# KAUST-IAMCS Workshop on Multiscale Modeling, Advanced Discretization Techniques, and Simulation of Wave Propagation

## Gerard Schuster, King Abdullah University of Science and Technology Multiscale and Multisource Phase Encoded Seismic Inversion

### Abstract

Full waveform inversion (FWI) of seismic data has the potential to provide unprecedented views of the earth's velocity and density distributions. The idea is to find the velocity and density models that can best predict all of the waveforms in observed seismic data $$d_{\text{obs}}$$ generated and recorded with seismic experiments. There are two significant problems with this method: lack of robust convergence to the true solution and enormous computational demands to generate simulated data $$d_{\text{syn}}$$ for millions of synthetic seismic traces. To partly overcome the problem of getting stuck in the local minima of the data misfit function $$\left\|d_{\text{obs}}-d_{\text{syn}}\right\|^{2}$$, multiscale methods initiate the iterative gradient optimization methods with low-pass filtered data. These low-pass filtered data have many fewer local minima in the misfit function and so the gradient method tends to converge rather quickly to a somewhat accurate representation of a smoothed earth model. Higher frequencies are then allowed into the input data and the gradient method will tend to converge to higher-wavenumber estimates of the model. This multiscale strategy is continued until acceptable earth models are computed. The second significant problem of enormous computational cost is tackled by a multisource phase-encoded inversion method. It is shown that the cost of FWI can be reduced by several orders of magnitude if the seismic data are phase-encoded and blended together to form a much smaller data set to be inverted. Examples of FWI are shown for both synthetic data and field data. The following issues are still a subject of research:

1. Comprehensive inclusion of the actual physics into the waveform simulations
2. Correct parameterization of the model to achieve a unique and accurate solution
3. Accurate assessment of solution reliability