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a6_fitbessel.m
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a6_fitbessel.m
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% Extract phase velocity dispersion between station pairs by fitting J0 bessel
% function to real(ccf)
% Uses cross spectral fitting technique of Menke & Jin (2015) BSSA
% DOI:10.1785/0120140245
%
% Define own starting phase velocity dispersion c manually or using
% functions/calc_Rayleigh_disp for a simple layered model (does not work for
% models with a water column).
%
% https://github.com/jbrussell
clear
close all;
global tN
global waxis
global twloc
global weight
setup_parameters;
%======================= PARAMETERS =======================%
comp = {'ZZ'}; %'RR'; 'ZZ'; 'TT'
windir = 'window3hr';
xspdir = 'phv_dir'; % output directory of phase velocities
frange = [1/5 1/10]; % frequency range over which to fit bessel function
N_wl = 1; % Number of wavelengths required
Npers = 21; % Number of periods
xlims = [1/12 1/3]; % limits for plotting
t_vec_all = 1./flip(linspace(frange(1) , frange(2) ,Npers)); % periods at which to extract phase velocity
damp = [1; 1; 1]; % [fit, smoothness, slope]
is_normbessel = 0; % normalize bessel function by analytic envelope?
% % Manually input phase velocity
% c = []';
is_resume = 0; % Resume from last processed file or overwrite
iswin = 1; % Use the time-domain windowed ccfs?
npts_smooth = 1; % 1 = no smoothing
isoutput = 1; % Save *.mat file with results?
nearstadist = 0;
IsFigure = 1;
isfigure2 = 0;
isfigure_snr = 1;
%% Make the initial phase velocity dispersion model
% % calc_Rayleigh_disp
% vec_h = [3 2 4 12]; % Layer thickness
% vec_vs = [1.1 1.2 2.8 3.7 4.6];
% vec_vp = vec_vs.*1.8; vec_pv(1) = 1.5;
% vec_rho = [1.03 1.5 3.02 3.027 3.342];
% vr = mat_disperse(vec_h,vec_rho,vec_vp,vec_vs,1./t_vec_all);
% c = vr(:,1)';
% c_start = c;
% Manually
% c = [3.4837 3.6341 3.7458 3.8223 3.8878 3.9451 4.0013 4.0522 4.0951 4.1337 4.1683 4.2098]; % 'test_1.6win' avg
% 10.0000 11.2063 12.5580 14.0729 15.7704 17.6727 19.8045 22.1935 24.8706 27.8706 31.2325 35.0000
% c = [3 3.2 3.3 3.4464 3.8400 3.9589 4.0097 4.0363 4.0515 4.0600 4.0644 4.0661];
% From MINEOS .q file (https://github.com/jbrussell/MINEOS_synthetics)
qfile = ['./qfiles/Nomelt_taper_eta_crust_INVpconstr_xi1.06_GRL19_ORCAiso_INV.s0to200.q'];
mode = 0;
if exist('c','var') == 0 % check if phase velocities exist, if not read them in
[~,~,c_all] = readMINEOS_qfile2(qfile,t_vec_all,mode);
end
c_start = c_all;
c_all_std = zeros(size(c_all));
%==========================================================%
% LIMITS
if comp{1}(1) == 'R'
ylims = [3.2 4.5];
elseif comp{1}(1) == 'Z' || comp{1}(1) == 'P'
ylims = [1.5 4.5];
elseif comp{1}(1) == 'T'
ylims = [3.5 4.8];
end
% LOAD DATA TO SEE HOW MANY POINTS
%%% --- Load in the ccf --- %%%
%ccf_path = ['./ccf/',windir,'/fullStack/ccf',comp{1},'/'];
ccf_path = [parameters.ccfpath,windir,'/fullStack/ccf',comp{1},'/'];
stalist = parameters.stalist;
sta1=char(stalist(1,:));
sta2=char(stalist(2,:));
sta1dir=[ccf_path,sta1]; % dir to have all cross terms about this central station
filename = sprintf('%s/%s_%s_f.mat',sta1dir,sta1,sta2);
if ~exist(filename,'file')
disp(['not exist ',filename])
% continue;
end
data1 = load(filename);
npts = length(data1.coh_sum_win);
% input path
%ccf_path = ['./ccf/',windir,'/fullStack/ccf',comp{1},'/'];
ccf_path = [parameters.ccfpath,windir,'/fullStack/ccf',comp{1},'/'];
% output path
XSP_path = ['./Xsp/',windir,'/fullStack/Xsp',comp{1},'/',num2str(1/frange(2)),'_',num2str(1/frange(1)),'s_',num2str(N_wl),'wl_',xspdir,'/'];
if ~exist(XSP_path)
if ~exist('./Xsp/')
mkdir('./Xsp/');
end
if ~exist(['./Xsp/',windir,'/'])
mkdir(['./Xsp/',windir,'/']);
end
if ~exist(['./Xsp/',windir,'/fullStack/'])
mkdir(['./Xsp/',windir,'/fullStack/']);
end
if ~exist(['./Xsp/',windir,'/fullStack/Xsp',comp{1},'/'])
mkdir(['./Xsp/',windir,'/fullStack/Xsp',comp{1},'/']);
end
mkdir(XSP_path)
end
% figure output path
if iswin
XSP_fig_path = ['./figs/',windir,'/fullStack/Xsp/',num2str(1/frange(2)),'_',num2str(1/frange(1)),'s_',num2str(N_wl),'wl_',xspdir,'/TEI19/'];
else
XSP_fig_path = ['./figs/',windir,'/fullStack/Xsp/',num2str(1/frange(2)),'_',num2str(1/frange(1)),'s_',num2str(N_wl),'wl_',xspdir,'/TEI19_nowin/'];
end
if ~exist(XSP_fig_path)
mkdir(XSP_fig_path);
end
warning off; %#ok<WNOFF>
stalist = parameters.stalist;
nsta=parameters.nsta; % number of target stations to calculate for
%%% --- Loop through station 1 --- %%%
for ista1=1:nsta
sta1=char(stalist(ista1,:));
sta1dir=[ccf_path,sta1]; % dir to have all cross terms about this central station
%%% --- Loop through station 2 --- %%%
for ista2 = 1: nsta % length(v_sta)
sta2 = char(stalist(ista2,:));
% if same station, skip
if(strcmp(sta1,sta2))
continue
end
% Check to see if we have already done this
if is_resume && exist([XSP_path,sta1,'_',sta2,'_xsp.mat'])
disp('Already fit this one!')
continue
end
clear data1 xcorf1 xsp1 filename
%%% --- Load in the ccf --- %%%
filename = sprintf('%s/%s_%s_f.mat',sta1dir,sta1,sta2);
if ~exist(filename,'file')
disp(['not exist ',filename])
continue;
end
data1 = load(filename);
r1 = distance(data1.stapairsinfo.lats(1),data1.stapairsinfo.lons(1),data1.stapairsinfo.lats(2),data1.stapairsinfo.lons(2),referenceEllipsoid('GRS80'))/1000;
groupv_max = data1.max_grv;
groupv_min = data1.min_grv;
if r1 < nearstadist
continue;
end
% Index wavelength criterion
I_wl = r1 ./ (t_vec_all .* c_all) > N_wl;
if sum(I_wl) <= 1
I_wl(1) = 1;
I_wl(2) = 1;
end
c = c_all(I_wl);
t_vec = t_vec_all(I_wl);
c_std = c_all_std(I_wl);
tN = length(t_vec);
wholesec = npts;
wvec1 = (2*pi)./t_vec;
wvec1 = wvec1';
% Get your axis correct
twloc=1./t_vec;
twloc = twloc*2*pi;
% waxis = (frange(1):1/wholesec:frange(2))*2*pi;
waxis = (1/max(t_vec):1/wholesec:1/min(t_vec))*2*pi;
%%% - Get the normalized ccf - %%%
if iswin
xcorf1 = data1.coh_sum_win./data1.coh_num;
else
xcorf1 = data1.coh_sum./data1.coh_num;
end
dumnan = find(isnan(xcorf1)==1);
if length(dumnan) > 10
disp([sta1,' and ',sta2,'is NaN! Moving on']);
continue
end
%N = 10000;
N = length(xcorf1);
if length(xcorf1) < N
disp('Dataset is too short! Moving on')
continue
end
xcorf = xcorf1;
xcorf1 = real(xcorf1(1:N));
xcorf1(1) = 0;
if isfigure2
figure(1)
T = length(xcorf1);
dt = 1;
temp_faxis = [0:1/T:1/dt/2,-1/dt/2+1/T:1/T:-1/T];
ind = find(temp_faxis>0);
subplot(2,1,1)
%plot(temp_faxis(ind),smooth(real(xcorf1(ind)),100));
plot(flip(temp_faxis(ind),smooth(real(xcorf1(ind)),50)));
xlim([frange(1) frange(2)])
hold on
subplot(2,1,2)
%plot(temp_faxis(ind),smooth(real(data1.coh_sum(ind)/data1.coh_num),100),'-r')
plot(temp_faxis(ind),smooth(real(data1.coh_sum(ind)/data1.coh_num),50),'-r');
xlim([frange(1) frange(2)])
end
%%% - Convert xcorf into spherical frequency - %%%
faxis = [0:N-1]*1/wholesec;
xsp1 = interp1(faxis*2*pi,xcorf1,waxis);
%xsp1 = smooth(xsp1,50);
xsp1 = smooth(xsp1,npts_smooth);
tw1 = ones(1,tN)*r1./c;
%%% - Invert for the bessel function 2x - %%%
options = optimoptions(@lsqnonlin,'TolFun',1e-12,'MaxIter',1500,'MaxFunEvals',1500);
weight = 1./waxis;
tw2 = lsqnonlin(@(x) besselerr(x,[xsp1],damp,is_normbessel),[tw1],[tw1]*0.8,[tw1]*1.2,options);
% tw2 = lsqnonlin(@(x) besselerr(x,[xsp1]),[tw1],[],[],options);
weight(:) = 1;
[tw,~,res,~,~,~,J] = lsqnonlin(@(x) besselerr(x,[xsp1],damp,is_normbessel),[tw2],[tw2]*0.8,[tw2]*1.2,options);
% tw = lsqnonlin(@(x) besselerr(x,[xsp1]),[tw2],[tw2]*0.8,[tw2]*1.2,options);
% tw = lsqnonlin(@(x) besselerr(x,[xsp1]),[tw2],[],[],options);
% ESTIMATE ERROR BARS ON MODEL! :: JBR - 2/2020
% Calculate data variance from residual following Menke QMDA book eq. (4.31)
% s_d^2 = E / (N-M)
sigma_d2 = res'*res / (length(res)-length(tw));
Cov_m = inv(J'*J)*sigma_d2;
sigma_m_tw = diag(Cov_m).^(1/2);
% Propogate model error to phase velocity
% c = r1./tw; therefore dc = |r*t^(-2) * dt|
sigma_m_c = abs(r1.*tw'.^(-2).*sigma_m_tw);
%%% - Set up the variable structure - %%%
xspinfo.sta1 = sta1;
xspinfo.sta2 = sta2;
xspinfo.lat1 = data1.stapairsinfo.lats(1);
xspinfo.lon1 = data1.stapairsinfo.lons(1);
xspinfo.lat2 = data1.stapairsinfo.lats(2);
xspinfo.lon2 = data1.stapairsinfo.lons(2);
xspinfo.r = r1;
xspinfo.tw = tw;
xspinfo.xsp = xsp1;
xspinfo.xsp_norm = xsp1./abs(hilbert(xsp1));
xspinfo.coherenum = data1.coh_num;
err = besselerr(tw,xsp1,damp,is_normbessel);
err = err(1:length(waxis));
if is_normbessel
xspinfo.sumerr = sum(err.^2)./sum((xspinfo.xsp_norm./weight(:)).^2);
else
xspinfo.sumerr = sum(err.^2)./sum((xsp1./weight(:)).^2);
end
xspinfo.err = err./weight(:);
xspinfo.tw1 = tw1;
xspinfo.twloc = twloc;
xspinfo.c = r1./tw;
xspinfo.c_std = sigma_m_c;
xspinfo.per = 1./(twloc/2/pi);
xspinfo.c_start = c_start;
xspinfo.c_std_start = c_all_std;
xspinfo.per_start = t_vec_all;
xspinfo.isgood_wl = I_wl;
data = r1./tw;
%% %%% Calculate SNR %%%
xcorf1 = data1.coh_sum./data1.coh_num;
xcorf1_filtered = tukey_filt( xcorf1,[min(t_vec) max(t_vec)],1,0.25 );
[snr, signal_ind] = calc_SNR(xcorf1_filtered,groupv_min,groupv_max,r1,isfigure_snr);
%%
xspinfo.filename = filename;
xspinfo.snr = snr;
% Calculate the predicted bessel function from the initial model
disp([filename,' fitted'])
if IsFigure
if 0 % plot initial bessel
tw_init = interp1(twloc,tw1(1:tN),waxis,'linear');
x_init = waxis.*tw_init;
A = 1;
binit = besselj(0,x_init)*A;
binit = binit./mean(abs(binit)).*mean([abs(xsp1)]);
plot(waxis/2/pi,binit,'-k','linewidth',2); hold on;
end
f3 = figure(3); clf; hold on;
set(gcf,'color','w','Position',[289 1 517 704]);
ax1 = subplot(3,1,1);
plot_SNR(xcorf1_filtered,groupv_min,groupv_max,r1,ax1);
set(ax1,'box','off');
% REAL PART (J0)
subplot(3,1,2); box off;
tww = interp1(twloc,tw(1:tN),waxis,'linear');
x = waxis.*tww;
A = 1;
b = besselj(0,x)*A;
b = b./mean(abs(b)).*mean([abs(xsp1)]);
T = length(data1.coh_sum);
dt = 1;
faxis = [0:1/T:1/dt/2,-1/dt/2+1/T:1/T:-1/T];
ind = find(faxis>0);
plot(faxis(ind),smooth(real(data1.coh_sum_win(ind)/data1.coh_num),npts_smooth),'-k','linewidth',3); hold on;
if ~iswin
plot(waxis/2/pi,xsp1,'-b','linewidth',1);
end
plot(waxis/2/pi,b,'-r','linewidth',2); hold on;
xlim(xlims);
xlims1 = get(gca,'XLim');
ylabel('J_{0}','fontsize',16);
ax1 = get(gca);
dx = 1;
dy = 0.95;
text(gca,diff(ax1.XLim)*dx+ax1.XLim(1),diff(ax1.YLim)*dy+ax1.YLim(1),...
sprintf('%.4f',xspinfo.sumerr),'color',[0 0 0],'fontsize',14);
set(gca,'fontsize',16,'linewidth',1.5);
box off;
title(['Distance : ',num2str(r1),'km'],'fontsize',16);
hold on
subplot(3,1,3);
errorbar(twloc/2/pi,r1./tw1,c_std,'o-','color',[0.5 0.5 0.5],'linewidth',2);hold on;
errorbar(twloc/2/pi,r1./tw,sigma_m_c*2,'o-','color',[1 0 0 ],'linewidth',2);
% errorbar(twloc/2/pi,r1./tw,xspinfo.err,'ro-','linewidth',2);
title([sta1,'-',sta2],'fontsize',16)
xlabel('Frequency (Hz)','fontsize',16);
ylabel('Phase Velocity (km/s)','fontsize',16);
set(gca,'fontsize',16,'linewidth',1.5);
ylim(ylims);
xlim(xlims1);
box off;
% Plot normalized bessel functions
if is_normbessel
figure(4); clf;
b_dat = smooth(real(data1.coh_sum_win(ind)/data1.coh_num),npts_smooth);
plot(faxis(ind),b_dat./abs(hilbert(b_dat)),'k','linewidth',3); hold on;
plot(waxis/2/pi,b./SmoothAnalyticEnv(waxis/2/pi,b),'-r','linewidth',2); hold on;
xlim(xlims);
xlims1 = get(gca,'XLim');
ylabel('J_{0}','fontsize',16);
ylim([-2 2]);
end
if isfigure2
f12 = figure(12);
clf
T = length(data1.coh_sum);
dt = 1;
faxis = [0:1/T:1/dt/2,-1/dt/2+1/T:1/T:-1/T];
ind = find(faxis>0);
plot(faxis(ind),smooth(real(data1.coh_sum(ind)/data1.coh_num),npts_smooth),'-r');
xlim([frange(1) frange(2)])
end
psfile = [XSP_fig_path,'Xsp_',comp{1}(1),'_',sta1,'_',sta2,'_J0J1.pdf'];
%print('-dpsc2',psfile);
drawnow
if isoutput
save2pdf(psfile,f3,250);
end
% pause;
end
if isoutput
save(sprintf('%s/%s_%s_xsp.mat',XSP_path,sta1,sta2),'xspinfo','twloc','waxis');
end
% pause;
end %end of station j
end %end of station i