Stability on the one-dimensional inverse source scattering problem in a two-layered medium

TL;DR

This paper investigates the stability of the inverse source scattering problem for the 1D Helmholtz equation in a two-layered medium, demonstrating that multi-frequency data at interval endpoints enhances stability.

Contribution

It introduces a method to achieve increasing stability using multi-frequency wave fields at the endpoints of the interval in a layered medium.

Findings

Multi-frequency data improves stability in inverse problems.

Stability increases with the use of boundary measurements at multiple frequencies.

The approach applies to one-dimensional layered media.

Abstract

This paper concerns the stability on the inverse source scattering problem for the one-dimensional Helmholtz equation in a two-layered medium. We show that the increasing stability can be achieved by using multi-frequency wave field at the two end points of the interval which contains the compact support of the source function.