Inversion of the crustal velocity model for Canterbury region

Problem Statement

For synthetic study of FWT, we use a 1-D velocity model of 60km X 40km X 20km as the true model. We use a homogenous model as the initial model and a test configuration including 12 receivers (3 X 4, equally spacing at every 10km) and 6 sources (2 X 3, equally spacing at every 10km) to generate the synthetic observed data for inversion. The wavefields are generated by numerical solutions of the 3-D elastodynamic/ visco-elastodynamic equations according to a specific velocity model and then compared with the synthetic observed data to extract the misfit between the current model with the true model. After a number of inversion iterations, the final inverted model using FWT has matched well with the given 1-D model.

Tasks

Forward modeling of the elastic wave propagation for the 1-D model to create the synthetic observed data.

• Choosing a 1-D velocity model as the true model.

• Choosing the cell size for the staggered grid using in forward simulation (0.2 km) and a stable time step according to the CFL criteria.

• Specifying station and source locations; recorded components of the wavefields at the station locations.

• Describing the source signal: using a Ricker wavelet with the central frequency of .5Hz, specifying the recorded time and the time delay for the source.

Inversion: specify the number of iterations, optimization method or optimal step length (if applicable) and follow the steps for doing inversion at one iteration:

• Forward modeling of the elastic wave propagation for the 1-D model to create the synthetic observed data and storing the forward velocity wavefields at every grid cell and for every subsampled time step.

• Calculate the displacement residual between the observed and estimated data.

• Backward propagation of the displacement residual at all stations for each and every source and store the backward velocity wavefields at every grid cell and for every subsampled time step.

• Calculation of the sensitive kernels (using 3 components of ground motion velocity wavefields or 6 components of stress wavefields).

• Preconditioning of the kernels to suppress the near source and receiver artifacts.

• Update of the model with the optimal search direction (using fixed or optimized step lengths; applying Conjugate Gradient or BFGS methods; implementing regularization).

Schedule

Verification

Verifying the inverted result using FWT - Adjoint Wavefield method with FWT-Scattering Integral or SASW methods.