Full Waveform Tomography page

Full Waveform Tomography (FWT) based on the Adjoint-Wavefield (AW-FWT) and Generalized Seismological Data Functionals (GSDF) methods to iteratively invert an initial 3-D crustal model for the Canterbury region. In FWT, 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 observed data to extract the misfit between the current model with the true model. For inversion, a number of misfit measurements based on 146 earthquake seismograms for 43 seismic stations in the Canterbury region are used as the observed data.

After a number of inversion iterations, the final inverted model using FWT has good potential for more accurate simulation of ground motion for the Canterbury region, and provides a platform for extension of this method to the wider New Zealand region.

Andrei Nguyen, Brendon Bradley, and Robin Lee

Description (Objectives / Outcomes)

1. Synthetic study of FWT for a 1-D velocity model.

2. Inversion of the crustal velocity model for Canterbury region.

Tasks

Forward modeling of the elastic wave propagation and storing the forward velocity wavefields at every grid cell and for every subsampled time step:

• Source description.

• Velocity model.

• Station list.

Development of the adjoint simulation based on backward propagation of the displacement residual at all stations or use of the time-reversed velocity field at one particular station as the adjoint source:

• Backward propagation of the displacement residual at all stations:

1. Calculate the displacement residual at all stations

2. Do backward simulation for NS (number of sources).

• Use of the time-reversed velocity field at one particular station as the adjoint source:

1. Pick-up part of the observed data for a specific channel (eg. SH wavefield or P-SV wavefield) to be used as the adjoint source.

2. Determine the station-specific GSDF adjoint fields , which involves NR (number of stations) of simulation.

Calculation of the sensitive kernels and update of the models:

• Do gradient calculation separately from the backward simulation OR do adjoint simulation together with reconstruction of the forward wavefield and calculation of the sensitive kernels.

• Do gradient preconditioning and regularization.

• Choose step lengths (fixed percentage of perturbing the current model or optimal step length).

• Choose stop criteria for the iteration process (after 20 iterations or no more optimal step length found).

Comparison of existing FWT methods

Schedule