PARAMETRIZED SHOOTING OF SEISMIC RAYS IN A SPHERICAL EARTH WITH DISCONTINUITIES

Abstract

The parametrized shooting method is extended to 3-D seismic ray tracing in a spherical earth with discontinuities. A shooting vector at a seismic source is iteratively updated by using numerical integrals of several variables and Snell's Law in spherical coordinates is matched at the discontinuities. The computational accuracy and efficiency of this method are demonstrated by tracing rays for various velocity models and comparing results with analytical solutions and results from the bending, pseudo-bending and finite difference methods. The parametrized shooting is very efficient in an earth with a smooth velocity field and it is reduced by the introduction of discontinuities or rapid velocity changes. Numerical instability can occur with the parametrized shooting in a velocity gradient greater than 10 per cent, but the degree of this instability is not as serious as in the bending method.