egroup - \fi - \endlist - \par\vspace{1.5\baselineskip}}} - \else%classical or indented - \if@abstractindented%% indented - \def\@@maketitlefinal{% - \vspace*{36mm}% - {\@maketitle@setup - \raggedright - {\LARGE\bfseries\if@sansserifface\sffamily\mathversion{sansbold}\else\mathversion{bold}\fi\color{textcol}% - \ifx\specialp@perstring\@undefined\else\textit{{\specialp@perstring} to}\break``\fi - \@title - \ifx\specialp@perstring\@undefined - \else - ''\if@noref,\else\space published in\fi\space - \@journalnameabbreviation, - \if@noref\@msnumber \else \@pvol, \@fpage\if@nolastpage\else{--\@lpage}\fi\fi, \@pyear - \fi - \par}% - \if@noauthor - \else - \vspace{\baselineskip}% - {\normalsize - \renewcommand\Authfont{\bfseries}% - \renewcommand\Affilfont{\mdseries}% - \setlength\affilsep{4pt}% - \let\and=\sw@and - \@author\par}% - \vskip-0.25\baselineskip - \fi - \@thanks} - %% NEU: - \ifnum\ifx\@corresp\@empty\ifx\@howtocite\@empty\if!\@recvd!\ifx\abstractexists\@undefined\ifx\@published\@undefined0\else1\fi\else1\fi\else1\fi\else1\fi\else1\fi=1\relax - \par\vskip1.5\baselineskip - \def\labelfont{\bfseries\if@sansserifface\sffamily\fi\upshape\noindent\color{textcol}}% - \list{}{\labelwidth35mm% - \leftmargin\labelwidth - \itemsep4mm - \labelsep\z@ - \xdef\@indescription{}% - \def\makelabel##1{\labelfont##1\hss}}% - \ifx\@corresp\@empty\else\item[{Correspondence:}]\@corresp\fi - \ifnum\ifx\@published\@undefined\ifx\specialp@perstring\@undefined\if!\@recvd!0\else1\fi\else0\fi\else1\fi=1\relax - \item[{Relevant dates:}]% - \fi - \bgroup\raggedright - \ifx\specialp@perstring\@undefined - \if!\@recvd! - \else - \strut\hbox{Received:\nobreakspace\@recvd}% - \def\datesep{ -- }% - \if@twostagejnl\ifx\@pubdiscuss\@empty\else - \datesep \hbox{Discussion started:\nobreakspace\@pubdiscuss}\def\datesep{\newline\def\datesep{ -- }}% - \fi\fi - \if!\@revsd!\else\datesep \hbox{Revised:\nobreakspace\@revsd}\fi - \if!\@accptd!\else\datesep \hbox{Accepted:\nobreakspace\@accptd}\fi - \ifx\@published\@undefined\else\datesep\fi - \fi - \fi - \ifx\@published\@undefined\else Published:\nobreakspace\@published\fi - \par\egroup - \ifx\@howtocite\@empty\else\item[{How to cite:}]\@howtocite\fi - \ifx\abstractexists\@undefined - \else - \item[\abstractname:]\@abstr% - \ifx\second@bstract\@undefined\else\item[\secabstractname:]\second@bstract\fi - \if!\@keyw!\else\item[Keywords:]\@keyw\fi - \fi - \endlist - \fi - \vspace{20pt}} - \else%% classical - \def\@@maketitlefinal{% - \vspace*{36mm}% - {\@maketitle@setup - \raggedright - {\LARGE\bfseries\if@sansserifface\if@sansserifface\sffamily\fi\mathversion{sansbold}\else\mathversion{bold}\fi\color{textcol}% - \ifx\specialp@perstring\@undefined\else\textit{{\specialp@perstring} to}\break``\fi - \@title - \ifx\specialp@perstring\@undefined - \else - ''\if@noref,\else\space published in\fi\space - \@journalnameabbreviation, - \if@noref\@msnumber \else \@pvol, \@fpage\if@nolastpage\else{--\@lpage}\fi\fi, \@pyear - \fi - \par}% - \if@noauthor - \else - \vspace{\baselineskip}% - {\normalsize - \renewcommand\Authfont{\bfseries}% - \renewcommand\Affilfont{\mdseries}% - \setlength\affilsep{4pt}% - \let\and=\sw@and - \@author\par}% - \vskip-0.25\baselineskip - \fi - \@thanks - \ifx\@corresp\@empty\else\vskip\baselineskip\textbf{{\if@sansserifface\sffamily\fi\upshape\noindent\color{textcol} Correspondence:}}\space\@corresp\fi - \ifx\@howtocite\@empty\else\vskip.75\baselineskip\textbf{{\if@sansserifface\sffamily\fi\upshape\noindent\color{textcol} How to cite:}}\space\@howtocite\fi - \par\vspace{10pt}% - \ifx\specialp@perstring\@undefined - \if!\@recvd! - \else - Received: \@recvd - \def\datesep{ -- }% - \if@twostagejnl\ifx\@pubdiscuss\@empty\else - \datesep Discussion started:\nobreakspace\@pubdiscuss\def\datesep{\newline\def\datesep{ -- }}% - \fi\fi - \if!\@revsd!\else\datesep Revised:\nobreakspace\@revsd\fi - \if!\@accptd!\else\datesep Accepted:\nobreakspace\@accptd\fi - \ifx\@published\@undefined\else\datesep\fi - \fi - \fi - \ifx\@published\@undefined\else Published: \@published\fi - \vspace{20pt}}} - \fi - \fi -\else%discussions - \def\titleheight#1{\def\@tithei{#1}} \def\@tithei{7.5cm}%reserved for future usage - \def\@maketitle{% - \global\@topnum\z@ - \if@cop@home\ifonline - \hypertarget{title}{}% - \hypersetup{pdfauthor={\@runauth}}% - \hypersetup{pdftitle={\@runtit}}% - \fi\fi - \begin{nolinenumbers}% - \if@cop@home - \ifx\@msnumber\@undefined - \CopernicusError{Please add \string\msnumber{...}}{You must provide the number of the manuscript}% - \global\let\@msnumber\@empty - \else - \ifx\@msnumber\@empty - \CopernicusError{Please fill \string\msnumber{...}}{You must provide the number of the manuscript}% - \fi\fi - \parbox[b]{107mm}{\fontsize{8}{11}\usefont{T1}{ma1}{m}{n}% - %\@journalInfo\\ - %\@journalurlInfo\\ - %\if@noref\else - % https://doi.org/10.5194/\@journalnameshortlower-\@pvol-\@fpage-\@pyear - %\fi\\ - %\@journalcopyright - \ifx\specialp@perstring\@undefined\else{\specialp@perstring} to\space\fi - \@journalnameabbreviation, % - \ifx\specialp@perstring\@undefined - \if@noref\else\doi{10.5194/\@msnumber}, \@pyear\fi\\ - Manuscript under review for journal \@journalnameabbreviationbase - \else - \@msnumber\\\@journalurl/\@msnumber/% - \fi - \\ - \ifx\specialp@perstring\@undefined - Published:\nobreakspace\@published - \else - \if@noref\else\doi{10.5194/\@msnumber-editorial-note}\fi - \fi - \\ - \copyright\ Author(s) \@pyear. CC-BY 3.0 License.% - %\\[1mm]\includegraphics[width=1.5cm]{CreativeCommons_Attribution_License.png}% - }% - \hfill - \setbox\z@\hbox{\@journallogo}\@tempdima\dimexpr\ht\z@-17mm\relax - \smash{\lower\dimexpr3mm+\@tempdima\relax\llap{\@journallogo}}%war2.5mm - \vskip5mm - \ifacp\vskip1.5mm\fi - \ifamt\vskip1.5mm\fi - \ifhess\vskip1.5mm\fi - {\fboxsep2mm - \colorbox{discussion_bartext_background} - {\advance\hsize-2\fboxsep - \parbox{\hsize} - {\color{discussion_bartext}\fontsize{9.5}{13}\usefont{T1}{ma1}{m}{n}% - \@sentenceDiscussion\par}}}% - \else - \parbox[t]{\textwidth}{\@manuscriptInfo}% - \fi - \vskip13.6\p@ - \raggedright - {\huge\bfseries\mathversion{bold}% - \ifx\specialp@perstring\@undefined\else{\large\specialp@perstring\space to\\}``\fi - \@title - \ifx\specialp@perstring\@undefined\else''\\[1mm]\large\@journalnameabbreviation, \@msnumber, \@pyear\fi - \\[5mm]}% - \if@noauthor\else - \def\Authfont{\rmfamily\bfseries}% - \def\Affilfont{\@affilfontsize\rmfamily\mdseries}% - \affilsep3mm - \@author\\[3mm] - \fi - \if@cop@home - {\small Received:\nobreakspace\@recvd\ -- Accepted:\nobreakspace\@accptd\ -- Published:\nobreakspace\@published\\*[2mm] - \if@noauthor\else Correspondence:\nobreakspace\@corresp\fi\\*[2mm] - \@sentence} - \else - \if@noauthor\else - {\small Correspondence: \@corresp}% - \fi - \fi - \end{nolinenumbers}% - \vfill - \clearpage} -\fi%stage -\if@stage@final - \if@sansserifface - \def\section{\@dolinesectrue\@startsection{section}{1}{\z@} - {-3.5ex\@plus-1ex\@minus-0.2ex} - {\if@secline2.3ex\else2.3ex\@plus0.2ex\fi} - {\raggedright\normalsize\sffamily\bfseries\mathversion{sansbold}\upshape\noindent\color{textcol}}} - \def\subsection{\@dolinesectrue\@startsection{subsection}{2}{\z@} - {\if@secline-3ex\@plus-1ex\@minus-0.2ex\else-3.25ex\@plus-1ex\@minus-0.2ex\fi} - {\if@secline1.25ex\else1.5ex\@plus0.2ex\fi} - {\raggedright\normalsize\sffamily\mdseries\mathversion{sans}\upshape\noindent\color{textcol}}} - \def\subsubsection{\@dolinesectrue\@startsection{subsubsection}{3}{\z@} - {\if@secline-3ex\@plus-1ex\@minus-0.2ex\else-3.25ex\@plus-1ex\@minus-0.2ex\fi} - {\if@secline1.25ex\else1.5ex\@plus0.2ex\fi} - {\raggedright\normalsize\sffamily\mdseries\mathversion{sans}\upshape\noindent\color{textcol}}} - \else%classical - \def\section{\@dolinesectrue\@startsection{section}{1}{\z@} - {-2em\@plus-1ex\@minus-.2ex} - {\if@secline1.15em\else1em\@plus.2ex\fi} - {\raggedright\normalfont\normalsize\bfseries\mathversion{bold}}} - \def\subsection{\@dolinesectrue\@startsection{subsection}{2}{\z@} - {-1em\@plus-0.25ex\@minus-.2ex} - {\if@secline1.15em\else1em\@plus.2ex\fi} - {\raggedright\normalfont\normalsize\bfseries\mathversion{bold}}} - \def\subsubsection{\@dolinesectrue\@startsection{subsubsection}{3}{\z@} - {-1em\@plus-0.25ex\@minus-.2ex} - {\if@secline1.15em\else1em\@plus.2ex\fi} - {\raggedright\normalsize\normalfont\bfseries\mathversion{bold}}} - \fi%final -\else%discussions - \def\section{\@dolinesectrue\@startsection{section}{1}{\z@} - {-2em\@plus-1ex\@minus-.2ex} - {1em\@plus.2ex} - {\raggedright\normalfont\normalsize\bfseries\mathversion{bold}}} - \def\subsection{\@dolinesectrue\@startsection{subsection}{2}{\z@} - {-1em\@plus-0.25ex\@minus-.2ex} - {1em\@plus.2ex} - {\raggedright\normalfont\normalsize\bfseries\mathversion{bold}}} - \def\subsubsection{\@dolinesectrue\@startsection{subsubsection}{3}{\z@} - {-1em\@plus-0.25ex\@minus-.2ex} - {1em\@plus.2ex} - {\raggedright\normalfont\normalsize\bfseries\mathversion{bold}}} -\fi -\def\@startsection#1#2#3#4#5#6{% - \gdef\cur@secdepth{#2}% - \if@noskipsec \leavevmode \fi - \par - \@tempskipa #4\relax - \@afterindenttrue - \ifdim \@tempskipa <\z@ - \@tempskipa -\@tempskipa \@afterindentfalse - \fi - \if@nobreak - \everypar{}% - \else - \addpenalty\@secpenalty\addvspace\@tempskipa - \fi - \if@secline\let\@secline@omitted\relax\fi - \@ifstar - {\@ssect{#3}{#4}{#5}{#6}}% - {\@dblarg{\@sect{#1}{#2}{#3}{#4}{#5}{#6}}}} -\def\@afterheading{% - \@nobreaktrue - \everypar{% - \if@nobreak - \@nobreakfalse - \clubpenalty \@M - \if@afterindent \else - {\setbox\z@\lastbox}% - \fi - \if@secline - \if@dolinesec - \if@sansserifface - \rlap{\smash{\expandafter\ifnum\cur@secdepth>\@ne\raise1.2\baselineskip\else\raise1.5\baselineskip\fi\hbox{\vrule width\hsize height\arrayrulewidth\relax}}}% - \else - \rlap{\smash{\raise1.5\baselineskip\hbox{\vrule width\hsize height\arrayrulewidth\relax}}}% - \fi - \fi% - \@dolinesecfalse - \global\let\@secline@omitted\@undefined - \fi - \else - \clubpenalty \@clubpenalty - \everypar{}% - \fi}% -} -\let\paragraph=\subsubsection -\let\subparagraph=\paragraph -\if@stage@final - \if@manuscript - \else - \leftmargini2em - \leftmarginii1.75em - \leftmarginiii1.5em - \leftmarginiv1em - \leftmarginv0.5em - \leftmarginvi0.5em - \fi -\fi -\def\labelitemi{\bfseries\textendash} -\def\labelitemii{\bfseries\textendash} -\def\labelitemiii{$\m@th\bullet$} -\def\labelitemiv{$\m@th\cdot$} -\def\itemize{% - \if@secline - \ifx\@secline@omitted\relax - \leavevmode - \nobreak - \vspace*{-1.72\baselineskip}% - \global\let\@secline@omitted\@undefined - \fi - \fi - \ifnum \@itemdepth >\thr@@\@toodeep\else - \advance\@itemdepth\@ne - \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}% - \expandafter - \list - \csname\@itemitem\endcsname - {\def\makelabel##1{\hss\llap{##1}}}% - \fi} -\let\@abslang\relax -\long\def\secondabstract#1{% - \subpdfbookmark{\secabstractname.}{\secabstractname.}% - \toks@{% - \if@abstractindented\else\if@stage@final - \noindent\textcolor{textcol}{\reset@font\normalsize\if@sansserifface\sffamily\fi\bfseries \secabstractname.} \ignorespaces\enskip - \fi\fi - #1} - \immediate\write\@auxout{\string\gdef\string\second@bstract{\the\toks@}}% - \if@abstractindented\else - \if@stage@final - \else - \section*{\secabstractname} - \second@bstract - \fi - \fi -} - -\if@stage@final - \ifnum\if@abstractcentered1\else\if@abstractindented1\else0\fi\fi=1\relax%modern oder indented - \long\def\abstract{% - \immediate\write\@auxout{\string\gdef\string\abstractexists{true}}% - \iflanguage{ngerman}{\@abslang}{\iflanguage{german}{\@abslang}{}}% - \subpdfbookmark{\abstractname}{abstract}% - \edef\ABS@{\@currenvir}% - \toks@{}\ABS@get@body} - \let\endabstract\relax - \long\def\ABS@get@body#1\end - {\toks@\expandafter{\the\toks@\parindent1em\relax#1}\ABS@find@end} - \def\ABS@find@end#1{% - \def\@tempa{#1}% - \ifx\@tempa\ABS@ - \expandafter\ABS@endabstract - \else - \toks@\expandafter{\the\toks@\end{#1}}\expandafter\ABS@get@body - \fi} - \def\ABS@{abstract} - \def\ABS@endabstract{% - \immediate\write\@auxout{\string\gdef\string\@abstr{\the\toks@}}% - \iflanguage{ngerman}% - {\gdef\@abslang{\selectlanguage{english}}}% - {\iflanguage{german}% - {\gdef\@abslang{\selectlanguage{english}}}% - {\gdef\@abslang{\selectlanguage{ngerman}}}} - \expandafter\end\expandafter{\ABS@}} - \else%classical - \renewenvironment{abstract} - {\gdef\abstractexists{true}% - \iflanguage{ngerman}{\@abslang}{\iflanguage{german}{\@abslang}{}}% - \reset@font\normalsize\par\noindent - \subpdfbookmark{\abstractname}{abstract}% - \textcolor{textcol}{\reset@font\normalsize\if@sansserifface\sffamily\fi\bfseries\abstractname.} \ignorespaces} - {% - \ifx\second@bstract\@undefined\else\vskip\baselineskip\second@bstract\fi - \if!\@keyw!\else - \par\vspace{1.7mm}\noindent - \textbf{Keywords.}\enspace\ignorespaces\@keyw - \fi - \if@manuscript\else\if@noline\else - \par\vskip\baselineskip - \fi\fi - \iflanguage{ngerman} - {\gdef\@abslang{\selectlanguage{english}}}% - {\iflanguage{german}% - {\gdef\@abslang{\selectlanguage{english}}}% - {\gdef\@abslang{\selectlanguage{german}}% - \if@manuscript\else\if@noline\else\hrule\fi\fi}}} - \fi -\else%discussions - \renewenvironment{abstract} - {\gdef\abstractexists{true}% - \iflanguage{ngerman}{\@abslang}{\iflanguage{german}{\@abslang}{}}% - \section*{\abstractname\if@cop@home\ifonline\hypertarget{abstr}{}\fi\fi}} - {\iflanguage{ngerman}% - {\gdef\@abslang{\selectlanguage{english}}}% - {\iflanguage{german}% - {\gdef\@abslang{\selectlanguage{english}}}% - {\gdef\@abslang{\selectlanguage{ngerman}}}}} -\fi%stage -%%make sure the author doesn't forget anything -\AtEndDocument{% - \@ifundefined{abstractexists} - {\NoSectionWarning{Abstract}} - {}} -\if@stage@final - \let\@oxfloat=\@xfloat -\else - \let\orig@xfloat\@xfloat - \def\@oxfloat#1[#2]{% - \clearpage - \@nodocument - \begin{nolinenumbers}% - \def\@captype{#1}% - \null\vfill} - \let\orig@end@float\end@float - \def\end@float{% - \vfill - \end{nolinenumbers}} -\fi -\def\@xfloat#1[#2]{% - \@oxfloat#1[#2]% - \if@stage@final\vspace*{2mm}\fi - \centering - \small} -\if@stage@final - \if@sansserifface - \def\fnum@figure{\sffamily\color{textcol}\figurename\nobreakspace\thefigure} - \def\fnum@table{\sffamily\color{textcol}\tablename\nobreakspace\thetable} - \fi -\else - \def\fnum@figure{\rmfamily\bfseries\figurename\nobreakspace\thefigure} - \def\fnum@table{\rmfamily\bfseries\tablename\nobreakspace\thetable} -\fi -\long\def\@makecaption#1#2{% - \def\@tempa{figure}\ifx\@captype\@tempa - \if@stage@final - \vskip0.7\abovecaptionskip - \else - \vskip\abovecaptionskip\goodbreak - \fi - \fi - {\reset@font\small{\bfseries#1.} #2\par}% - \if@cop@home\ifonline\ifnum\csname c@\@captype\endcsname=1 % for 1st fig or tab only - \immediate\write\@auxout{\string\gdef\string\@num\@captype{}}% - \hypertarget{\@captype}{}% - \fi\fi\fi - \def\@tempa{table}\ifx\@captype\@tempa - \vskip\abovecaptionskip - \if@stage@final\else\goodbreak\fi - \fi} -\if@stage@final - \if@manuscript - \else - \columnsep7mm\relax - \fi -\else - \columnsep7mm\relax -\fi -\if@stage@final - \if@manuscript - \pagestyle{plain} - \else - \pagestyle{headings} - \fi -\else - \pagestyle{headings} -\fi -\if@stage@final - \if@manuscript - \else - \@twosidetrue - \@twocolumntrue - \sloppy - \flushbottom - \fi -\fi -\RequirePackage[normalem]{ulem}% -\RequirePackage[T1]{fontenc} -\RequirePackage{textcomp} -\if@cop@home - \RequirePackage{fontawesome5} - \RequirePackage{fontawesome} -\fi -\ifx\xmltexversion\@undefined - \RequirePackage[utf8]{inputenc} - \def\strip@x#1x#2\@nil{#1}% - \IfFileExists{ucharacters.sty}{% - \def\DefineCharacter##1##2##3{\expandafter\def\expandafter\@argii\expandafter{\strip@x##2x\@nil}\DeclareUnicodeCharacter{\@argii}{##3}}% - \usepackage{ucharacters}% - }{}% -\fi -\def\cmrng{{\fontfamily{cmr}\selectfont\ng}} -\let\old@classoptionslist\@classoptionslist -\edef\@classoptionslist{english,\old@classoptionslist} -\RequirePackage{babel} -\let\@classoptionslist\old@classoptionslist -\def\@tempa{french}\ifx\bbl@main@language\@tempa - \StandardLayout - %% Switch to quotation marks with additional horizontal spacing - \bbl@frenchguillemets - \global\let\flqq\og \global\let\frqq\fg - \ifx\xmltexversion\@undefined\else - \begingroup - \catcode`\!=\active\gdef!{\utfeightax!}% - \catcode`\?=\active\gdef?{\utfeightax?}% - \catcode`\:=\active\gdef:{\utfeightax:}% - \catcode`\;=\active\gdef;{\utfeightax;}% - \endgroup - \fi -\fi -\expandafter\ifx\csname l@ngerman\endcsname\relax - \chardef\l@ngerman="FD -\fi -\expandafter\ifx\csname l@german\endcsname\relax - \chardef\l@german="FE -\fi -\def\@tempa{% - \def\introductionname{Introduction}% - \def\secabstractname{Kurzfassung}% - \def\conclusionname{Conclusions}% - \def\copyrightstatementname{Copyright statement}% - \def\codeavailabilityname{Code availability}% - \def\dataavailabilityname{Data availability}% - \def\codedataavailabilityname{Code and data availability}% - \def\sampleavailabilityname{Sample availability}% - \def\authorcontributionname{Author contributions}% - \def\competinginterestsname{Competing interests}% - \def\videosupplementname{Video supplement}% - \def\dosupplementname{Supplement}% - \def\teamlistname{Team list}% - \def\disclaimername{Disclaimer}% - \def\sistatementname{Special issue statement}% - \def\financialsupportname{Financial support}% - \def\reviewstatementname{Review statement}% - \def\acknowledgementname{Acknowledgement}% - \def\acknowledgementsname{Acknowledgements}% - \if@cop@home - \def\equationname{Eq.}% - \def\sectionname{Sect.}% - \fi} -\expandafter\addto\expandafter\captionsbritish\expandafter{\@tempa} -\expandafter\addto\expandafter\captionsUKenglish\expandafter{\@tempa} -\expandafter\addto\expandafter\captionsenglish\expandafter{\@tempa} -\expandafter\addto\expandafter\captionsamerican\expandafter{\@tempa} -\expandafter\addto\expandafter\captionsUSenglish\expandafter{\@tempa} -\def\@tempa{% - \def\figurename{Abb.}% - \def\abstractname{Kurzfassung}% - \def\secabstractname{Abstract}% - \def\introductionname{Einleitung}% - \def\conclusionname{Fazit}% - \def\copyrightstatementname{Urheberrechtserklärung}% - \def\codeavailabilityname{Codeverfügbarkeit}% - \def\dataavailabilityname{Datenverfügbarkeit}% - \def\codedataavailabilityname{Code- und Datenverfügbarkeit}% - \def\sampleavailabilityname{Probenverfügbarkeit}% - \def\authorcontributionname{Autorenmitwirkung}% - \def\competinginterestsname{Interessenkonflikt}% - \def\videosupplementname{Videoanhang}% - \def\dosupplementname{Supplement}% - \def\teamlistname{Gruppenautorenschaft}% - \def\disclaimername{Haftungsausschluss}% - \def\sistatementname{Erklärung zum Sonderheft}% - %% TBD - \def\financialsupportname{Finanzierung}% - \def\reviewstatementname{Begutachtung}% - \def\acknowledgementname{Danksagung}% - \def\acknowledgementsname{Danksagung}% - \if@cop@home - \def\equationname{Gl.}% - \def\sectionname{Kap.}% - \fi} -\expandafter\addto\expandafter\captionsngerman\expandafter{\@tempa} -\expandafter\addto\expandafter\captionsgerman\expandafter{\@tempa} -\def\@tempa{% - \def\figurename{Figure}% - \def\tablename{Tableau}% - \def\secabstractname{Kurzfassung}% - \def\introductionname{Introduction}% - \def\conclusionname{Conclusion}% - \def\copyrightstatementname{Affirmation du droit d'auteur}% - \def\codeavailabilityname{Disponibilité du code}% - \def\dataavailabilityname{Disponibilité des données}% - \def\sampleavailabilityname{Disponibilité des examples}% - \def\codedataavailabilityname{Disponibilité du code et des données}% - \def\authorcontributionname{Collaborateurs}% - \def\competinginterestsname{Intérêts concurrents}% - \def\videosupplementname{Annexes vidéo}% - \def\dosupplementname{Supplement}% - \def\teamlistname{Liste d'auteurs}% - \def\disclaimername{Clause de non-responsabilité}% - \def\sistatementname{Déclaration de la numéro special}% - %% TBD - \def\financialsupportname{Financement}% - \def\reviewstatementname{Contr\^{o}le par les pairs}% - \def\acknowledgementname{Remerciements}% - \def\acknowledgementsname{Remerciements}% - \if@cop@home - \def\equationname{Éq.}% - \def\sectionname{Sect.}% - \fi} -\expandafter\addto\expandafter\captionsfrench\expandafter{\@tempa} -\expandafter\addto\expandafter\captionsfrancais\expandafter{\@tempa} -\expandafter\addto\expandafter\captionscanadien\expandafter{\@tempa} -\expandafter\addto\expandafter\captionsacadian\expandafter{\@tempa} -\RequirePackage{array} -\def\@cline#1-#2\@nil{% - \noalign{% - \ifx\@clinecorr\@undefined - \vskip0.5mm% - \global\let\@clinecorr\relax - \else - \vskip-1.5mm% - \fi}% - \omit - \@multicnt#1% - \advance\@multispan\m@ne - \ifnum\@multicnt=\@ne\@firstofone{&\omit}\fi - \@multicnt#2% - \advance\@multicnt-#1% - \advance\@multispan\@ne - \leaders\hrule\@height\arrayrulewidth\hfill - \cr - \noalign{% - \vskip-\arrayrulewidth - \vskip1.5mm}} -\def\@arraycr{\relax\iffalse{\fi\ifnum 0=`}\fi - \global\let\@clinecorr\@undefined - \@ifstar \@xarraycr \@xarraycr} -\RequirePackage{tabularx} -\IfFileExists{graphicx.sty} - {\RequirePackage{graphicx}% - \ifnum\pdfoutput=\z@ - \DeclareGraphicsExtensions{.eps,.ps}% - \else - \DeclareGraphicsExtensions{.pdf,.png,.jpg} - \fi} - {\CopernicusWarningNoLine{Cannot find graphicx.sty; proceeding without it}} -\IfFileExists{color.sty} - {\RequirePackage{color}} - {\CopernicusWarningNoLine{Cannot find color.sty; proceeding without it}} -\IfFileExists{amssymb.sty} - {\RequirePackage{amssymb}} - {\CopernicusWarningNoLine{Cannot find amssymb.sty; proceeding without it}} -\IfFileExists{amsmath.sty} - {\RequirePackage[intlimits,fleqn,tbtags]{amsmath} - \ifx\xmltexversion\@undefined - \else - \renewcommand{\allowdisplaybreaks}[1][4]{% - \global\interdisplaylinepenalty\getdsp@pen{##1}\relax}% - \fi} - {\CopernicusWarningNoLine{Cannot find amsmath.sty; proceeding without it}} -\RequirePackage{amsthm} -\newcommand\Authfont{\normalfont} -\newcommand\Affilfont{\normalfont} -\newcommand\Authsep{, } -\newcommand\Authands{, and } -\newcommand\Authand{ and } -\newlength\affilsep\setlength{\affilsep}{1em} -\newlength\@affilsep -\newcounter{Maxaffil} -\setcounter{Maxaffil}{2} -\newcounter{authors} -\newcounter{affil} -\newif\ifnewaffil \newaffiltrue -\newcommand\AB@authnote[1]{\textsuperscript{\normalfont#1}} -\newcommand\AB@affilnote[1]{\textsuperscript{\normalfont#1}} -\providecommand\textsuperscript[1]{$^{#1}$} -\newcommand\AB@blk@and{\protect\Authfont\protect\AB@setsep} -\newcommand\AB@pand{\protect\and \protect\Authfont \protect\AB@setsep} -\@namedef{@sep1}{} -\@namedef{@sep2}{\Authand} -\newcommand\AB@affilsep{\protect\Affilfont} -\newcommand\AB@affilsepx{\protect\\\protect\Affilfont} -\newcommand\AB@setsep{\setlength{\@affilsep}{\affilsep}} -\newcommand\AB@resetsep{\setlength{\@affilsep}{\z@}} -\newcommand\AB@authlist{} -\newcommand\AB@affillist{} -\newcommand\AB@authors{} -\newcommand\AB@empty{} -\xdef\AB@author{\noexpand\AB@blk@and\@author} -\def\true{true}% -\newcounter{authnum} -\global\let\@@deceased\relax -\global\let\@@econtrib\relax - -\renewcommand\author[2][]% - {\ifnewaffil\addtocounter{affil}{1}% - \xdef\AB@thenote{\arabic{affil}}\fi - \global\advance\c@authnum\@ne - \if@cop@home - \expandafter\ifx\csname deceased@\the\c@authnum\endcsname\true\relax\def\@@deceased{$^{,\text{\faCross}}$}\fi - \expandafter\ifx\csname econtrib@\the\c@authnum\endcsname\true\relax\def\@@econtrib{$^{,\text{\faStar}}$}\fi - \fi - \def\@tempa{#1}\ifx\@tempa\@empty\def\AB@note{\AB@thenote}\else\def\AB@note{#1}% - \setcounter{Maxaffil}{0}\fi - \ifnum\value{authors}>1\relax - \expandafter\gdef\csname @sep\number\c@authors\endcsname{\Authsep}% - \fi - \addtocounter{authors}{1}% - \begingroup - \let\protect\@unexpandable@protect \let\and\AB@pand - \def\thanks{\protect\thanks}\def\footnote{\protect\footnote}% - \@temptokena=\expandafter{\AB@authors}% - {\def\\{\protect\\[\@affilsep]\protect\Affilfont - \protect\AB@resetsep}% - \protected@xdef\AB@author{\AB@blk@and#2}% - \ifnewaffil\gdef\AB@las{}\gdef\AB@lasx{\protect\Authand}\gdef\AB@as{}% - \xdef\AB@authors{\the\@temptokena\AB@blk@and}% - \else - \xdef\AB@authors{\the\@temptokena\AB@as\AB@au@str}% - \global\let\AB@las\AB@lasx\gdef\AB@lasx{\protect\Authands}% - \gdef\AB@as{\Authsep}% - \fi - \gdef\AB@au@str{#2}}% - \@temptokena=\expandafter{\AB@authlist}% - \let\\=\authorcr - \protected@xdef\AB@authlist{\the\@temptokena - \protect\@nameuse{@sep\number\c@authors}% - \protect\Authfont#2\AB@authnote{\AB@note}% - \@@econtrib - \@@deceased}% - \endgroup - \ifnum\value{authors}>2\relax - \expandafter\gdef\csname @sep\number\c@authors\endcsname{\Authands}% - \fi - \newaffilfalse -\global\let\@@deceased\relax\global\let\@@econtrib\relax} -\newcommand\authorcr{\protect\\ \protect\Authfont \protect\AB@setsep}% -\newcommand\affil[2][]% - {\newaffiltrue\let\AB@blk@and\AB@pand - \def\@tempa{#1}\ifx\@tempa\@empty\def\AB@note{\AB@thenote}\else\def\AB@note{#1}% - \setcounter{Maxaffil}{0}\fi - \begingroup - \let\protect\@unexpandable@protect - \def\thanks{\protect\thanks}\def\footnote{\protect\footnote}% - \@temptokena=\expandafter{\AB@authors}% - {\def\\{\protect\\\protect\Affilfont}\protected@xdef\AB@temp{#2}}% - \protected@xdef\AB@authors{\the\@temptokena\AB@las\AB@au@str - \protect\\[\affilsep]\protect\Affilfont\AB@temp}% - \gdef\AB@las{}\gdef\AB@au@str{}% - {\def\\{, \ignorespaces}\protected@xdef\AB@temp{#2}}% - \@temptokena=\expandafter{\AB@affillist}% - \protected@xdef\AB@affillist{\the\@temptokena \AB@affilsep - \AB@affilnote{\AB@note}\protect\Affilfont\AB@temp}% - \endgroup - \let\AB@affilsep\AB@affilsepx -} -\def\@author{} -\renewcommand\@author{% - \let\no@par\relax - \ifx\AB@affillist\AB@empty\AB@author\else - \ifnum\value{affil}>\value{Maxaffil}% - \AB@authlist\\[\affilsep]\AB@affillist - \else - \AB@authors - \fi - \fi} - -\def\deceased@sep#1,#2\@nil{% - \immediate\write\@auxout{\string\expandafter\string\gdef\string\csname\space deceased@#1\endcsname{true}}% - \if!#2!\else\deceased@sep#2\@nil\fi} -\def\econtrib@sep#1,#2\@nil{% - \immediate\write\@auxout{\string\expandafter\string\gdef\string\csname\space econtrib@#1\endcsname{true}}% - \if!#2!\else\econtrib@sep#2\@nil\fi} - -\newcommand\deceased[2][]{\gdef\@deceasedtext{#1}\@deceased{#2}} -\if@cop@home -\def\@deceased#1{% - \ifx\@deceasedtext\@empty\gdef\@deceasedNote{deceased}\else\gdef\@deceasedNote{deceased, \@deceasedtext}\fi - \deceased@sep#1,\@nil - \@temptokena=\expandafter{\AB@affillist}% - \protected@xdef\AB@affillist{\the\@temptokena \AB@affilsep - \AB@affilnote{\faCross}\protect\Affilfont\@deceasedNote}% - } -\newcommand\equalcontrib[1]{% - \gdef\@econtribNote{These authors contributed equally to this work.}% - \econtrib@sep#1,\@nil - \@temptokena=\expandafter{\AB@affillist}% - \protected@xdef\AB@affillist{\the\@temptokena \AB@affilsep - \AB@affilnote{\faStar}\protect\Affilfont\@econtribNote}% - } -\else - \let\equalcontrib\@gobble - \let\@deceased\@gobble -\fi -\def\Author{\@ifnextchar[\@Author{\@Author[]}}%] -\def\@Author[#1]{% - \def\@tempa{#1}% - \@ifnextchar(\@@Author{\@@Author()}}%)} -\def\@@Author(#1){% - \def\@tempb{#1}% - \@ifnextchar(\@@@Author{\@@@Author()}}%)} -\def\@@@Author(#1)#2#3{% - \def\@tempc{#1}% - \protected@edef\@tempd{% - \ifx\@tempb\@empty\else\@tempb\nobreakspace\fi - #2\nobreakspace - #3% - \ifx\@tempc\@empty\else\nobreakspace\@tempc\fi}% - \expandafter\expandafter\expandafter\author\expandafter\expandafter\expandafter - [\expandafter\@tempa\expandafter]\expandafter{\@tempd}} -\providecommand\appendixname{Appendix} -\let\orisection=\section -\let\theolds=\thesection -\let\theoldss=\thesubsection -\def\appendix{\par - \setcounter{section}{0}% - \setcounter{subsection}{0}% - \def\thesection{\@Alph\c@section}% - \def\thesubsection{\thesection\@arabic\c@subsection}% - \setcounter{secnumdepth}{4}% - \@addtoreset{equation}{section}% - \setcounter{equation}{0}% - \setcounter{reaction}{0}% - \def\theequation{\thesection\@arabic\c@equation}% - \def\thereaction{\thesection R\@arabic\c@reaction}% - \let\c@org@eq\c@equation% - \let\org@theeq\theequation% - \if@stage@final - \@addtoreset{figure}{section}% - \setcounter{figure}{0}% - \def\thefigure{\thesection\@arabic\c@figure}% - \@addtoreset{table}{section}% - \setcounter{table}{0}% - \def\thetable{\thesection\@arabic\c@table}% - \fi - \global\let\old@sect\@sect - \def\@sect##1##2##3##4##5##6[##7]##8{% - \ifnum ##2>\c@secnumdepth - \let\@svsec\@empty - \else - \refstepcounter{##1}% - \ifnum ##2=\@ne - \def\@tempa{##8}% - \protected@edef\@svsec{% - \appendixname\space\csname the##1\endcsname - \ifx\@tempa\@empty\else:\enskip\fi\relax}% - \else - \protected@edef\@svsec{\@seccntformat{##1}\relax}% - \fi - \fi - \@tempskipa ##5\relax - \ifdim \@tempskipa>\z@ - \begingroup - \ifnum ##2=\@ne\let\@hangfrom\noindent\fi - ##6{% - \@hangfrom{\hskip ##3\relax\@svsec}% - \interlinepenalty \@M ##8\@@par}% - \endgroup - \csname ##1mark\endcsname{##7}% - \addcontentsline{toc}{##1}{% - \appendixname\space\csname the##1\endcsname\if!##7!\else:\space\fi%for bookmarks - ##7}% - \else - \def\@svsechd{% - ##6{\hskip ##3\relax - \@svsec ##8}% - \csname ##1mark\endcsname{##7}% - \addcontentsline{toc}{##1}{% - \appendixname\space\csname the##1\endcsname\if!##7!\else:\space\fi%for bookmarks - ##7}}% - \fi - \@xsect{##5}} - \global\let\old@ssect\@ssect - \def\@ssect##1##2##3##4##5{% - \@tempskipa ##3\relax - \ifdim \@tempskipa>\z@ - \begingroup - ##4{% - \@hangfrom{\hskip ##1}% - \@tempskipa##2\relax - \ifdim\@tempskipa<-17\p@%check for sectionlevel=1 - \appendixname - \def\@tempa{##5}\ifx\@tempa\@empty\else:\enskip\fi - \fi - \interlinepenalty \@M ##5\@@par}% - \endgroup - \else - \def\@svsechd{##4{\hskip ##1\relax ##5}}% - \fi - \@xsect{##3}}} -\def\noappendix{\setcounter{secnumdepth}{0}% - \global\let\section=\orisection - \global\let\thesection=\theolds - \global\let\thesubsection=\theoldss - \ifx\old@sect\@undefined\else\global\let\@sect\old@sect\fi - \ifx\old@ssect\@undefined\else\global\let\@ssect\old@ssect\fi - \def\thefigure{\@arabic\c@figure}% - \def\thetable{\@arabic\c@table}} -\IfFileExists{url.sty} - {\RequirePackage{url}\urlstyle{same}}% - {\CopernicusWarningNoLine{Cannot find url.sty; proceeding without it}% - \def\url#1{% - \CopernicusError{To use \string\url, you must have url.sty}{Install url.sty}}} -\newcommand\doitext{https://doi.org/} -\newcommand*\doi{% - \begingroup - \lccode`\~=`\#\relax - \lowercase{\def~{\#}}% - \lccode`\~=`\_\relax - \lowercase{\def~{\_}}% - \lccode`\~=`\<\relax - \lowercase{\def~{\textless}}% - \lccode`\~=`\>\relax - \lowercase{\def~{\textgreater}}% - \lccode`\~=0\relax - \catcode`\#=\active - \catcode`\_=\active - \catcode`\<=\active - \catcode`\>=\active - %catcode change won't work after \bibitem while backref.sty - % grabs for the whole entry - \@doi} -\def\@doi#1{% - \let\#\relax - \let\_\relax - \let\textless\relax - \let\textgreater\relax - \edef\x{\toks0={{#1}}}% - \x - \edef\#{\@percentchar23}% - \edef\_{_}% - \edef\textless{\@percentchar3C}% instead of {\string<} for Apple - \edef\textgreater{\@percentchar3E}% instead of {\sting>} for Apple - \edef\x{\toks1={\noexpand\href{https://doi.org/#1}}}% - \x - \edef\x{\endgroup\doitext\the\toks1 \the\toks0}% - \x} -\IfFileExists{accents.sty} - {\RequirePackage{accents}} - {\CopernicusWarningNoLine{Cannot find accents.sty; proceeding without it}} -\IfFileExists{cancel.sty} - {\RequirePackage{cancel}} - {\CopernicusWarningNoLine{Cannot find cancel.sty; proceeding without it}} -\IfFileExists{multirow.sty} - {\RequirePackage{multirow}} - {\CopernicusWarningNoLine{Cannot find multirow.sty; proceeding without it}} -\IfFileExists{supertabular.sty} - {\RequirePackage{supertabular}% - \let\old@tablecaption\tablecaption - \def\tablecaption{\def\@captype{table}\old@tablecaption} - \let\old@supertabular\supertabular - \def\supertabular{% - \clearpage - \centering - \small - \old@supertabular} - \@namedef{supertabular*}##1{% - \clearpage - \centering - \small - \@ifnextchar[{\@nameuse{@supertabular*}{##1}}% - {\@nameuse{@supertabular*}{##1}[]}%] - } - \let\old@endsupertabular\endsupertabular - \def\ud@captype{\let\@captype\@undefined} - \def\ud@cr{\let\\\@normalcr} - \long\def\endsupertabular{% - \old@endsupertabular\par - \global\let\@table@first@head\undefined - \global\let\@table@last@tail\undefined - \tablehead{}% - \tabletail{}% - \aftergroup\ud@captype - \aftergroup\ud@cr} - \expandafter\let\csname endsupertabular*\endcsname\endsupertabular} - {\CopernicusWarningNoLine{Cannot find supertabular.sty; proceeding without it}} -\IfFileExists{algorithmic.sty} - {\RequirePackage{algorithmic}} - {\CopernicusWarningNoLine{Cannot find algorithmic.sty; proceeding without it}} -\IfFileExists{algorithm.sty} - {\if@stage@final - \else - \def\extra@float##1{% - \@ifnextchar[%] - {\orig@xfloat{##1}}% - {\edef\reserved@a{\noexpand\orig@xfloat{##1}[\csname fps@##1\endcsname]}% - \reserved@a}} - \RequirePackage{float}% - \def\float@restyle##1{\expandafter\edef\csname - fst@##1\endcsname{\expandafter\noexpand\csname - fs@\float@style\endcsname}% - \@namedef{##1}{\@nameuse{fst@##1}% - \@float@setevery{##1}\extra@float{##1}}% - \@namedef{##1*}{\@nameuse{fst@##1}% - \@float@setevery{##1}\@dblfloat{##1}}% - \expandafter\let\csname end##1\endcsname\float@end - \expandafter\let\csname end##1*\endcsname\float@dblend - \expandafter\let\csname @float@c@##1\endcsname=\float@caption - \@ifundefined{@float@every@##1}{% - \expandafter\newtoks\csname @float@every@##1\endcsname}{}% - \@nameuse{@float@every@##1}={}} - \def\float@end{\@endfloatbox - \global\setbox\@currbox\float@makebox\columnwidth - \let\@endfloatbox\relax\orig@end@float} - \fi - \RequirePackage{algorithm} - \def\theHalgorithm{\@arabic\c@algorithm}} - {\CopernicusWarningNoLine{Cannot find algorithm.sty; proceeding without it}} -\let\cop@makecaption\@makecaption -\let\c@org@fig\c@figure -\let\@orgfigurename\figurename -\def\setfigures{\global\let\c@figure\c@org@fig\global\let\figurename\@orgfigurename} -\@definecounter{figscheme} -\def\schemename{Scheme} -\let\figschemename\schemename -\def\setschemes{\global\let\c@figure\c@figscheme\global\let\figurename\figschemename} -\@definecounter{plates} -\def\platesname{Plate} -\def\setplates{\global\let\c@figure\c@plates\global\let\figurename\platesname} -\@definecounter{listings} -\def\listingsname{Listing} -\def\setlistings{\global\let\c@figure\c@listings\global\let\figurename\listingsname} -\@definecounter{boxes} -\def\boxesname{Box} -\def\setboxes{\global\let\c@figure\c@boxes\global\let\figurename\boxesname} -\if@stage@final - \IfFileExists{caption.sty} - {\RequirePackage{caption}} - {\CopernicusWarningNoLine{Cannot find caption.sty; proceeding without it}} -\else - \IfFileExists{subfig.sty} - {\RequirePackage{subfig}} - {\CopernicusWarningNoLine{Cannot find subfig.sty; proceeding without it}} -\fi -\let\@makecaption\cop@makecaption -\IfFileExists{subfloat.sty} - {\RequirePackage{subfloat}% - \protected@xdef\themainfigure{\thefigure}% - \protected@xdef\themaintable{\thetable}% - \g@addto@macro\subfiguresbegin{\global\let\theHfigure\thesubfloatfigure} - \g@addto@macro\subtablesbegin{\global\let\theHtable\thesubfloattable} - \g@addto@macro\subfiguresend{\global\let\theHfigure\thefigure@original} - \g@addto@macro\subtablesend{\global\let\theHtable\thetable@original}} - {\CopernicusWarningNoLine{Cannot find subfloat.sty; proceeding without it}} -\RequirePackage[authoryear,round]{natbib} -\def\NAT@sort{0}\def\NAT@cmprs{0} -\renewcommand\NAT@sep{;} \renewcommand\NAT@cmt{, } -\renewcommand\NAT@aysep{,} \renewcommand\NAT@yrsep{, } -\setlength\bibsep\z@ -\let\bibfont\small -\NAT@numbersfalse -\NAT@set@cites -\let\NAT@set@cites\relax -\AtBeginDocument{\let\@citex\NAT@citex} -\newcommand\urlprefix{} -\renewenvironment{thebibliography}[1] - {\bibsection - \if@secline\leavevmode\vspace*{-\baselineskip}\nobreak\fi - \parindent\z@ - \bibpreamble - \bibfont - \list{\@biblabel{\arabic{NAT@ctr}}}{\@bibsetup{#1}% - \setcounter{NAT@ctr}{0}}% - \ifNAT@openbib - \renewcommand\newblock{\par} - \else - \renewcommand\newblock{\hskip .11em \@plus.33em \@minus.07em}% - \fi - \sloppy - %\clubpenalty4000\widowpenalty4000 - \sfcode`\.=1000\relax - \let\citeN\cite \let\shortcite\cite - \let\citeasnoun\cite} - {\def\@noitemerr{% - \PackageWarning{natbib}{Empty `thebibliography' environment}}% - \endlist\vskip-\lastskip} -\def\bibsection{% - \if@stage@final - \if@manuscript\newpage\fi - \pdfbookmark[1]{\refname}{biblio}% - \fi - \noappendix\section*{\refname\if@cop@home\ifonline\hypertarget{references}{}\fi\fi}} -\RequirePackage{rotating} -\def\@rotxdblfloat#1[#2]{% - \@float{#1}[#2]% - \hsize\textwidth\linewidth\textwidth - \begin{lrbox}\rot@float@box - \begin{minipage}\textheight -} -\IfFileExists{lineno.sty} - {\RequirePackage[mathlines,modulo]{lineno}% - \if@stage@final - \if@manuscript - \linenumbers\renewcommand\linenumberfont{\normalfont\small\sffamily}% - \else - \setpagewiselinenumbers\switchlinenumbers%cf. the switch option - \linenumbersep3\p@ - \if@cop@home - \nolinenumbers - \else%new, 2015-12-14 - \linenumbers - \fi - \fi - \else - \setpagewiselinenumbers - \if@cop@home\linenumbers\fi - \fi - \g@addto@macro\nolinenumbers{\linenopenalty\z@}%avoids problems with \patchAmsMathEnvironmentForLinenoX while \nolinenumbers - \newcommand*\patchAmsMathEnvironmentForLineno[1]{% - \expandafter\let\csname old##1\expandafter\endcsname\csname ##1\endcsname - \expandafter\let\csname oldend##1\expandafter\endcsname\csname end##1\endcsname - \renewenvironment{##1}% - {\linenomath\csname old##1\endcsname}% - {\csname oldend##1\endcsname\endlinenomath}}% - \newcommand*\patchBothAmsMathEnvironmentsForLineno[1]{% - \patchAmsMathEnvironmentForLineno{##1}% - \patchAmsMathEnvironmentForLineno{##1*}}% - \newcommand*\patchAmsMathEnvironmentForLinenoX[1]{% - \expandafter\let\csname old##1\expandafter\endcsname\csname ##1\endcsname - \expandafter\let\csname oldend##1\expandafter\endcsname\csname end##1\endcsname - \renewenvironment{##1}% - {\linenomath\advance - \postdisplaypenalty-\linenopenalty - \csname old##1\endcsname}% - {\csname oldend##1\endcsname\endlinenomath}}% - \newcommand*\patchBothAmsMathEnvironmentsForLinenoX[1]{% - \patchAmsMathEnvironmentForLinenoX{##1}% - \patchAmsMathEnvironmentForLinenoX{##1*}}% - \AtBeginDocument{% - \patchBothAmsMathEnvironmentsForLineno{equation}% - \patchBothAmsMathEnvironmentsForLinenoX{align}% - \patchBothAmsMathEnvironmentsForLinenoX{flalign}% - \patchBothAmsMathEnvironmentsForLinenoX{alignat}% - \patchBothAmsMathEnvironmentsForLinenoX{gather}% - \patchBothAmsMathEnvironmentsForLinenoX{multline}}} - {\CopernicusWarningNoLine{Cannot find lineno.sty; proceeding without it}% - \let\nolinenumbers\bgroup\let\endnolinenumbers\egroup} -\IfFileExists{times.sty} - {\RequirePackage{times} - \def\Hv@scale{0.95}} - {\CopernicusWarningNoLine{Cannot find times.sty; proceeding without it}} -\if@stage@final - \if@cop@home - \let\vec\@undefined - \let\grave\@undefined - \let\acute\@undefined - \let\check\@undefined - \let\breve\@undefined - \let\bar\@undefined - \let\hat\@undefined - \let\dot\@undefined - \let\tilde\@undefined - \let\ddot\@undefined - \ifx\xmltexversion\@undefined\else{\catcode`\_=\active\global\let\xmltexUndersc@re_}\fi - \def\provide@orig@symbol#1{\expandafter\let\csname orig#1\expandafter\endcsname\csname#1\endcsname} - \provide@orig@symbol{Gamma} - \provide@orig@symbol{Delta} - \provide@orig@symbol{Theta} - \provide@orig@symbol{Lambda} - \provide@orig@symbol{Xi} - \provide@orig@symbol{Pi} - \provide@orig@symbol{Sigma} - \provide@orig@symbol{Upsilon} - \provide@orig@symbol{Phi} - \provide@orig@symbol{Psi} - \provide@orig@symbol{Omega} - \RequirePackage[mtbold]{mathtime} - \DeclareSymbolFont{largesymbolsA}{U}{esint}{m}{n}%from esint.sty - \DeclareMathSymbol{\oiintop}{\mathop}{largesymbolsA}{'015}%from esint.sty - \def\oiint{\oiintop\nolimits}%from esint.sty - \DeclareMathSymbol{\fintop}{\mathop}{largesymbolsA}{'037}%from esint.sty - \def\fint{\fintop\nolimits}%from esint.sty - \ifx\xmltexversion\@undefined\else{\catcode`\_=\active\global\let_\xmltexUndersc@re}\fi - \if@sansserifface - \DeclareMathVersion{sans} - \DeclareMathVersion{sansbold} - \def\mversion@sans{sans}\def\mversion@sansbold{sansbold} - \SetSymbolFont{operators}{sans}{OT1}{hvr}{m}{n}% - \SetSymbolFont{letters}{sans}{OML}{hvm}{m}{it}% - \SetSymbolFont{symbols} {sans}{MY2}{mtt}{m}{n}%because +=; reencoded in mathtime.sty - \SetSymbolFont{largesymbols}{sans}{OMX}{hvex}{m}{n}% - \SetSymbolFont{operators}{sansbold}{OT1}{hvr}{bx}{n}% - \SetSymbolFont{letters}{sansbold}{OML}{hvm}{b}{it}% - \SetSymbolFont{symbols} {sansbold}{MY2}{mtt}{b}{n}%because +=; reencoded in mathtime.sty - \def\provide@fontspec@symbol#1{% - \expandafter\let\csname mt#1\expandafter\endcsname\csname#1\endcsname - \expandafter\DeclareRobustCommand\expandafter*\csname #1\endcsname{% - \ifx\math@version\mversion@sans\csname orig#1\endcsname - \else\ifx\math@version\mversion@sansbold\csname orig#1\endcsname - \else\csname mt#1\endcsname\fi\fi}} - \provide@fontspec@symbol{Gamma} - \provide@fontspec@symbol{Delta} - \provide@fontspec@symbol{Theta} - \provide@fontspec@symbol{Lambda} - \provide@fontspec@symbol{Xi} - \provide@fontspec@symbol{Pi} - \provide@fontspec@symbol{Sigma} - \provide@fontspec@symbol{Upsilon} - \provide@fontspec@symbol{Phi} - \provide@fontspec@symbol{Psi} - \provide@fontspec@symbol{Omega} - \DeclareMathDelimiter{(}{\mathopen} {operators}{"28}{largesymbols}{"00}%was reencoded in mathtime.sty - \DeclareMathDelimiter{)}{\mathclose}{operators}{"29}{largesymbols}{"01}%was reencoded in mathtime.sty - \SetMathAlphabet\mathrm{sans}{OT1}{hvr}{m}{n}%mind! (gives more flexibility) - \SetMathAlphabet\mathrm{sansbold}{OT1}{hvr}{bx}{n}%mind! (gives more flexibility) - \SetMathAlphabet\mathit{sans}{OT1}{hvr}{m}{it}% - \SetMathAlphabet\mathit{sansbold}{OT1}{hvr}{bx}{it}% - \SetMathAlphabet\mathbf{sans}{OT1}{hvr}{bx}{n}% - \SetMathAlphabet\mathbf{sansbold}{OT1}{hvr}{bx}{n}% - \RequirePackage{hvams} - %neu: - \DeclareFontShape{U}{msb}{m}{n}{<-6>msbm5<6-8>msbm7<8->msbm10}{}%aus amsfonts.sty - \DeclareFontFamily{U}{msbhv}{}%umbenannt aus hvams.sty - \DeclareFontShape{U}{msbhv}{m}{n}{<->\@l@scale hvbm10}{}%umbenannt aus hvams.sty - \SetMathAlphabet\mathbb{sans}{U}{msbhv}{m}{n}% - \SetMathAlphabet\mathbb{sansbold}{U}{msbhv}{m}{n}% - %Ende neu - \DeclareMathAlphabet\mathbold{MY1}{mtt}{b}{\greekshape}% - \SetMathAlphabet\mathbold{sans}{OML}{hvm}{b}{it}% - \SetMathAlphabet\mathbold{sansbold}{OML}{hvm}{bx}{it}% - \fi - \else - \if@sansserifface - \DeclareMathVersion{sans} - \DeclareMathVersion{sansbold} - \SetSymbolFont{operators}{sansbold}{OT1}{cmr} {bx}{n} - \SetSymbolFont{letters} {sansbold}{OML}{cmm} {b}{it} - \SetSymbolFont{symbols} {sansbold}{OMS}{cmsy}{b}{n} - \SetMathAlphabet\mathsf{sansbold}{OT1}{cmss}{bx}{n} - \SetMathAlphabet\mathit{sansbold}{OT1}{cmr}{bx}{it} - \DeclareMathAlphabet\mathbold{OML}{cmm}{b}{it}% - \fi - \fi -\else%discussions - \if@cop@home - \if@hvmath - \RequirePackage{hvmath} - \expandafter\let\csname\expandafter\string\csname T1\endcsname\string\'-\string y\endcsname\relax%patching wrong glyph in hvr, slot 253 - \DeclareMathSymbol{,}{\mathpunct}{operators}{"2C} - \DeclareMathSymbol{.}{\mathord}{operators}{"2E} - \RequirePackage{hvams} - \else - \let\rmdefault\sfdefault - \DeclareSymbolFont{operators}{OT1}{cmss} {m}{n} - \DeclareMathAlphabet{\mathbf}{OT1}{cmss}{bx}{n} - \fi - \else - \let\rmdefault\sfdefault - \DeclareSymbolFont{operators}{OT1}{cmss} {m}{n} - \DeclareMathAlphabet{\mathbf}{OT1}{cmss}{bx}{n} - \fi -\fi -\DeclareMathAlphabet{\mathblackbold}{U}{dsrom}{m}{n} -\RequirePackage{pifont} -\if@cop@home - \if@nohyperref - \else - \if@stage@final\else - \PassOptionsToPackage{pagebackref,pdffitwindow}{hyperref} - \fi - \usepackage[\ifcopyediting bookmarks=false\else bookmarks=true\fi,colorlinks]{hyperref} - \hypersetup{anchorcolor=black,citecolor=black,filecolor=black,linkcolor=black,% - menucolor=black,pagecolor=black,urlcolor=black} - \let\old@Hy@backout\Hy@backout\def\Hy@backout{\leavevmode\old@Hy@backout}%bug-fixing, to be checked - \ifnum\pdfoutput=\z@\RequirePackage{breakurl}\fi - \pdfstringdefDisableCommands{\let\boldsymbol\relax\let\vec\relax} - \fi - \edef\@pdfcreator{% - copernicus.cls% - \space version \csname ver@copernicus.cls\endcsname - \ifx\xmltexversion\@undefined\else, produced from XML\fi} - \if@nohyperref\pdfinfo{/Creator (\@pdfcreator)}\fi -\else - \usepackage[bookmarks=false,pdfborder={0 0 0}]{hyperref} - \pdfstringdefDisableCommands{\let\boldsymbol\relax\let\vec\relax} -\fi -\ifx\xmltexversion\@undefined -\else - \ifnum\pdfoutput=\z@ - \def\ReadBookmarks{% - \begingroup - \escapechar=`\\% - \let\escapechar\@gobble % - \def\@@BOOKMARK[##1][##2]##3##4##5{\calc@bm@number{##5}}% - 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\Hy@OutlineName{}\Hy@pstringName{% - ##2\check@bm@number{##3}% - }{% - \expandafter\strip@prefix\meaning\Hy@temp - }% - }% - {% - \def\WriteBookmarks{0}% - \@inputtoc{\jobname.out}{}{}% - }% - %{\escapechar\m@ne\InputIfFileExists{\jobname.out}{}{}}% - \ifx\WriteBookmarks\relax - \else - \if@filesw - \newwrite\@outlinefile - \immediate\openout\@outlinefile=\jobname.out\relax - \ifHy@typexml - \immediate\write\@outlinefile{\relax}% - \fi - \fi - \fi - \endgroup} - \fi -\fi -\if@stage@final\else - \if@cop@home - \ifonline - \let\orig@psheadings\ps@headings - \let\orig@abstractname\abstractname - \let\orig@pdfcreator\@pdfcreator - \usepackage[screen,rightpanel]{pdfscreencop} - \let\ps@headings\orig@psheadings \pagestyle{headings}%because pdfscreencop overwrites it - \let\abstractname\orig@abstractname%because pdfscreencop overwrites it - \let\@pdfcreator\orig@pdfcreator%because pdfscreencop overwrites it - \setcounter{secnumdepth}{3}%because pdfscreencop sets it to 4 - \setlength\footskip{5mm}%because pdfscreencop overwrites it - \def\addButton#1#2{\begingroup\normalsfcodes\fboxsep\z@ - \sffamily\colorbox{buttonbackground}{\hbox to#1{\hfil\Black\st#2\hfil}}\endgroup} - \hypersetup{anchorcolor=black,citecolor=black,filecolor=black,linkcolor=black,% - menucolor=black,pagecolor=black,urlcolor=black,% - pdfcenterwindow=false,pdfmenubar=true,pdftoolbar=true,pdfwindowui=true} - %because pdfscreencop overwrites it - \def\PDFSCR@Warning#1{}% no more "No overlay specified" warnings - \setlength\panelwidth{5cm}% - \newlength\bigbutton\setlength\bigbutton{0.75\panelwidth}% - \newlength\buttongap\setlength\buttongap{0.06\panelwidth}% - \newlength\smallbutton\setlength\smallbutton{0.5\bigbutton}% - \addtolength\smallbutton{-0.5\buttongap-0.5pt}% - \def\panelfont{\rmfamily\scriptsize}% - \margins{10mm}{10mm}{7mm}{7mm}% - \screensize{15.9cm}{21.6cm}% - \definecolor{backgroundcolor}{rgb}{1.,1.,1.}%white - \backgroundcolor{backgroundcolor}% - \definecolor{section0}{rgb}{0.,0.,0.}%black - \definecolor{section1}{rgb}{0.,0.,0.}%black - \definecolor{section2}{rgb}{0.,0.,0.}%black - \definecolor{section3}{rgb}{0.,0.,0.}%black - \definecolor{section4}{rgb}{0.,0.,0.}%black - \def\panel{% - \colorbox[rgb]{0.94,0.95,0.95}% - {\begin{minipage}[t][\paperheight][t]{\panelwidth} - %% set default font for panel: - \fontseries{m}\fontshape{n}\fontsize{11}{13.7pt}\rmfamily - %% journal name, volume, pages, year, runningtitle, runningauthor: - \null\vspace*{7mm}% - \centering - \parbox[t]{0.8\panelwidth}% - {\centering\color{paneltext}% - {\Large\bfseries - %overwrite of default urlcolor=black to journal-specific color @journalname - %for the @journalnameshort link to the journal webpage on the panel - \hypersetup{urlcolor=journalname}% - \href{http://\@journalurl}{\@journalnameshort}}\\[2mm] - \if@noref - \else - {\fontsize{8.7}{11}\selectfont - %\@pvol, \@fpage\if@nolastpage\else{--\@lpage}\fi, \@pyear - \hypersetup{urlcolor=paneltext}\doi{10.5194/\@msnumber}% - }\\[1mm]% - \fi - \rule{0.8\panelwidth}{1.1pt}\\[1mm] - {\bfseries\mathversion{bold}% - \leavevmode\null - \ifx\firstruntit@utput\@undefined - \global\let\firstruntit@utput\relax - \else - \def\blackb@x[##1]##2{\relax}% - \fi - \@runtit}% - \if@noauthor\else\\[3mm]{\small\leavevmode\null\@runauth}\fi - \\[0mm]% - \rule{0.8\panelwidth}{1.1pt}\\[5mm]} %keep this blank! - %% the buttons: - \addButton{\bigbutton} - {\hyperlink{title}{\hfill\color{buttontext}Title Page\hfill}}% - \\[1.5mm] - \addButton{\smallbutton} - {\hyperlink{abstr}{\hfill\color{buttontext}Abstract\hfill}}% - \hspace{\buttongap}% - \ifessd - \addButton{\smallbutton} - {\hyperlink{instru}{\hfill\color{buttontext}Instruments\hfill}}% - \\[1.5mm] - \else - \addButton{\smallbutton} - {\hyperlink{intro}{\hfill\color{buttontext}Introduction\hfill}}% - \\[1.5mm] - \fi - \ifessd - \addButton{\bigbutton} - {\hyperlink{datastruct}{\hfill\color{buttontext}Data Provenance \& Structure\hfill}}% - \\[1.5mm] - \else - \addButton{\smallbutton} - {\hyperlink{conclusions}{\hfill\color{buttontext}Conclusions\hfill}}% - \hspace{\buttongap}% - \addButton{\smallbutton} - {\hyperlink{references}{\hfill\color{buttontext}References\hfill}}% - \\[1.5mm] - \fi - \addButton{\smallbutton} - {\@ifundefined{@numtable}%automatically defined via \@num\@captype - {\hfill\color{buttontext}Tables\hfill} - {\hyperlink{table}{\hfill\color{buttontext}Tables\hfill}}}% - \hspace{\buttongap}% - \addButton{\smallbutton} - {\@ifundefined{@numfigure}% automatically defined via \@num\@captype - {\hfill\color{buttontext}Figures\hfill} - {\hyperlink{figure}{\hfill\color{buttontext}Figures\hfill}}}% - \\[4mm]% - \Acrobatmenu{FirstPage}{\addButton{\smallbutton}% - {\color{buttontext}$\rule[-0.144ex]{0.35ex}{1.244ex}\!\blacktriangleleft$}}% - \hspace{\buttongap}% - \Acrobatmenu{LastPage} - {\addButton{\smallbutton}% - {\color{buttontext}$\blacktriangleright\!\rule[-0.144ex]{0.35ex}{1.244ex}$}}% - \\[1.5mm] - \Acrobatmenu{PrevPage} - {\addButton{\smallbutton}{\color{buttontext}$\blacktriangleleft$}}% - \hspace{\buttongap}% - \Acrobatmenu{NextPage} - {\addButton{\smallbutton}{\color{buttontext}$\blacktriangleright$}}% - \\[1.5mm] - \Acrobatmenu{GoBack}{\addButton{\smallbutton}{\color{buttontext}Back}}% - \hspace{\buttongap}% - \Acrobatmenu{Close}{\addButton{\smallbutton}{\color{buttontext}Close}}% - \\[1.5mm] - \Acrobatmenu{FullScreen}{\addButton{\bigbutton}{\color{buttontext}Full Screen / Esc}}% - \\[4mm] - \addButton{\bigbutton} - {\href{http://\@journalurl/\@pvol/\@fpage/\@pyear/\@journalnameshortlower-\@pvol-\@fpage-\@pyear-print.pdf}% - {\hfill\color{buttontext}Printer-friendly Version\hfill}}% - \\[1.5mm] - \addButton{\bigbutton} - {\href{http://\@journalurl/\@pvol/\@fpage/\@pyear/\@journalnameshortlower-\@pvol-\@fpage-\@pyear-discussion.html}% - {\hfill\color{buttontext}Interactive Discussion\hfill}}% - \\[4mm] - \href{http://creativecommons.org/licenses/by/3.0/}{\includegraphics[width=1.7cm]{CreativeCommons_Attribution_License.png}}% - \null\vspace*{10mm}% - \end{minipage}}} - \fi - \fi -\fi -%% some of the following commands are only active if \@cop@hometrue -\def\texlicencestatement#1{\gdef\@texlicencestatement{#1}}% - \def\@texlicencestatement{\CopernicusError{Please add \string\texlicencestatement}{You must provide the licence statement before \string\maketitle"}} -\def\received#1{\if@cop@home\def\@recvd{#1}\fi} \def\@recvd{}%+1,+2,+d -\def\pubdiscuss#1{\if@cop@home\def\@pubdiscuss{#1}\fi} \def\@pubdiscuss{}%+1,+2,-d -- twostagejnltrue -\def\revised#1{\if@cop@home\def\@revsd{#1}\fi} \def\@revsd{}%+1,+2,-d -\def\accepted#1{\if@cop@home\def\@accptd{#1}\fi} \def\@accptd{}%+1,+2,+d -\def\published#1{\if@cop@home\gdef\@published{#1}\fi} \if@stage@final\else\def\@published{}\fi%+1,+2,+d -\def\firstpage#1{\if@cop@home\ifx\specialp@perstring\@undefined\ifx\citati@nbyarticlenumber\@undefined\gdef\@fpage{#1}\fi\fi\fi} - \def\@fpage{1}%+1,+2,+d -\def\articlenumber#1{\if@cop@home\ifx\specialp@perstring\@undefined\ifx\citati@nbyarticlenumber\relax\gdef\@fpage{#1}\gdef\article@number{#1}\fi\fi\fi} -\def\citationbyarticlenumber{% - \@nolastpagetrue - \let\citati@nbyarticlenumber\relax - \def\@fpage{-1}} -\ifx\xmltexversion\@undefined - \@onlypreamble\citationbyarticlenumber -\fi -\def\pubyear#1{\if@cop@home\ifx\specialp@perstring\@undefined\gdef\@pyear{#1}\fi\gdef\@cyear{#1}\fi} - \def\@pyear{\number\year}%+1,+2,+d - \let\@cyear\@pyear -\def\pubvol#1{\if@cop@home\ifx\specialp@perstring\@undefined\gdef\@pvol{#1}\fi\fi}%+1,+2,+d -\let\pubnum\@gobble%not for TeX, only for secondary data use -\def\correspondence#1{\gdef\@corresp{#1}} \def\@corresp{}%+1,+2,+d -\def\citationstatement#1{% - \edef\@@doi{https://doi.org/10.5194/\@journalnameshortlower-\@pvol-\@fpage-\@pyear}% - \def\@tempa{#1}% - \ifx\@tempa\@empty - \gdef\@howtocite{}% - \else - \ifcopyediting - \gdef\@howtocite{}% - \else - \gdef\@howtocite{#1, \@journalnameabbreviation, \@pvol, \@fpage--\@lpage, \expandafter\url{\@@doi}, \@pyear.}% - \fi - \fi -}\def\@howtocite{}%+1,+2,+d -\def\msnumber#1{\if@cop@home\gdef\@msnumber{#1}\fi} -\if@stage@final -\else - \def\affilfontsize#1{\def\@affilfontsize{#1}} - \def\@affilfontsize{\small} -\fi -\if@stage@final - \def\bartext#1{\gdef\@btext{#1}} \def\@btext{} -\fi -\if@cop@home - \newcounter{jnlvolume}%the journal volume - \setcounter{jnlvolume}{\number\year} - \addtocounter{jnlvolume}{1} - \AtBeginDocument{\addtocounter{jnlvolume}{-\@journalstartyear}} - \def\@pvol{\arabic{jnlvolume}} - \if@stage@final - \ifadgeo\def\@pvol{1}\fi - \ifasr\def\@pvol{1}\fi - \fi - \AtBeginDocument{% - \ifx\specialp@perstring\@undefined\else - \def\origfirstpage#1{\ifx\citati@nbyarticlenumber\@undefined\gdef\@fpage{#1}\fi} - \def\origlastpage#1{\gdef\@lpage{#1}} - \def\origpubyear#1{\gdef\@pyear{#1}} - \def\origpubvol#1{\gdef\@pvol{#1}} - \def\origarticlenumber#1{\ifx\citati@nbyarticlenumber\relax\gdef\@fpage{#1}\fi} - \fi} -\else - \def\@pvol{0} -\fi -\if@stage@final - \def\keywords#1{\def\@keyw{#1}} - \def\@keyw{} -\else - \def\keywords#1{% - \CopernicusWarningNoLine{Keywords are not supported.}% - \vspace{1.7mm}\par\noindent\textbf{Keywords.}\enspace\ignorespaces#1} -\fi -\newcommand*\editorthanks[3] - {\ifthenelse{\equal{#2}{}}% check if the first referee exits, if not write: - {\\ \hspace*{4mm} Topical Editor\ #1\ thanks two unknown referees % - for their help in evaluating this paper.} - {\ifthenelse{\equal{#3}{}}% check if second referee exist, if not write: - {\\ \hspace*{4mm}Topical Editor\ #1\ thanks\ #2\ and another % - referee for their help in evaluating this paper.}% - {\\ \hspace*{4mm}Topical Editor\ #1\ thanks\ #2\ and\ #3\ for their % - help in evaluating this paper.}}} -\def\runningauthor#1{\def\@runauth{#1}} -\def\@runauth{} -\def\runningtitle#1{\def\@runtit{#1}} -\def\@runtit{} -\if@stage@final - \def\runninghead#1{\def\@runhd{#1}} - \def\@runhd{% - \ifx\firstrunhd@utput\@undefined - \global\let\firstrunhd@utput\relax - \else - \def\blackb@x[##1]##2{\relax}% - \fi - \if@noauthor\else\@runauth: \fi\@runtit} -\fi -\DeclareRobustCommand*\degree{\ensuremath{^{\circ}}} -\DeclareRobustCommand*\permil{\ifmmode\text{\textperthousand}\else\textperthousand\fi} -\def\@Radical{\put(2.0,2.0){\circle*{1.5}}\kern3.5\p@} -\def\@RadicalC{\raise0.25ex\hbox{\@Radical}} -\DeclareRobustCommand*\Radical{% - \ifmmode\mathchoice{\@RadicalC}{\@RadicalC}{\@Radical}{\@Radical}\else\@RadicalC\fi} -\def\testbx{bx} -\DeclareRobustCommand*\chem[1] - {\ensuremath{% - {\mathcode`\-="0200\mathcode`\=="003D% no space around "-" and "=" - \ifx\f@series\testbx\mathbf{#1}\else\mathrm{#1}\fi}}} -\@ifpackageloaded{hyperref} - {\begingroup - \toks0=\expandafter{\pdfstringdefPreHook}% - \xdef\pdfstringdefPreHook{% - \the\toks0 % - \let\noexpand\hack\noexpand\@gobble - \let\noexpand\chem\noexpand\@firstofone}% - \endgroup} - {\relax} -\DeclareRobustCommand*\unit[1] - {\ensuremath{% - {\thinmuskip3mu\relax - \def\mu{\text{\textmu}}\def~{\,}% - \ifx\f@series\testbx\mathbf{#1}\else\mathrm{#1}\fi}}} -\@definecounter{reaction} -\def\thereaction{R\@arabic\c@reaction} -\let\c@org@eq\c@equation -\let\org@theeq\theequation -\def\setreaction{% - \global\let\c@equation\c@reaction - \global\let\theequation\thereaction} -\def\setequation{% - \global\let\c@equation\c@org@eq - \global\let\theequation\org@theeq} -\newenvironment{reaction} - {\let\c@equation\c@reaction - \let\theequation\thereaction - \incr@eqnum - \mathdisplay@push - \st@rredfalse \global\@eqnswtrue - \mathdisplay{equation}} - {\endmathdisplay{equation}% - \mathdisplay@pop - \ignorespacesafterend} -\IfFileExists{lineno.sty} - {\AtBeginDocument{% - \patchAmsMathEnvironmentForLineno{reaction}}} - {} -\newenvironment{rxnarray} - {\let\c@equation\c@reaction - \let\theequation\thereaction - \eqnarray} - {\endeqnarray - \let\c@equation\c@reaction - \let\theequation\thereaction} -\if@stage@final\else - \newcounter{parentreaction} - \newenvironment{subreactions} - {\refstepcounter{reaction}% - \protected@edef\theparentreaction{\thereaction}% - \setcounter{parentreaction}{\value{reaction}}% - \setcounter{reaction}{0}% - \def\thereaction{\theparentreaction\alph{reaction}}% - \ignorespaces} - {\setcounter{reaction}{\value{parentreaction}}% - \ignorespacesafterend} -\fi -\newcommand\tophline{\hline\noalign{\vspace{1mm}}} -\newcommand\middlehline{\noalign{\vspace{1mm}}\hline\noalign{\vspace{1mm}}} -\newcommand\bottomhline{\noalign{\vspace{1mm}}\hline} -\newcommand\hhline{\noalign{\vspace{1mm}}\hline\noalign{\vspace{1mm}}} -\newdimen\tabularwidth -\def\@tabular{% - 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This template should be used for copernicus.cls -%% The class file and some style files are bundled in the Copernicus Latex Package, which can be downloaded from the different journal webpages. -%% For further assistance please contact Copernicus Publications at: production@copernicus.org -%% https://publications.copernicus.org/for_authors/manuscript_preparation.html - - -%% Please use the following documentclass and journal abbreviations for preprints and final revised papers. - -%%2-column papers and preprints -\documentclass[journal abbreviation, manuscript]{copernicus} - - - -%% Journal abbreviations (please use the same for preprints and final revised papers) - - -% Advances in Geosciences (adgeo) -% Advances in Radio Science (ars) -% Advances in Science and Research (asr) -% Advances in Statistical Climatology, Meteorology and Oceanography (ascmo) -% Annales Geophysicae (angeo) -% Archives Animal Breeding (aab) -% ASTRA Proceedings (ap) -% Atmospheric Chemistry and Physics (acp) 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(pb) -% Proceedings of the International Association of Hydrological Sciences (piahs) -% Scientific Drilling (sd) -% SOIL (soil) -% Solid Earth (se) -% The Cryosphere (tc) -% Weather and Climate Dynamics (wcd) -% Web Ecology (we) -% Wind Energy Science (wes) - - -%% \usepackage commands included in the copernicus.cls: -%\usepackage[german, english]{babel} -%\usepackage{tabularx} -%\usepackage{cancel} -%\usepackage{multirow} -%\usepackage{supertabular} -%\usepackage{algorithmic} -%\usepackage{algorithm} -%\usepackage{amsthm} -%\usepackage{float} -%\usepackage{subfig} -%\usepackage{rotating} - - - -\begin{document} - - -\title{DisReserv (v1.0): Analytical displacement solution due to reservoir compaction with arbitrary geometry and under arbitrary pressure changes} - - -% \Author[affil]{given_name}{surname} - -\Author[1]{Valeria}{C. F. Barbosa} -\Author[1]{Vanderlei}{C. Oliveira Jr.} -\Author[1,2]{Andre}{D. Arelaro} - -\affil[1]{Department of Geophysics, Observat\'{o}rio Nacional, Rio de Janeiro, Brazil} -\affil[2]{PETROBRAS, Rio de Janeiro, Brazil} - - -%% The [] brackets identify the author with the corresponding affiliation. 1, 2, 3, etc. should be inserted. - -%% If an author is deceased, please mark the respective author name(s) with a dagger, e.g. "\Author[2,$\dag$]{Anton}{Aman}", and add a further "\affil[$\dag$]{deceased, 1 July 2019}". - -%% If authors contributed equally, please mark the respective author names with an asterisk, e.g. "\Author[2,*]{Anton}{Aman}" and "\Author[3,*]{Bradley}{Bman}" and add a further affiliation: "\affil[*]{These authors contributed equally to this work.}". - - -\correspondence{Valeria C. F. Barbosa (valcris@on.br)} - -\runningtitle{Displacement due to reservoir compaction} - -\runningauthor{Barbosa, V. C. F., Oliveira Jr., V. C. and Arelaro, A. D.} - - - -\received{} -\pubdiscuss{} %% only important for two-stage journals -\revised{} -\accepted{} -\published{} - -%% These dates will be inserted by Copernicus Publications during the typesetting process. - - -\firstpage{1} - -\maketitle - - -%%\twocolumn -\begin{abstract} -We have presented analytical solutions for the displacement due to reservoir compaction with arbitrary geometry and under arbitrary pressure changes. -These solutions are based on the similarity between the gravitational potential yielded -by a volume source under a density variation and the thermoelastic displacement -potential yielded by a volume source in a half-space under a pressure variation. -This similarity enables the use of closed expressions of the gravitational potential -and its derivatives for calculating the displacement and stress fields due to a volume -source under a pressure variation. -We discretized the reservoir as a grid of 3D right rectangular prisms juxtaposed in -the horizontal and vertical directions. -Each prism has homogeneous pressure; however, pressure variations among different -prisms are allowed. -This parametrization of the reservoir yields a piecewise-constant distribution of -pressure in the subsurface. -The discrete reservoir modeling to calculate the displacement and stress fields due to -this pressure variation follows the nucleus-of-strain concept. -The nucleus of strain is considered an infinitesimal reservoir volume element. -The displacement and stress fields due each prism are calculated by integrating the -nucleus of strain over the volume of the prism. -Finally, the displacement and stress due to the reservoir are computed by the sum of -the contributions of each prism. -We provide a Python implementation (DisReserv) of our method to calculate the -displacement and stress fields due to a reservoir with arbitrary shape and distribution -of pressure changes. -Our expressions are valid both inside and outside the reservoir. -We calculate the displacement and stress fields in three scenarios: i) cylindrical -reservoir under uniform depletion; ii) cylindrical reservoir under non uniform -depletion and iii) reservoir with arbitrary geometry and under arbitrary pressure -distribution. -The results obtained for the three scenarios show that our method produces null -stress field components at the free surface. -\end{abstract} - - -\copyrightstatement{} - - -\introduction %% \introduction[modified heading if necessary] -The surface subsidence due to oil or gas withdrawal from a reservoir in the subsurface may occur as a result of geomechanical changes caused by pressure drop. -The phenomenon of subsidence by fluid extraction has been observed in a variety of oil fields, e.g., the Ekofisk field, southern North Sea \citep{Borges2020} and the Groningen gas field in the northeast Netherlands \citep{vanThienen-visser&Fokker17}. -Because the subsidence close to hydrocarbon fields under production can induce earthquakes (e.g., \citeauthor{Dahmetal15}, \citeyear{Dahmetal15}; \citeauthor{Grigolietal17}, \citeyear{Grigolietal17}), the petroleum companies have been an increased interest in monitoring the magnitude and distribution of subsidence resulting from reservoir depletion. -The subsidence monitoring is accomplished by means of calculating the displacement field for a given set of reservoir properties. - -The possibility of occurrence of catastrophic events, related to subsidence due to extraction or injection of fluids in reservoir, has stimulated efforts to develop analytical methods for modeling the displacement and stress fields due to reservoir compactation. -The physical foundation of the displacement, stress and strain fields in the subsurface due to a reduction of pressure in the reservoir comes from the theory of thermoelasticity. -Theory of thermoelasticity has been laid in the first half of the nineteenth century to describe the interaction between the thermal field and elastic bodies. -In the uncoupled thermoelasticity theory for quasi-static problems (i.e., problems with negligible inertia effects), \cite{Goodier37} employed the method of superposition using -displacement potential functions and introduced the concept of nucleus of thermoelastic strain in an infinite space. -Specifically, Goodier’s (\citeyear{Goodier37}) method simplified the thermoelastic problem by replacing it by an isothermal elastic problem with different boundary conditions together with the solution of a Poisson’s equation \citep{Tao71}. -\cite{Mindlin&Cheng50} and \cite{Sen51} extended the Goodier's method to a homogenous half-space. -\cite{Sharma56} deduced the displacement and stress fields in an infinite elastic plate due to a nucleus of thermoelastic strain located at a point inside it by using infinite integrals involving Bessel functions. - -The subsidence resulting from reservoir depletion is in the context of poroelastic theory. -\cite{Geertsma57} remarked the analogy between the theories of thermoelasticity and poroelasticity. -To our knowledge, \cite{Geertsma73} was the first to solve the poroelastic problem by using the nucleus-of-strain concept in the half-space, which in turn was proposed by \cite{Mindlin&Cheng50} and \cite{Sen51} in the theory of thermoelasticity. -\cite{Geertsma73} derived analytical expressions for the stress and displacement fields for a thin disk-shaped reservoir. -\cite{Segall92} followed \cite{Geertsma73} and extended the analytical solutions of the displacement and stress fields assuming general axisymmetric geometries and an arbitrary radial pressure distribution. - -\cite{Geertsma&Opstal73} applied the nucleus-of-strain concept in the half-space -to calculate the spatial subsidence distribution due to the production of reservoir with an arbitrary 3D shape. -By assuming a producing reservoir embedded in an a homogeneous, isotropic, and elastic medium, and a reservoir model in which the pressure perturbations are related to the displacement field by a linear relationship, \cite{Geertsma&Opstal73} discretized the reservoir into a grid of prisms and calculated the displacement due to the pressure change in the whole reservoir by the superposition of the displacement due to the constant pressure change in each prism. -\cite{Tempone10} adopted the same reservoir model used in \cite{Geertsma&Opstal73} and -extended the nucleus-of-strain concept in the half-space to consider the effects of a rigid basement. -Similarly, \cite{Tempone10} assumed a reservoir embedded in an a homogeneous, isotropic, and elastic medium and calculated the displacement, stress and strain fields subject to uniform depletion. -The main drawbacks in \cite{Geertsma&Opstal73} and \cite{Tempone10} are the assumption of homogeneous reservoir and the solution is only valid outside the reservoir. -In this case, the displacements within the reservoir are calculated by a linear interpolation of the displacements at the upper and lower edges of the reservoir \citep{Tempone12}. - -Considering an inhomogeneous poroelastic model consists of layered stratigraphy, \cite{Mehrabian&Abousleiman15} developed closed-form formulae for the displacement and stress fields outside and inside of the reservoir embedded within elastic strata with different mechanical properties and subjected to pore pressure disturbances due to fluid extraction or injection. -By assuming a linear elastic semi-infinite medium, \cite{Munoz&Roehl17} developed analytical solution for the displacement field outside and inside of an arbitrarily-shaped reservoir under arbitrary distribution of pressure changes. -\cite{Munoz&Roehl17} parametrized the reservoir into a grid of 3D prisms and used the nucleus-of-strain concept. -The nucleus of strain is taking as an infinitesimal volume element for each prism and the displacement solution due to each prism is obtained by a three-dimensional integration over the prism volume. -The displacement field outside and inside of the reservoir is given by the summation of the displacement fields of the displacements produced by all prisms setting up the reservoir model. - -The present work assumes a linear elastic semi-infinite medium and provides an analytical solution for displacement field due to an arbitrarily-shaped reservoir under arbitrary distribution of pressure changes. -Like \cite{Munoz&Roehl17} we used the nucleus-of-strain concept and discretized the -reservoir into a grid of 3D prisms along the $x-$, $y-$ and $-z$ directions. -We also consider the nucleus of strain as an infinitesimal volume element for each prism and the displacement solution due to each prism is obtained by a three-dimensional integration over the prism volume. -The final displacement field due to the whole reservoir is the sum of the displacements produced by the prisms. -In contrast with \cite{Munoz&Roehl17}'s method we take advantage the similarity between -the equations for calculating the displacement field due to a volume source in a half-space under a pressure variation and the gravitational potential due to a volume source under a density variation. -This similarity makes possible the use of closed expressions of the gravitational potential and its derivatives produced by the 3D right rectangular prism derived by \cite{Nagyetal2000} and (\citeyear{Nagyetal2002}) and \cite{Fukushima2020} for calculating the displacement field due to a volume source under a pressure variation. -The adopted exact analytical formulae of the gravitational field are valid expressions either outside or inside the prisms because the implemented expressions make use of modified arctangent function proposed by \cite{Fukushima2020}. -We present routines written in Python language (Python 3.7.6) to calculate the displacement fields due to a reservoir with arbitrary shape and distribution of pressure changes. -We validate our equations by verifying that at the free surface the stress fields are null. -Tests with synthetic data validate our approach. - -\section{THEORY} - -The displacement, stress and strain fields in the subsurface caused by reservoir compactation due to hydrocarbon production are grounded on the theory of thermoelasticity. - -The Goodier’s thermoelastic displacement potential $\phi$ satisfies the Poisson's equation \citep{Goodier37}, i.e.: -\begin{equation} -\nabla^{2} \phi = m \: T, -\label{eq:poisson} -\end{equation} -where $\nabla^{2}$ is the Laplacian operator, $T $ is the temperature variation and -\begin{equation} -m = \: \alpha \: \frac{1 + \nu}{ 1 -\nu}, -\label{eq:m} -\end{equation} -where $\alpha$ is the coefficient of linear thermal expansion and $\nu$ is the Poisson's ratio. - -From the potential theory, a particular solution of equation \ref{eq:poisson} is -\begin{equation} -\phi(x,y,z) = - \frac{m}{4 \pi} \int\int\limits_{v}\int \frac{T(x^{\prime}, y^{\prime}, z^{\prime} )}{\sqrt{(x - x^{\prime})^{2} + (y - y^{\prime})^{2} + (z - z^{\prime})^{2}}} \: dv^{\prime}, -\label{eq:phi} -\end{equation} -where $\phi(x,y,z)$ represents the Newtonian gravitational potential \citep{Kellogg29} that would be produced at the coordinates $x, y$ and $z$ by a continuous density distribution $- \frac{m}{4 \pi} \: T( x^{\prime}, y^{\prime}, z^{\prime} )$. -The integral in equation \ref{eq:phi} is conducted over the coordinates $x^{\prime}$,$y^{\prime}$ and $z^{\prime}$, denoting, respectively, the $x-$, $y-$ and $-z$ coordinates of an arbitrary point belonging to the interior of the volume $v$ of the solid. - - -From equation \ref{eq:phi} and the potential theory, \citet{Goodier37} showed that, if an element of volume $dv$ in the infinite solid is at a temperature $T(x^{\prime}, y^{\prime}, z^{\prime}) $, the remainder being at temperature zero, the displacement vector $\bf{u}$ caused by this temperature is the gradient of the Goodier’s thermoelastic displacement potential, i.e., -\begin{equation} -{\bf{u}} = {\bf {\nabla}} \phi(x,y,z) \: , -\label{eq:displacement-general} -\end{equation} -where $\bf{\nabla}$ is the gradient operator. - -To a homogenous half-space, \citet{Mindlin&Cheng50} showed that the method proposed by \citet{Goodier37} can be extended by the displacement solution given by: -\begin{equation} -\bf{u} = {\bf{\nabla}} \: \phi_{1} \: + \: {\bf{{\nabla}_{2}}} \phi_{2}, -\label{eq:displacement-solution} -\end{equation} -where $\phi_{1} \equiv \phi_{1}(x,y,z)$ is the potential defined in equation \ref{eq:phi}, -$\phi_{2} \equiv \phi_{2}(x,y,z)$ -is defined as "image potential" \citep{Segall92} due to a image point at the coordinates -$(x^{\prime}, y^{\prime}, -z^{\prime} )$ and the operator $\bf{{\nabla}_{2}}$ is expressed by -\begin{equation} -{\bf{{\nabla}_{2}}} = (3 - 4\nu){\bf{\nabla}} + 2 {\bf{\nabla}} z \frac{\partial }{\partial z} - 4(1- \nu){\bf{\hat{z}}} {\bf{{\nabla}^{2}_{z}}}, -\label{eq:nabla2} -\end{equation} -where ${\bf{\hat{z}}}$ is the unit vector in the $z-$direction and -${\bf{{\nabla}^{2}_{z}}}$ is a scalar operator in which the operand is firstly -multiplied by $z$ and then operated upon by the Laplacian ${\bf{\nabla}^{2}}$. - -Equation \ref{eq:displacement-solution} is the displacement solution for the variation of temperature due to a single nucleus of strain buried at depth $z^{\prime}$ in a -semi-infinite homogeneous medium. -In the right hand side of equation \ref{eq:displacement-solution}, the first term -$ {\bf{\nabla}} \: \phi_{1} $ represents the displacement in an infinite medium, and the second term represents a correction of the displacement due a half-space, also known as "image nucleus solution". - -\section{METHODOLOGY} - -Let's assume that a reservoir in the interior of the Earth is subject to a compactation due to hydrocarbon production. -The compactation is caused by the pressure change within the reservoir, which in turn causes a surface subsidence (or surface displacement). -Here, we use a Cartesian coordinate system with the $x-$axis pointing to north, the $y-$axis pointing to east and the $z-$axis pointing downward. -We discretize the reservoir into an $ m_{x} \times m_{y} \times m_{z} $ grid of 3D vertical juxtaposed prisms $(m_{x} \cdot m_{y} \cdot m_{z} = M)$ along the -$x$, $y$ and $z$ axes, respectively, in which the pressure within each prism is -assumed to be constant and known. -Each prism in the reservoir model may undergo a distinct pressure change. -The subsidence effect is the displacement field due to the pressure change throughout the reservoir and is calculated by the sum of the displacement produced by each prism. - - -The discrete forward modeling to calculate the displacement and stress fields due to a piecewise-constant distribution of the pressure contrast within a reservoir follows the nucleus-of-strain approach. -We assume that a nucleus of strain represents an infinitesimal reservoir volume -element. The displacement solution for a single nucleus of strain in a homogeneous elastic semi-infinite medium (equation \ref{eq:displacement-solution}) will be used as an element of the displacement. -Then we calculate the displacement field due to the pressure contrast of a prism by integrating the nucleus of strain over its volume. The same approach is used to -compute the stress field due to a prism. - - -\subsection{The discrete forward modeling due to a nucleus of strain in a homogeneous elastic semi-infinite medium}\label{solution-nucleus} - -By considering the discrete form of equation \ref{eq:displacement-solution}, the displacement vector $ {\bf{u}}_{ij} \equiv {\bf{u}}(x_{i}, y_{i}, z_{i}, x^{\prime}_{j}, y^{\prime}_{j}, z^{\prime}_{j})$ at an arbitrary point $(x_{i}, y_{i}, z_{i})$ due to the $j$th nucleus of strain at the coordinates -$(x^{\prime}_{j}, y^{\prime}_{j}, z^{\prime}_{j})$ will be calculated by -\begin{equation} -{\bf{u}}_{ij} = {\bf{u_{1}}}_{ij} + {\bf{u_{2}}}_{ij} \: , -\label{eq:displacement_ui} -\end{equation} -where ${\bf{u_{1}}}_{ij}$ is the displacement vector at the point $(x_{i}, y_{i}, z_{i})$ due to the $j$th single nucleus in the infinite space and ${\bf{u_{2}}}_{ij}$ -is the correction of the displacement considering a semi-space (image nucleus solution). -The term ${\bf{u_{1}}}_{ij}$ (equation \ref{eq:displacement_ui}) is given by -\begin{equation} -{\bf{u_{1}}}_{ij} = \frac{A \: (1 + \nu)}{E} \: {\bf{\nabla}} \bigg( {\frac{1}{{R_1}_{ij}}} \bigg) -\: \Delta p_{j} \: \:dv_j^{\prime} -\label{eq:nucleus-u1} -\end{equation} -and represents the gradient of the potential -\begin{equation} -\phi_{1} = - \frac{C_m}{4 \pi} \frac{\Delta p_{j} \: \:dv_j^{\prime}}{ {R_1}_{ij} } \: . -\label{eq:nucleus-phi1} -\end{equation} -The term ${\bf{u_{2}}}_{ij}$ (equation \ref{eq:displacement_ui}) is given by -\begin{equation} -{\bf{u_{2}}}_{ij} = \frac{A \: (1 + \nu)}{E} \: -\bigg[ -(3 - 4\nu){\bf{\nabla}} \bigg( {\frac{1}{{R_2}_{ij}}} \bigg) -+ 2 {\bf{\nabla}} \bigg( z \frac{\partial }{\partial z} {\frac{1}{{R_2}_{ij}}} \bigg) -- 4(1- \nu){\bf{\hat{z}}} {\bf{{\nabla}^{2}}} \bigg( {\frac{z}{{R_2}_{ij}}} \bigg) -\bigg] \: \Delta p_{j} \:dv_j^{\prime} -\label{eq:nucleus-u2} -\end{equation} -and is obtained by applying the operator ${\bf{{\nabla}_{2}}}$ (equation -\ref{eq:nabla2}) to the image potential -\begin{equation} -\phi_{2} = - \frac{C_m}{4 \pi} \frac{\Delta p_{j} \: \:dv_j^{\prime}}{ {R_2}_{ij} } \: . -\label{eq:nucleus-phi2} -\end{equation} -In equations \ref{eq:nucleus-u1}--\ref{eq:nucleus-phi2}, -all derivatives are computed with respect to the coordinates of the point -$(x_{i}, y_{i}, z_{i})$, -$\Delta p_j$ is the pressure contrast of the $j$th nucleus, $dv_j^{\prime}$ is an -infinitesimal element of volume centered at the $j$th nucleus of strain -$(x^{\prime}_{j}, y^{\prime}_{j}, z^{\prime}_{j})$, $A$ is the constant -\begin{equation} -A = - \frac{C_m E}{4 \pi (1 + \nu)} \: , -\label{eq:nucleus-A} -\end{equation} -$C_m$ is the uniaxial compaction coefficient (see \citeauthor{Geertsma66}, -\citeyear{Geertsma66}; \citeauthor{Tempone10}, \citeyear{Tempone10} and -\citeauthor{Munoz&Roehl17}, \citeyear{Munoz&Roehl17}) -\begin{equation} -C_m = \frac{1}{E} \: \frac{(1 + \nu) (1 - 2\nu)}{(1-\nu)} \: , -\label{eq:Cm} -\end{equation} -and $E$ is the Young’s modulus. -In equation \ref{eq:nucleus-phi1}, $ {R_1}_{ij}$ is the distance from the $i$th point $ (x_{i}, y_{i}, z_{i})$ to the $j$th nucleus of strain $(x^{\prime}_{j}, y^{\prime}_{j}, z^{\prime}_{j})$, i.e.: -\begin{equation} -{R_1}_{ij} = {\sqrt{(x_{i}- x^{\prime}_{j})^{2} + (y_{i} - y^{\prime}_{j})^{2} + -(z_{i} - z^{\prime}_{j})^{2}}}. -\label{eq:R1} -\end{equation} -In equation \ref{eq:nucleus-phi2}, $ {R_2}_{ij}$ is the distance from the $i$th point $ (x_{i}, y_{i}, z_{i})$ to the $j$th image nucleus $(x^{\prime}_{j}, y^{\prime}_{j}, - z^{\prime}_{j})$, i.e.: -\begin{equation} -{R_2}_{ij} = {\sqrt{(x_{i}- x^{\prime}_{j})^{2} + (y_{i} - y^{\prime}_{j})^{2} + -(z_{i} + z^{\prime}_{j})^{2}}} \: . -\label{eq:R2} -\end{equation} -Figure \ref{fig:nucleus_strain} shows a schematic representation of the geometry -of the nucleus of strain problem in a semi-infinite medium. -The horizontal plane $z = 0$ is called "free surface". -The $x-$, $y-$ and $z-$components of the vectors ${\bf{u_{1}}}_{ij}$ (equation \ref{eq:nucleus-u1}) and ${\bf{u_{2}}}_{ij}$ (equation \ref{eq:nucleus-u2}) -can be explicitly defined as follows: -\begin{equation} -{\bf{u_{1}}}_{ij} = -\frac{A \: (1 + \nu)}{E} \: -\begin{bmatrix} -\frac{\partial }{\partial x} {\frac{1}{{R_1}_{ij}}} \\ -\frac{\partial }{\partial y} {\frac{1}{{R_1}_{ij}}} \\ -\frac{\partial }{\partial z} {\frac{1}{{R_1}_{ij}}} -\end{bmatrix} - \: \Delta p_{j} \: \:dv_j^{\prime} -\label{eq:nucleus-u1-vector} -\end{equation} -and -\begin{equation} -{\bf{u_{2}}}_{ij} = -\frac{A \: (1 + \nu)}{E} \: \left\{ (3 - 4 \nu) -\begin{bmatrix} - \: \frac{\partial }{\partial x} {\frac{1}{{R_2}_{ij}}} \\ - \: \frac{\partial }{\partial y} {\frac{1}{{R_2}_{ij}}} \\ - - \frac{\partial }{\partial z} {\frac{1}{{R_2}_{ij}}} -\end{bmatrix} -+ 2 \: z_{i} -\begin{bmatrix} -\frac{\partial^{2} }{\partial x \partial z} {\frac{1}{{R_2}_{ij}}} \\ -\frac{\partial^{2} }{\partial y \partial z} {\frac{1}{{R_2}_{ij}}} \\ -\frac{\partial^{2} }{\partial z^{2}} {\frac{1}{{R_2}_{ij}}} -\end{bmatrix} -\right\} -\: \Delta p_{j} \: \:dv_j^{\prime} \: . -\label{eq:nucleus-u2-vector} -\end{equation} - -By following \cite{Sharma56} and \cite{Tempone10}, -the stress vector -$\mbox{\boldmath$\sigma$}_{ij} \equiv \mbox{\boldmath$\sigma$}(x_{i}, y_{i}, z_{i}, x^{\prime}_{j}, y^{\prime}_{j}, z^{\prime}_{j})$ -at the point $(x_{i}, y_{i}, z_{i})$ due to the $j$th single nucleus of strain buried -in the half space is given by -\begin{equation} -\mbox{\boldmath$\sigma$}_{ij} = \mbox{\boldmath$\sigma_{1}$}_{ij} + -\mbox{\boldmath$\sigma_{2}$}_{ij} \: , -\label{eq:stress_nucleus} -\end{equation} -where -$\mbox{\boldmath$\sigma_{1}$}_{ij} \equiv \mbox{\boldmath$\sigma_{1}$}(x_{i}, y_{i}, z_{i}, x^{\prime}_{j}, y^{\prime}_{j}, z^{\prime}_{j})$ is the stress vector -at the point $(x_{i}, y_{i}, z_{i})$ due to the $j$th single nucleus in the infinite space and $\mbox{\boldmath$\sigma_{2}$}_{ij} \equiv \mbox{\boldmath$\sigma_{2}$}(x_{i}, y_{i}, z_{i}, x^{\prime}_{j}, y^{\prime}_{j}, z^{\prime}_{j})$ is the stress vector -at the point $(x_{i}, y_{i}, z_{i})$ that gives the correction of the stress due to the -$j$th image nucleus considering a semi-space. These two vectors are given by -\begin{equation} -\mbox{\boldmath$\sigma_{1}$}_{ij} = -A \: -\begin{bmatrix} -\frac{\partial^{2} }{\partial x \partial z} {\frac{1}{{R_1}_{ij}}} \\ -\frac{\partial^{2} }{\partial y \partial z} {\frac{1}{{R_1}_{ij}}} \\ -\frac{\partial^{2} }{\partial z^{2}} {\frac{1}{{R_1}_{ij}}} -\end{bmatrix} -\: \Delta p_{j} \: \:dv_j^{\prime} \: , -\label{eq:nucleus-stress1-vector} -\end{equation} -and -\begin{equation} -\mbox{\boldmath$\sigma_{2}$}_{ij} = -A \: -\left\{ -\begin{bmatrix} -\frac{\partial^{2} }{\partial x \partial z} {\frac{1}{{R_2}_{ij}}} \\ -\frac{\partial^{2} }{\partial y \partial z} {\frac{1}{{R_2}_{ij}}} \\ -- \frac{\partial^{2} }{\partial z^{2}} {\frac{1}{{R_2}_{ij}}} -\end{bmatrix} -+ 2 \: z_{i} -\begin{bmatrix} -\frac{\partial^{3} }{\partial x \partial z^{2}} {\frac{1}{{R_2}_{ij}}} \\ -\frac{\partial^{3} }{\partial y \partial z^{2}} {\frac{1}{{R_2}_{ij}}} \\ -\frac{\partial^{3} }{\partial z^{3}} {\frac{1}{{R_2}_{ij}}} -\end{bmatrix} -\right\} -\: \Delta p_{j} \: \:dv_j^{\prime} \: . -\label{eq:nucleus-stress2-vector} -\end{equation} -According to \cite{Sharma56} and \cite{Tempone10}, the Beltrami’s equations \citep{Beltrami} and the equilibrium equations must be satisfied to obtain the contribution of the stress field in the half space. -Additionally, the boundary condition -$\mbox{\boldmath$\sigma$}_{ij} = \mbox{ \boldmath$0$}$ (equation \ref{eq:stress_nucleus}), where $\mbox{ \boldmath$0$}$ is the zero vector, must be satisfied at the free surface ($z_i = 0$). -%\begin{equation} -%\mbox{\boldmath$\sigma$}_{ij} = \mbox{\boldmath$\sigma_{1}$}_{ij} + -%\mbox{\boldmath$\sigma_{2}$}_{ij} = \mbox{ \boldmath$0$}, -%\label{eq:null_stress} -%\end{equation} -%where $\mbox{ \boldmath$0$}$ is the null vector. -This condition can be easily verified by adding the vectors -$\mbox{\boldmath$\sigma_{1}$}_{ij}$ (equation \ref{eq:nucleus-stress1-vector}) and -$\mbox{\boldmath$\sigma_{2}$}_{ij}$ (equation \ref{eq:nucleus-stress2-vector}) -computed at any point on the free surface $(x_i, y_i, z_i = 0)$. - - -\subsection{The discrete displacement forward modeling due to a reservoir in a homogeneous elastic semi-infinite medium} \label{u-model} - - -We parameterize the reservoir as a grid of juxtaposed right rectangular prisms. -Each grid prism has a constant pressure contrast $\Delta p_{j}$; however, pressure variations among different prisms are allowed. -To calculate the displacement field produced by the $j$th prism -at the $i$th coordinates $(x_i, y_i, z_i)$, we integrate the solution deduced for a single nucleus of strain (equation \ref{eq:displacement_ui}) -over its volume and obtain -\begin{equation} -{\bf{\tilde{u}}}_{ij} = -\iiint\limits_{{v_{1}}_{j}} -{\bf{u_{1}}}_{ij} \: \: dv_{j}^{\prime} -\: + \: -\iiint\limits_{{v_{2}}_{j}} -{\bf{u_{2}}}_{ij} \:\: dv_{j}^{\prime} \: , -\label{eq:nucleus-ui_jth_prism} -\end{equation} -where both integrals are conducted with respect to the variables -$(x^{\prime}_{j}, y^{\prime}_{j}, z^{\prime}_{j})$. The first integral in equation -\ref{eq:nucleus-ui_jth_prism} is conducted over the volume ${v_{1}}_{j}$ of the $j$th -prism and the second is conducted over the volume -${v_{2}}_{j}$ of a different prism symmetrically positioned above the free surface -and conveniently called $j$th "image prism". -Volume ${v_{1}}_{j}$ is defined by ${x_1}_{j}$, ${x_2}_{j}$, ${y_1}_{j}$, ${y_2}_{j}$, -${z_1}_{j}$, and ${z_2}_{j}$, which represent, respectively, the south, north, west, -east, top, and bottom borders of the $j$th prism. -Volume ${v_{2}}_{j}$ of the $j$th image prism is defined in a similar way, but with -top and bottom given by ${z_1}_{j} - 2 \, {z_c}_{j}$ and ${z_2}_{j} - 2 \, {z_c}_{j}$, where -${z_c}_{j} = \frac{1}{2}({z_1}_{j} + {z_2}_{j})$ is the center depth of the $j$th prism. - -The total displacement vector at the point $(x_i, y_i, z_i)$ due to the -pressure change in the whole reservoir is defined as the sum of the displacements -${\bf{u}}_{ij}$ (equation \ref{eq:nucleus-ui_jth_prism}) yielded by each prism -with constant pressure $\Delta p_{j}$: -\begin{equation} -{\bf{\tilde{u}}}_{i} = \sum_{j=1}^{M} {\bf{\tilde{u}}}_{ij} \: , -\label{eq:nucleus-ui_M_prisms} -\end{equation} -where $M$ is the number of prisms setting up the reservoir model. -The horizontal component of the total displacement vector ${\bf{\tilde{u}}}_{i}$ -(equation \ref{eq:nucleus-ui_M_prisms}) is calculated by -\begin{equation} -{\tilde{u}}_{{i}_h} = \sqrt{ {\tilde{u}}_{{i}_x}^{2} + {\tilde{u}}_{{i}_y}^{2} } -\: , -\label{eq:horizontal_displacement} -\end{equation} -where ${\tilde{u}}_{{i}_x}$ and ${\tilde{u}}_{{i}_y}$ are the $x-$ and $y-$ components. - -By substituting equations \ref{eq:nucleus-u1-vector} and \ref{eq:nucleus-u2-vector} -into equation \ref{eq:nucleus-ui_jth_prism}, we obtain -\begin{equation} -{\tilde{u}}_{{ij}_\alpha} = \frac{A \: (1 + \nu)}{E} -\: \Delta p_{j} \: \left[ \iiint\limits_{{v_{1}}_{j}} -\frac{\partial }{\partial \alpha} {\frac{1}{{R_1}_{ij}}} \: dv_{j}^{\prime} -\: + \: -(3 - 4 \nu) \iiint\limits_{{v_{2}}_{j}} -\: \frac{\partial }{\partial \alpha} {\frac{1}{{R_2}_{ij}}}\: dv_j -+ \: 2 \: z_{i} \: \iiint\limits_{{v_{2}}_{j}} -\frac{\partial^{2} }{\partial \alpha \partial z} {\frac{1}{{R_2}_{ij}}} \:\: dv_{j}^{\prime} -\right] \: , -\label{eq:u_til_alpha} -\end{equation} -where $\alpha = x, y$, and -\begin{equation} -{\tilde{u}}_{{ij}_z} = \frac{A \: (1 + \nu)}{E} -\: \Delta p_{j} \: \left[ \iiint\limits_{{v_{1}}_{j}} -\frac{\partial }{\partial z} {\frac{1}{{R_1}_{ij}}} \: dv_{j}^{\prime} -\: - \: (3 - 4 \nu) \iiint\limits_{{v_{2}}_{j}} -\: \frac{\partial }{\partial z} {\frac{1}{{R_2}_{ij}}}\: dv_{j}^{\prime} -+ \: 2 \: z_{i} \: \iiint\limits_{{v_{2}}_{j}} -\frac{\partial^{2} }{\partial z^{2}} {\frac{1}{{R_2}_{ij}}} \:\: dv_{j}^{\prime} -\right] \: . -\label{eq:u_til_z} -\end{equation} -In the right-hand side of equations \ref{eq:u_til_alpha} and \ref{eq:u_til_z}, the three integrals have the same form of derivatives of the gravitational potential produced by the $j$th prism and image prism. -The first integral corresponds to the $\alpha-$component of the gravitational attraction -produced by the $j$th prism. -The second and third integrals correspond, respectively, to the $\alpha-$component of the gravitational attraction and to the $\alpha \:z-$component of the gravitational -gradient tensor produced by the $j$th image prism. -The similarity between the displacement fields due to a volume source in a half-space and the gravitational field allows the use of closed expressions of the gravitational potential and its derivatives produced by the 3D right rectangular prism. - -In equations \ref{eq:u_til_alpha} and \ref{eq:u_til_z}, the integrals depending on -first derivatives of ${\frac{1}{{R_1}_{ij}}}$ have the following closed solutions -\citep{Nagyetal2000, Nagyetal2002}: -\begin{equation} -\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} \int\limits_{{z_{1}}_{j}}^{{z_{2}}_{j}} -\frac{\partial }{\partial x} {\frac{1}{{R_1}_{ij}}} dv_{j}^{\prime} = -\Bigg|\Bigg|\Bigg| -y \ln(z + R) + z \ln(y + R) - x \tan^{-1} \Bigg( \frac{yz}{x \: R} \Bigg) -\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} \quad , -\label{dx1} -\end{equation} -\begin{equation} -\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} \int\limits_{{z_{1}}_{j}}^{{z_{2}}_{j}} -\frac{\partial }{\partial y} {\frac{1}{{R_1}_{ij}}} dv_{j}^{\prime} = -\Bigg|\Bigg|\Bigg| -x \ln(z + R) + z \ln(x + R) - y \tan^{-1} \Bigg( \frac{xz}{y \: R} -\Bigg) -\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} \quad , -\label{dy1} -\end{equation} -and -\begin{equation} -\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} \int\limits_{{z_{1}}_{j}}^{{z_{2}}_{j}} -\frac{\partial }{\partial z} {\frac{1}{{R_1}_{ij}}} dv_{j}^{\prime} = -\Bigg|\Bigg|\Bigg| -x \ln(y + R) + y \ln(x + R) - z \tan^{-1} \Bigg( \frac{xy}{z \: R} \Bigg) -\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} \quad , -\label{dz1} -\end{equation} -where all derivatives are computed with respect to the coordinates of the $i$th point -$(x_i, y_i, z_i)$, $R = \sqrt{x^{2} + y^{2} + z^{2}}$, and -\begin{equation} -\begin{array}{ll} -{X_1}_{j} &= x_i - {x_1}_{j} \\ -{X_2}_{j} &= x_i - {x_2}_{j} \\ -{Y_1}_{j} &= y_i - {y_1}_{j} \\ -{Y_2}_{j} &= y_i - {y_2}_{j} \\ -{Z_1}_{j} &= z_i - {z_1}_{j} \\ -{Z_2}_{j} &= z_i - {z_2}_{j} -\end{array} \quad . -\label{eq:Nagy_limits_1} -\end{equation} -The remaining integrals, in the right-hand side of equations -\ref{eq:u_til_alpha} and \ref{eq:u_til_z}, depend on first and second derivatives -of ${\frac{1}{{R_2}_{ij}}}$. -These integrals are conducted over the volume ${v_{2}}_{j}$ of the $j$th image prism and have the following closed solutions \citep{Nagyetal2000, Nagyetal2002}: -\begin{equation} -\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} \int\limits_{{z_{1}}_{j} - 2 \, z_c}^{{z_{2}}_{j} - 2 \, z_c} -\frac{\partial }{\partial x} {\frac{1}{{R_2}_{ij}}} dv_{j}^{\prime} = -\Bigg|\Bigg|\Bigg| -y \ln(z + R) + z \ln(y + R) - x \tan^{-1} \Bigg( \frac{yz}{x \: R} \Bigg) -\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} \quad , -\label{dx2} -\end{equation} -\begin{equation} -\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} \int\limits_{{z_{1}}_{j} - 2 \, z_c}^{{z_{2}}_{j} - 2 \, z_c} -\frac{\partial }{\partial y} {\frac{1}{{R_2}_{ij}}} dv_{j}^{\prime} = -\Bigg|\Bigg|\Bigg| -x \ln(z + R) + z \ln(x + R) - y \tan^{-1} \Bigg( \frac{xz}{y \: R} -\Bigg) -\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} \quad , -\label{dy2} -\end{equation} -\begin{equation} -\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} \int\limits_{{z_{1}}_{j} - 2 \, z_c}^{{z_{2}}_{j} - 2 \, z_c} -\frac{\partial }{\partial z} {\frac{1}{{R_2}_{ij}}} dv_{j}^{\prime} = -\Bigg|\Bigg|\Bigg| -x \ln(y + R) + y \ln(x + R) - z \tan^{-1} \Bigg( \frac{xy}{z \: R} \Bigg) -\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} \quad , -\label{dz2} -\end{equation} -\begin{equation} -\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} \int\limits_{{z_{1}}_{j} - 2 \, z_c}^{{z_{2}}_{j} - 2 \, z_c} -\frac{\partial^{2} }{\partial x \partial z} {\frac{1}{{R_2}_{ij}}} dv_{j}^{\prime} = \Bigg|\Bigg|\Bigg| -\ln(y + R) -\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} \quad , -\label{dxz2} -\end{equation} -\begin{equation} -\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} \int\limits_{{z_{1}}_{j} - 2 \, z_c}^{{z_{2}}_{j} - 2 \, z_c} -\frac{\partial^{2} }{\partial y \partial z} {\frac{1}{{R_2}_{ij}}} dv_{j}^{\prime} = -\Bigg|\Bigg|\Bigg| -\ln(x + R) -\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} \quad , -\label{dyz2} -\end{equation} -and -\begin{equation} -\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} \int\limits_{{z_{1}}_{j} - 2 \, z_c}^{{z_{2}}_{j} - 2 \, z_c} -\frac{\partial^{2} }{\partial z \partial z} {\frac{1}{{R_2}_{ij}}} dv_{j}^{\prime} = -\Bigg|\Bigg|\Bigg| -- \tan^{-1} \Bigg( \frac{xy}{z \: R} \Bigg) -\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} \quad . -\label{dzz2} -\end{equation} -In these integrals related to the $j$th image prism -(equations \ref{dx2}--\ref{dzz2}), the integration limits along the $z$ direction -are given by -\begin{equation} -\begin{array}{ll} -{Z_1}_{j} &= z_i - {z_1}_{j} + 2 \, {z_c}_{j} \\ -{Z_2}_{j} &= z_i - {z_2}_{j} + 2 \, {z_c}_{j} -\end{array} \quad , -\label{eq:Nagy_limits_2} -\end{equation} -where ${z_c}_{j} = \frac{1}{2}({z_1}_{j} + {z_2}_{j})$ is the center depth of the $j$th prism. -The remaining limits along $x$ and $y$ directions are the same defined by equation -\ref{eq:Nagy_limits_1}. - - -\subsection{The discrete stress forward modeling due to a reservoir in a homogeneous elastic semi-infinite medium} - -By following the similar approach used in the previous subsection, the stress field of each prism assuming constant pressure is calculated by integrating solution for a -nucleus of strain (equations \ref{eq:stress_nucleus}, \ref{eq:nucleus-stress1-vector}, -and \ref{eq:nucleus-stress2-vector}) over its volume. -This integration leads to a stress vector -$\mbox{\boldmath$\tilde{\sigma}$}_{ij} \equiv \mbox{\boldmath$\tilde{\sigma}$}(x_{i}, y_{i}, z_{i}, x^{\prime}_{j}, y^{\prime}_{j}, z^{\prime}_{j})$ given by -\begin{equation} -\mbox{\boldmath$\tilde{\sigma}$}_{ij} = -\iiint\limits_{{v_{1}}_{j}} -\mbox{\boldmath$\sigma_{1}$}_{ij} \: \: dv_{j}^{\prime} -\: + \: -\iiint\limits_{{v_{2}}_{j}} -\mbox{\boldmath$\sigma_{2}$}_{ij} \:\: dv_{j}^{\prime} \: , -\label{eq:nucleus-stress_jth_prism} -\end{equation} -where the first and second integrals are conducted, respectively, over the volumes -${v_{1}}_{j}$ and ${v_{2}}_{j}$ of the $j$th prism and the $j$th image prism. -The total stress vector at the $i$th coordinates $(x_i, y_i, z_i)$ due to the -pressure change in the whole reservoir is calculated by -\begin{equation} -\mbox{\boldmath$\tilde{\sigma}$}_{i} = -\sum_{j=1}^{M} \mbox{\boldmath$\tilde{\sigma}$}_{ij} \: . -\label{eq:nucleus-stress_M_prisms} -\end{equation} - -By substituting equation \ref{eq:nucleus-stress1-vector} and -\ref{eq:nucleus-stress2-vector} into equation \ref{eq:nucleus-stress_jth_prism}, -we obtain the $\alpha-$component (where $\alpha = x$ and $y$) and the $z-$ component -of the stress vector $\mbox{\boldmath$\tilde{\sigma}$}_{ij}$ as follows: -\begin{equation} -{\tilde{\sigma}}_{{ij}_\alpha} = A \: \Delta p_{j} \: \left[ -\iiint\limits_{{v_{1}}_{j}} -\frac{\partial^{2}}{\partial \alpha \partial z} {\frac{1}{{R_1}_{ij}}} \: dv_{j}^{\prime} -\: + \iiint\limits_{{v_{2}}_{j}} -\: \frac{\partial^{2} }{\partial \alpha \partial z} {\frac{1}{{R_2}_{ij}}} \: -dv_{j}^{\prime} -+ \: 2 \: z_{i} \: \iiint\limits_{{v_{2}}_{j}} -\frac{\partial^{3} }{\partial \alpha \partial z ^{2}} {\frac{1}{{R_2}_{ij}}} \:\: -dv_{j}^{\prime} \right] -\label{eq:stress_til_alpha} -\end{equation} -and -\begin{equation} -{\tilde{\sigma}}_{{ij}_{z}} = A \: \Delta p_{j} \: \left[ -\iiint\limits_{{v_{1}}_{j}} -\frac{\partial^{2}}{\partial z^{2}} {\frac{1}{{R_1}_{ij}}} \: dv_{j}^{\prime} -\: + \iiint\limits_{{v_{2}}_{j}} -\: \frac{\partial^{2} }{\partial z^{2}} {\frac{1}{{R_2}_{ij}}} \: -dv_{j}^{\prime} -+ \: 2 \: z_{i} \: \iiint\limits_{{v_{2}}_{j}} -\frac{\partial^{3} }{\partial z^{3}} {\frac{1}{{R_2}_{ij}}} \:\: -dv_{j}^{\prime} \right] \: . -\label{eq:stress_til_z} -\end{equation} - -Similarly to the displacement field (equations \ref{eq:u_til_alpha} and \ref{eq:u_til_z}), the three integrals in the right-hand side of equations \ref{eq:stress_til_alpha} and \ref{eq:stress_til_z} have the same form of -derivatives of the gravitational potential produced by the $j$th prism and image prism. -The integrals depending on $\frac{1}{{R_1}_{ij}}$ have the following closed -solutions \citep{Nagyetal2000, Nagyetal2002}: -\begin{equation} -\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} \int\limits_{{z_{1}}_{j}}^{{z_{2}}_{j}} -\frac{\partial^{2} }{\partial x \partial z} {\frac{1}{{R_1}_{ij}}} dv_{j}^{\prime} = \Bigg|\Bigg|\Bigg| -\ln(y + R) -\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} \quad , -\label{dxz1} -\end{equation} -\begin{equation} -\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} \int\limits_{{z_{1}}_{j}}^{{z_{2}}_{j}} -\frac{\partial^{2} }{\partial y \partial z} {\frac{1}{{R_1}_{ij}}} dv_{j}^{\prime} = -\Bigg|\Bigg|\Bigg| -\ln(x + R) -\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} \quad , -\label{dyz1} -\end{equation} -and -\begin{equation} -\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} \int\limits_{{z_{1}}_{j}}^{{z_{2}}_{j}} -\frac{\partial^{2} }{\partial z \partial z} {\frac{1}{{R_1}_{ij}}} dv_{j}^{\prime} = -\Bigg|\Bigg|\Bigg| -- \tan^{-1} \Bigg( \frac{xy}{z \: R} \Bigg) -\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} \quad , -\label{dzz1} -\end{equation} -where the limits ${X_1}_{j}$, ${X_2}_{j}$, ${Y_1}_{j}$, ${Y_2}_{j}$, ${Z_1}_{j}$, and ${Z_2}_{j}$ are defined by equation \ref{eq:Nagy_limits_1}. -The integrals depending on second derivatives of $\frac{1}{{R_2}_{ij}}$ in the -right-hand side of equations \ref{eq:stress_til_alpha} and \ref{eq:stress_til_z} -have closed solutions defined by equations \ref{dxz2}, \ref{dyz2}, and \ref{dzz2}. -Finally, the remaining integrals depending on third derivatives of -$\frac{1}{{R_2}_{ij}}$ have closed solutions given by -\citep{Nagyetal2000, Nagyetal2002}: -\begin{equation} -\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} \int\limits_{{z_{1}}_{j} - 2 \, z_c}^{{z_{2}}_{j} - 2 \, z_c} -\frac{\partial^{3}}{\partial x \partial z^{2}} {\frac{1}{{R_2}_{ij}}} dv_{j}^{\prime} = -\Bigg|\Bigg|\Bigg| -\frac{- y z}{R} -\left( \frac{1}{x^{2} + z^{2}} \right) -\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} \quad , -\label{sxzz} -\end{equation} -\begin{equation} -\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} \int\limits_{{z_{1}}_{j} - 2 \, z_c}^{{z_{2}}_{j} - 2 \, z_c} -\frac{\partial^{2} }{\partial y \partial z^{2}} {\frac{1}{{R_2}_{ij}}} dv_{j}^{\prime} = -\Bigg|\Bigg|\Bigg| -\frac{- x z}{R} -\left( \frac{1}{y^{2} + z^{2}} \right) -\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} \quad , -\label{syzz} -\end{equation} -\begin{equation} -\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} \int\limits_{{z_{1}}_{j} - 2 \, z_c}^{{z_{2}}_{j} - 2 \, z_c} -\frac{\partial^{3} }{\partial z^{3}} {\frac{1}{{R_2}_{ij}}} dv_{j}^{\prime} = -\Bigg|\Bigg|\Bigg| -\frac{ x y}{R} -\left( \frac{1}{x^{2} + z^{2}} + \frac{1}{y^{2} + z^{2}} \right) -\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} \quad , -\label{sz3} -\end{equation} -where the limits ${X_1}_{j}$, ${X_2}_{j}$, ${Y_1}_{j}$, and ${Y_2}_{j}$, are defined -by equation \ref{eq:Nagy_limits_1} and the limits ${Z_1}_{j}$, and ${Z_2}_{j}$ by -equation \ref{eq:Nagy_limits_2}. - -\subsection{Computation notes} - -In equations \ref{dx1}--\ref{dz1}, \ref{dx2}--\ref{dzz2} and \ref{dxz1}--\ref{dzz1}, we adopted the modifications proposed by \cite{Fukushima2020}. -To overcome the zero division in evaluating the arguments of the arctangent function, \cite{Fukushima2020} replaced $\tan^{-1} \big( \frac{S}{T} \big)$ by -\begin{equation} -arctan2(S,T) = \begin{cases} - %\left\{ \begin{aligned} - atan (S/T) & \:\: \mbox{if} \: \:\: T \neq 0 \\ - \pi /2 & \:\: \mbox{if} \: \:\: T = 0 \: \: \mbox{and} \: \:S > 0 \\ - -\pi /2 & \:\: \mbox{if} \: \:\: T = 0 \: \: \mbox{and} \: \:S < 0 \\ - 0 & \:\: \mbox{if} \: \:\: T = 0 \: \: \mbox{and} \: \:S = 0 \\ - %\end{aligned} \right\}. - \end{cases} -\label{eq:arctan2} -\end{equation} -Additionally, if the argument of the logarithm is less than $10^{-10}$, the logarithm is replaced by zero; otherwise the logarithm is calculated regularly - - - -\section{NUMERICAL APPLICATIONS} - -\subsubsection{Disk-shaped reservoir under uniform depletion} - -Embedded in a semi-infinite homogenous medium, we simulated a vertical cylinder-like reservoir (Figure \ref{fig:cylinder}) with a radius of 500 m and whose horizontal coordinates of its center along the north-south and east-west directions are 0 m and 0 m, respectively. -The depths to the top and to the bottom of the simulated reservoir are 750 m and 850 m, respectively. -The reservoir is uniformly depleted by $\Delta p = -10$ MPa. -The Young’s modulus is 3300 (in MPa), the Poisson's coefficient is 0.25, and -the uniaxial compaction coefficient $C_{m}$ (equation \ref{eq:Cm}) is -$2.2525 \: 10^{-4}$ $\textrm{ MPa}^{-1}$. - -To apply our methodology, we discretized the cylinder along the $x-$ and $y-$ directions into an $20 \times 20$ grid of prisms. Hence, we totalized 400 prisms all of them centered at 800 m deep, with depths to the top and to the bottom at 750 m and 850 m and with pressure contrast $\Delta p_j$, $j = 1, ..., 400$ equal to $-10$ MPa. -To apply the Geertsma’s method \citep{Geertsma73}, we used the disk-shaped reservoir described in \cite{Fjaer08} with dimensions and physical properties defined above. - -Figures \ref{fig:displacement} and \ref{fig:displacement_Geertsma} show cross-sections at -$x = 0$ m of the displacement fields in 2D contour plots due to the pressure change in the whole cylindrical reservoir by using our methodology and Geertsma’s method \citep{Geertsma73}, respectively. - -Because we defined the $z-$axis as positive downwards, the positive vertical displacement means a subsidence and the negative vertical displacement means an uplift. -Figure \ref{fig:displacement} shows the horizontal and vertical displacements calculated, respectively, with equations \ref{eq:horizontal_displacement} and \ref{eq:u_til_z} by our methodology that uses the closed expressions of the full integrations (equations \ref{eq:u_til_alpha} and \ref{eq:u_til_z}) of \cite{Nagyetal2000} and \cite{Nagyetal2002} (equations \ref{dx1} $-$ \ref{dzz2} ). - -Figure \ref{fig:displacement_Geertsma} shows the radial and vertical displacements using Geertsma’s method \citep{Geertsma73} considering an elastic homogeneous cylindrical reservoir under uniform depletion based on the nucleus-of-strain concept in the half-space, which in turn was proposed by \cite{Mindlin&Cheng50} and \cite{Sen51} in the theory of thermoelasticity. - -In both cases (Figures \ref{fig:displacement}b and \ref{fig:displacement_Geertsma}b) the vertical displacements due to the entire the disk-shaped reservoir display a subsidence (positive values) above the reservoir and an uplift (negative values) below the reservoir. -We stress that the proposed volume integrations (equations \ref{dx1} $-$ \ref{dzz2}) allowed to evaluate the vertical displacement (Figure \ref{fig:displacement}b) throughout the entire reservoir including inside and outside the reservoir. -Rather, the vertical displacement using Geertsma’s method -(Figure \ref{fig:displacement_Geertsma}b) is only valid outside the reservoir. - -The radial displacement using Geertsma’s method -(Figure \ref{fig:displacement_Geertsma}a) shows positive values at the edges of the reservoir ($y= -500$ and $y = 500$) with a singularity at the center of the reservoir -($x= 0, \: y = 0$ and $z = 800$ m). -The horizontal displacement with the proposed full integration -(Figures \ref{fig:displacement}a) shows positive values at the edges of the reservoir ($y= -500$ and $y = 500$); however, it does not present sigularities inside the reservoir. - -Figure \ref{fig:displacement_z_levels} shows the $x-$component displacement and vertical displacement by our methodology that uses a full volume integrations. -These displacements are calculated along the $x-$axis, at $y = 0$ m and considering four surfaces located at the following depths: seafloor ($z = 0$ m), reservoir top ($z = 750$ m), reservoir center ($z = 800$ m) and reservoir bottom ($z = 850$ m). -In the $x$-component of the displacement (Figure \ref{fig:displacement_z_levels}a), we can note an increased horizontal contraction from the center of the reservoir ($x = 0$) toward the reservoir edge ($x= 500$ m) where the maximum contraction of all surfaces occur. -In the vertical displacement (Figure \ref{fig:displacement_z_levels}b), we can note a subsidence of the seafloor and the reservoir top (positive values) and an uplift of the reservoir bottom (negative values). -The vertical displacements of the seafloor, the top and bottom of the reservoir for Geertsma’s method (Figure \ref{fig:displacement_z_levels_Geertsma}) show a similar behavior of those obtained by our methodology that uses a full volume integrations (Figure \ref{fig:displacement_z_levels}b). -However, we note that the subsidence of the seafloor is more attenuated in the Geertsma’s method than in our method. -This fact is important because the moviment of the seafloor should be monitored in hydrocarbon fields under production. - -Figure \ref{fig:Null_stress} shows the null stress through the free surface at the -plane $z=0$ m due to reservoir under uniform depletion. - - - -\subsubsection{Disk-shaped reservoir under non uniform depletion} - -Here, we kept the same dimensions of the cylindrical reservoir simulated previously. -We also kept the reservoir properties, except the pressure. -We simulated a non-uniform depletion scenario where the cylindrical reservoir is composed by two vertically juxtaposed cylinders, each one with a uniform depletion. -The deepest cylinder is uniformly depleted by $\Delta p = -20$ MPa with its top and bottom at, respectively, 800 and 850 m deep. -The shallowest cylinder is uniformly depleted by $\Delta p = -40$ MPa with its top and bottom at, respectively, 750 and 800 m deep. - -We discretized the cylinders along the $x-$, $y-$ and $z-$ directions into an $20 \times 20 \times 2$ grid of prisms. -This simulation totalized 800 prisms whose thicknesses are 50 m. -The 400 deepest prisms are centered at 825 deep, with pressure contrast equal to $-20$ MPa and the 400 shalowest prisms are centered at 775 deep, with pressure contrast equal to $-40$ MPa - -We calculate the displacement fields due to the pressure change in the whole cylindrical reservoir under non uniform depletion. -Figure \ref{fig:displacement_non_uniform_depletion} shows cross-sections at $x = 0$ m of the horizontal and vertical displacements, in 2D contour plots, calculated in the whole reservoir by using our methodology. -Figure \ref{fig:displacement_z_levels_non_uniform_depletion} shows the $x-$component displacement and vertical displacement that are calculated by our methodology along the -$x-$axis, at $y = 0$ m and considering four surfaces located at the following depths: seafloor ($z = 0$ m), reservoir top ($z = 750$ m), reservoir center ($z = 800$ m) and reservoir bottom ($z = 850$ m). - -By comparing Figure \ref{fig:displacement_non_uniform_depletion} with Figures \ref{fig:displacement}, we can note similar behaviours of the displacement fields. -However, the displacement fields of reservoir under non uniform depletion (Figure \ref{fig:displacement_non_uniform_depletion}) attain higher values because the higher variation of the pressure in the whole cylindrical reservoir. - -In general, the displacements on the seafloor, the top, the center and the bottom of the reservoir under non uniform depletion -(Figure \ref{fig:displacement_z_levels_non_uniform_depletion}) show similar behaviors to the corresponding surfaces of the reservoir under uniform depletion -(Figure \ref{fig:displacement_z_levels}). -However, we can note higher displacements of these surfaces in the reservoir under non uniform depletion (Figure \ref{fig:displacement_z_levels_non_uniform_depletion}) due to the higher variation of the pressure in the whole cylindrical reservoir. -Moreover, we can observe that the $x-$component displacements -(Figure \ref{fig:displacement_z_levels_non_uniform_depletion}a) -produced by the top (black line) and the bottom (red line) of the reservoir under non uniform depletion are not coincident to each other and the vertical displacement on the center of the reservoir under non uniform depletion (blue line in (Figure \ref{fig:displacement_z_levels_non_uniform_depletion}b) varies along the $x-$axis. -Finally, we stress that the subsidence on the seafloor due to the reservoir under non uniform depletion -(green line in Figure \ref{fig:displacement_z_levels_non_uniform_depletion}b) attains higher values (close to 20 cm) than the subsidence of the seafloor due to the reservoir under uniform depletion (green line in Figure \ref{fig:displacement_z_levels}b). - -We verify that the zero stress condition is satisfied at the free surface -%(equations \ref{eq:null_stress} and \ref{eq:null_stress_i}) -due to reservoir under a non uniform depletion as shown in Figure \ref{fig:Null_stress_non_uniform_depletion}. - -\subsubsection{Reservoir with arbitrary geometry and under arbitrary pressure changes} - -In this numerical application, the reservoir model is a simplification of a realistic reservoir located in a production oil field in offshore Brazil. -The entire reservoir model comprises dimensions of 14 km in the north-axis, 13 km in the -east-axis, and 0.6 km in the down-axis. -The depths to the top and bottom of the reservoir model are 2,712 m and 3,312 m, respectively. -The components of the displacements are calculated at 0 m deep, -on a regular grid of 100 $\times$ 80 observation points along the north- and east-directions, respectively. -We discretized the reservoir along the $x-$, $y-$ and $z-$ directions into an $14 \times 13 \times 2$ grid of prisms. -The Young’s modulus is 3300 (in MPa), the Poisson's coefficient is 0.25, and -the uniaxial compaction coefficient $C_{m}$ (equation \ref{eq:Cm}) is $2.2525 \: 10^{-4}$ -$\textrm{ MPa}^{-1}$. -In the 3D perspective view of the pore pressure distribution of the simulated reservoir shown in Figure \ref{fig:pressure_complex_reservoir}, we can see that the pressures vary from $0$ to $-0.72$ MPa. -Figure \ref{fig:displacement_complex_reservoir} shows cross-sections at $x = 8$ km of the horizontal and vertical displacements, in 2D contour plots, calculated in the whole reservoir by using our methodology. -Figure \ref{fig:Null_stress_complex_reservoir} shows the null stress through the free surface -%(equations \ref{eq:null_stress} and \ref{eq:null_stress_i}) -due to reservoir with arbitrary geometry and under arbitrary pressure disribution. - - -\conclusions %% \conclusions[modified heading if necessary] -Grounded on the similarity between the gravitational potential produced by a volume source under a density variation and the displacement field produced by a volume source in a half-space under a pressure variation, we have presented the analytical solution for the displacement field due to reservoir compaction with arbitrary geometry and under non-uniform pressure distribution. -Our approach calculates the displacement field due to a reservoir by approximating its 3D pressure distribution through a piecewise constant function defined on a user-specified grid of 3D vertical prisms juxtaposed in the $x-$, $y-$ and $z-$directions. -By using the nucleus of strain as an infinitesimal volume element for each prism, -we have calculated the displacement solution yielded by each prism through a 3D integration over the prism volume. -The sum of the displacements produced by the prisms is the final displacement field due to the whole reservoir. -The adopted exact analytical formulae, based on the gravitational field, to carry out the full integrations and calculate the displacement field due to reservoir compaction are valid expressions either outside or inside the prisms because the implemented expressions make use of modified arctangent function. -We have demonstrated the use of these exact analytical expressions by applying them to calculate the displacement fields due to cylindrical reservoirs with uniform and non-uniform pressure distributions and to realistic reservoir model of a production oil field in offshore Brazil with arbitrary geometry and under arbitrary pressure distribution. -All the numerical applications produced null stress fields at the free surface -showing that the condition of null tractions at the free surface has been met. -We have presented routines written in Python language (Python 3.7.6) to calculate the displacement and stress fields due to a reservoir with arbitrary shape and non-uniform distribution of pressure changes. -The numerical applications and figures showing the results in this article were produced in -Jupyter Notebook. - -%% The following commands are for the statements about the availability of data sets and/or software code corresponding to the manuscript. -%% It is strongly recommended to make use of these sections in case data sets and/or software code have been part of your research the article is based on. - - -\codedataavailability{ -The current version of our code is freely distributed under the BSD 3-clause licence and it is available for download at Zenodo: http://doi.org/10.5281/zenodo.4041985 . -The latest development version of our code can be freely downloaded from a repository on GitHub (https://github.com/pinga-lab/DisReserv). -Instructions for running the current version of our code are also provided on the repository. -The code is still being improved and we encourage the user to work with the latest development version. -The code was developed as an open-source Python language (Python 3.7.6). -The numerical applications were produced in Jupyter Notebook. -The data of the pore pressure distribution simulating a realistic reservoir -$(realistic-model.pickle)$ are available in the above-mentioned repositories. -} %% use this section when having data sets and software code available - - -%\appendix -%\section{} %% Appendix A - -%\subsection{} %% Appendix A1, A2, etc. - - -%\noappendix %% use this to mark the end of the appendix section. Otherwise the figures might be numbered incorrectly (e.g. 10 instead of 1). - -%% Regarding figures and tables in appendices, the following two options are possible depending on your general handling of figures and tables in the manuscript environment: - -%% Option 1: If you sorted all figures and tables into the sections of the text, please also sort the appendix figures and appendix tables into the respective appendix sections. -%% They will be correctly named automatically. - -%% Option 2: If you put all figures after the reference list, please insert appendix tables and figures after the normal tables and figures. -%% To rename them correctly to A1, A2, etc., please add the following commands in front of them: - -%\appendixfigures %% needs to be added in front of appendix figures - -%\appendixtables %% needs to be added in front of appendix tables - -%% Please add \clearpage between each table and/or figure. Further guidelines on figures and tables can be found below. - - - -\authorcontribution{ -VCFB and VCOJr deduced the equations in this paper. -VCFB and ADA implemented the numerical applications presented in this paper. -Most of the python codes were developed by VCOJr with some participation of VCFB. -All authors contributed to the writing of the paper. -} %% this section is mandatory - -\competinginterests{The authors declare that they have no conflict of interest.} %% this section is mandatory even if you declare that no competing interests are present - - -\begin{acknowledgements} -Andre D. Arelaro thanks Petrobras, especially, the Multiphysics Group. -Valeria C.F. Barbosa was supported by fellowships from: CNPq (grant 307135/2014- 4) and FAPERJ (grant E-26/202.582/2019). -Vanderlei C. Oliveira Jr. was supported by fellowships from: CNPq (grant 308945/2017-4) and FAPERJ (grant E-26/202.729/2018). -\end{acknowledgements} - -\financialsupport{This work is supported by the Brazilian research agencies -Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) and -Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ).} - -%% REFERENCES - -%% The reference list is compiled as follows: - -\begin{thebibliography}{} - - -\bibitem[Beltrami(1902–1920)]{Beltrami} -Beltrami, E.: Opere Matematiche, Hoepli, Milano, 1902–1920. - -\bibitem[Borges et al.(2020)]{Borges2020} -Borges, F., Landro M., and Duffaut, K.: Time-lapse seismic analysis of overburden water injection at the Ekofisk field, southern North Sea, GEOPHYSICS, 85, B9–B21, 2020 - -\bibitem[Dahm et al.(2015)]{Dahmetal15} -Dahm, T., Cesca, S., Hainzl, S., Braun, T., and Krüger, F.: Discrimination -between induced, triggered, and natural earthquakes close to hydrocarbon reservoirs: A probabilistic approach based on the modeling of depletion-induced stress changes -and seismological source parameters, J. Geophys. Res. Solid Earth, 120, -2491–2509, 2015. - - -\bibitem[Fjaer et al.(2008)]{Fjaer08} -Faer, E., Holt, R. M., Horsrud,P., Raaen, A.M., and Risnes, R.: Petroleum related rock mechanics: Elsevier, 53, 2008. - - -\bibitem[Fukushima(2020)]{Fukushima2020} -Fukushima, T.: Speed and accuracy improvements in standard algorithm for prismatic gravitational field, Geophys. J. Int., 222, 1898–1908, 2020. - - -\bibitem[Geertsma(1957)]{Geertsma57} -Geertsma, J.: A remark on the analogy between thermoelasticity and the -elasticity of saturated porous media. J. Mech. Phys. Solids, 6, 13–16, 1957 - -\bibitem[Geertsma(1966)]{Geertsma66} -Geertsma, J.: Problems of rock mechanics in petroleum production engineering, in: Proc. First Cong. Int. Soc. Rock Mech., 1, 585–594, 1966. - -\bibitem[Geertsma(1973)]{Geertsma73} -Geertsma, J.: Land Subsidence above compacting oil and gas reservoirs, J. Pet. Tech. 25, 734-744, 1973. - -\bibitem[Geertsma and van Opstal(1973)]{Geertsma&Opstal73} -Geertsma, J., and van Opstal, G.: A numerical technique for predicting subsidence above compacting reservoirs, based on the nucleus of strain concept,” Verhandelingen Kon. -Ned. Geol. Mijnbouwk., 28, 63–78, 1973. - - -\bibitem[Goodier(1937)]{Goodier37} -Goodier, J. N.: On the Integration of the Thermo-elasti equations, Phil. Mag. 7, 1017-1032, 1937. - -\bibitem[Grigoli et al.(2017)]{Grigolietal17} -Grigoli, F., Cesca, S., Priolo. E., Rinaldi, A.P., Clinton, J.F., Stabile, T.A., Dost, B., Fernandez, M.G., Wiemer, S. and, Dahm T.: Current challenges in monitoring, discrimination, and management of induced seismicity related to underground industrial activities: a European perspective, Rev, Geophys., 55, 310–340, 2017 - - -\bibitem[Kellogg(1929)]{Kellogg29} -Kellogg, O. D.: Foundations of Potential Theory, rederick Ungar Publishing Company, 1929. - -\bibitem[Mehrabian and Abousleiman(2015)]{Mehrabian&Abousleiman15} -Mehrabian, A., and Abousleiman, Y.A.: Geertsma’s subsidence solution extended to layered stratigraphy, J. Pet. Sci. Eng., 130, 68–76, 2015. - -\bibitem[Mindlin and Cheng(1950)]{Mindlin&Cheng50} -Mindlin, R.D. and Cheng, D.H.: Thermoelastic stress in the semi-infinite solid, J. Appl. Phys. 21, 931–933, 1950. - -\bibitem[Muñoz and Roehl(2017)]{Munoz&Roehl17} -Muñoz, L.F.P. and Roehl, D: An analytical solution for displacements due to reservoir -compaction under arbitrary pressure changes, Appl. Math. Modell., 52, 145–159, 2017. - - -\bibitem[Nagy et al.(2000)]{Nagyetal2000} -Nagy, D., Papp, G., and Benedek, J.: The gravitational potential and its -derivatives for the prism: Journal of Geodesy, 74, 552–560, 2000. - - -\bibitem[Nagy et al.(2002)]{Nagyetal2002} -Nagy, D., Papp, G., and Benedek, J.: Corrections to "The gravitational potential and its -derivatives for the prism": Journal of Geodesy, 76, 475, 2002. - -\bibitem[Segall(1992)]{Segall92} -Segall, P.: Induced stresses due to fluid extraction from -axisymmetric reservoirs. Pure Appl. Phys. 139, 536–560, 1992. - -\bibitem[Sen(1951)]{Sen51} -Sen, B.: Note on the Stresses Produced by Nuclei of Thermoelastic Strain -in a Semi-infinite Solid, Quart. Appl. Math., 8, 365–369, 1951. - -\bibitem[Sharma(1956)]{Sharma56} -Sharma, B.D.: Stresses in an infinite slab due to a nucleus of thermoelastic strain in it, Z. Angew. Math. Mech., 36, 565–589, 1956. - -\bibitem[Tao(1971)]{Tao71} -Tao, L.N: Integration of the dynamic thermoelastic equations, -Int. J. Eng. Sci., 9, 489–505, 1971 - -\bibitem[Tempone et al.(2010)]{Tempone10} -Tempone, P., Fjaer, E., and Landro, M.: Improved solution of displacements due to a compacting reservoir over a rigid basement, Appl. Math. Modell. 34, 3352–3362, 2010. - -\bibitem[Tempone et al.(2012)]{Tempone12} -Tempone, P., Landro, M., and Fjaer, E.: 4D gravity response of compacting reservoirs: Analytical approach, Geophysics, 77, G45–G54, 2012. - - -\bibitem[van Thienen-visser and Fokker(2017)]{vanThienen-visser&Fokker17} -van Thienen-Visser, K. and Fokker, P. A.:The future of subsidence modelling: compaction and subsidence due to gas depletion of the Groningen gas field in the Netherlands, 96, Netherlands Journal of Geosciences, 96, s105–s116, 2017. - -\end{thebibliography} - -\clearpage - -\begin{figure}[ht] -\includegraphics[width=8.3cm]{Fig/Figure_Nucleus_Strain.png} -\caption{Schematic representation of the geometry of the nucleus of strain in a semi-infinite medium. After \cite{Munoz&Roehl17}. -The adopted Cartesian coordinate system considered the $x-$axis pointing to north, the $y-$axis pointing to east and the $z-$axis pointing downward.} -\label{fig:nucleus_strain} -\end{figure} - -%%% First Test: Disk-shaped reservoir under non uniform depletion - -\begin{figure}[ht] -\includegraphics[width=8.3cm]{Fig/Figure_Cylinder.png} -\caption{Disk-shaped reservoir under uniform depletion with a radius of 500 m} -\label{fig:cylinder} -\end{figure} - -\begin{figure}[ht] -\includegraphics[width=8.3cm]{Fig/Figure_Displacement.png} -\caption{Reservoir under uniform depletion: (a) Horizontal displacement (equation \ref{eq:horizontal_displacement}) and (b) vertical displacement (equation \ref{eq:u_til_z}) by our methodology that uses the closed expressions of the volume integrations given by \cite{Nagyetal2000} and \cite{Nagyetal2002} (equations \ref{dx1}-\ref{dzz2})} -\label{fig:displacement} -\end{figure} - -\begin{figure}[h] -\includegraphics[width=8.3cm]{Fig/Figure_Displacement_Geertsma.png} -\caption{Reservoir under uniform depletion: (a) Radial displacement and (b) vertical displacement using Geertsma’s method \citep{Geertsma73} considering an elastic homogeneous cylindrical reservoir under uniform depletion \citep{Fjaer08}} -\label{fig:displacement_Geertsma} -\end{figure} - -\begin{figure}[ht] -\includegraphics[width=8.3cm]{Fig/Figure_Displacement_z_levels.png} -\caption{Reservoir under uniform depletion: (a) Horizontal x-component displacement and (b) vertical displacement by our methodology that uses the closed expressions of the volume integrations given by \cite{Nagyetal2000} and \cite{Nagyetal2002} (equations \ref{dx1}-\ref{dzz2}). -These displacements are calculated along the x-axis, at $y = 0$ m and $z$ located at the depths of: seafloor ($z = 0$ m), reservoir top ($z = 750$ m), reservoir center ($z = 800$ m) and reservoir bottom ($z = 850$ m).} -\label{fig:displacement_z_levels} -\end{figure} - -\begin{figure}[ht] -\includegraphics[width=8.3cm]{Fig/Figure_Displacement_z_levels_Geertsma.png} -\caption{Reservoir under uniform depletion: Vertical displacement using Geertsma’s method \citep{Geertsma73} considering an elastic homogeneous cylindrical reservoir under uniform depletion \citep{Fjaer08}. -The displacement is calculated along the x-axis, at $y = 0$ m and $z$ located at the depths of: seafloor ($z = 0$ m), reservoir top ($z = 750$ m), and reservoir bottom -($z = 850$ m).} -\label{fig:displacement_z_levels_Geertsma} -\end{figure} - - -\begin{figure}[ht] -\includegraphics[width=12cm]{Fig/Figure_Null_stress.png} -\caption{Reservoir under uniform depletion: (a) $x-$, (b) $y-$, and (c) $z-$components of the stress at the free surface.} -\label{fig:Null_stress} -\end{figure} - - -%%% Second test: Disk-shaped reservoir under non uniform depletion - - -\begin{figure}[ht] -\includegraphics[width=8.3cm]{Fig/Figure_Displacement_non_uniform_depletion.png} -\caption{Reservoir under non uniform depletion: (a) Horizontal displacement (equation \ref{eq:horizontal_displacement}) and (b) vertical displacement (equation \ref{eq:u_til_z}) by our methodology that uses the closed expressions of the volume integrations given by \cite{Nagyetal2000} and \cite{Nagyetal2002} (equations \ref{dx1}--\ref{dzz2})} -\label{fig:displacement_non_uniform_depletion} -\end{figure} - -\begin{figure}[ht] -\includegraphics[width=8.3cm]{Fig/Figure_Displacement_z_levels_non_uniform_depletion.png} -\caption{Reservoir under non uniform depletion: (a) Horizontal x-component displacement and (b) vertical displacement by our methodology that uses the closed expressions of the volume integrations given by \cite{Nagyetal2000} and \cite{Nagyetal2002} (equations \ref{dx1}--\ref{dzz2}). -These displacements are calculated along the x-axis, at $y = 0$ m and $z$ located at the depths of: seafloor ($z = 0$ m), reservoir top ($z = 750$ m), reservoir center ($z = 800$ m) and reservoir bottom ($z = 850$ m).} -\label{fig:displacement_z_levels_non_uniform_depletion} -\end{figure} - - -\begin{figure}[ht] -\includegraphics[width=12cm]{Fig/Figure_Null_stress_non_uniform_depletion.png} -\caption{Reservoir under non uniform depletion: (a) $x-$, (b) $y-$, and (c) $z-$components of the stress at the free surface.} -\label{fig:Null_stress_non_uniform_depletion} -\end{figure} - -%% Third test: Reservoir with arbitrary geometry and under arbitrary pressure changes - - -\begin{figure}[ht] -\includegraphics[width=8.3cm]{Fig/Figure_Pressure_complex_reservoir.png} -\caption{Reservoir with arbitrary geometry and under arbitrary pressure changes: 3D perspective view of the pore pressure distribution of a realistic reservoir -located in a production oil field in offshore Brazil.} -\label{fig:pressure_complex_reservoir} -\end{figure} - -\begin{figure}[ht] -\includegraphics[width=8.3cm]{Fig/Figure_Displacement_complex_reservoir.png} -\caption{Reservoir with arbitrary geometry and under arbitrary pressure changes: (a) Horizontal displacement (equation \ref{eq:horizontal_displacement}) and (b) vertical displacement (equation \ref{eq:u_til_z}) by our methodology that uses the closed expressions of the volume integrations given by \cite{Nagyetal2000} and \cite{Nagyetal2002} (equations \ref{dx1}--\ref{dzz2})} -\label{fig:displacement_complex_reservoir} -\end{figure} - -\begin{figure}[ht] -\includegraphics[width=12cm]{Fig/Figure_Null_stress_complex_reservoir.png} -\caption{Reservoir with arbitrary geometry and under arbitrary pressure changes: (a) $x-$, (b) $y-$, and (c) $z-$components of the stress at the free surface.} -\label{fig:Null_stress_complex_reservoir} -\end{figure} - - -%% Since the Copernicus LaTeX package includes the BibTeX style file copernicus.bst, -%% authors experienced with BibTeX only have to include the following two lines: -%% -%% \bibliographystyle{copernicus} -%% \bibliography{example.bib} -%% -%% URLs and DOIs can be entered in your BibTeX file as: -%% -%% URL = {http://www.xyz.org/~jones/idx_g.htm} -%% DOI = {10.5194/xyz} - - -%% LITERATURE CITATIONS -%% -%% command & example result -%% \citet{jones90}| & Jones et al. 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F. Barbosa,\affil{1} Vanderlei C. Oliveira Jr,\affil{1} +Andre D. Arelaro\affil{1,2} and Filipe Borges\affil{2} } +\shortauthors{Barbosa et al.} +\correspondent{Valeria C. F. Barbosa} +% +\keywords{gravitational potential, reservoir compaction, hydrocarbon production, nucleus-of-strain solution, mathematical and numerical modeling} + +\ano{2022} + +% + +\begin{document} +%%%%% +% The \affiliation command has two arguments: the affiliation number and the institution. Make sure that the affiliation +% numbers correspond to those put in the \affil commands. +% The \affiliation commands must be placed immediately after \begin{document}. + +%\affil{1}{Observat\'{o}rio Nacional, Rio de Janeiro, Brazil} +%\affil{2}{Petróleo Brasileiro S.A. (PETROBRAS), Rio de Janeiro, Brazil} + +\affiliation{1}{Observat\'{o}rio Nacional, Rio de Janeiro, Brazil} +\affiliation{2}{Petróleo Brasileiro S.A. (PETROBRAS), Rio de Janeiro, Brazil} + +% +\begin{abstract} +We have presented alternative solutions for the displacement and stress fields outside and inside of a 3D right rectangular prism under constant pressure. These solutions are obtained by integrating the well-known nucleus-of-strain solution over the volume of the prism. They are based on the similarity between the gravitational potential yielded by a volume source under a density variation and the thermoelastic displacement potential yielded by a volume source in a half-space under a pressure variation. This similarity enables the use of closed expressions of the gravitational potential +and its derivatives. We use our solution for approximating the displacement and stress fields +due to a reservoir with arbitrary shape and under arbitrary pressure changes. +We discretized the reservoir as a grid of 3D right rectangular prisms juxtaposed in the horizontal and vertical directions. Each prism has homogeneous pressure; however, pressure variations among different prisms are allowed. This parametrization of the reservoir yields a piecewise-constant distribution of pressure in the subsurface. We validate the resultant displacement and stress fields due to the reservoir by numerical simulations including a reservoir with arbitrary geometry and under arbitrary pressure distribution, based on a production oil field in offshore Brazil. +\end{abstract} + +\begin{resumo} +We have presented alternative solutions for the displacement and stress fields outside and inside of a 3D right rectangular prism under constant pressure. These solutions are obtained by integrating the well-known nucleus-of-strain solution over the volume of the prism. They are based on the similarity between the gravitational potential yielded by a volume source under a density variation and the thermoelastic displacement potential yielded by a volume source in a half-space under a pressure variation. This similarity enables the use of closed expressions of the gravitational potential +and its derivatives. We use our solution for approximating the displacement and stress fields +due to a reservoir with arbitrary shape and under arbitrary pressure changes. +We discretized the reservoir as a grid of 3D right rectangular prisms juxtaposed in the horizontal and vertical directions. Each prism has homogeneous pressure; however, pressure variations among different prisms are allowed. This parametrization of the reservoir yields a piecewise-constant distribution of pressure in the subsurface. We validate the resultant displacement and stress fields due to the reservoir by numerical simulations including a reservoir with arbitrary geometry and under arbitrary pressure distribution, based on a production oil field in offshore Brazil. +\end{resumo} + + +\section*{Introduction} +The surface subsidence due to oil or gas withdrawal from a reservoir in the subsurface may occur as a result of geomechanical changes caused by pressure drop. +The phenomenon of subsidence by fluid extraction has been observed in a variety of oil fields, e.g., the Ekofisk field, southern North Sea \citep{Borges2020} and the Groningen gas field in the northeast Netherlands \citep{vanThienenFokker17}. +Because the subsidence close to hydrocarbon fields under production can induce earthquakes (e.g., \citeauthor{Dahmetal15}, \citeyear{Dahmetal15}; \citeauthor{Grigolietal17}, \citeyear{Grigolietal17}), the petroleum companies have been an increased interest in monitoring the magnitude and distribution of subsidence resulting from reservoir depletion. +This monitoring is accomplished by means of the numerical modeling of the displacement field. +The physical foundation of the displacement, stress and strain fields in the subsurface due to a reduction of pressure in the reservoir comes from the theory of thermoelasticity. +In the uncoupled thermoelasticity theory for quasi-static problems (i.e., problems with negligible inertia effects), \cite{Goodier37} employed the method of superposition using +displacement potential functions and introduced the concept of nucleus of thermoelastic strain in an infinite space. +Specifically, Goodiee’s (\citeyear{Goodier37}) method simplified the thermoelastic problem by replacing it by an isothermal elastic problem with different boundary conditions together with the solution of a Poisson’s equation \citep{Tao71}. +\cite{Mindlin-Cheng50} and \cite{Sen51} extended the Goodiee's method to a homogenous half-space. +\cite{Sharma56} deduced the displacement and stress fields in an infinite elastic plate due to a nucleus of thermoelastic strain located at a point inside it by using infinite integrals involving Bessel functions. + +The subsidence resulting from reservoir depletion is in the context of poroelastic theory. +\cite{Geertsma57} remarked the analogy between the theories of thermoelasticity and poroelasticity. +To our knowledge, \cite{Geertsma73} was the first to solve the poroelastic problem by using the nucleus-of-strain concept in the half-space, which in turn was proposed by \cite{Mindlin-Cheng50} and \cite{Sen51} in the theory of thermoelasticity. +Geertsma's approach presumes that the total displacement field due to the compaction of a +compacting region in subsurface is the superposition of the displacement field due to +its constituting points. +Each constituting point, in turn, is represented by a small sphere called nucleus-of-strain. +By using this idea, \cite{Geertsma73} derived analytical expressions by integrating the +nucleus-of-strain solution over the volume of a thin disk-shaped reservoir. +\cite{Segall92} followed \cite{Geertsma73} and extended the analytical solutions of the displacement and stress fields assuming general axisymmetric geometries and an arbitrary radial pressure distribution. +\cite{Geertsma-Opstal73} applied the nucleus-of-strain concept in the half-space +to calculate the spatial subsidence distribution due to the production of reservoir with an arbitrary 3D shape. +By assuming a producing reservoir embedded in an a homogeneous, isotropic, and elastic medium, and a reservoir model in which the pressure perturbations are related to the displacement field by a linear relationship, \cite{Geertsma-Opstal73} discretized the reservoir into a grid of nuclei-of-strain and calculated the displacement due to the pressure change in the whole reservoir by the superposition of the displacement due to the constant pressure change in each nucleus. +\cite{Tempone10} followed \cite{Geertsma-Opstal73} and +extended the nucleus-of-strain concept in the half-space to consider the effects of a rigid basement. +The main drawbacks in \cite{Geertsma-Opstal73} and \cite{Tempone10} are the assumption of homogeneous reservoir and the fact that the solution is only valid outside the reservoir. +In this case, the displacements within the reservoir are calculated by a linear interpolation of the displacements at the upper and lower edges of the reservoir \citep{Tempone12}. +Considering an inhomogeneous poroelastic model consists of layered stratigraphy, \cite{Mehrabian-Abousleiman15} developed closed-form formulae for the displacement and stress fields outside and inside of the reservoir embedded within elastic strata with different mechanical properties and subjected to pore pressure disturbances due to fluid extraction or injection. +\cite{Munoz-Roehl17} assume a linear elastic semi-infinite medium to develop an analytical solution for the displacement field outside and inside of a rectangular prism having a constant pressure change. +Their approach consists in integrating the Geertsma's nucleus-of-strain solution over the volume of the prism. Then, they discretize an arbitrarily-shaped reservoir under arbitrary distribution of pressure changes into a grid of prisms having different constant pressure changes. +Finally, they compute the total displacement field outside and inside of the reservoir by adding the displacement fields produced by all prisms setting up the reservoir model. + +The present work assumes a linear elastic semi-infinite medium and provides an alternative solution for the displacement field outside and inside of a rectangular prism with constant pressure change. +Like \cite{Munoz-Roehl17}, we integrate the Geertsma's nucleus-of-strain over the prism volume. +We also use our alternative solution to approximate the displacement field due to an arbitrarily-shaped +reservoir under arbitrary pressures changes by the superposition of the displacement fields produced by +a grid of prisms. +Like \cite{Vasco1987}, we take advantage of the similarity between the equations for calculating the displacement field due to a volume source in a half-space under a pressure variation and the gravitational potential due to a volume source under a density variation. +In contrast with \cite{Vasco1987}, our approach calculates the displacement field due to a 3D volume source +at the whole subsurface whereas \cite{Vasco1987} calculated the displacement field due to a 2D volume source +at the Earth surface. +We use closed expressions of the gravitational potential and its derivatives produced by the 3D right rectangular prism derived by \cite{Nagyetal2000}, \cite{Nagyetal2002} and \cite{Fukushima2020} for calculating the displacement field due to a 3D prism +under a constant pressure variation. +%\vspace{-0.5cm} +\section*{Theory} +%\vspace{-0.5cm} +The displacement, stress and strain fields in the subsurface caused by reservoir compactation due to hydrocarbon production are grounded on the theory of thermoelasticity. +The Goodiee’s thermoelastic displacement potential $\phi$ satisfies the Poisson's equation \citep{Goodier37}, i.e.: +%\vspace{-1cm} +\begin{equation} +\nabla^{2} \phi = m \: T, +\label{eq:poisson} +\end{equation} +where $\nabla^{2}$ is the Laplacian operator, $T $ is the temperature variation and +$m = \: \alpha \: \frac{1 + \nu}{ 1 -\nu},$ +%\begin{equation} +%m = \: \alpha \: \frac{1 + \nu}{ 1 -\nu}, +%\label{eq:m} +%\end{equation} +where $\alpha$ is the coefficient of linear thermal expansion and $\nu$ is the Poisson's ratio. +From the potential theory, a particular solution of equation \ref{eq:poisson} is +%\vspace{-1cm} +\begin{equation} +\begin{aligned} +\phi(x,y,z) = & - \frac{m}{4 \pi} \int\int\limits_{v}\int \\ + & \frac{T(x^{\prime}, y^{\prime}, z^{\prime} )} + {\sqrt{(x - x^{\prime})^{2} + (y - y^{\prime})^{2} + (z - z^{\prime})^{2}}} \: dv^{\prime}, +\end{aligned} +\label{eq:phi} +\end{equation} +where $\phi(x,y,z)$ represents the Newtonian gravitational potential \citep{Kellogg29} that would be produced at the coordinates $x, y$ and $z$ by a continuous density distribution $- \frac{m}{4 \pi} \: T( x^{\prime}, y^{\prime}, z^{\prime} )$. +The integral in equation \ref{eq:phi} is conducted over the coordinates $x^{\prime}$,$y^{\prime}$ and $z^{\prime}$, denoting, respectively, the $x-$, $y-$ and $-z$ coordinates of an arbitrary point belonging to the interior of the volume $v$ of the solid. +From equation \ref{eq:phi} and the potential theory, \citet{Goodier37} showed that, if an element of volume $dv$ in the infinite solid is at a temperature $T(x^{\prime}, y^{\prime}, z^{\prime}) $, the remainder being at temperature zero, the displacement vector $\bf{u}$ caused by this temperature is the gradient of the Goodiee’s thermoelastic displacement potential, i.e., +%\vspace{-1cm} +\begin{equation} +{\bf{u}} = {\bf {\nabla}} \phi(x,y,z) \: , +\label{eq:displacement-general} +\end{equation} +where $\bf{\nabla}$ is the gradient operator. +To a homogenous half-space, \citet{Mindlin-Cheng50} showed that the method proposed by \citet{Goodier37} can be extended by the displacement solution given by: +%\vspace{-1cm} +\begin{equation} +\bf{u} = {\bf{\nabla}} \: \phi_{1} \: + \: {\bf{{\nabla}_{2}}} \phi_{2}, +\label{eq:displacement-solution} +\end{equation} +where $\phi_{1} \equiv \phi_{1}(x,y,z)$ is the potential defined in equation \ref{eq:phi}, +$\phi_{2} \equiv \phi_{2}(x,y,z)$ +is defined as "image potential" \citep{Segall92} due to a image point at the coordinates +$(x^{\prime}, y^{\prime}, -z^{\prime} )$ and the operator $\bf{{\nabla}_{2}}$ is +%\vspace{-1cm} +\begin{equation} +{\bf{{\nabla}_{2}}} = (3 - 4\nu){\bf{\nabla}} + 2 {\bf{\nabla}} z \frac{\partial }{\partial z} - 4(1- \nu){\bf{\hat{z}}} {\bf{{\nabla}^{2}_{z}}}, +\label{eq:nabla2} +\end{equation} +where ${\bf{\hat{z}}}$ is the unit vector in the $z-$direction and +${\bf{{\nabla}^{2}_{z}}}$ is a scalar operator in which the operand is firstly +multiplied by $z$ and then operated upon by the Laplacian ${\bf{\nabla}^{2}}$. +Equation \ref{eq:displacement-solution} is the displacement solution for the variation of temperature due to a single nucleus of strain buried at depth $z^{\prime}$ in a +semi-infinite homogeneous medium. +In the right hand side of equation \ref{eq:displacement-solution}, the first term +$ {\bf{\nabla}} \: \phi_{1} $ represents the displacement in an infinite medium, and the second term represents a correction of the displacement due a half-space, also known as "image nucleus solution". + +\section*{Methodology} +%\vspace{-1.0cm} +Let's assume that a reservoir in the interior of the Earth is subject to a compactation due to hydrocarbon production. +The compactation is caused by the pressure change within the reservoir, which in turn causes a surface subsidence (or surface displacement). +Here, we use a Cartesian coordinate system with the $x-$axis pointing to north, the $y-$axis pointing to east and the $z-$axis pointing downward. +We discretize the reservoir into an $ m_{x} \times m_{y} \times m_{z} $ grid of 3D vertical juxtaposed prisms $(m_{x} \cdot m_{y} \cdot m_{z} = M)$ along the +$x$, $y$ and $z$ axes, respectively, in which the pressure within each prism is +assumed to be constant and known. +Each prism in the reservoir model may undergo a distinct pressure change. +The subsidence effect is the displacement field due to the pressure change throughout the reservoir and is calculated by the sum of the displacement produced by each prism. +The discrete forward modeling to calculate the displacement and stress fields due to a piecewise-constant distribution of the pressure variation within a reservoir follows the nucleus-of-strain approach. +We assume that a nucleus of strain represents an infinitesimal reservoir volume +element. The displacement solution for a single nucleus of strain in a homogeneous elastic semi-infinite medium (equation \ref{eq:displacement-solution}) will be used as an element of the displacement. +We calculate the displacement (stress) field due to the pressure variation of a prism by integrating the nucleus of strain over its volume. + +\noindent{\textbf{The discrete forward modeling due to a nucleus of strain in a homogeneous elastic semi-infinite medium}} +%====================================================================================== +%\subsection*{The discrete forward modeling due to a nucleus of strain %in a homogeneous elastic semi-infinite medium}\label{solution-nucleus} +%====================================================================================== + +By considering the discrete form of equation \ref{eq:displacement-solution}, the displacement vector $ {\bf{u}}_{ij} \equiv {\bf{u}}(x_{i}, y_{i}, z_{i}, x^{\prime}_{j}, y^{\prime}_{j}, z^{\prime}_{j})$ at an arbitrary point $(x_{i}, y_{i}, z_{i})$ due to a change of pressure in the $j$th nucleus of strain at the coordinates $(x^{\prime}_{j}, y^{\prime}_{j}, z^{\prime}_{j})$ will be calculated by +%\vspace{-1cm} +\begin{equation} +{\bf{u}}_{ij} = {\bf{u_{1}}}_{ij} + {\bf{u_{2}}}_{ij} \: , +\label{eq:displacement_ui} +\end{equation} +where ${\bf{u_{1}}}_{ij}$ is the displacement vector at the point $(x_{i}, y_{i}, z_{i})$ due to the $j$th single nucleus in the infinite space and ${\bf{u_{2}}}_{ij}$ +is the correction of the displacement considering a semi-space (image nucleus solution). +The term ${\bf{u_{1}}}_{ij}$ (equation \ref{eq:displacement_ui}) is given by +%\vspace{-1cm} +\begin{equation} +{\bf{u_{1}}}_{ij} = A_{E} \: {\bf{\nabla}} \bigg( {\frac{1}{{R_1}_{ij}}} \bigg) +\: \Delta p_{j} \: \:dv_j^{\prime} +\label{eq:nucleus-u1} +\end{equation} +and represents the gradient of the potential +%\vspace{-1cm} +\begin{equation} +\phi_{1} = - \frac{C_m}{4 \pi} \frac{\Delta p_{j} \: \:dv_j^{\prime}}{ {R_1}_{ij} } \: . +\label{eq:nucleus-phi1} +\end{equation} +The term ${\bf{u_{2}}}_{ij}$ (equation \ref{eq:displacement_ui}) is given by +%\vspace{-1cm} +\begin{equation} +\begin{aligned} +{\bf{u_{2}}}_{ij} \!= & +A_{E} \! +\bigg[ +C_{\nu} \: {\bf{\nabla}} \bigg( {\frac{1}{{R_2}_{ij}}} \bigg) +\! + 2 {\bf{\nabla}} \bigg( \! z \frac{\partial }{\partial z} {\frac{1}{{R_2}_{ij}}} \bigg) \\ +& - 4(1- \nu){\bf{\hat{z}}} {\bf{{\nabla}^{2}}} \bigg(\! {\frac{z}{{R_2}_{ij}}} \bigg) +\bigg] \! \Delta p_{j} dv_j^{\prime} +\end{aligned} +\label{eq:nucleus-u2} +\end{equation} +and is obtained by applying the operator ${\bf{{\nabla}_{2}}}$ (equation +\ref{eq:nabla2}) to the image potential +%\vspace{-1cm} +\begin{equation} +\phi_{2} = - \frac{C_m}{4 \pi} \frac{\Delta p_{j} \: \:dv_j^{\prime}}{ {R_2}_{ij} } \: . +\label{eq:nucleus-phi2} +\end{equation} +In equations \ref{eq:nucleus-u1}--\ref{eq:nucleus-phi2}, +all derivatives are computed with respect to the coordinates of the point +$(x_{i}, y_{i}, z_{i})$, +$\Delta p_j$ is the pressure change of the $j$th nucleus, $dv_j^{\prime}$ is an +infinitesimal element of volume centered at the $j$th nucleus of strain +$(x^{\prime}_{j}, y^{\prime}_{j}, z^{\prime}_{j})$, +$C_{\nu} = (3 - 4\nu)$, +$A_{E} = \frac{A (1 + \nu)}{E}$, +where $A$ is the constant +%\vspace{-1cm} +\begin{equation} +A = - \frac{C_m E}{4 \pi (1 + \nu)} \: , +\label{eq:nucleus-A} +\end{equation} +$E$ is the Young’s modulus and $C_m$ is the uniaxial compaction coefficient (see \citeauthor{Geertsma66}, +\citeyear{Geertsma66}) +%\vspace{-1cm} +\begin{equation} +C_m = \frac{1}{E} \: \frac{(1 + \nu) (1 - 2\nu)}{(1-\nu)} \: . +\label{eq:Cm} +\end{equation} +In equation \ref{eq:nucleus-phi1}, $ {R_1}_{ij}$ is the distance from the $i$th point $ (x_{i}, y_{i}, z_{i})$ to the $j$th nucleus of strain $(x^{\prime}_{j}, y^{\prime}_{j}, z^{\prime}_{j})$, i.e.: +${R_1}_{ij} = {\sqrt{(x_{i}- x^{\prime}_{j})^{2} + (y_{i} - y^{\prime}_{j})^{2} + +(z_{i} - z^{\prime}_{j})^{2}}}.$ +%\begin{equation} +%{R_1}_{ij} = {\sqrt{(x_{i}- x^{\prime}_{j})^{2} + (y_{i} - y^{\prime}_{j})^{2} + +%(z_{i} - z^{\prime}_{j})^{2}}}. +%\label{eq:R1} +%\end{equation} +In equation \ref{eq:nucleus-phi2}, $ {R_2}_{ij}$ is the distance from the $i$th point $ (x_{i}, y_{i}, z_{i})$ to the $j$th image nucleus $(x^{\prime}_{j}, y^{\prime}_{j}, - z^{\prime}_{j})$, i.e.: +${R_2}_{ij} = {\sqrt{(x_{i}- x^{\prime}_{j})^{2} + (y_{i} - y^{\prime}_{j})^{2} + +(z_{i} + z^{\prime}_{j})^{2}}}.$ +%\begin{equation} +%{R_2}_{ij} = {\sqrt{(x_{i}- x^{\prime}_{j})^{2} + (y_{i} - y^{\prime}_{j})^{2} + +%(z_{i} + z^{\prime}_{j})^{2}}} \: . +%\label{eq:R2} +%\end{equation} +Figure \ref{fig:nucleus_strain} shows a schematic representation of the geometry of the nucleus of strain problem in a semi-infinite medium. +The horizontal plane $z = 0$ is called "free surface". +The $x-$, $y-$ and $z-$components of the vectors ${\bf{u_{1}}}_{ij}$ (equation \ref{eq:nucleus-u1}) and ${\bf{u_{2}}}_{ij}$ (equation \ref{eq:nucleus-u2}) can be explicitly defined as follows: +\begin{equation} +{\bf{u_{1}}}_{ij} = A_{E} +\begin{bmatrix} +\frac{\partial }{\partial x} {\frac{1}{{R_1}_{ij}}} \\ +\frac{\partial }{\partial y} {\frac{1}{{R_1}_{ij}}} \\ +\frac{\partial }{\partial z} {\frac{1}{{R_1}_{ij}}} +\end{bmatrix} + \Delta p_{j} \:dv_j^{\prime} +\label{eq:nucleus-u1-vector} +\end{equation} +and +%\vspace{-1cm} +\begin{equation} +{\bf{u_{2}}}_{ij} \! = \! +A_{E} \! \left\{\! C_{\nu} \! +\begin{bmatrix} + \frac{\partial}{\partial x} {\frac{1}{{R_2}_{ij}}} \\ + \frac{\partial}{\partial y} {\frac{1}{{R_2}_{ij}}} \\ + -\frac{\partial}{\partial z} {\frac{1}{{R_2}_{ij}}} +\end{bmatrix} +\! + \! 2 z_{i} \! +\begin{bmatrix} +\frac{\partial^{2}}{\partial x \partial z} {\frac{1}{{R_2}_{ij}}} \\ +\frac{\partial^{2}}{\partial y \partial z} {\frac{1}{{R_2}_{ij}}} \\ +\frac{\partial^{2}}{\partial z^{2}} {\frac{1}{{R_2}_{ij}}} +\end{bmatrix} \! +\right\} \! \! +\Delta p_{j} dv_j^{\prime}. +\label{eq:nucleus-u2-vector} +\end{equation} +By following \cite{Sharma56} and \cite{Tempone10}, +the stress vector +$\mbox{\boldmath$\sigma$}_{ij} \equiv \mbox{\boldmath$\sigma$}(x_{i}, y_{i}, z_{i}, x^{\prime}_{j}, y^{\prime}_{j}, z^{\prime}_{j})$ +at the point $(x_{i}, y_{i}, z_{i})$ due to the $j$th single nucleus of strain buried +in the half space is given by +%\vspace{-1cm} +\begin{equation} +\mbox{\boldmath$\sigma$}_{ij} = \mbox{\boldmath$\sigma_{1}$}_{ij} + +\mbox{\boldmath$\sigma_{2}$}_{ij} \: , +\label{eq:stress_nucleus} +\end{equation} +where $\mbox{\boldmath$\sigma_{1}$}_{ij} \equiv \mbox{\boldmath$\sigma_{1}$}(x_{i}, y_{i}, z_{i}, x^{\prime}_{j}, y^{\prime}_{j}, z^{\prime}_{j})$ is the stress vector +at the point $(x_{i}, y_{i}, z_{i})$ due to the $j$th single nucleus in the infinite space and $\mbox{\boldmath$\sigma_{2}$}_{ij} \equiv \mbox{\boldmath$\sigma_{2}$}(x_{i}, y_{i}, z_{i}, x^{\prime}_{j}, y^{\prime}_{j}, z^{\prime}_{j})$ is the stress vector +at the point $(x_{i}, y_{i}, z_{i})$ that gives the correction of the stress due to the +$j$th image nucleus considering a semi-space. These two vectors are given by +\begin{equation} +\mbox{\boldmath$\sigma_{1}$}_{ij} = +A \! +\begin{bmatrix} +\frac{\partial^{2} }{\partial x \partial z} {\frac{1}{{R_1}_{ij}}} \\ +\frac{\partial^{2} }{\partial y \partial z} {\frac{1}{{R_1}_{ij}}} \\ +\frac{\partial^{2} }{\partial z^{2}} {\frac{1}{{R_1}_{ij}}} +\end{bmatrix} +\Delta p_{j} dv_j^{\prime}, +\label{eq:nucleus-stress1-vector} +\end{equation} +%\vspace{-0.5cm} +and +\begin{equation} +\mbox{\boldmath$\sigma_{2}$}_{ij} = \! +A \! +\left\{ +\begin{bmatrix} +\frac{\partial^{2} }{\partial x \partial z} {\frac{1}{{R_2}_{ij}}} \\ +\frac{\partial^{2} }{\partial y \partial z} {\frac{1}{{R_2}_{ij}}} \\ +- \frac{\partial^{2} }{\partial z^{2}} {\frac{1}{{R_2}_{ij}}} +\end{bmatrix} +\! + \! 2 z_{i} \! +\begin{bmatrix} +\frac{\partial^{3} }{\partial x \partial z^{2}} {\frac{1}{{R_2}_{ij}}} \\ +\frac{\partial^{3} }{\partial y \partial z^{2}} {\frac{1}{{R_2}_{ij}}} \\ +\frac{\partial^{3} }{\partial z^{3}} {\frac{1}{{R_2}_{ij}}} +\end{bmatrix} +\right\} +\Delta p_{j}dv_j^{\prime}. +\label{eq:nucleus-stress2-vector} +\end{equation} +According to \cite{Sharma56} and \cite{Tempone10}, the Beltrami’s equations \citep{Beltrami} and the equilibrium equations must be satisfied to obtain the contribution of the stress field in the half-space. +Additionally, the boundary condition +$\mbox{\boldmath$\sigma$}_{ij} = \mbox{ \boldmath$0$}$ (equation \ref{eq:stress_nucleus}), where $\mbox{ \boldmath$0$}$ is the zero vector, must be satisfied at the free surface ($z_i = 0$). +%\begin{equation} +%\mbox{\boldmath$\sigma$}_{ij} = \mbox{\boldmath$\sigma_{1}$}_{ij} + +%\mbox{\boldmath$\sigma_{2}$}_{ij} = \mbox{ \boldmath$0$}, +%\label{eq:null_stress} +%\end{equation} +%where $\mbox{ \boldmath$0$}$ is the null vector. +This condition can be easily verified by adding the vectors +$\mbox{\boldmath$\sigma_{1}$}_{ij}$ (equation \ref{eq:nucleus-stress1-vector}) and +$\mbox{\boldmath$\sigma_{2}$}_{ij}$ (equation \ref{eq:nucleus-stress2-vector}) +computed at any point on the free surface $(x_i, y_i, z_i = 0)$. +\begin{figure}[t] + \centering + \includegraphics[scale=0.90]{figures/Figure_Nucleus_Strain.png} + \vspace{-2.5cm} + \caption{Schematic representation of the geometry of the nucleus of strain in a semi-infinite medium. + After \cite{Munoz-Roehl17}. + The adopted Cartesian coordinate system considered the $x-$axis pointing to north, the $y-$axis pointing + to east and the $z-$axis pointing downward.} + \label{fig:nucleus_strain} +\end{figure} + +\noindent{\textbf{The discrete displacement forward modeling due to a reservoir in a homogeneous elastic semi-infinite medium}} +%====================================================================================== +%\subsection*{The discrete displacement forward modeling due to a %reservoir in a homogeneous elastic semi-infinite medium} \label{u-%model} +%====================================================================================== + +We parameterize the reservoir as a grid of juxtaposed right rectangular prisms. +Each grid prism undergoes a constant pressure change $\Delta p_{j}$; however, $\Delta p_{j}$ +can be different for every prism. +To calculate the displacement field produced by the $j$th prism +at the $i$th coordinates $(x_i, y_i, z_i)$, we integrate the solution deduced for a single nucleus of strain (equation \ref{eq:displacement_ui}) +over its volume and obtain +%\vspace{-1cm} +\begin{equation} +{\bf{\tilde{u}}}_{ij} = +\iiint\limits_{{v_{1}}_{j}} +{\bf{u_{1}}}_{ij} dv_{j}^{\prime} + + +\iiint\limits_{{v_{2}}_{j}} +{\bf{u_{2}}}_{ij} \:\: dv_{j}^{\prime}, +\label{eq:nucleus-ui_jth_prism} +\end{equation} +where both integrals are conducted with respect to the variables +$(x^{\prime}_{j}, y^{\prime}_{j}, z^{\prime}_{j})$. The first integral in equation +\ref{eq:nucleus-ui_jth_prism} is conducted over the volume ${v_{1}}_{j}$ of the $j$th +prism and the second is conducted over the volume +${v_{2}}_{j}$ of a different prism symmetrically positioned above the free surface +and conveniently called $j$th "image prism". +Volume ${v_{1}}_{j}$ is defined by ${x_1}_{j}$, ${x_2}_{j}$, ${y_1}_{j}$, ${y_2}_{j}$, +${z_1}_{j}$, and ${z_2}_{j}$, which represent, respectively, the south, north, west, +east, top, and bottom borders of the $j$th prism. +Volume ${v_{2}}_{j}$ of the $j$th image prism is defined in a similar way, but with +top and bottom given by ${z_1}_{j} - 2 \, {z_c}_{j}$ and ${z_2}_{j} - 2 \, {z_c}_{j}$, where +${z_c}_{j} = \frac{1}{2}({z_1}_{j} + {z_2}_{j})$ is the center depth of the $j$th prism. +The total displacement vector at the point $(x_i, y_i, z_i)$ due to the +pressure change in the whole reservoir is defined as the sum of the displacements +${\bf{u}}_{ij}$ (equation \ref{eq:nucleus-ui_jth_prism}) yielded by each prism +with constant pressure $\Delta p_{j}$: +%\vspace{-0.5cm} +\begin{equation} +{\bf{\tilde{u}}}_{i} = \sum_{j=1}^{M} {\bf{\tilde{u}}}_{ij}, +\label{eq:nucleus-ui_M_prisms} +\end{equation} +where $M$ is the number of prisms setting up the reservoir model. +The horizontal component of the total displacement vector ${\bf{\tilde{u}}}_{i}$ +(equation \ref{eq:nucleus-ui_M_prisms}) is calculated by +%\vspace{-1cm} +\begin{equation} +{\tilde{u}}_{{i}_h} = \sqrt{ {\tilde{u}}_{{i}_x}^{2} + {\tilde{u}}_{{i}_y}^{2} }, +\label{eq:horizontal_displacement} +\end{equation} +where ${\tilde{u}}_{{i}_x}$ and ${\tilde{u}}_{{i}_y}$ are the $x-$ and $y-$ components. +By substituting equations \ref{eq:nucleus-u1-vector} and \ref{eq:nucleus-u2-vector} +into equation \ref{eq:nucleus-ui_jth_prism}, we obtain +%\vspace{-1cm} +\begin{equation} +\begin{aligned} +{\tilde{u}}_{{ij}_\alpha} = + A_{E} + & \Delta p_{j} + \bigg[ \iiint\limits_{{v_{1}}_{j}} +\frac{\partial }{\partial \alpha} {\frac{1}{{R_1}_{ij}}} dv_{j}^{\prime} \: + \\ +& C_{\nu} \: \iiint\limits_{{v_{2}}_{j}} +\frac{\partial }{\partial \alpha} {\frac{1}{{R_2}_{ij}}} dv_j \: + \\ +& 2 z_{i} \iiint\limits_{{v_{2}}_{j}} +\frac{\partial^{2} }{\partial \alpha \partial z} {\frac{1}{{R_2}_{ij}}} dv_{j}^{\prime} \bigg], +\end{aligned} +\label{eq:u_til_alpha} +\end{equation} +where $\alpha = x, y$, and +%\vspace{-1cm} +\begin{equation} +\begin{aligned} +{\tilde{u}}_{{ij}_z} = +A_{E} +& \Delta p_{j} \bigg[ \iiint\limits_{{v_{1}}_{j}} +\frac{\partial }{\partial z} {\frac{1}{{R_1}_{ij}}} dv_{j}^{\prime} \: - \\ +& C_{\nu} \: \iiint\limits_{{v_{2}}_{j}} +\frac{\partial }{\partial z} {\frac{1}{{R_2}_{ij}}} dv_{j}^{\prime} \: + \\ +& 2 z_{i} \iiint\limits_{{v_{2}}_{j}} +\frac{\partial^{2} }{\partial z^{2}} {\frac{1}{{R_2}_{ij}}} dv_{j}^{\prime} \bigg] . +\end{aligned} +\label{eq:u_til_z} +\end{equation} +In the right-hand side of equations \ref{eq:u_til_alpha} and \ref{eq:u_til_z}, the three integrals have the same form of derivatives of the gravitational potential produced by the $j$th prism and image prism. +The first integral corresponds to the $\alpha-$component of the gravitational attraction +produced by the $j$th prism. +The second and third integrals correspond, respectively, to the $\alpha-$component of the gravitational attraction and to the $\alpha \:z-$component of the gravitational +gradient tensor produced by the $j$th image prism. +The similarity between the displacement fields due to a volume source in a half-space and the gravitational field allows the use of closed expressions of the gravitational potential and its derivatives produced by the 3D right rectangular prism. +We draw the readers' attention to the fact that \cite{Vasco1987} were the pioneer in taking the advantage of the similarity between the the displacement fields due to a source in a half-space and the gravitational field and calculating displacement field due to a 2D volume source at the Earth surface. +Here, our approach also takes the advantage of this similarity, but it calculates the displacement field due to a 3D volume source at the whole subsurface. +In equations \ref{eq:u_til_alpha} and \ref{eq:u_til_z}, the integrals depending on +first derivatives of ${\frac{1}{{R_1}_{ij}}}$ have the following closed solutions +\citep{Nagyetal2000, Nagyetal2002}: +%\vspace{-0.5cm} +\begin{equation} +\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} \int\limits_{{z_{1}}_{j}}^{{z_{2}}_{j}} +\frac{\partial }{\partial x} {\frac{1}{{R_1}_{ij}}} dv_{j}^{\prime} \! = \! +\Bigg|\Bigg|\Bigg| +y L_z + z L_y - x T_{yz} +\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} \quad , +\label{dx1} +\end{equation} +\vspace{-0.5cm} +\begin{equation} +\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} \int\limits_{{z_{1}}_{j}}^{{z_{2}}_{j}} +\frac{\partial }{\partial y} {\frac{1}{{R_1}_{ij}}} dv_{j}^{\prime} \! = \! +\Bigg|\Bigg|\Bigg| +x L_z + z L_x - y T_{xz} +\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} \quad , +\label{dy1} +\end{equation} +and +%\vspace{-0.5cm} +\begin{equation} +\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} \int\limits_{{z_{1}}_{j}}^{{z_{2}}_{j}} +\frac{\partial }{\partial z} {\frac{1}{{R_1}_{ij}}} dv_{j}^{\prime} \! = \! +\Bigg|\Bigg|\Bigg| +x L_y + y L_x - z T_{xy} +\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} \quad , +\label{dz1} +\end{equation} +where all derivatives are computed with respect to the coordinates of the $i$th point +$(x_i, y_i, z_i)$, and $L_x = \ln(x + R), L_y = \ln(y + R) \textrm{and} L_z = \ln(z + R)$, +$T_{yz} = \tan^{-1} \big( \frac{yz}{x \: R} \big), T_{xz} = \tan^{-1} \big( \frac{xz}{y \: R} \big)$ +and $T_{xy} = \tan^{-1} \big( \frac{xy}{z \: R} \big)$, +$R = \sqrt{x^{2} + y^{2} + z^{2}}$. +The integration limits in equations \ref{dx1}--`\ref{dz1} are +%\vspace{-1cm} +%\begin{equation} +%{X_1}_{j} = x_i - {x_1}_{j}, \: +%{X_2}_{j} = x_i - {x_2}_{j}, \: +%{Y_1}_{j} = y_i - {y_1}_{j}, \: +%{Y_2}_{j} = y_i - {y_2}_{j}, \: +%{Z_1}_{j} = z_i - {z_1}_{j}, \: \textrm{and} \: +%{Z_2}_{j} = z_i - {z_2}_{j}. +%\label{eq:Nagy_limits_1} +%\end{equation} +\begin{equation} +\begin{array}{ll} +{X_1}_{j} &= x_i - {x_1}_{j} , \\ +{X_2}_{j} &= x_i - {x_2}_{j} , \\ +{Y_1}_{j} &= y_i - {y_1}_{j} , \\ +{Y_2}_{j} &= y_i - {y_2}_{j} , \\ +{Z_1}_{j} &= z_i - {z_1}_{j} , \: \: \: \textrm{and} \\ +{Z_2}_{j} &= z_i - {z_2}_{j}. +\end{array} \quad +\label{eq:Nagy_limits_1} +\end{equation} +The remaining integrals, in the right-hand side of equations +\ref{eq:u_til_alpha} and \ref{eq:u_til_z}, depend on first and second derivatives +of ${\frac{1}{{R_2}_{ij}}}$. +These integrals are conducted over the volume ${v_{2}}_{j}$ of the $j$th image prism and have the following closed solutions \citep{Nagyetal2000, Nagyetal2002}: +%\vspace{-0.5cm} +\begin{equation} +\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \! +\int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} \! +\int\limits_{{z_{1}}_{j} - 2 \, z_c}^{{z_{2}}_{j} - 2 \, z_c} +\! \! \! \! \! \! \! +\frac{\partial}{\partial x} \! {\frac{1}{{R_2}_{ij}}} dv_{j}^{\prime} \! = \! +\Bigg|\Bigg|\Bigg| +y L_z + z L_y - x T_{yz} \! +\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \! \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \! \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}}, +\label{dx2} +\end{equation} +\vspace{-0.5cm} +\begin{equation} +\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \! +\int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} +\int\limits_{{z_{1}}_{j} - 2 \, z_c}^{{z_{2}}_{j} - 2 \, z_c} +\! \! \! \! \! \! \! \! +\frac{\partial}{\partial y} {\frac{1}{{R_2}_{ij}}} dv_{j}^{\prime} \! = \! +\Bigg|\Bigg|\Bigg| +xL_z + zL_x - y T_{xz} \! +\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \! \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \! \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}}, +\label{dy2} +\end{equation} +\vspace{-0.5cm} +\begin{equation} +\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \! +\int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} +\int\limits_{{z_{1}}_{j} - 2 \, z_c}^{{z_{2}}_{j} - 2 \, z_c} +\! \! \! \! \! \! \! \! +\frac{\partial }{\partial z} {\frac{1}{{R_2}_{ij}}} dv_{j}^{\prime} \! = \! +\Bigg|\Bigg|\Bigg| +x L_y + y L_x - z T_{xy} \! +\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \! \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \! \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} , +\label{dz2} +\end{equation} +\vspace{-0.5cm} +\begin{equation} +\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \! +\int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} +\int\limits_{{z_{1}}_{j} - 2 \, z_c}^{{z_{2}}_{j} - 2 \, z_c} +\! \! \! \! \! \! \! \! +\frac{\partial^{2}}{\partial x \partial z} {\frac{1}{{R_2}_{ij}}} dv_{j}^{\prime} \! = \! +\Bigg|\Bigg|\Bigg| +L_y \! +\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \! \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \! \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} , +\label{dxz2} +\end{equation} +%\vspace{-0.5cm} +\begin{equation} +\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \! +\int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} +\int\limits_{{z_{1}}_{j} - 2 \, z_c}^{{z_{2}}_{j} - 2 \, z_c} +\! \! \! \! \! \! \! \! +\frac{\partial^{2}}{\partial y \partial z} {\frac{1}{{R_2}_{ij}}} dv_{j}^{\prime} \! = \! +\Bigg|\Bigg|\Bigg| +L_x \! +\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \! \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \! \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} , +\label{dyz2} +\end{equation} +and +%\vspace{-0.5cm} +\begin{equation} +\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \! +\int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} +\int\limits_{{z_{1}}_{j} - 2 \, z_c}^{{z_{2}}_{j} - 2 \, z_c} +\! \! \! \! \! \! \! \! +\frac{\partial^{2}}{\partial z \partial z} {\frac{1}{{R_2}_{ij}}} dv_{j}^{\prime} \! = \! +\Bigg|\Bigg|\Bigg| +- T_{xy} +\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \! \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \! \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} \quad . +\label{dzz2} +\end{equation} +In these integrals related to the $j$th image prism +(equations \ref{dx2}--\ref{dz2}), the integration limits along the $z$ direction +are given by +%\vspace{-1cm} +\begin{equation} +{Z_1}_{j} = z_i - {z_1}_{j} + 2 \, {z_c}_{j} \:\: \: \textrm{and} \: \: \: +{Z_2}_{j} = z_i - {z_2}_{j} + 2 \, {z_c}_{j} \:, +\label{eq:Nagy_limits_2} +\end{equation} +%\begin{equation} +%\begin{array}{ll} +%{Z_1}_{j} &= z_i - {z_1}_{j} + 2 \, {z_c}_{j} \\ +%{Z_2}_{j} &= z_i - {z_2}_{j} + 2 \, {z_c}_{j} +%\end{array} \quad , +%\label{eq:Nagy_limits_2} +%\end{equation} +where ${z_c}_{j} = \frac{1}{2}({z_1}_{j} + {z_2}_{j})$ is the center depth of the $j$th prism. +The remaining limits along $x$ and $y$ directions are the same defined by equation \ref{eq:Nagy_limits_1}. + +\vspace{0.5cm} +\noindent{\textbf{The discrete stress forward modeling due to a reservoir in a homogeneous elastic semi-infinite medium}} +%====================================================================================== +%\subsection*{The discrete stress forward modeling due to a reservoir %in a homogeneous elastic semi-infinite medium} +%====================================================================================== + +By following the similar approach used in the previous subsection, the stress field of each prism assuming constant pressure is calculated by integrating solution for a +nucleus of strain (equations \ref{eq:stress_nucleus}, \ref{eq:nucleus-stress1-vector}, +and \ref{eq:nucleus-stress2-vector}) over its volume. +This integration leads to a stress vector +$\mbox{\boldmath$\tilde{\sigma}$}_{ij} \equiv \mbox{\boldmath$\tilde{\sigma}$}(x_{i}, y_{i}, z_{i}, x^{\prime}_{j}, y^{\prime}_{j}, z^{\prime}_{j})$ given by +%\vspace{-1cm} +\begin{equation} +\mbox{\boldmath$\tilde{\sigma}$}_{ij} = +\iiint\limits_{{v_{1}}_{j}} +\mbox{\boldmath$\sigma_{1}$}_{ij} dv_{j}^{\prime} ++ +\iiint\limits_{{v_{2}}_{j}} +\mbox{\boldmath$\sigma_{2}$}_{ij} dv_{j}^{\prime}, +\label{eq:nucleus-stress_jth_prism} +\end{equation} +where the first and second integrals are conducted, respectively, over the volumes +${v_{1}}_{j}$ and ${v_{2}}_{j}$ of the $j$th prism and the $j$th image prism. +The total stress vector at the $i$th coordinates $(x_i, y_i, z_i)$ due to the pressure change in the whole reservoir is calculated by the sum of all stress vector $\mbox{\boldmath$\tilde{\sigma}$}_{ij}$ (equation \ref{eq:nucleus-stress_jth_prism}), i.e., +%\vspace{-1cm} +\begin{equation} +\mbox{\boldmath$\tilde{\sigma}$}_{i} = +\sum_{j=1}^{M} \mbox{\boldmath$\tilde{\sigma}$}_{ij} \: . +\label{eq:nucleus-stress_M_prisms} +\end{equation} +By substituting equation \ref{eq:nucleus-stress1-vector} and +\ref{eq:nucleus-stress2-vector} into equation \ref{eq:nucleus-stress_jth_prism}, +we obtain the $\alpha-$component (where $\alpha = x$ and $y$) and the $z-$ component +of the stress vector $\mbox{\boldmath$\tilde{\sigma}$}_{ij}$ as follows: +%\vspace{-0.5cm} +\begin{equation} +\begin{aligned} +{\tilde{\sigma}}_{{ij}_\alpha} \! = \! A +& \Delta p_{j} \! \Bigg[ +\iiint\limits_{{v_{1}}_{j}} \!\! +\frac{\partial^{2}}{\partial \alpha \partial z} {\frac{1}{{R_1}_{ij}}} dv_{j}^{\prime} +\! + \! \iiint\limits_{{v_{2}}_{j}} +\frac{\partial^{2} }{\partial \alpha \partial z} {\frac{1}{{R_2}_{ij}}} dv_{j}^{\prime} \\ +& + 2 z_{i} \iiint\limits_{{v_{2}}_{j}} +\frac{\partial^{3}}{\partial \alpha \partial z ^{2}} {\frac{1}{{R_2}_{ij}}} dv_{j}^{\prime} \Bigg] +\end{aligned} +\label{eq:stress_til_alpha} +\end{equation} +and +%\vspace{-0.5cm} +\begin{equation} +\begin{aligned} +{\tilde{\sigma}}_{{ij}_{z}} \! = \! A +& \Delta p_{j} \! \Bigg[ +\iiint\limits_{{v_{1}}_{j}} \! \! +\frac{\partial^{2}}{\partial z^{2}} {\frac{1}{{R_1}_{ij}}} dv_{j}^{\prime} +\! + \!\iiint\limits_{{v_{2}}_{j}} +\frac{\partial^{2} }{\partial z^{2}} {\frac{1}{{R_2}_{ij}}} dv_{j}^{\prime} \\ +& + 2 z_{i} \iiint\limits_{{v_{2}}_{j}} +\frac{\partial^{3} }{\partial z^{3}} {\frac{1}{{R_2}_{ij}}} +dv_{j}^{\prime} \Bigg]. +\end{aligned} +\label{eq:stress_til_z} +\end{equation} +Similarly to the displacement field (equations \ref{eq:u_til_alpha} and \ref{eq:u_til_z}), the three integrals in the right-hand side of equations \ref{eq:stress_til_alpha} and \ref{eq:stress_til_z} have the same form of +derivatives of the gravitational potential produced by the $j$th prism and image prism. +The integrals depending on $\frac{1}{{R_1}_{ij}}$ have the following closed +solutions \citep{Nagyetal2000, Nagyetal2002}: +%\vspace{-0.5cm} +\begin{equation} +\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} \int\limits_{{z_{1}}_{j}}^{{z_{2}}_{j}} +\! \! \! +\frac{\partial^{2} }{\partial x \partial z}{\frac{1}{{R_1}_{ij}}} dv_{j}^{\prime} = +\Bigg|\Bigg|\Bigg| L_y +\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} \quad , +\label{dxz1} +\end{equation} +%\vspace{-0.5cm} +\begin{equation} +\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} \int\limits_{{z_{1}}_{j}}^{{z_{2}}_{j}} +\! \! \! +\frac{\partial^{2} }{\partial y \partial z} {\frac{1}{{R_1}_{ij}}} dv_{j}^{\prime} = +\Bigg|\Bigg|\Bigg| +L_x +\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} \quad , +\label{dyz1} +\end{equation} +and +%\vspace{-0.5cm} +\begin{equation} +\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} \int\limits_{{z_{1}}_{j}}^{{z_{2}}_{j}} +\! \! \! +\frac{\partial^{2} }{\partial z \partial z} {\frac{1}{{R_1}_{ij}}} dv_{j}^{\prime} = +\Bigg|\Bigg|\Bigg| +- T_{xy} \Bigg) +\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} \quad , +\label{dzz1} +\end{equation} +where the limits ${X_1}_{j}$, ${X_2}_{j}$, ${Y_1}_{j}$, ${Y_2}_{j}$, ${Z_1}_{j}$, and ${Z_2}_{j}$ are defined by equation \ref{eq:Nagy_limits_1}. +The integrals depending on second derivatives of $\frac{1}{{R_2}_{ij}}$ in the +right-hand side of equations \ref{eq:stress_til_alpha} and \ref{eq:stress_til_z} +have closed solutions defined by equations \ref{dxz2}, \ref{dyz2}, and \ref{dzz2}. +Finally, the remaining integrals depending on third derivatives of +$\frac{1}{{R_2}_{ij}}$ have closed solutions given by +\citep{Nagyetal2000, Nagyetal2002}: +%\vspace{-0.5cm} +\begin{equation} +\begin{aligned} +\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} +\int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} +\int\limits_{{z_{1}}_{j} - 2 \, z_c}^{{z_{2}}_{j} - 2 \, z_c} +\! \! \! \! \! \! \! \! +& \frac{\partial^{3}}{\partial x \partial z^{2}} +{\frac{1}{{R_2}_{ij}}} dv_{j}^{\prime} \! = \! \\ +& \Bigg|\Bigg|\Bigg| +\frac{- y z}{R} +\left( \frac{1}{x^{2} + z^{2}} \right) +\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} \quad , +\end{aligned} +\label{sxzz} +\end{equation} +%\vspace{-0.5cm} +\begin{equation} +\begin{aligned} +\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} +\int\limits_{{z_{1}}_{j} - 2 \, z_c}^{{z_{2}}_{j} - 2 \, z_c} +\! \! \! \! \! \! \! \! +& \frac{\partial^{2} }{\partial y \partial z^{2}} +{\frac{1}{{R_2}_{ij}}} dv_{j}^{\prime} \! = \! \\ +& \Bigg|\Bigg|\Bigg| +\frac{- x z}{R} +\left( \frac{1}{y^{2} + z^{2}} \right) +\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} \quad , +\end{aligned} +\label{syzz} +\end{equation} +and +%\vspace{-0.5cm} +\begin{equation} +\begin{aligned} +\int\limits_{{x_{1}}_{j}}^{{x_{2}}_{j}} \int\limits_{{y_{1}}_{j}}^{{y_{2}}_{j}} \int\limits_{{z_{1}}_{j} - 2 \, z_c}^{{z_{2}}_{j} - 2 \, z_c} +\! \! \! \! \! \! \! \! +& \frac{\partial^{3} }{\partial z^{3}} +{\frac{1}{{R_2}_{ij}}} dv_{j}^{\prime} \! = \! \\ +& \Bigg|\Bigg|\Bigg| +\frac{ x y}{R} +\left( \frac{1}{x^{2} + z^{2}} + \frac{1}{y^{2} + z^{2}} \right) +\Bigg|_{{X_1}_{j}}^{{X_2}_{j}} \Bigg|_{{Y_1}_{j}}^{{Y_2}_{j}} \Bigg|_{{Z_1}_{j}}^{{Z_2}_{j}} \quad , +\end{aligned} +\label{sz3} +\end{equation} +where the limits ${X_1}_{j}$, ${X_2}_{j}$, ${Y_1}_{j}$, and ${Y_2}_{j}$, are defined by equation \ref{eq:Nagy_limits_1} and ${Z_1}_{j}$, and ${Z_2}_{j}$ by equation \ref{eq:Nagy_limits_2}. +Our method was implemented in Python programming language and it is based on Harmonica \citep{Uieda2020}. +The horizontal and vertical displacements are calculated by using +the volume integrations (equations \ref{eq:u_til_alpha} and \ref{eq:u_til_z}), whose solutions +are given by equations \ref{dx1}--\ref{dzz2}. +The horizontal and vertical stresses are calculated by using the volume integrations (equations \ref{eq:stress_til_alpha} and \ref{eq:stress_til_z}), +whose solutions are given by equations \ref{dxz1}--\ref{sz3}. +We used \cite{Fukushima2020} to overcome the zero division in evaluating the arguments of the arctangent function. +%\noindent{\textbf{Software implementation}} +%====================================================================================== +%\subsection*{Software implementation} +%====================================================================================== + +%The method proposed here was implemented in Python programming language and it is based on Harmonica \citep{Uieda2020}. +%The horizontal and vertical displacements are calculated by using +%the full volume integrations (equations \ref{eq:u_til_alpha} and \ref{eq:u_til_z}), whose +%closed solutions are given by equations \ref{dx1}--\ref{dzz2}. +%Moreover, the horizontal and vertical stresses are calculated by using +%the full volume integrations (equations \ref{eq:stress_til_alpha} and \ref{eq:stress_til_z}), +%whose closed solutions are given by equations \ref{dxz1}--\ref{sz3}. +%In equations \ref{dx1}--\ref{dz1}, \ref{dx2}--\ref{dzz2} and \ref{dxz1}--\ref{dzz1}, we adopted the modifications proposed by \cite{Fukushima2020}. +%To overcome the zero division in evaluating the arguments of the arctangent function, \cite{Fukushima2020} replaced $\tan^{-1} \big( \frac{S}{T} \big)$ by +%\begin{equation} +%arctan2(S,T) = \begin{cases} + %\left\{ \begin{aligned} +% atan (S/T) & \:\: \mbox{if} \: \:\: T \neq 0 \\ +% \pi /2 & \:\: \mbox{if} \: \:\: T = 0 \: \: \mbox{and} \: \:S > %0 \\ +% -\pi /2 & \:\: \mbox{if} \: \:\: T = 0 \: \: \mbox{and} \: \:S %0 \\ +% 0 & \:\: \mbox{if} \: \:\: T = 0 \: \: \mbox{and} \: \:S = 0 \\ +% %\end{aligned} \right\}. +% \end{cases} +%\label{eq:arctan2} +%\end{equation} +%Additionally, if the argument of the logarithm is less than $10^{-10}%$, the logarithm is replaced by zero; otherwise the logarithm is calculated regularly. +%\vspace{-0.5cm} +\section*{Numerical Applications} + +\noindent{\textbf{Disk-shaped reservoir under uniform depletion}} +%\subsection*{Disk-shaped reservoir under uniform depletion} + +Embedded in a semi-infinite homogenous medium, we simulated a vertical cylinder-like reservoir (not shown) with a radius of 500 m and whose horizontal coordinates of its center along the north-south and east-west directions are 0 m and 0 m, respectively. +The depths to the top and to the bottom of the simulated reservoir are 750 m and 850 m, respectively. +The reservoir is uniformly depleted by $\Delta p = -10$ MPa. +The Young’s modulus is 3300 (in MPa), the Poisson's coefficient is 0.25, and +the uniaxial compaction coefficient $C_{m}$ (equation \ref{eq:Cm}) is +$2.2525 \: 10^{-4}$ $\textrm{ MPa}^{-1}$. +%\begin{figure} +% \centering +% \includegraphics[scale=1.0]{figures/Figure_Cylinder.png} +% \caption{Disk-shaped reservoir under uniform depletion with a radius of 500 m.} +% \label{fig:cylinder} +%\end{figure} +To apply our methodology, we discretized the cylinder along the $x-$ and $y-$ directions into an $20 \times 20$ grid of prisms. Hence, we totalized 400 prisms all of them centered at 800 m deep, with depths to the top and to the bottom at 750 m and 850 m and with pressure change $\Delta p_j$, $j = 1, ..., 400$ equal to $-10$ MPa. +To apply the Geertsma’s method \citep{Geertsma73}, we used the disk-shaped reservoir +described in \cite{Fjaer08} with dimensions and physical properties defined above. +Figures \ref{fig:displacement} and \ref{fig:displacement_Geertsma} show cross-sections at +$x = 0$ m of the displacement fields in 2D contour plots due to the pressure change in the whole cylindrical reservoir by using our methodology and Geertsma’s method, respectively. +Because we defined the $z-$axis as positive downwards, the positive vertical displacement means a subsidence and the negative vertical displacement means an uplift. +Figure \ref{fig:displacement} shows the horizontal and vertical displacements calculated, respectively, with equations \ref{eq:horizontal_displacement} and \ref{eq:u_til_z} by our methodology. +Figure \ref{fig:displacement_Geertsma} shows the radial and vertical displacements using Geertsma’s method considering an elastic homogeneous cylindrical reservoir under uniform depletion based on the nucleus-of-strain concept in the half-space. +In both cases (Figures \ref{fig:displacement}b and \ref{fig:displacement_Geertsma}b) the vertical displacements due to the entire the disk-shaped reservoir display a subsidence (positive values) above the reservoir and an uplift (negative values) below the reservoir. +We stress that the proposed volume integrations (equations \ref{dx1} $-$ \ref{dzz2}) allowed to evaluate the vertical displacement (Figure \ref{fig:displacement}b) throughout the entire reservoir. +Rather, the vertical displacement using Geertsma’s method +(Figure \ref{fig:displacement_Geertsma}b) is only valid outside the reservoir. +The radial displacement using Geertsma’s method +(Figure \ref{fig:displacement_Geertsma}a) shows positive values at the edges of the reservoir ($y= -500$ and $y = 500$) with a singularity at the center of the reservoir +($x= 0, \: y = 0$ and $z = 800$ m). +The horizontal displacement with the proposed full integration +(Figures \ref{fig:displacement}a) shows positive values at the edges of the reservoir ($y= -500$ and $y = 500$); however, it does not present sigularities inside the reservoir. +Figure \ref{fig:displacement_z_levels} shows the $x-$component displacement and vertical displacement by our methodology that uses a full volume integrations. +These displacements are calculated along the $x-$axis, at $y = 0$ m and considering four surfaces located at the following depths: seafloor ($z = 0$ m), reservoir top ($z = 750$ m), reservoir center ($z = 800$ m) and reservoir bottom ($z = 850$ m). +In the $x$-component of the displacement (Figure \ref{fig:displacement_z_levels}a), we can note an increased horizontal contraction from the center of the reservoir ($x = 0$) toward the reservoir edge ($x= 500$ m) where the maximum contraction of all surfaces occur. +In the vertical displacement (Figure \ref{fig:displacement_z_levels}b), we can note a subsidence of the seafloor and the reservoir top (positive values) and an uplift of the reservoir bottom (negative values). +The vertical displacements of the seafloor, the top and bottom of the reservoir for Geertsma’s method (Figure \ref{fig:displacement_z_levels_Geertsma}) show a similar behavior of those obtained by our methodology that uses a full volume integrations (Figure \ref{fig:displacement_z_levels}b). +However, we note that the subsidence of the seafloor is more attenuated in the Geertsma’s method than in our method because we calculate the total displacement field outside and inside of the reservoir. +This fact is important because the moviment of the seafloor should be monitored in hydrocarbon fields under production. +Figure \ref{fig:Null_stress} shows the null stress through the free surface at the plane $z=0$ m due to reservoir under uniform depletion. +\begin{figure}[h] + \centering + \includegraphics[scale=0.40]{figures/Figure_Displacement.png} + \caption{Reservoir under uniform depletion: (a) horizontal displacement (equation + \ref{eq:horizontal_displacement}) and (b) vertical displacement (equation \ref{eq:u_til_z}) by our + methodology that uses the closed expressions of the volume integrations (equations \ref{eq:u_til_alpha} + and \ref{eq:u_til_z}), whose closed solutions are given by equations \ref{dx1}--\ref{dzz2}.} + \label{fig:displacement} +\end{figure} +\vspace{0.00mm} +\begin{figure}[h] + \centering + \includegraphics[scale=0.40]{figures/Figure_Displacement_Geertsma.png} + \caption{Reservoir under uniform depletion: (a) Radial displacement and (b) vertical displacement using + Geertsma’s method \citep{Geertsma73} considering an elastic homogeneous cylindrical reservoir under + uniform depletion \citep{Fjaer08}.} + \label{fig:displacement_Geertsma} +\end{figure} +\begin{figure}[h] + \centering + \includegraphics[scale=0.40]{figures/Figure_Displacement_z_levels.png} + \caption{Reservoir under uniform depletion: (a) horizontal $x$-component displacement and (b) vertical + displacement by our methodology that uses the closed expressions of the volume integrations (equations + \ref{eq:u_til_alpha} and \ref{eq:u_til_z}), whose closed solutions are given by equations \ref{dx1}--\ref{dzz2}. + These displacements are calculated along the $x$-axis, at $y = 0$ m and $z$ located at the depths of: + seafloor ($z = 0$ m), reservoir top ($z = 750$ m), reservoir center ($z = 800$ m) and reservoir bottom ($z = 850$ m).} + \label{fig:displacement_z_levels} +\end{figure} +%\vspace{0.0cm} +\begin{figure}[!h] + \centering + \includegraphics[scale=0.40]{figures/Figure_Displacement_z_levels_Geertsma.png} + \caption{Reservoir under uniform depletion: vertical displacement using Geertsma’s method + \citep{Geertsma73} + considering an elastic homogeneous cylindrical reservoir under uniform depletion \citep{Fjaer08}. + The displacement is calculated along the x-axis, at $y = 0$ m and $z$ located at the depths of: seafloor + ($z = 0$ m), reservoir top ($z = 750$ m), and reservoir bottom ($z = 850$ m).} + \label{fig:displacement_z_levels_Geertsma} +\end{figure} +%\vspace{-0.5cm} +\begin{figure*}[!t] + \centering + \includegraphics[width=\textwidth]{figures/Figure_Null_stress.png} + \vspace{-2cm} + \caption{Reservoir under uniform depletion: (a) $x-$, (b) $y-$, and + (c) $z-$components of the stress at the free surface. + The horizontal and vertical stresses are calculated by using + the full volume integrations (equations \ref{eq:stress_til_alpha} + and \ref{eq:stress_til_z}), + whose closed solutions are given by equations \ref{dxz1}-- + \ref{sz3}.} + \label{fig:Null_stress} +\end{figure*} + + +%\newpage +\vspace{0.5cm} +\noindent{\textbf{Reservoir with arbitrary geometry and under arbitrary pressure changes}} +%\subsection*{Reservoir with arbitrary geometry and under arbitrary pressure changes} +%\vspace{-0.5cm} + +In this numerical application, the reservoir model is a simplification of a realistic reservoir located in a production oil field in offshore Brazil. +The entire reservoir model comprises dimensions of 14 km in the north-axis, 13 km in the +east-axis, and 0.6 km in the down-axis. +The depths to the top and bottom of the reservoir model are 2,712 m and 3,312 m, respectively. +The components of the displacements are calculated at 0 m deep, +on a regular grid of 100 $\times$ 80 observation points along the north- and east-directions, respectively. +We discretized the reservoir along the $x-$, $y-$ and $z-$ directions into an $14 \times 13 \times 2$ grid of prisms. +The Young’s modulus is 3300 (in MPa), the Poisson's coefficient is 0.25, and +the uniaxial compaction coefficient $C_{m}$ (equation \ref{eq:Cm}) is $2.2525 \: 10^{-4}$ +$\textrm{ MPa}^{-1}$. +Figure \ref{fig:pressure_complex_reservoir} shows the pore pressure distribution of the reservoir whose pressures vary from $0$ to $-0.72$ MPa. +Figure \ref{fig:displacement_complex_reservoir} shows cross-sections at $x = 8$ km of the horizontal and vertical displacements, calculated in the whole reservoir by using our methodology. +Figure \ref{fig:Null_stress_complex_reservoir} shows the null stress through the free surface +due to reservoir shown in Figure \ref{fig:pressure_complex_reservoir}. +%The reservoir (Figure \ref{fig:pressure_complex_reservoir}) yields null stress (not shown) at the free surface +\begin{figure}[h] + \centering + \includegraphics[scale=0.40]{figures/Figure_Pressure_complex_reservoir.png} + \caption{Reservoir with arbitrary geometry and under arbitrary pressure changes: 3D perspective view of + the pore pressure distribution based on a reservoir located in a production oil field in offshore Brazil.} + \label{fig:pressure_complex_reservoir} +\end{figure} +\begin{figure}[t] + \centering + \includegraphics[scale=0.40]{figures/Figure_Displacement_complex_reservoir.png} + \vspace{-0.5cm} + \caption{Reservoir with arbitrary geometry and under arbitrary pressure changes: + (a) horizontal displacement (equation \ref{eq:horizontal_displacement}) and (b) vertical displacement + (equation \ref{eq:u_til_z}) by our methodology that uses the closed expressions of the volume integrations + (equations \ref{eq:u_til_alpha} and \ref{eq:u_til_z}), whose closed solutions are given by equations + \ref{dx1}--\ref{dzz2}.} + \label{fig:displacement_complex_reservoir} +\end{figure} + + +%\vspace{-1.0cm} +\section*{Conclusion} +%\vspace{-0.5cm} +Grounded on the similarity between the gravitational potential produced by a volume source under a density variation and the displacement field produced by a volume source in a half-space under a pressure variation, we have presented an alternative solution for the displacement and stress fields outside and inside of a 3D right rectangular prism with constant pressure change. +Our solution is obtained by integrating the well-known nucleus-of-strain solution over the volume of the prism. +We also use our solution to approximate the displacement and stress fields due to a reservoir compaction with arbitrary geometry and under non-uniform pressure distribution. +Our approach consists in approximating the reservoir 3D pressure distribution through a piecewise constant function defined on a user-specified grid of 3D prisms juxtaposed in the $x-$, $y-$ and $z-$directions. +The sum of the displacements(stresses) produced by the prisms is the resultant displacement(stress) field due to the whole reservoir. +Our expressions are valid either outside or inside the prisms. +We have demonstrated the use of these expressions by applying them to calculate the displacement and stress fields due to cylindrical reservoirs with uniform and non-uniform pressure distributions and to a reservoir model of a production oil field in offshore Brazil. +All the numerical applications produced null stress fields at the free surface showing that the condition of null tractions at the free surface has been met. +%\footnote{Note for editor and reviewers: Following the concept of reproducible science which requires the +%open-source code, the computer codes, supporting documentation and numerical applications showing the results %will be freely available through online repositories at the end of the review process.} + +\section*{Acknowledgments} +We thank the editor George Sand L.A. de Fran\c{c}a and the reviewers for their criticisms and suggestions. +Barbosa V.C.F. and Oliveira Jr V.C. were supported by fellowships from the Brazilian research agencies: CNPq (grants 309624/2021-5 and 315768/2020-7) and FAPERJ (grants E-26/202.582/2019 and E-26/202.729/2018). +Arelaro A.D. and Borges F. thank PETROBRAS. + +\section*{Code and data availability} +The current version of our code is freely distributed under the BSD 3-clause licence and it is available for download at Zenodo: \texttt{https://doi.org/10.5281/zenodo.4041984}. +The latest development version of our code can be freely downloaded from a repository on GitHub (\texttt{https://github.com/pinga-lab/DisReserv}). +Instructions for running the current version of our code are also provided on the repository. +The code is still being improved and we encourage the user to work with the latest development version. +The code was developed as an open-source Python language (Python 3.7.x). +The numerical applications were produced in Jupyter Notebook. +The data of the pore pressure distribution simulating a reservoir with arbitrary geometry and under arbitrary pressure changes +(\textit{realistic-model.pickle}) are available in the above-mentioned repositories. + +\begin{figure*}[!t] + \centering + \includegraphics[width=\textwidth]{figures/Figure_Null_stress_complex_reservoir.png} + \vspace{-2.0cm} + \caption{Reservoir with arbitrary geometry and under arbitrary pressure changes: + (a) $x-$, (b) $y-$, and (c) $z-$components of the stress at the free surface. + The horizontal and vertical stresses are calculated by using + the full volume integrations (equations \ref{eq:stress_til_alpha} and \ref{eq:stress_til_z}), + whose closed solutions are given by equations \ref{dxz1}--\ref{sz3}.} + \label{fig:Null_stress_complex_reservoir} +\end{figure*} + +%%%%%%%%%%%%%% +\bibliographystyle{rbgf} +\bibliography{references_RBGF} +%\bibliography{ref_teste} + + + +\end{document} \ No newline at end of file diff --git a/manuscript/natbib.sty b/manuscript/natbib.sty deleted file mode 100644 index ff2b326..0000000 --- a/manuscript/natbib.sty +++ /dev/null @@ -1,835 +0,0 @@ -%% -%% This is file `natbib.sty', -%% generated with the docstrip utility. -%% -%% The original source files were: -%% -%% natbib.dtx (with options: `package,all') -%% ============================================= -%% IMPORTANT NOTICE: -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN -%% archives in directory macros/latex/base/lppl.txt; either -%% version 1 of the License, or any later version. -%% -%% This is a generated file. -%% It may not be distributed without the original source file natbib.dtx. -%% -%% Full documentation can be obtained by LaTeXing that original file. -%% Only a few abbreviated comments remain here to describe the usage. -%% ============================================= -%% Copyright 1993-2006 Patrick W Daly -%% Max-Planck-Institut f\"ur Sonnensystemforschung -%% Max-Planck-Str. 2 -%% D-37191 Katlenburg-Lindau -%% Germany -%% E-mail: daly@linmpi.mpg.de -\NeedsTeXFormat{LaTeX2e}[1995/06/01] -\ProvidesPackage{natbib} - [2006/09/06 7.4a (PWD)] - % This package reimplements the LaTeX \cite command to be used for various - % citation styles, both author-year and numerical. 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