Source estimation with incoherent waves in random waveguides

TL;DR

This paper investigates an inverse source problem in a random waveguide, utilizing incoherent wave measurements to estimate the source, accounting for boundary and medium fluctuations that cause scattering and wave decoherence.

Contribution

It introduces a method to estimate sources from incoherent wave data in random waveguides, leveraging the theory of wave propagation and mode energy transport.

Findings

High fidelity estimates of waveguide mode energy can be obtained from incoherent measurements.

The invertibility of the transport system enables accurate source reconstruction.

Random fluctuations cause exponential decay of coherent wave components, emphasizing the importance of incoherent analysis.

Abstract

We study an inverse source problem for the acoustic wave equation in a random waveguide. The goal is to estimate the source of waves from measurements of the acoustic pressure at a remote array of sensors. The waveguide effect is due to boundaries that trap the waves and guide them in a preferred (range) direction, the waveguide axis, along which the medium is unbounded. The random waveguide is a model of perturbed ideal waveguides which have flat boundaries and are filled with known media that do not change with range. The perturbation consists of fluctuations of the boundary and of the wave speed due to numerous small inhomogeneities in the medium. The fluctuations are uncertain in applications, which is why we model them with random processes, and they cause significant cumulative scattering at long ranges from the source. The scattering effect manifests mathematically as an exponential decay of the expectation of the acoustic pressure, the coherent part of the wave. The incoherent wave is modeled by the random fluctuations of the acoustic pressure, which dominate the expectation at long ranges from the source. We use the existing theory of wave propagation in random waveguides to analyze the inverse problem of estimating the source from incoherent wave recordings at remote arrays. We show how to obtain from the incoherent measurements high fidelity estimates of the time resolved energy carried by the waveguide modes, and study the invertibility of the system of transport equations that model energy propagation in order to estimate the source.