Early-Warning Inverse Source Problem for the Elasto-Gravitational Equations

Through coupled physics, we study an early-warning inverse source problem for the constant-coefficient 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.