During a seismic event, the rupture and the propagation of seismic waves redistribute masses within the Earth. This mass redistribution generates in turn a dynamic long-range perturbation of the Earth gravitational potential, which can be recorded before the arrival of the direct seismic waves. A ground-based seismometer then records a gravity-induced inertial acceleration in addition to the gravitational potential perturbation: we refer to the overall signal as elasto-gravitational perturbation. We present a normal-mode simulation of elasto-gravitational perturbations, as recorded by a ground-based seismometer. The normal-mode approach enables the computation of elasto-gravitational signals in uniform and layered spherical Earth models, wi...