An Improved Representation of Boundary Conditions in Finite Difference Schemes for Seismological Problems

Abstract

A finite difference scheme is developed for seismological problems, containing a new treatment of surface and interface boundary conditions. The new representations of boundary conditions are associated with truncation errors of the second order, while previous representations were of the first order only. We show by comparison with analytical solutions that increasing the accuracy of the representation of boundary conditions increases the order of accuracy of the whole solution. The present scheme can be programmed easily and applied to seismological problems. We illustrate this by solving the problem of pulse propagation in two models of rift valley, and in the vicinity of an elastic wedge embedded in another elastic space.