On the reconstruction of parameters of a moving fluid from the Dirichlet-to-Neumann map

TL;DR

This paper develops formulas to uniquely recover fluid parameters in acoustic tomography by eliminating gauge ambiguities using multi-frequency boundary measurements, building on previous partial reconstructions.

Contribution

It introduces a method to remove gauge non-uniqueness and recover all fluid parameters from boundary data at multiple frequencies, extending prior partial results.

Findings

Formulas for gauge elimination in inverse problems

Recovery of fluid parameters at multiple frequencies

Extension of existing reconstruction methods

Abstract

We consider an inverse boundary value problem for a model time-harmonic equation of acoustic tomography of moving fluid with variable current velocity, sound speed, density and absorption. In the present article it is assumed that at fixed frequency the coefficients of this equation are already recovered modulo an appropriate gauge transformation using some reconstruction method from boundary measurements presented in the literature. Our main result consists in formulas and equations that allow to get rid of this gauge non-uniqueness and recover the fluid parameters using boundary measurements at several frequencies.