  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.
