THE ACCURACY OF THE ODOHERTY-ANSTEY APPROXIMATION FOR WAVE-PROPAGATION IN HIGHLY DISORDERED STRATIFIED MEDIA

A pulse propagates normally through a stratified medium. It is known f rom numerical experiments and heuristic arguments that under certain c ircumstances, including those arising in seismic exploration, the shap e and precise travel time of the forward propagating pulse as it trave ls over large distances depends to a good approximation only upon the autocorrelation function of the medium properties. The expression for this dependence is surprisingly simple and is known as the O'Doherty-A nstey approximation after the authors who first derived it in 1971. We give a theoretical estimate of the error committed in making this app roximation. The analysis proceeds by first obtaining a closed equation governing the evolution of the propagation mode of interest. There is an interesting interplay of frequency- and time-domain considerations . Thus the error is frequency dependent, but depends also on the lengt h of time for which the signal is to be computed. In contrast to earli er related work we give a rigorous error estimate, which is derived in a deterministic context, without the use of small or large parameters . Some previous results involving limits as small parameters tend to z ero are recovered by application of our general estimate.