Contents

Analytic solutions

test against analytic solutions, see testing_analytic.m

tmp = dlmread(['../results/testing/error_mod.dat']);
h   = tmp(:,1);
e   = tmp(:,2);

% plot error
figure;
loglog(h,e,'k',h,.3*h.^2,'k--');xlim([2,20])
xlabel('h');ylabel('error');

% plot solutions
[D1,o,d,n] = odnread(['../results/testing/D1.odn']);
[D2,o,d,n] = odnread(['../results/testing/D2.odn']);
[z,x] = odn2grid(o,d,n);

D1 = reshape(D1,n);
D2 = reshape(D2,n);

iz = floor(length(z)/2) + 1;

figure;
plot(x,real(D1(iz,:)),'k',x,real(D2(iz,:)),'r',x,imag(D1(iz,:)),'k--',x,imag(D2(iz,:)),'r--');
legend('Re(numerical)','Re(analytic)','Im(numerical)','Im(analytic)');
xlabel('x [m]');ylabel('z [m]');
title(['solutions at z = ' num2str(z(iz)) 'm']);


[G1,o,d,n] = odnread(['../results/testing/G1.odn']);
[G2,o,d,n] = odnread(['../results/testing/G2.odn']);
[z,x] = odn2grid(o,d,n);
G1 = reshape(G1,n);
G2 = reshape(G2,n);

figure;
imagesc(1e-3*x,1e-3*z,real(G1),[-10 10]);axis equal tight;
xlabel('x [km]');ylabel('z [km]');
title('Numerical solution for linear velocity profile')

figure;
imagesc(1e-3*x,1e-3*z,real(G2),[-10 10]);axis equal tight;
xlabel('x [km]');ylabel('z [km]');
title('Analytic solution for linear velocity profile')

Jacobian test

Accuracy of the Jacobian, see testing_jacobian.m

tmp = dlmread(['../results/testing/error_jac.dat']);
h   = tmp(:,1);
e   = tmp(:,2);

% plot error
figure;
loglog(h,e,'k',h,1e3*h.^2,'k--');
xlabel('h');ylabel('error');

Adjoint test

Adjoint test of the Jacobian. See testing_adjoint.m

adjoint_table = dlmread(['../results/testing/error_adj.dat']);

fprintf(1,'<Ax,y>   , <x,A''y>  ,error\n');
fprintf(1,'%2.3e, %2.3e, %1.2e \n',adjoint_table');

<Ax,y>   , <x,A'y>  ,error
2.453e+07, 2.453e+07, 2.22e-14 
1.762e+08, 1.762e+08, 3.55e-15 
1.896e+08, 1.896e+08, 1.42e-14 
-4.903e+07, -4.903e+07, 7.19e-14 
1.296e+08, 1.296e+08, 3.20e-14 
-4.529e+08, -4.529e+08, 3.20e-14 
-1.712e+08, -1.712e+08, 3.21e-13 
-3.417e+08, -3.417e+08, 0.00e+00 
-8.159e+08, -8.159e+08, 1.42e-14 
3.125e+07, 3.125e+07, 7.99e-15 

Scalability

Compute data for a model of size 1201 x 404, for 64 frequencies and 10 sources. See testing_parallel.m

par_table=dlmread('../results/testing/time.dat');
par_table(:,3) = par_table(1,2)./(par_table(:,2).*par_table(:,1));

fprintf(1,'Np, time [s], efficiency\n');
fprintf(1,'%2d, %6.2f , %1.2f\n',par_table');

Np, time [s], efficiency
 1, 2459.50 , 1.00
 2, 1224.10 , 1.00
 4, 615.60 , 1.00
 8, 313.10 , 0.98
16, 188.80 , 0.81
32, 109.50 , 0.70