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data_generation.m
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data_generation.m
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function [filename, grid_gen, K_true, phi_true, sigma_true, K, sigma, Sigma, gen] = data_generation(gen)
% DATA_GENERATION is basically creating all the data required for a simulation.
% INPUT:
% GRID
% * xmax: length of the grid_gen of x [unit]
% * ymax: length of the grid_gen of y [unit]
% * sx: scale level. number of cell is 2^gen.scale.x(i)+1
% * sy: scale level. number of cell is 2^gen.scale.y(i)+1
% STRUCTURE
% * method: method of generation: 'fromRho', ''
% * samp: Method of sampling of K and g | 1: borehole, 2:random. For fromK or from Rho only
% * samp_n: Number of well or number of point
% * covar:
% * modele covariance structure
% * c
% * mu parameter of the first field.
% * std
% RHO R2
% * Rho.grid_gen.nx = 300;
% * Rho.grid_gen.ny = 60; % log-spaced grid_gen.
% * Rho.elec.spacing = 2; % in grid_gen spacing unit.
% * Rho.elec.config_max = 6000; % number of configuration of electrode maximal
% * Rho.method = 'R2';
% OTHER
% * plotit = false; % display graphic or not (you can still display later with |script_plot.m|)
% * saveit = true; % save the generated file or not, this will be turn off if mehod Paolo or filename are selected
% * name = 'Small_range';
% * seed = 123456;
% OUTPUT:
% - K_true: Hydraulic conductivity true field, matrix (grid_gen.nx x grid_gen.ny) (data or generated)
% - rho_true: Electrical conductivity true field, matrix (grid_gen.nx x grid_gen.ny) (data or from K_true)
% - K: Hydraulic conductivity at some point, structure: location (K.x, K.y) of data (K.d) (sampled from K_true)
% - g: Electrical conductivity at some point, structure: location (g.x, g.y) of data (g.d) (sampled from rho_true)
% - G: Electrical conductivity measured grid_gen, matrix (G.nx x G.ny) of data (G.d) (ERT inverse)
%
% Author: Raphael Nussbaumer
%% * *INPUT CEHCKING*
assert(isfield(gen, 'xmax'))
assert(isfield(gen, 'ymax'))
assert(isfield(gen, 'nx'))
assert(isfield(gen, 'ny'))
if ~isfield(gen, 'method'); gen.method = 'Random'; end
if ~isfield(gen, 'samp'); gen.samp = 2; end
if ~isfield(gen, 'samp_n'); gen.samp_n = 1/100 * (2^gen.sx+1)*(2^gen.sy+1); end
if ~isfield(gen, 'mu'); gen.mu = 0; end
if ~isfield(gen, 'std'); gen.std = 1; end
% Other
if ~isfield(gen, 'plotit'); gen.plotit = 0; end
if ~isfield(gen, 'saveit'); gen.saveit = 1; end
if ~isfield(gen, 'name'); gen.name = ''; end
if ~isfield(gen, 'seed'); gen.seed = 'default'; end
if ~isfield(gen, 'plot'); gen.plot = true; end
tic
rng(gen.seed)
%% * 2. *construction of the grid_gen*
grid_gen.nx = gen.nx;
grid_gen.ny = gen.ny;
grid_gen.nxy = grid_gen.nx*grid_gen.ny; % total number of cells
grid_gen.dx=gen.xmax/(grid_gen.nx-1);
grid_gen.dy=gen.ymax/(grid_gen.ny-1);
grid_gen.x=linspace(0, gen.xmax, grid_gen.nx); % coordinate of cells center
grid_gen.y=linspace(0, gen.ymax, grid_gen.ny);
grid_gen.xy=1:grid_gen.nxy;
[grid_gen.X, grid_gen.Y] = meshgrid(grid_gen.x,grid_gen.y); % matrix coordinate
%% * 2. *handle function for generating a fiel and all phsical relationship*
f_Heinz = @(phi,a,b) 10.^(a *phi - b); % log_10(K) = 6.66 \phi - 4.97 + noise (Heinz et al., 2003)
f_Heinz_inv = @(K) (log10(K)+4.97)/ 6.66 ; % log_10(K) = 6.66 \phi - 4.97 + noise (Heinz et al., 2003)
f_Archie = @(phi) 43*real(phi.^1.4); % \sigma = \sigma_W \phi ^m + noise (Archie, 1942) where sigma_W can go up to .075, 1.2<m<1.6
f_Archie_inv = @(sigma) (sigma/43).^(1/1.4) ; % \sigma = \sigma_W \phi ^m + noise (Archie, 1942)
f_Kozeny = @(phi,d) d^2/180*phi^3/(1-phi)^2;
f_Kozeny = @(K,d) roots([-d^2/180/K 1 -2 1]);
f_KC = @(phi,d10) 9810/0.001002 * phi.^3./(1-phi).^2 .* d10^2/180; % Kozeny-Carman @20°C
%% * 3. *Generate field*
switch gen.method
case 'Normal-Random'
sigma_true = gen.mu + gen.std*fftma_perso(gen.covar, grid_gen);
phi_true = f_Archie_inv(sigma_true);
K_true = f_Heinz(phi_true,6.66,4.97);
rho_true = 1000./sigma_true;
case 'Log-Random'
sigma_true = 10.^(gen.mu + gen.std*fftma_perso(gen.covar, grid_gen));
phi_true = f_Archie_inv(sigma_true);
K_true = f_Heinz(phi_true,6.66,4.97);
rho_true = 1000./sigma_true;
case 'fromPhi'
phi_true = gen.mu + gen.std*fftma_perso(gen.covar, grid_gen);
assert(all(phi_true(:)>0),'All phi_true are not greater than 0')
% K_true = f_Heinz(phi_true,6.66,4.97);
% K_true_2 = f_Heinz(phi_true,7,4.5);
% mask = fftma_perso(gen.covar, grid_gen);
% K_true =K_true_1;
% K_true(mask<0) = K_true_2(mask<0);
sigma_true = f_Archie(phi_true); % archie gives conductivity, I want resisitivitiy
rho_true = 1000./sigma_true;
case 'fromLogPhi'
phi_true = exp(gen.mu + gen.std*fftma_perso(gen.covar, grid_gen));
assert(all(phi_true(:)>0),'All phi_true are not greater than 0')
% K_true = f_Heinz(phi_true,6.66,4.97);
% K_true_2 = f_Heinz(phi_true,7,4.5);
% mask = fftma_perso(gen.covar, grid_gen);
% K_true =K_true_1;
% K_true(mask<0) = K_true_2(mask<0);
sigma_true = f_Archie(phi_true); % archie gives conductivity, I want resisitivitiy
rho_true = 1000./sigma_true;
otherwise
error('method not define.')
end
%% Sampling
sigma = sampling_pt(grid_gen,sigma_true,gen.samp,gen.samp_n);
% K = sampling_pt(grid_gen,K_true,gen.samp,gen.samp_n);
% Plot
if gen.plotit
sigma_true_t = (log(sigma_true) - mean(log(sigma_true(:)))) ./ std(log(sigma_true(:)));
sigma_dt = (log(sigma.d) - mean(log(sigma_true(:)))) ./ std(log(sigma_true(:)));
figure(1);clf; subplot(2,1,1); hold on;axis equal; title('Electrical Conductivity [mS/m]');xlabel('x [m]'); ylabel('y [m]')
imagesc(grid_gen.x,grid_gen.y,sigma_true_t);colorbar; scatter(sigma.x,sigma.y,sigma.d); legend({'Sampled location'})
subplot(2,1,2); hold on; title('Histogram'); xlabel('Electrical Conductivity [mS/m]');
ksdensity(sigma_true_t(:)); ksdensity(sigma_dt(:)); legend({'True','Sampled'})
[gamma_x, gamma_y] = variogram_gridded_perso(sigma_true_t);
figure(2); clf; subplot(2,1,1); hold on; title('Horizontal (x) Variogram')
plot(grid_gen.x(1:end/2),gamma_x(1:end/2)./std(sigma_true_t(:))^2);
% plot([gen.covar.modele(1,2) gen.covar.modele(1,2)],[0 1])
plot(grid_gen.x(1:end/2),1-gen.covar.g(grid_gen.x(1:end/2)/gen.covar.range(2)),'linewidth',2)
subplot(2,1,2); hold on; title('Vertical (y) Variogram')
plot(grid_gen.y(1:end/2),gamma_y(1:end/2)./std(sigma_true_t(:))^2);
% plot([gen.covar.modele(1,3) gen.covar.modele(1,3)],[0 1])
plot(grid_gen.y(1:end/2),1-gen.covar.g(grid_gen.y(1:end/2)/gen.covar.range(1)),'linewidth',2)
keyboard;close all; % try different initial data if wanted
end
%%
filepath = 'data_gen/IO-file/';
delete([filepath '*']);
% Forward Grid
f = gen.Rho.f;
f.grid.x = grid_gen.x;
f.grid.y = grid_gen.y;
cell2vertex = @(x) [x(1)-(x(2)-x(1))/2 x(1:end-1)+diff(x)/2 x(end)+(x(end)-x(end-1))/2];
f.grid.x_n = cell2vertex(f.grid.x);
f.grid.y_n = cell2vertex(f.grid.y);
% Electrod config
elec = gen.Rho.elec;
[~,min_spacing] = min(abs(f.grid.x-elec.spacing));
elec.spacing = f.grid.x(min_spacing);
f.elec_spacing = min_spacing-1;
f.elec_id = f.elec_spacing*(elec.bufzone)+1 : f.elec_spacing : numel(f.grid.x_n)-elec.bufzone*f.elec_spacing;
elec.x = f.grid.x_n(f.elec_id);
elec.n = numel(elec.x);
% elec.config_max = 3000;
elec.method = 'dipole-dipole';
elec.depth_max = ceil(elec.n*f.grid.y(end)/f.grid.x(end));
elec.selection = 5; %1: k-mean, 2:iterative removal of the closest neighboohood 3:iterative removal of the averaged closest point 4:voronoi 5:random
elec = config_elec(elec); % create the data configuration.
% Inverse Grid
i = gen.Rho.i;
i.elec_spacing = floor(i.grid.nx/(elec.n+2*elec.bufzone-1));
i.grid.x_n = f.grid.x_n(1:f.elec_spacing/i.elec_spacing:end);
i.grid.x = i.grid.x_n(1:end-1)+diff(i.grid.x_n)/2;
i.grid.y_n = logspace(log10(f.grid.y_n(1)+5),log10(f.grid.y_n(end)+5),i.grid.ny+1)-5; % cell center
i.grid.y = i.grid.y_n(1:end-1)+diff(i.grid.y_n)/2;
i.elec_id = find(sum(bsxfun(@eq,i.grid.x_n',elec.x),2));
% Forward
f.header = 'Forward'; % title of up to 80 characters
f.job_type = 0;
f.filepath = filepath;
f.readonly = 0;
f.alpha_aniso = gen.covar.range0(2)/gen.covar.range0(1);
% Rho value
% f = griddedInterpolant({grid.y,grid.x},rho_true,'nearest','nearest');
f.rho = rho_true; % f({grid_Rho.y,grid_Rho.x});
% f.filename = 'gtrue.dat';
f.num_regions = 1+numel(f.rho);
f.rho_min = min(rho_true(:));
f.rho_avg = mean(rho_true(:));
f.rho_max = max(rho_true(:))*2;
f = Matlat2R2(f,elec); % write file and run forward modeling
% Add some error to the observation
i.a_wgt = 0;%0.01;
i.b_wgt = 0.02;
% var(R) = (a_wgt*a_wgt) + (b_wgt*b_wgt) * (R*R)
f.output.resistancewitherror = i.a_wgt.*randn(numel(f.output.resistance),1) + (1+i.b_wgt*randn(numel(f.output.resistance),1)).*f.output.resistance;
%f.output.resistancewitherror(f.output.resistancewitherror>0) = -f.output.resistancewitherror(f.output.resistancewitherror>0);
%f.output.resistancewitherror(f.output.resistancewitherror<-10) = -10;
fid = fopen([f.filepath 'R2_forward.dat'],'r');
A = textscan(fid,'%f %f %f %f %f %f %f');fclose(fid);
A{end-1}(2:end) = f.output.resistancewitherror;
fid=fopen([f.filepath 'R2_forward.dat'],'w');
A2=[A{:}];
fprintf(fid,'%d\n',A2(1,1));
for u=2:size(A2,1)
fprintf(fid,'%d %d %d %d %d %f %f\n',A2(u,:));
end
fclose(fid);
if 0==1
figure(4); clf; hold on;
[X,Y] = meshgrid(f.grid.x_n,f.grid.y_n);
mesh(X,Y,0*X,'EdgeColor','b','facecolor','none')
[X,Y] = meshgrid(i.grid.x_n,i.grid.y_n);
mesh(X,Y,0*X,'EdgeColor','r','facecolor','none')
[X,Y] = meshgrid(f.grid.x,f.grid.y);
scatter(X(:),Y(:),'b')
[X,Y] = meshgrid(i.grid.x,i.grid.y);
scatter(X(:),Y(:),'r')
plot(elec.x,f.grid.y_n(1),'xk')
view(2); axis tight; set(gca,'Ydir','reverse');
end
% Inverse
i.header = 'Inverse'; % title of up to 80 characters
i.job_type = 1;
i.filepath = filepath;
i.readonly = 0;
i.alpha_aniso = f.alpha_aniso;
i.num_regions = 1;
i.tolerance = 1;
i.rho_avg = f.rho_avg;
i = Matlat2R2(i,elec);
%% Ouput Sigma
Sigma.d = 1000./flipud(i.output.res);
if i.res_matrix == 1 && any(~isnan(i.output.sen(:)))
Sigma.sen = 1000./flipud(i.output.sen);
elseif i.res_matrix == 2 && any(~isnan(i.output.rad(:)))
Sigma.rad = flipud(i.output.rad);
elseif i.res_matrix == 3 && any(~isnan(i.output.Res(:)))
Sigma.res=i.output.Res;
Sigma.res(~i.output.inside,:)=[]; Sigma.res(:,~i.output.inside(:))=[];
Sigma.res_out=i.output.Res;
Sigma.res_out(~i.output.inside,:)=[]; Sigma.res_out(:,i.output.inside(:))=[];
Sigma.res_out = sum(Sigma.res_out,2);
end
rmpath data_gen/R2
Sigma.x = i.grid.x;
Sigma.y = i.grid.y;
[Sigma.X,Sigma.Y] = meshgrid(Sigma.x, Sigma.y);
gen.Rho.i = i;
gen.Rho.f = f;
gen.Rho.elec = elec;
%% * 4.*SAVING*
if gen.saveit
filename = ['data_gen/data/GEN-', gen.name ,'_', datestr(now,'yyyy-mm-dd_HH-MM'), '.mat'];
save(filename, 'phi_true', 'sigma_true', 'Sigma','grid_gen', 'gen') %'sigma',
end
fprintf(' -> finish in %g sec\n', toc)
end