Simulation of P-Wave Propagation in a Heterogeneous Spherical Earth: I. Numerical Method

To be able to simulate P-wave propagation in a heterogeneous spherical Earth, we solve the acoustic wave equation in spherical coordinates numerically for axi-symmetric media. We employ a high-order nite-diierence scheme which allows us to simulate arbitrary heterogeneous structures with wavelengths as small as 10km. A standard regular gridding in spherical coordinates leads to a continuously decreasing eeective grid increment towards the Earth's center. To avoid the resulting stability problems we regrid the lateral domain several times thereby drastically improving the stability criterium for whole Earth models. Treatment of the Earth's center in a Carte-sian system allows us to model wave propagation through the center of the Earth. While it is clearly desirable to extend this scheme to elastic media we present the algorithm in the acoustic approximation and show its applicability to simulate whole Earth P-wave propaga-1 tion. In the present implementation waveeelds with cutoo periods of about 4 seconds can be simulated. This suggests that the simulation of short-period P-wave propagation through laterally heterogeneous global Earth models (i.e. in the axi-symmetric approximation) may soon become reality.