# Forward and inverse acoustic scattering problems involving the mass density

## TL;DR

This paper investigates the inverse problem of retrieving the mass density or wavespeed of a layered medium in 2D acoustic scattering, using explicit solutions and perturbation techniques to improve retrieval accuracy.

## Contribution

It introduces a perturbation-based series solution for the inverse problem, enabling more accurate retrieval of layer properties in acoustic scattering.

## Key findings

- Perturbation series effectively estimates mass density contrast.
- Explicit solutions facilitate inverse problem analysis.
- Numerical results confirm the method's accuracy.

## Abstract

This investigation is concerned with the 2D acoustic scattering problem of a plane wave propagating in a non-lossy fluid host and soliciting a linear, isotropic, macroscopically-homogeneous, lossy, flat-plane layer in which the mass density and wavespeed are different from those of the host. The focus is on the inverse problem of the retrieval of either the layer mass density or the real part of the layer wavespeed. The data is the transmitted pressure field, obtained by simulation (resolution of the forward problem) in exact, explicit form via separation of variables. Another form of this solution, which is exact and more explicit in terms of the mass-density contrast (between the host and layer), is obtained by a domain-integral method. A perturbation technique enables this solution to be cast as a series of powers of the mass density contrast, the first three terms of which are employed as the trial models in the treatment of the inverse problem. The aptitude of these models to retrieve the mass density contrast and real part of the layer wavespeed is demonstrated both theoretically and numerically. Keywords: 2D acoustics, forward scattering, inverse scattering, domain integral equation, constant mass density assumption, small density contrast, retrieval accuracy