## Frozen Gaussian approximation with applications in seismology

- Feb. 20, 2017
- 1:15 p.m.
- LeConte 312

## Abstract

We propose the frozen Gaussian approximation (FGA) for the computation of high frequency wave propagation. This method approximates the solution to the wave equation by an integral representation. We also present a systematic introduction on applying FGA to compute synthetic seismograms in three-dimensional earth models. In the method, seismic wavefield is decomposed into frozen (fixed-width) Gaussian functions, which propagate along ray paths. Rather than the coherent state solution to the wave equation, this method is rigorously derived by asymptotic expansion on phase plane, with analysis of its accuracy determined by the ratio of short wavelength over large domain size. Similar to other ray-based beam methods (e.g. Gaussian beam methods), one can use relatively small number of Gaussians to get accurate approximations of high-frequency wavefield. The algorithm is embarrassingly parallel, which can drastically speed up the computation with a multicore-processor computer station. Furthermore, we incorporate the Snell's law into the FGA formulation, and asymptotically derive reflection, transmission and free surface conditions for FGA to compute high-frequency seismic wave propagation in high contrast media. We numerically test these conditions by computing traveltime kernels of different phases in the 3D crust-over-mantle model. This is joint work with Lihui Chai and Ping Tong.