Reciprocity principle and the approximate solution of the wave equation

Abstract In this paper, we examine the validity of reciprocity when certain approximations are applied to the wave equation. We focus on some of the approximation techniques which are frequently used in investigating seismic waves, particularly in the context of synthetic seismograms, namely, asymptotic ray theory and finite difference methods. The main result is that the reciprocity property is not necessarily preserved when an approximation is used. This conclusion is shown to be valid for both ray theory and finite difference techniques. We give some concrete examples as well as numerical results to illustrate the practical effect of nonreciprocity. We also show that reciprocity breaks down when analytical approximation is required to solve the problem in question .