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main_pseudo_KDEDMS.m
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%% Creat synthetic well data
addpath(genpath('SeReM'))
addpath(genpath('utils'))
load('data\pseudowell.mat')
Depth = WELL.curves(:,1);
facies = WELL.curves(:,2);
Phi = WELL.curves(:,3); Phi(Phi<=0.001) = 0.001;
v_clay = WELL.curves(:,5); v_clay(v_clay <=0.001) = 0.001;
sw = WELL.curves(:,4); sw (sw <=0.001) = 0.001;
[Vp, Vs, Rho] = RPM(Phi ,v_clay, sw); Vp = 1000*Vp; Vs = 1000*Vs;
std_vp = 100;
std_vs = 50;
std_rho = 0.05;
correlation_function = construct_correlation_function_beta(30,1,Vp,2);
Vp = Vp + std_vp*FFT_MA_3D(correlation_function, randn(size(Vp)));
Vs = Vs + std_vs*FFT_MA_3D(correlation_function, randn(size(Vp)));
Rho = Rho + std_rho*FFT_MA_3D(correlation_function, randn(size(Vp)));
AI = Vp.*Rho;
figure(1)
subplot(221)
scatter(Phi, Vp, 25, facies);
axis([0.05 0.3 2500 4000])
subplot(222)
scatter(AI, Vp./Vs, 25, sw);
figure
subplot(121)
plot_histogram(AI, facies);
subplot(122)
plot_histogram(Vp./Vs, facies);
%% PRIOR SAMPLING
n_sim = 50000;
mtrain = [];
dtrain = [];
for facie = 1:length(unique(facies))
idx_facie = (facies==facie);
Phi_train = mean(Phi(idx_facie)) + std(Phi(idx_facie))*randn(n_sim,1);
v_clay_train = mean(v_clay(idx_facie)) + std(v_clay(idx_facie))*randn(n_sim,1);
sw_train = mean(sw(idx_facie)) + std(sw(idx_facie))*randn(n_sim,1);
mtrain = [ mtrain; Phi_train, v_clay_train, sw_train];
[Vp_train, Vs_train, Rho_train] = RPM(Phi_train, v_clay_train, sw_train); Vp_train = 1000*Vp_train; Vs_train = 1000*Vs_train;
Vp_train = Vp_train + std_vp*FFT_MA_3D(correlation_function, randn(size(Vp_train)));
Vs_train = Vs_train + std_vs*FFT_MA_3D(correlation_function, randn(size(Vs_train)));
Rho_train = Rho_train + std_rho*FFT_MA_3D(correlation_function, randn(size(Rho_train )));
dtrain = [ dtrain; Vp_train, Vs_train, Rho_train];
end
figure(1)
subplot(223)
scatter(mtrain(:,1), dtrain(:,1), 25);
axis([0.05 0.3 2500 4000])
subplot(224)
scatter(dtrain(:,1).*dtrain(:,3), dtrain(:,1)./dtrain(:,2), 25);
%% Non-parametric case (Kernel density estimation)
%
% % petrophysical domain discretization
% ndiscr = 25;
% phidomain = linspace(0, 0.4, ndiscr)';
% cdomain = linspace(0, 1, ndiscr)';
% swdomain = linspace(0, 1, ndiscr)';
% mdomain = [phidomain cdomain swdomain];
% % elastic domain discretization
% vpdomain = linspace(min(Vp), max(Vp),ndiscr)';
% vsdomain = linspace(min(Vs), max(Vs),ndiscr)';
% rhodomain = linspace(min(Rho), max(Rho),ndiscr)';
% ddomain =[vpdomain vsdomain rhodomain];
% % kernel bandwidths
% h = 5;
% hm(1) = (max(phidomain)-min(phidomain))/h;
% hm(2) = (max(cdomain)-min(cdomain))/h;
% hm(3) = (max(swdomain)-min(swdomain))/h;
% hd(1) = (max(vpdomain)-min(vpdomain))/h;
% hd(2) = (max(vsdomain)-min(vsdomain))/h;
% hd(3) = (max(rhodomain)-min(rhodomain))/h;
%
%
% % measured data (elastic logs)
% dcond = [Vp Vs Rho];
% ns = size(dcond,1);
%
% % inversion
% Ppost = RockPhysicsKDEInversion(mtrain, dtrain, mdomain, ddomain, dcond, hm, hd);
%
% % marginal posterior distributions
% Ppostphi = zeros(ns,length(phidomain));
% Ppostclay = zeros(ns,length(cdomain));
% Ppostsw = zeros(ns,length(swdomain));
% Phimap = zeros(ns,1);
% Cmap = zeros(ns,1);
% Swmap = zeros(ns,1);
% for i=1:ns
% Ppostjoint=reshape(Ppost(i,:),length(phidomain),length(cdomain),length(swdomain));
% Ppostphi(i,:)=sum(squeeze(sum(squeeze(Ppostjoint),3)),2);
% Ppostclay(i,:)=sum(squeeze(sum(squeeze(Ppostjoint),3)),1);
% Ppostsw(i,:)=sum(squeeze(sum(squeeze(Ppostjoint),2)),1);
% Ppostphi(i,:)=Ppostphi(i,:)/sum(Ppostphi(i,:));
% Ppostclay(i,:)=Ppostclay(i,:)/sum(Ppostclay(i,:));
% Ppostsw(i,:)=Ppostsw(i,:)/sum(Ppostsw(i,:));
% [~,Phimapind]=max(Ppostphi(i,:));
% [~,Cmapind]=max(Ppostclay(i,:));
% [~,Swmapind]=max(Ppostsw(i,:));
% Phimap(i)=phidomain(Phimapind);
% Cmap(i)=cdomain(Cmapind);
% Swmap(i)=swdomain(Swmapind);
% end
%
% % plots
% figure
% subplot(141)
% imagesc(1, Depth, facies);
% ylabel('Depth (m)');
% subplot(142)
% pcolor(phidomain, Depth, Ppostphi);
% set(gca, 'YDir','reverse')
% hold on; shading interp; %colorbar;
% plot(Phi, Depth, 'k', 'LineWidth', 2);
% xlabel('Porosity (v/v)'); xlim([0 0.4]);
% plot(Phimap, Depth, 'r', 'LineWidth', 2);
% subplot(143)
% pcolor(cdomain, Depth, Ppostclay);
% set(gca, 'YDir','reverse')
% hold on; shading interp; %colorbar;
% plot(v_clay, Depth, 'k', 'LineWidth', 2);
% xlabel('Clay volume (v/v)'); xlim([0 0.8]);
% plot(Cmap, Depth, 'r', 'LineWidth', 2);
% subplot(144)
% pcolor(swdomain, Depth, Ppostsw);
% set(gca, 'YDir','reverse')
% hold on; shading interp; %colorbar;
% plot(sw, Depth, 'k', 'LineWidth', 2);
% plot(Swmap, Depth, 'r', 'LineWidth', 2);
% xlabel('Water saturation (v/v)'); xlim([0 1]);
%% Non-parametric case (Kernel density estimation) - DMS approach
dcond = [Vp Vs Rho];
[ mean_marginal, conditioned_data ] = RockPhysicsKDEInversion_DMS(mtrain, dtrain, dcond, 25, 400);
n_bins = 30;
hist_edges = [linspace(0,0.4,n_bins ); linspace(0,1,n_bins ); linspace(0,1,n_bins )]';
hist_edges = hist_edges - mean(diff(hist_edges))/2;
for d = 1:size(conditioned_data,1)
if d == 490
para = 1;
end
for p = 1:size(conditioned_data,2)
data2hist = squeeze(conditioned_data(d, p, :));
data2hist(data2hist == 0) = [];
histograms(d, p, :) = histcounts(data2hist, hist_edges(:,p),'Normalization', 'probability' );
end
end
Ppostphi = squeeze(histograms(:, 1, :));
Ppostclay = squeeze(histograms(:, 2, :));
Ppostsw = squeeze(histograms(:, 3, :));
phidomain = hist_edges(1:end-1,1);
cdomain = hist_edges(1:end-1,2);
swdomain = hist_edges(1:end-1,2);
Phimean = mean_marginal(:,1);
Cmean = mean_marginal(:,2);
Smean = mean_marginal(:,3);
[~,Phimapind] = max(Ppostphi');
[~,Cmapind] = max(Ppostclay');
[~,Swmapind] = max(Ppostsw');
Phimap = phidomain(Phimapind);
Cmap = cdomain(Cmapind);
Swmap = swdomain(Swmapind);
% % plots
figure
ax1 = subplot(141)
imagesc(1, Depth, facies);
ylabel('Depth (m)');
ax2 = subplot(142)
pcolor(phidomain, Depth, Ppostphi);
set(gca, 'YDir','reverse')
hold on; shading interp; %colorbar;
plot(Phi, Depth, 'k', 'LineWidth', 2);
xlabel('Porosity (v/v)'); xlim([0 0.4]);
plot(Phimean, Depth, 'r', 'LineWidth', 2);
ax3 = subplot(143)
pcolor(cdomain, Depth, Ppostclay);
set(gca, 'YDir','reverse')
hold on; shading interp; %colorbar;
plot(v_clay, Depth, 'k', 'LineWidth', 2);
xlabel('Clay volume (v/v)'); xlim([0 0.8]);
plot(Cmean, Depth, 'r', 'LineWidth', 2);
ax4 = subplot(144)
pcolor(swdomain, Depth, Ppostsw);
set(gca, 'YDir','reverse')
hold on; shading interp; %colorbar;
plot(sw, Depth, 'k', 'LineWidth', 2);
plot(Smean, Depth, 'r', 'LineWidth', 2);
xlabel('Water saturation (v/v)'); xlim([0 1]);
linkaxes([ax1, ax2, ax3, ax4], 'y');