Forward Modeling

A forward calculation predicts surface-wave travel times for a given model. It can be used to compute residuals for a reference model, or to build the synthetic observations of a checkerboard test.

Command SURFATT_tomo -f

This command predict synthetic traveltime from existing model.

 Usage: SURFATT_tomo -i para_file [-f] [-h]

 Adjoint-state travel time tomography for surface wave

 required arguments:
  -i para_file  Path to parameter file in yaml format

 optional arguments:
  -f            Forward simulate travel time instead of inversion (default: false)
  -h            Print help message

With -f, the run stops after one forward calculation:

mpirun -np 8 SURFATT_tomo -i input_params.yml -f

Set model.init_model_type: 2 and model.init_model_path to run the forward calculation through an existing 3-D model, for example the final_model.h5 of a previous inversion.

Command SURFATT_cb_fwd

This command create a checkerboard model and predict synthetic traveltime data from it.

 Usage: SURFATT_cb_fwd -i para_file -n nx/ny/nz [-h] [-m margin_degree] [-p pert] [-s anom_size_km]

 Create checkerboard and forward simulate travel time for surface wave

 required arguments:
  -i para_file             Path to parameter file in yaml format
  -n nx/ny/nz              Number of anomalies along X, Y and Z

 optional arguments:
  -h                       Print help message
  -a nx/ny/nz[/angle]      Add azimuthal anisotropy anomalies with optional angle (deg, default: 120)
  -r                       Use radial anisotropy instead of azimuthal (cannot be used with -a)
  -v                       Only perturb Vs model, default: false
  -m margin_degree         Margin between anomalies to boundary in degrees (default: 0)
  -p pert_vel[/pert_ani]   Magnitude of velocity/anisotropy perturbations
                           For azimuthal: -p pert_vel[/pert_gc_gs] (default: 0.08)
                           For radial: -p pert_vs[/pert_zeta] (default: 0.08)
  -s anom_size_km          Size of top anomalies in km (default: uniform)

How the checkerboard is built

• -n nx/ny/nz gives the number of anomalies along longitude, latitude, and depth. The perturbation is the product of one sinusoid per direction.
• -m margin_degree leaves an unperturbed band of the given width in degrees along the horizontal edges of the model, which keeps the anomalies away from the poorly covered boundary.
• -s anom_size_km indicates the thickness of the shallow layer anomaly. Default setting is each layer has even thickness.
• -v perturbs $V_s$ only. By default, $V_p$ and $\rho$ are recomputed from the perturbed $V_s$ with the empirical Brocher (2005) relations.

Anisotropic checkerboards

• -a nx/ny/nz[/angle] adds azimuthal anisotropy anomalies with their own block layout and a fast axis at angle degrees. Blocks of the opposite sign get a fast axis rotated by $90^\circ$. Their amplitude is set by the second value of -p.
• -r adds radial anisotropy. The $\zeta$ perturbation uses the same block layout as $V_s$, and its amplitude is the second value of -p.

Outputs

Both commands write to output.output_path:

• src_rec_file_forward_<TAG>.csv: the synthetic travel times, one file per activated data set. <TAG> is RL_PH, RL_GR, LV_PH, or LV_GR. The file has the same columns as the input table, with tt, dist, and vel filled with the calculated values.
• initial_model.h5: the unperturbed starting model, when output.output_initial_model is True.
• target_model.h5: the perturbed checkerboard model. Written by SURFATT_cb_fwd only.

Example: synthetic data for a checkerboard test

The examples first copy the observed geometry to the file name that the parameter file declares, then let the forward run replace its travel times:

mkdir -p OUTPUT_FILES
cp src_rec_file_ph.csv OUTPUT_FILES/src_rec_file_forward_RL_PH.csv
 
# 2 x 3 x 2 isotropic checkerboard, 8% Vs perturbation, 0.2 degree margin
mpirun -np 8 SURFATT_cb_fwd -i input_params.yml -n 2/3/2 -m 0.2 -p 0.08
 
# invert the synthetic travel times
mpirun -np 8 SURFATT_tomo -i input_params.yml

For a radial-anisotropy test, both Rayleigh and Love data are activated, and -r adds a $\zeta$ checkerboard:

mkdir -p OUTPUT_FILES
cp src_rec_file_ph.csv OUTPUT_FILES/src_rec_file_forward_RL_PH.csv
cp src_rec_file_ph.csv OUTPUT_FILES/src_rec_file_forward_LV_PH.csv
 
mpirun -np 8 SURFATT_cb_fwd -i input_params.yml -n 2/3/2 -s 2 -r -m 0.2 -p 0.08/0.08

Complete cases are described in the Synthetic Examples section.