Acoustic nonlinearity parameter tomography with the Jordan-Moore-Gibson-Thompson equation in frequency domain

TL;DR

This paper develops a frequency domain approach using the Jordan-Moore-Gibson-Thompson equation to achieve local uniqueness in reconstructing the nonlinear acoustic parameter from boundary data, with potential for practical inversion methods.

Contribution

It introduces a novel frequency domain formulation for acoustic nonlinearity tomography based on the JMGT equation, proving local uniqueness and discussing a regularized Newton reconstruction method.

Findings

Proved local uniqueness of the nonlinearity parameter from boundary measurements.

Established convergence of a regularized Newton method for parameter reconstruction.

Demonstrated the effectiveness of the frequency domain approach in nonlinear acoustics.

Abstract

This paper aims to combine the advantages of the Jordan-Moore-Gibson-Thompson JMGT equation as an advanced model in nonlinear acoustics with a frequency domain formulation of the forward and inverse problem of acoustic nonlinearity parameter tomography, enabling the multiplication of information by nonlinearity. Our main result is local uniqueness of the space dependent nonlinearity parameter from boundary measurements, which we achieve by linearized uniqueness with an Implicit Function type perturbation argument in appropriately chosen topologies. Moreover, we shortly dwell on the application of a regularized Newton type method for reconstructing the nonlinearity coefficient, whose convergence can be established by means of the linear uniqueness result.