chenyong910920 / fd2d

2D finite-difference code for noise correlations and kernels

fd2d

2D staggered rid finite differences of the wave equation

Die Anleitung:

GENERAL INPUT PARAMETERS: /input/input_parameters.m

• size of the computational domain

• number of grid points

• length and number of time steps

• finite-difference order

• model type as defines in /code/propagation/define_material_parameters.m

• source time function (only relevant for simulation_mode=forward)

• simulation_mode (type of forward or adjoint simulation)

• source and receiver positions

• absorbing boundaries (where and how wide)

COMPUTING NOISE CORRELATIONS

The computation of noise correlations proceeds in two steps.

STEP 1: Computation of the Green’s function with source at the reference station

• Edit the simulation parameters in input_parameters.m (domain, time step, receivers, …).
• The source (in earthquake simulations) acts as the reference station in noise correlation simulations.
• Set the simulation_mode to “forward_green”.
• Go to /input/interferometry/input_interferometry.m and edit the frequency sampling of the Green’s function. (If the sampling is too low in the frequency domain, then artefacts appear on the correlation source function. Trial and error?)
• Go to /code/ and run “run_forward()”.
• This will compute the forward Green’s function.
• The Fourier transform of the Green’s function is computed on-the-fly, i.e. during the simulation.
• The Fourier transform is then stored as “G_2.mat” in the directory /output/interferometry/“

STEP 2: Computing the actual correlation function

• Go to /input/interferometry/make_noise_source.m and edit the noise source spectrum and the noise source geometry.
• Go to /input/input_parameters.m and set the simulation_mode to “correlation”.
• Go to /code/ and run “[u,t,rec_x,rec_z]=run_forward();”
• The resulting correlation functions will be written to “u”. Neither “u” nor “t” are automatically stored!
• Go to /tools/ and use “plot_recordings(u,t,'vel’)” to plot velocity correlations or “plot_recordings(u,t,’dis’)” to plot displacement correlations.

COMPUTING NOISE SOURCE KERNELS

The computation of noise source kernels proceeds in two steps, as well.

STEP 1: Make measurements and compute adjoint sources

• Go to /tools/. Without actual data (or at least fake data), one can only compute data-independent adjoint sources, for instance adjoint sources for cross-correlation traveltimes. For this, run “make_adjoint_sources(u,0*u,t,'vel','cc_time_shift’)”. This will compute the adjoint source for cross-correlation time shifts performed on velocity correlations. These adjoint sources are written to /input/sources/adjoint/.

STEP 2: Computing the actual kernels

• Go to /input/input_parameters.m and set the simulation_mode to “noise_source_kernel”.
• Go to /code/ and run “[X,Z,K_s]=run_noise_source_kernel();”.
• The kernel as a function of “X” and “Z” is then in “K_s”.
• Go to /tools/ and use “plot_noise_source_kernels(X,Z,K_s)” to plot noise source kernels for specific frequency bands.

COMPUTING NOISE STRUCTURE KERNELS

The computation of noise structure kernels proceeds in three steps.

STEP 1: Make measurements and compute adjoint sources, just as for the computation of noise source kernels.

STEP 2: Compute kernel for the reference station

• Go to /input/input_parameters.m and set the simulation_mode to “noise_structure_kernel”.
• Go to /code/ and run “[X,Z,K_rho]=run_noise_structure_kernel();”
• You can plot the kernel with “pcolor(X,Z,K_rho’)”.

STEP 3: Repeat the same procedure with source (reference station) and receiver (target station) interchanged. Then add both kernels to obtain the complete kernel.