Problem Statement |
For full-scale field data inversion of the crustal velocity model for Canterbury region, we use the velocity model (140km X 120km X 46km) developed by Lee. et al (2017) as the initial model and a test configuration including 43 seismic stations (not equally spacing at every 10km) and 146 earthquake to start the inversion. The observed data are processed including filtering from 0.02Hz to .5Hz, windowing to use only significant part of the signals. The source locations, magnitudes and shapes are determined prior to the inversion. A visco-elastic forward modelling is applied with consideration of the spatial attenuation from the observed data. After a number of inversion iterations, the final inverted model using FWT has matched well with the given 1-D model and the misfit error has significantly decreased. |
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).
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Schedule |
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Verification |
Verifying the inverted result using FWT - Adjoint Wavefield method with FWT-Scattering Integral or SASW methods. |