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example_CompareMethods_fast.m
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example_CompareMethods_fast.m
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% Compare Radon transform methods applied to synthetic multimode (0T-4T)
% Love waves. The velocity model used to calculate the synethic waveforms in this
% example is PA5 (Gaherty et al. 1996). The synthetic station configuration
% is a linear array extending 30 degrees.
%
% Fast Linear Radon Transform methods:
% - L2 (Schultz, 2012)
% - CGsimple (Ji, 2006)
% - CGG_weight (Ji, 2006) *This one seems to work the best on real data
% - CGhestenes (Ji, 2006; Claerbout, 1992)
%
% J. Russell
% github.com/jbrussell
clear;
addpath('./functions/')
addpath('./functions/CG_methods')
% Load variables.
load('./pa5_5km/Synth_120W_150W.mat','-mat');
isnoise = 1; % add gaussian noise?
Delta = deg2km(Delta');
% t - time axis.
% Delta - distance (offset) axis.
% M - Amplitudes of phase arrivals.
% indicies - list of indicies relevent to the S670S phase.
load('./pa5_5km/dispersion_pa5_5km_b5.mat');
BRANCHES=5;
for ii = 1:BRANCHES
DISP(ii).n = ii-1;
DISP(ii).cv = dat{ii}(:,6);
DISP(ii).gv = dat{ii}(:,7);
DISP(ii).cvq = dat{ii}(:,8);
DISP(ii).Tq = dat{ii}(:,9);
DISP(ii).T = dat{ii}(:,10);
% plot(Tq(1:10:end),cvq(1:10:end),'--','color',[.5 .5 .5],'linewidth',1);
end
% Define some variables for RT.
maxiter = 10; %100;
rthresh = 1e-6;
mu=5e-2; %5e-2;
P_axis=10:0.1:40; % s/deg
P_axis = P_axis / 111; %(s/km);
delta=mean(Delta);
f_min = 1/150;
f_max = 1/20;
v_min = 4;
v_max = 8;
% Add noise to data
std_noise = rms(M(:))*0.5;
if isnoise
M = M + normrnd(0,std_noise,size(M));
end
% Invert to Radon domain using several different methods with varying
% degrees of sparseness
tic;
% [R,Rfft,f]=Radon_inverse_disp(t, Delta, M, P_axis, ones(size(Delta)), delta, 'Linear', 'L2', mu);
[R,Rfft,f]=Radon_inverse_disp_fast(t, Delta, M, P_axis, ones(size(Delta)), delta, f_min,f_max,'Linear', 'L2', mu);
toc
tic;
% [ Rfft_2,f_2 ] = Radon_conjgrad(P_axis,t,M,Delta,maxiter,rthresh,'CGsimple');
[ Rfft_2,f_2 ] = Radon_conjgrad_fast(P_axis,t,M,Delta,f_min,f_max,maxiter,rthresh,'CGsimple');
toc
tic;
% [ Rfft_3,f_3 ] = Radon_conjgrad(P_axis,t,M,Delta,maxiter,rthresh,'CGG_weight');
[ Rfft_3,f_3 ] = Radon_conjgrad_fast(P_axis,t,M,Delta,f_min,f_max,maxiter,rthresh,'CGG_weight');
toc
tic;
% [ Rfft_4,f_4 ] = Radon_conjgrad(P_axis,t,M,Delta,maxiter,rthresh,'CGhestenes');
[ Rfft_4,f_4 ] = Radon_conjgrad_fast(P_axis,t,M,Delta,f_min,f_max,maxiter,rthresh,'CGhestenes');
toc
[~,I_fmin_plot] = min(abs(f-f_min)); [~,I_fmax_plot] = min(abs(f-f_max));
I_fmin_plot=I_fmin_plot-1; I_fmax_plot=I_fmax_plot+1;
fplot = f(I_fmin_plot:I_fmax_plot);
[~,I_pmin_plot] = min(abs(P_axis-1/v_max)); [~,I_pmax_plot] = min(abs(P_axis-1/v_min));
I_pmin_plot=I_pmin_plot-1; I_pmax_plot=I_pmax_plot+1;
P_axisplot = P_axis(I_pmin_plot:I_pmax_plot);
Rfftplot = Rfft(I_pmin_plot:I_pmax_plot,I_fmin_plot:I_fmax_plot);
[ perplot,vplot,R_Tv ] = FreqSlow2PeriodVeloc( fplot,P_axisplot,abs(Rfftplot));
[ ~,~,R_Tv_2 ] = FreqSlow2PeriodVeloc( fplot,P_axisplot,abs(Rfft_2(I_pmin_plot:I_pmax_plot,I_fmin_plot:I_fmax_plot)));
[ ~,~,R_Tv_3 ] = FreqSlow2PeriodVeloc( fplot,P_axisplot,abs(Rfft_3(I_pmin_plot:I_pmax_plot,I_fmin_plot:I_fmax_plot)));
[ ~,~,R_Tv_4 ] = FreqSlow2PeriodVeloc( fplot,P_axisplot,abs(Rfft_4(I_pmin_plot:I_pmax_plot,I_fmin_plot:I_fmax_plot)));
%%
% Plot figures. Normalize each frequency separately for plotting purposes.
figure(3); clf;
subplot(2,3,1);
[Delta_srt,I_srt] = sort(Delta);
imagesc(t,Delta_srt,M(I_srt,:)); hold on;
for ii = 1:length(Delta)
plot(t,M(ii,:)/max(M(ii,:))*30+Delta(ii),'-k','linewidth',1);
end
title('Love waves (0T-4T)'); xlabel('Time (s)'); ylabel('Distance (km)');
subplot(232); imagesc(perplot(1,1:end), vplot(1:end,1), abs(R_Tv(:,1:length(perplot))')'./max(abs(R_Tv(:,1:length(perplot))')')); hold on;
for ii = 1:BRANCHES
plot(DISP(ii).Tq(1:10:end),DISP(ii).cvq(1:10:end),'-','color',[0 0.8 0],'linewidth',1);
end
% colorbar;
caxis([0 1]);
xlim([min(perplot(1,1:end)) max(perplot(1,1:end))]);
ylim([v_min v_max]);
title('Schultz & Gu'); ylabel('Velocity (km/s)'); xlabel('Period (s)');
set(gca,'YDir','normal');
subplot(233); imagesc(perplot(1,1:end), vplot(1:end,1), abs(R_Tv_2(:,1:length(perplot))')'./max(abs(R_Tv_2(:,1:length(perplot))')')); hold on;
for ii = 1:BRANCHES
plot(DISP(ii).Tq(1:10:end),DISP(ii).cvq(1:10:end),'-','color',[0 0.8 0],'linewidth',1);
end
% colorbar;
caxis([0 0.6]);
xlim([min(perplot(1,1:end)) max(perplot(1,1:end))]);
ylim([v_min v_max]);
title('CG simple'); ylabel('Velocity (km/s)'); xlabel('Period (s)');
set(gca,'YDir','normal');
subplot(234); imagesc(perplot(1,1:end), vplot(1:end,1), abs(R_Tv_3(:,1:length(perplot))')'./max(abs(R_Tv_3(:,1:length(perplot))')')); hold on;
for ii = 1:BRANCHES
plot(DISP(ii).Tq(1:10:end),DISP(ii).cvq(1:10:end),'-','color',[0 0.8 0],'linewidth',1);
end
% colorbar;
caxis([0 1]);
xlim([min(perplot(1,1:end)) max(perplot(1,1:end))]);
ylim([v_min v_max]);
title('CGG weight'); ylabel('Velocity (km/s)'); xlabel('Period (s)');
set(gca,'YDir','normal');
subplot(235); imagesc(perplot(1,1:end), vplot(1:end,1), abs(R_Tv_4(:,1:length(perplot))')'./max(abs(R_Tv_4(:,1:length(perplot))')')); hold on;
for ii = 1:BRANCHES
plot(DISP(ii).Tq(1:10:end),DISP(ii).cvq(1:10:end),'-','color',[0 0.8 0],'linewidth',1);
end
% colorbar;
caxis([0 1]);
xlim([min(perplot(1,1:end)) max(perplot(1,1:end))]);
ylim([v_min v_max]);
title('CG Hestenes'); ylabel('Velocity (km/s)'); xlabel('Period (s)');
set(gca,'YDir','normal');
%%%%%%%%%%%% make colormap %%%%%%%%%%%%
colmap1 = cmap('steelblue',10,10,15);
colmap2 = cmap('orange',6,40,20);
colmap3 = rgb('orangered');
colmap4 = cmap('red',8,1,45);
colmap = [colmap1;flipud(colmap2);colmap3;flipud(colmap4)];
colormap(colmap);