On features of starting earthquakes at rigid contacts of lithospheric plates with the base
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O R I G I NA L PA P E R
Vladimir A. Babeshko Olga M. Babeshko
· Olga V. Evdokimova ·
On features of starting earthquakes at rigid contacts of lithospheric plates with the base
Received: 8 June 2020 / Revised: 21 August 2020 / Accepted: 5 September 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
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.
1 Introduction In earlier works of the authors, the problem of forecasting a recently classified new type of earthquakes, called the “starting one”, was considered. They occur in the Earth’s crust at the time of complete convergence of lithospheric plates. Their origin is related to the concentration of contact stresses under the plates. The problem was considered under the assumption that the lithospheric plates and layered bases under them are linear elastic. The layered bases are modeled by three-dimensional bodies, while the lithospheric plates, according to scales of the Earth, are considered as Kirchhoff plates. The concentration of stresses under the plates for their different mutual positions at their convergence ends is investigated. Contact conditions are considered, either without tangential stresses, or without normal stresses between the plates and the base. Vladimir A. Babeshko (B) · Olga V. Evdokimova Southern Scientific Center of Russian Academy of Science, Chekhov st., 41, Rostov-on-Don, Russia 344006 E-mail: [email protected] Olga V. Evdokimova E-mail: [email protected] Olga M. Babeshko Kuban State University, Stavropolskaya, 149, Krasn
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