Stochastic Strike-Slip Fault as Earthquake Source Model

It is known that the source of a tectonic earthquake in the framework of the theory of elasticity and viscoelasticity is considered to be displacement along a certain fault surface. Usually, when describing a source, the geometry of the fault surface is simplified to a flat rectangular area. The displacement vector is assumed to be constant. In this paper, we propose a model of an earthquake source in the form of a displacement with a constant vector along a stochastic uneven surface. A number of standard assumptions are made during the modeling. We take into account only the elastic properties of the medium. We consider the Earth's crust as a half-space and assume that the medium is homogeneous and isotropic. For the mathematical description of the earthquake source, we use the classical force equivalent of displacement along the fault. This is the distribution of double pairs of forces. The field of displacements under the action of body forces is found through a combination of Mindlin nuclei of strain. The paper presents numerical analytic solutions for displacement along the strike-slip fault corresponding to one of an earthquake source mechanism. We propose to introduce a random deformation of a rectangular flat fault surface. The paper shows the results of a computational experiment comparing the levels and regions of relative deformations of the Earth's crust in the case of displacement along a flat fault surface and along a stochastic uneven one. In the case of a stochastic fault surface, the regions of relative deformations become asymmetric. Such differences from the classical case can be useful for an explanation as to why in some cases the simulation results differ from the results of observations.