Stability of a one-dimensional inverse source scattering problem in a multi-layered medium

Abstract

In this paper, a stability result on an inverse source scattering problem is shown for Helmholtz equation in a multi-layered medium. The stability estimate consists of a Lipschitz stability term for low frequencies and a logarithmically unstable term for high frequencies, based on the Green's function of the problem. Moreover, the logarithmic term decreases as the frequency grows, which indicates the stability is almost Lipschitz. This result demonstrates that increasing stability for inverse source scattering problems can be achieved by utilizing multi-frequency measurement data.