Inverse random source scattering for the Helmholtz equation with attenuation

TL;DR

This paper introduces a novel inverse scattering model for the Helmholtz equation with attenuation, linking fractional Gaussian sources to wave measurements for unique source characterization.

Contribution

It establishes the connection between fractional Gaussian fields and rough sources, proves well-posedness of the direct problem, and shows unique determination of source micro-correlation from passive measurements.

Findings

Connected fractional Gaussian fields to rough sources.

Proved well-posedness of the direct scattering problem.

Demonstrated unique recovery of source properties from measurements.

Abstract

In this paper, a new model is proposed for the inverse random source scattering problem of the Helmholtz equation with attenuation. The source is assumed to be driven by a fractional Gaussian field whose covariance is represented by a classical pseudo-differential operator. The work contains three contributions. First, the connection is established between fractional Gaussian fields and rough sources characterized by their principal symbols. Second, the direct source scattering problem is shown to be well-posed in the distribution sense. Third, we demonstrate that the micro-correlation strength of the random source can be uniquely determined by the passive measurements of the wave field in a set which is disjoint with the support of the strength function. The analysis relies on careful studies on the Green function and Fourier integrals for the Helmholtz equation.