Early-warning inverse source problem for the elasto-gravitational equations

TL;DR

This paper investigates an early-warning inverse source problem for elasto-gravitational equations, proving uniqueness and stability in recovering source details from early gravitational measurements, relevant for earthquake warning systems.

Contribution

It introduces a novel inverse problem framework for coupled hyperbolic-elliptic PDEs and establishes theoretical guarantees for source reconstruction under the Cowling approximation.

Findings

Proved uniqueness of source recovery from early gravitational data

Established Lipschitz stability for the inverse problem

Motivated by applications in gravity-based earthquake early warning

Abstract

Through coupled physics, we study an early-warning inverse source problem for the elasto-gravitational equations. It consists of a mixed hyperbolic-elliptic system of partial differential equations describing elastic wave displacement and gravity perturbations produced by a source in a homogeneous bounded medium. Within the Cowling approximation, we prove uniqueness and Lipschitz stability for the inverse problem of recovering the moment tensor and the location of the source from early-time measurements of the changes of the gravitational field. The setup studied in this paper is motivated by gravity-based earthquake early warning systems, which are gaining much attention recently.