A comparison of finite difference and reflectivity seismograms for marine models

Abstract

Finite difference and reflectivity synthetic seismograms are compared for laterally homogeneous seafloor models with step and ramp discontinuities in elastic properties. Given suitable numerical parameters in each case excellent agreement can be obtained. For step discontinuities between a liquid and a solid the explicit finite difference formulation of the elastic wave equation for heterogeneous media is unstable. It is necessary to introduce the boundary conditions specifically at the interface and suitable formulations correct to first and second order in the space increment are given. For ramp discontinuities between a liquid and a solid the finite difference formulation for heterogeneous media is stable and agrees with the reflectivity method when, in the latter case, the gradient is approximated by homogeneous layers thinner than one‐fifth of the minimum compressional wavelength at the upper half‐power frequency. For a step discontinuity between two solids the explicit finite difference formulation of the elastic wave equation for heterogeneous media, although stable, is inaccurate and boundary conditions must again be specifically introduced. Copyright © 1983, Wiley Blackwell. All rights reserved