# A logarithmic estimate for inverse source scattering problem with attenuation in a two-layered medium

## TL;DR

This paper establishes a logarithmic stability estimate for the inverse source problem of the 1D Helmholtz equation with attenuation in a two-layer medium, using multiple frequencies at domain endpoints.

## Contribution

It introduces a new stability estimate for the inverse source problem in a layered medium with attenuation, leveraging multi-frequency data at boundary points.

## Key findings

- Logarithmic stability estimate derived for the inverse problem.
- Effective use of multiple frequencies enhances stability.
- Applicable to layered media with attenuation effects.

## Abstract

The paper aims a logarithmic stability estimate for the inverse source problem of the one-dimensional Helmholtz equation with attenuation factor in a two layer medium. We establish a stability by using multiple frequencies at the two end points of the domain which contains the compact support of the source functions.