Wave propagation and imaging in moving random media

TL;DR

This paper develops a transport theory for sound wave propagation in moving, random media and applies it to inverse source imaging, including methods to estimate medium velocity and statistical properties from measurements.

Contribution

It introduces a novel transport framework for waves in moving random media and demonstrates how to perform source imaging and estimate medium parameters from remote measurements.

Findings

Transport theory accurately models wave energy in moving random media.

Source location can be reconstructed using measurements and estimated medium velocity.

Medium velocity estimation is robust even with strong scattering and unknown statistics.

Abstract

We present a study of sound wave propagation in a time dependent random medium and an application to imaging. The medium is modeled by small temporal and spatial random fluctuations in the wave speed and density, and it moves due to an ambient flow. We develop a transport theory for the energy density of the waves, in a forward scattering regime, within a cone (beam) of propagation with small opening angle. We apply the transport theory to the inverse problem of estimating a stationary wave source from measurements at a remote array of receivers. The estimation requires knowledge of the mean velocity of the ambient flow and the second-order statistics of the random medium. If these are not known, we show how they may be estimated from additional measurements gathered at the array, using a few known sources. We also show how the transport theory can be used to estimate the mean velocity of the medium. If the array has large aperture and the scattering in the random medium is strong, this estimate does not depend on the knowledge of the statistics of the random medium.