Recent Movements of the Earth’s Surface and Stress Propagation in the Elastic Upper Crust

Abstract

The Earth’s crust is modeled by a thin elastic plate, whereas the underlying lithosphere by a half-space with viscous fluid rheology. For this system, with the use of the Fourier transform with respect to horizontal coordinates and the Laplace transform with respect to time, the solutions of continuum mechanics equations are obtained in the form of the diffusion type waves which propagate with strong attenuation from the initial perturbation domain across the Earth’s surface and cause its displacements. Analytical formula for these waves is obtained for the case of a point initial perturbation, which explicitly links the Earth’s surface displacements and stresses in the elastic crust with the horizontal coordinates and time. The diffusion waves (inertialess Rayleigh and Love waves) can be considered as a mechanism of recent vertical and horizontal movements of the Earth’s crust. The inertialess Rayleigh waves restore the isostatic equilibrium of the Earth’s crust which is disturbed by the initial vertical displacement of the Earth’s surface. In the case when an inertialess Love wave propagates along a locked fault from a segment where the fault has ruptured which was accompanied by an earthquake, this wave lowers the normal stress applied to the fault’s side and, hence, reduces the friction force thus facilitating rupture on a remote part of the locked fault and causing a new earthquake.