A comparison of synthetic seismograms of core phases generated by the full wave theory and by the reflectivity method

Abstract

Summary. Because the computation of synthetic seismograms has become an invaluable tool for the study of the Earth, it is of major interest to know whether two different methods, the reflectivity method and the full wave theory, generate identical record sections when applied to the same body wave problem. The full wave theory employs approximations by assuming decoupling of P and SV potentials in arbitrarily thick radially inhomogeneous layers and by representing radial eigenfunctions by the first term in a uniformly asymptotic series. The reflectivity method employs approximations by transforming depth-dependent variables of a spherically symmetric Earth to those of a plane-layered medium and by replacing this medium by a stack of homogenous layers. We have compared record sections generated by the two methods using the same Earth model, source parameters, distance ranges and body waves. Specifically, we examined core phases, which should provide a stringent comparison because they contain a wide range of frequencydependent phenomena including diffraction and the effects that arise from a cusp and a caustic. It is found that the synthetic record sections of the two techniques are identical when displacements are low-pass filtered. This is the case for many practical purposes, for displacement generally must be convolved with an instrument response and a source function of several seconds