# Local recovery of the compressional and shear speeds from the hyperbolic DN map

## TL;DR

This paper demonstrates that local boundary measurements can uniquely determine the compressional and shear wave speeds in an elastic medium, given certain geometric conditions, advancing inverse boundary value problem theory.

## Contribution

It establishes unique local recovery of elastic wave speeds from boundary data under convex foliation conditions, a novel result in inverse elastic problems.

## Key findings

- Local boundary data determines p-wave speed with convex foliation.
- Local boundary data determines s-wave speed with convex foliation.
- Unique determination of wave speeds from boundary measurements.

## Abstract

We study the isotropic elastic wave equation in a bounded domain with boundary. We show that local knowledge of the Dirichlet-to-Neumann map determines uniquely the speed of the p-wave locally if there is a strictly convex foliation with respect to it, and similarly for the s-wave speed.