Increasing stability for inverse acoustic source problems

TL;DR

This paper demonstrates increasing stability in inverse acoustic source problems in three-dimensional space, showing that stability improves with longer observation times due to decay in the source's high time tail.

Contribution

It establishes increasing stability estimates for the acoustic source function in the time domain, linking stability to the separation of variables and source support.

Findings

Stability improves as observation time increases.

High time tail of sources diminishes, enhancing stability.

Provides explicit stability estimates for inverse source problems.

Abstract

In this paper, we show the increasing stability of the inverse source problems for the acoustic wave equation in the full space R3.The goal is to understand increasing stability for wave equation in the time domain. If the time and spatial variables of the source term can be separated with compact support, the increasing stability estimates of the $L^2$-norm of the acoustic source function can be established. The stability estimates consist of two parts: the Lipschitz type data discrepancy and the high time tail of the source functions. As the time increases, the latter decreases and thus becomes negligible.