# On finding a buried obstacle in a layered medium via the time domain enclosure method

## TL;DR

This paper develops a method to detect and analyze a penetrable obstacle in a layered medium using wave observations in the time domain, providing insights into the obstacle's geometry and properties.

## Contribution

It introduces an indicator function based on the time domain enclosure method for inverse obstacle problems in layered media, revealing geometric and qualitative obstacle information.

## Key findings

- The indicator function can determine the obstacle's shape and location.
- Asymptotic analysis yields qualitative properties of the obstacle.
- Method applicable to penetrable obstacles in layered environments.

## Abstract

An inverse obstacle problem for the wave equation in a two layered medium is considered. It is assumed that the unknown obstacle is penetrable and embedded in the lower half-space. The wave as a solution of the wave equation is generated by an initial data whose support is in the upper half-space and observed at the same place as the support over a finite time interval. From the observed wave an indicator function in the time domain enclosure method is constructed. It is shown that, one can find some information about the geometry of the obstacle together with the qualitative property in the asymptotic behavior of the indicator function.