About one new precursor of increased seismicity

Abstract

The relevance of the work consists in the need for further development of the use of highprecision mechanical and mathematical methods in the problem of forecasting the increase in seismicity. The aim of the research was to solve the problem of identifying the conditions of resonant behavior of harmoniously oscillating lithospheric plates caused by periodic tidal impacts of the Moon. Methods. Application of the latest mathematical developments in the field of mechanics of deformable stamps published in highly rated journals. The case is being studied when the fault is large enough and the lithospheric plates are removed by the ends. Each of the lithospheric plates turns out to be autonomous and can be considered as a deformable stamp. The latest theory of deformable stamps developed by the block element method is applied. In the course of the research, a new universal modeling method was used that allows solutions of vector boundary value problems for systems of partial differential equations describing materials of complex rheologies to be decomposed according to solutions of individual scalar boundary value problems As a result of the study, the recently developed theory of contact problems with deformable stamps acting on a layered base allowed us to explicitly identify the relations describing the resonant frequencies of harmonically oscillating stamps. The results is applied to a lithospheric plate in the form of a strip of finite width lying on a layered base, modeled by a deformable stamp. For this case, a ratio has been found that allows us to calculate the resonant frequencies indicating the possible destruction of the plate, that is, an earthquake. The appearance of a discrete resonant frequency in contact problems on the action of deformable stamps on a layered medium was predicted in the works of Academician I. I. Vorovich. The need to involve mechanical approaches in the problem of earthquake prediction was expressed by academician G.A. Gamburtsev. Academician M.A. Sadovsky has a position related to the need to take into account the lumpy structure of the earth’s crust, that is, the block structure, in matters of earthquake prediction and the identification of new weather phenomena. Thus, using the new methods used in the work, the possibility of obtaining ratios that allow assessing the degree of danger of destruction of lithospheric plates is proved, since it is possible to obtain all the missing ratios for this.