The fundamental nature of a transient elastic response to prompt gravity perturbations

SUMMARY Seismic waves radiated from an earthquake induce mass redistribution in the Earth, which in turn generates prompt gravity perturbations at all distances before the arrival of seismic waves. Here, we obtain an analytic solution for the transient elastic response to prompt gravity perturbations induced by a portion of earthquake mass redistribution in an infinite homogeneous isotropic non-self-gravitation elastic medium. This solution reveals the fundamental nature of an unusual net-inner-force-free deformation regime that emerges between the onset of an earthquake and P-wave arrival, which we find inherent in action at a distance with the inverse-square law. These results provide physical insights into why a gravimeter installed in the Earth is characterized by significantly decreased sensitivity to earthquake-induced prompt gravity perturbations.