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Highlights from
Large Data in MATLAB: A Seismic Data Processing Case Study

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Large Data in MATLAB: A Seismic Data Processing Case Study

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These are the files used in the webinar on Feb. 23, 2011.

Seismic Migration Example - Fault Model

Seismic Migration Example - Fault Model

Contents

Data source

This example is derived from Gerard Schuster's MATLAB example and book Seismic Interferometry

addpath faultModelData
addpath migration

Read in velocity model data and plot it

load velocityModel
[nz,nx] = size(velocityModel);

dx = 10;
dz = 10;
x = (1:nx)*dx;
z = (1:nz)*dz;

subplot(2,2,1)
imagesc(x,z,velocityModel)
xlabel('Distance (m)'); ylabel('Depth (m)');
title('Velocity Model');
hold on
hshot = plot(x(1),z(1),'w*');
hold off
colormap(seismic)

Create shot gathers

Use the velocity model to simulate a seismic survey. The wave equations is solved using finite differences for a defined initial wavefield.

% calculate time step dt from stability crierion for finite difference
% solution of the wave equation.
dt = 0.9*min(min(dz./velocityModel/sqrt(2)));

% determine time samples nt from wave travelime to depth and back to
% surface
vmin = min(velocityModel(:));
nt = round(sqrt((dx*nx)^2 + (dz*nx)^2)*2/vmin/dt + 1);
t  = (0:nt-1).*dt;

% add region around model for applying absorbing boundary conditions (20
% nodes wide)
V = [repmat(velocityModel(:,1),1,20) velocityModel repmat(velocityModel(:,end),1,20)];
V(end+1:end+20,:) = repmat(V(end,:),20,1);

% Define frequency parameter for ricker wavelet
f  = 20;

Generate shots and save to file and video

%vidObj = VideoWriter('FaultModelShots.avi');
%open(vidObj);
data = zeros(size(nt,nx));
figure(gcf)
for ixs = 21:nx+20 % shot loop
    % initial wavefield
    rw = ricker(f,nz+40,dt,dt*ixs,0);
    rw = rw(1:nz+20,:);

    % plot initial wavefield
    set(hshot,'XData',x(ixs-20),'YData',z(1));
    subplot(2,2,2)
    imagesc(x,z,rw(1:end-20,21:end-20))
    xlabel('Distance (m)'); ylabel('Depth (m)');
    title(['Shot ',num2str(ixs-20),' at ',num2str(x(ixs-20)),' m']);
    colormap(seismic)

    % generate shot record
    tic
    [data snapshot] = fm2d(V,rw,nz,dz,nx,dx,nt,dt);
    toc
    %save(['faultModelData\snapshot',num2str(ixs-20),'.mat'],'snapshot');
    %save(['faultModelData\shotfdm',num2str(ixs-20),'.mat'],'data')

    data = data(21:end-20,:)';

    if ismember(ixs-20,[1 nx/2 nx])
        start = 1;
    else
        start = nt;
    end

    for i = start:nt
        % plot shot record evolution
        ds = zeros(nt,nx);
        ds(1:i,:) = data(1:i,:);
        subplot(2,2,3)
        imagesc(x,t,ds)
        xlabel('Distance (m)'), ylabel('Time (s)')
        title('Shot Record')
        caxis([-0.1 0.1])

        % plot wave propagation
        subplot(2,2,4)
        imagesc(x,z,snapshot(1:end-20,21:end-20,i))
        xlabel('Distance (m)'), ylabel('Depth (m)')
        title(['Wave Propagation t = ',num2str(t(i),'%10.3f')])
        caxis([-0.14 1])

        %writeVideo(vidObj,getframe(gcf));
        drawnow;
    end %shot loop
end
%close(vidObj);
Elapsed time is 0.901365 seconds.
Elapsed time is 0.877529 seconds.
Elapsed time is 0.871672 seconds.
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Traveltime by 2D ray-tracing

Generate the traveltime field for all z = 0 locations

%vidObj = VideoWriter('FaultModelTravelTime.avi');
%open(vidObj);
travelTime = zeros(nz,nx,nx);
subplot(2,2,2)
for ixs = 1:nx
    travelTime(:,:,ixs) = ray2d(velocityModel,[1 ixs],dx);
    imagesc(x,z,travelTime(:,:,ixs))
    xlabel('Distance (m)'), ylabel('Depth (m)')
    title(['Traveltime for shot ',num2str(ixs)])
    set(hshot,'XData',x(ixs));
    drawnow
    %writeVideo(vidObj,getframe(gcf));
end
%close(vidObj)
%save results for later re-use
%save('faultModelData\travelTime.mat', 'travelTime')

Process Shots - Kirchhoff Migration

%vidObj = VideoWriter('FaultModelKirchhoff.avi');
%open(vidObj);
load('travelTime.mat');
Stacked = zeros(nz,nx);
figure(gcf)
colormap  seismic %bone
for ixs = 1:nx
    load(['shotfdm',num2str(ixs),'.mat'])
    shot = data(21:end-20,:)';
    M = migrate(travelTime,shot,dt,nz,ixs,nx);
    Stacked = Stacked + M;

    subplot(2,2,2)
    imagesc(x,z,Stacked)
    xlabel('Distance (m)'); ylabel('Depth (m)');
    title('Stacked Image');
    caxis([-135 135])

    subplot(2,2,3)
    imagesc(x,t,shot)
    xlabel('Distance (m)'); ylabel('Time (s)');
    title(['Current Shot ',num2str(ixs)]);
    caxis([-0.1 0.1])

    subplot(2,2,4)
    imagesc(x,t,M)
    xlabel('Distance (m)'); ylabel('Time (s)');
    title(['Current Migrated Shot ',num2str(ixs)]);
    caxis([-5 5])

    set(hshot,'XData',x(ixs));

    drawnow
    %writeVideo(vidObj,getframe(gcf));
end
%close(vidObj);
Elapsed time is 0.281017 seconds.
Elapsed time is 0.077068 seconds.
Elapsed time is 0.065901 seconds.
Elapsed time is 0.070564 seconds.
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Process Shots - Reverse Time Migration

%vidObj = VideoWriter('FaultModelRTM.avi');
%open(vidObj);
Stacked = zeros(nz+20,nx+40);
colormap seismic %bone
for ixs = 1:nx
    load(['shotfdm',num2str(ixs),'.mat'])
    shot = data(21:end-20,:)';

    tic
    [~, rtmsnapshot] = rtm2d(V,data,nz,dz,nx,dx,nt,dt);
    toc
    %save(['faultModelData\rtmsnapshot',num2str(ixs),'.mat'],'rtmsnapshot');

    load(['snapshot',num2str(ixs),'.mat']);

    M = 0;
    s2 = 0;
    for i = 1:nt
        M = snapshot(:,:,i).*rtmsnapshot(:,:,nt-i+1)+M;
        s2 = snapshot(:,:,i).^2+s2;

        if ismember(ixs,[1 nx/2 nx])
            subplot(2,2,3)
            imagesc(x,z,snapshot(1:end-20,21:end-20,i))
            xlabel('Distance (m)'); ylabel('Depth (m)');
            title(['Forward Time Wave Propagation t = ',num2str(t(i),'%10.3f')])
            caxis([-0.14 1])

            subplot(2,2,4)
            imagesc(x,z,rtmsnapshot(1:end-20,21:end-20,nt-i+1))
            xlabel('Distance (m)'); ylabel('Depth (m)');
            title('Reverse Time Wave Propagation')
            caxis([-0.14 1])

            subplot(2,2,2)
            imagesc(x,z,diff(M(1:end-20,21:end-20)./s2(1:end-20,21:end-20),2,1))
            xlabel('Distance (m)'); ylabel('Depth (m)');
            title(['Current Migrated Shot ',num2str(ixs)]);
            caxis([-.05 .05])

            drawnow
            %writeVideo(vidObj,getframe(gcf));
        end
    end

    Stacked = Stacked + M;
    subplot(2,2,2)
    imagesc(x,z,diff(Stacked(1:end-20,21:end-20),2,1))
    xlabel('Distance (m)'); ylabel('Depth (m)');
    title('Stacked Image');
    caxis([-30 30])

    subplot(2,2,3)
    imagesc(x,t,shot)
    xlabel('Distance (m)'); ylabel('Time (s)');
    title(['Current Shot ',num2str(ixs)]);
    caxis([-0.1 0.1])

    subplot(2,2,4)
    imagesc(x,t,diff(M(1:end-20,21:end-20),2,1))
    xlabel('Distance (m)'); ylabel('Time (s)');
    title(['Current Migrated Shot ',num2str(ixs)]);
    caxis([-1 1])

    set(hshot,'XData',x(ixs));
    drawnow
    %writeVideo(vidObj,getframe(gcf));
end
%close(vidObj);
Elapsed time is 2.300806 seconds.
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