Pulse propagation in random media

Abstract

Wave propagation in randomly fluctuating media is a problem of continuing interest in ocean acoustics. Usually the work done in this field is carried out in the frequency domain since there are powerful techniques to study wave scattering in the frequency domain, while time-domain formulations are notoriously more difficult to use and obtain results. Nevertheless, our intuition about wave phenomena is much better when discussing such phenomena in a space-time formulation than in a space-frequency formulation. In this presentation wave propagation in a weakly and randomly fluctuating medium is discussed entirely within the space-time formulation. McDonald and Kuperman derived from the wave equation an approximate time-domain progressive wave equation which is the equivalent in the space-time formulation of the well-known parabolic wave equation in the space-frequency formulation. A path integral representation for the solution of this equation is used here to study wave propagation in random media. The weakly inhomogeneity assumption yields an approximate evaluation of the path integral for the Green’s function thus allowing an analysis of the time-dependent statistics of acoustic fields propagating through random media. [Work supported by ONR.]