Stable determination of polyhedral interfaces from boundary data for the Helmholtz equation

TL;DR

This paper establishes a Lipschitz stability estimate for determining polyhedral interfaces in the Helmholtz equation from boundary measurements, advancing inverse boundary value problem theory.

Contribution

It provides the first Lipschitz stability result for reconstructing tetrahedral partitions with piecewise constant wavespeeds from boundary data.

Findings

Lipschitz stability estimate derived for tetrahedral partitions

Unique determination of interfaces from boundary measurements

Quantitative bounds on partition reconstruction accuracy

Abstract

We study an inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map as the data. We consider piecewise constant wavespeeds on an unknown tetrahedral partition and prove a Lipschitz stability estimate in terms of the Hausdorff distance between partitions.