On features of starting earthquakes at rigid contacts of lithospheric plates with the base

Abstract

The paper reports the results of a study of the strength of fragments of a lithospheric plate with a fault under the assumption that a granite lithospheric plate is rigidly connected to a basalt base along the Conrad border. In this case, one vertical and two horizontal contact stress components arise in the contact zone. Two types of faults are considered. In the first case, the fault banks are at a certain distance, whereas in the second case they are in contact. When solving the boundary value problem by the block element method, the problem of differential factorization of a third-order matrix function is solved exactly. In the process of solving the posed boundary problem, it is possible to accurately implement all the steps of the block element method, which allows us to obtain an exact analytical solution of the boundary problem. As a result, the problem of concentration of contact stresses for two types of faults is accurately solved. In the first case of nonzero distance between the plates, the concentration of contact stresses results in a finite energy of the system. In the second case of contact of the plates, the stress concentrations in each component of the vector of contact stresses leads to infinite energy in the system that is treated as an earthquake. Calculation of the Earth surface displacement in the epicenter zone in the case of a starting earthquake shows that surface motion occurs simultaneously in three directions. This explains the fact that such earthquakes cause greatest seismic damage on the Earth surface.