Introduction

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Introduction

Reciprocity principles in wave propagation problems are well known and mathematical aspects are detailed in Morse and Feshbach [(Morse and Feshbach,1953)] and with applications to seismic data in Aki and Richards [(Aki and Richards,1980)]. Those descriptions are based on a symmetry property of the Green's funtions for the underlying wave propagation operator. Full wave equation theory is the basis for those investigations. Knopoff and Gangi [(Knopoff and Gangi,1959)] and Gangi [(Gangi,1980)] verify reciprocity principles in measurements for seismic waves on the laboratory scale. Fenati and Rocca [(Fenati and Rocca,1984)] demonstrate reciprocity in field data to a remarkable degree, even though their source and receiver geometry/type were not exactly reciprocal. All these investigations have been concerned with full dynamic reciprocity principles, not just traveltime, but full waveform reciprocity. Razavy and Lenoachca [(Razavy and Lenoachca,1986)] have investigated the influence of analytical and numerical approximations on reciprocity principles, which becomes important when using approximate solutions and reciprocity arguments together in a wave propagation problem.

Based on these findings, I will show that my particular finite-difference approximation to the elastic wave equations maintains reciprocity and I will show two field data examples of 9 component data showing reciprocity (or lack thereof).