Imaging nonlinearity coefficient and sound speed with the JMGT equation in frequency domain

TL;DR

This paper establishes the uniqueness and stability of reconstructing sound speed and nonlinearity coefficients in the JMGT equation using frequency domain observations, advancing nonlinear acoustics imaging techniques.

Contribution

It introduces a multiharmonic expansion approach for coefficient reconstruction in the JMGT equation, connecting nonlinear acoustics with frequency domain analysis.

Findings

Proved uniqueness and stability of coefficient reconstruction.

Derived regularization properties as relaxation time tends to zero.

Linked JMGT and Westervelt equations through reconstruction analysis.

Abstract

In this paper we prove uniqueness and stability of reconstruction of two coefficients (sound speed and nonlinearity parameter) in the Jordan-Moore-Gibson-Thompson JMGT equation of nonlinear acoustics, relying on observations resulting from only two sources. A key tool for this purpose is a multiharmonic expansion of the PDE solution, which reflects the physical phenomenon of higher harmonics appearing due to nonlinearity and allows us to work in frequency domain. Based on this result, we derive a regularization property of reconstruction with JMGT as the relexation time tends to zero (in the spirit of a quasi reversibility method) for reconstruction from the classical Westervelt equation.