Numerical testing in determination of sound speed from a part of boundary by the BC-method

TL;DR

This paper demonstrates numerical testing for determining the sound speed in an acoustic medium using the boundary control method, focusing on partial boundary data and time-optimal recovery within the covered subdomain.

Contribution

It provides a numerical validation of the BC-method for inverse acoustic problems with partial boundary data, emphasizing time-optimal determination of sound speed.

Findings

Sound speed can be numerically recovered in subdomains covered by acoustic rays.

The method is effective with partial boundary data.

Longer observation times expand the recoverable subdomain.

Abstract

We present the results of numerical testing on determination of the sound speed $c$ in the acoustic equation $u_{tt}-c^2\Delta u=0$ by the ${\it boundary}$ ${control}$ ${method}$. The inverse data is a response operator (a hyperbolic Dirichlet-to-Neumann map) given on controls, which are supported on ${\it a part}$ of the boundary. The speed is determined in the subdomain covered by acoustic rays, which are emanated from the points of this part orthogonally to the boundary. The determination is ${\it time-optimal}$: the longer is the observation time, the larger is the subdomain, in which $c$ is recovered. The numerical results are preceded with brief exposition of the relevant variant of the BC-method.