Seismic wavefield calculation for laterally heterogeneous whole earth models using the pseudospectral method

Abstract

SUMMARY A method for simulating seismic wave propagation in a laterally heterogeneous whole earth model is presented by solving the elastodynamic equations in 2-D cylindrical coordinates using the pseudospectral method (PSM). The PSM is an attractive timedomain technique that uses the fast Fourier transform for an accurate diierentiation of ¢eld variables in the equations. Since no dispersion error arises in Fourier diierentiation, even when using a large grid spacing, computer memoryand time are reduced by several orders of magnitude compared to traditional ¢nite-diierence methods. In order to examine body-wave phases with current computing resources, a slice through the sphere is approximated with a 2-D cylindrical model. An irregular grid spacing is used in the vertical coordinate to improve the treatment of the various structural boundaries appearing in the earth model by matching the heterogeneity in the model. Synthetic seismograms obtained by the PSM calculation are compared with those calculated from an exact simulation method for a spherically homogeneous (1-D) earth model and achieve good agreement. The PSM method is illustrated by constructing the seismic P^SV wave¢eld for strongly heterogeneous earth models including a shield structure near the free surface and velocity perturbations just above the core^mantle boundary. The visualization of the evolution of seismic P and S waves in time and space is tracked using a sequence of snapshots and synthetic seismograms. These displays allow direct insight into the nature of the complex seismic wave behaviour in the Earth’s interior.