Inverting the power spectrum for a heterogeneous medium

Abstract

SUMMARY The delta-correlated assumption of the random medium is of considerable significance in statistical wave propagation problems. Assuming the Rytov and parabolic approximations, this work completed an exact derivation of the transverse coherence functions without using the delta-correlated approximation. The error introduced by this approximation is shown to be negligible when the source‐receiver distance is large. Our new formulation shows that the TCF does have limited vertical spectral resolution, in contrast to previous results. We define a new observational variable whose Fourier transform directly yields the power spectral density function of the random medium. This enables a simultaneous determination of the scale and statistical distribution of heterogeneities without assuming the power spectral function a priori.