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gmpe_sb_2014_ratios.m
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gmpe_sb_2014_ratios.m
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function [ ratio, sigma, phi, tau ] = gmpeSB_2014_ratios( T )
% Created by Jack Baker, August 21, 2015
% Updated 12 October, 2015, to include Phi and Tau values
%
% Compute Sa_RotD100/Sa_RotD50 ratios, from the following model:
%
% Shahi, S. K., and Baker, J. W. (2014). "NGA-West2 models for ground-
% motion directionality." Earthquake Spectra, 30(3), 1285-1300.
%
% INPUTS:
%
% T = Period(s) of interest (sec)
%
% OUTPUTS:
%
% ratio = geometric mean of Sa_RotD100/Sa_RotD50
%
% sigma = standard deviation of log(Sa_RotD100/Sa_RotD50)
%
% phi = within-event standard deviation
%
% tau = between-event standard deviation
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Model coefficient values from Table 1 of the above-reference paper
periods_orig = [0.0100000000000000,0.0200000000000000, 0.0300000000000000, 0.0500000000000000, 0.0750000000000000, 0.100000000000000, 0.150000000000000, 0.200000000000000, 0.250000000000000, 0.300000000000000, 0.400000000000000, 0.500000000000000, 0.750000000000000, 1, 1.50000000000000, 2, 3, 4, 5, 7.50000000000000, 10];
ratios_orig = [1.19243805900000, 1.19124621700000, 1.18767783300000, 1.18649074900000, 1.18767783300000, 1.18767783300000, 1.19961419400000, 1.20562728500000, 1.21652690500000, 1.21896239400000, 1.22875320400000, 1.22875320400000, 1.23738465100000, 1.24110237900000, 1.24234410200000, 1.24358706800000, 1.24732343100000, 1.25985923900000, 1.264908769000, 1.28531008400000, 1.29433881900000];
sigma_orig = [0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08];
phi_orig = [0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.07];
tau_orig = [0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.02, 0.02, 0.03];
% Interpolate to compute values for the user-specified periods
ratio = interp1(log(periods_orig), ratios_orig, log(T));
sigma = interp1(log(periods_orig), sigma_orig, log(T));
phi = interp1(log(periods_orig), phi_orig, log(T));
tau = interp1(log(periods_orig), tau_orig, log(T));
end