Increasing stability for inverse acoustic source problems in the time domain

Abstract

This paper is concerned with the inverse source problems for the acoustic wave equation in the full space $R^3$, where the source term is compactly supported in both time and spatial variables. The main goal is to investigate increasing stability for the wave equation in terms of the interval length of given parameters (e.g., frequency bandwith of the temporal component of the source function). We establish increasing stability estimates of the $L^2$-norm of the source function by using only the Dirichlet boundary data. Our method relies on the Huygens' principle, the Fourier transform and explicit bounds for the continuation of analytic functions.