The purpose of this work is the development of mechanical and mathematical methods for identifying faults as seismogenerating zones in the system of block divisibility of the earth's crust. In this paper we present an approach to study of the stress-strain state of lithospheric structures near faults based on their modeling with Kirchhoff plates on an elastic foundation. We implemented method for solving problems for models of rectilinear faults in spatial and plane formulations based on the transformation of a differential operator. The method is represented by the example of the problem of vibration under the effect of the concentrated surface load of two extended plates with a common boundary on the surface of an elastic layer. The system of integro-differential equations is derived from the plates displacement equations, the relations between displacements and stresses on the surface of the elastic substrate, and the conditions of its conjugation with the coating, the transformation of the operator of this system of equations allows us to reduce it to a system of functional equations solved by the Wiener-Hopf method. The described approach provides an analytical representation of the solution of the posed problem and can be used as a control method when checking the limit solutions of the problems for faults of complex shape based on the topological method of the block element. Numerical implementation of the developed algorithm made it possible to carry out model calculations and analyze the results with varying physical and mechanical characteristics of the plates and the elastic substrate. The proposed approach makes it possible to analyze the resulting surface displacements under vibration effects for different contact conditions in the fault region. Using of the described method will make it possible to draw conclusions applicable for studying the structure of faults in the upper part of the earth's crust about the influence of the fault type, physical and mechanical properties of the lithospheric structures on the nature of the wave process in the geological environment, in particular the waveform after passing through the fault.

В работе представлен подход к исследованию напряженно-деформированного состояния литосферных структур вблизи разломов посредством моделирования их пластинами Кирхгофа на упругом основании. Реализован метод решения задач, описывающих модели для прямолинейных разломов, в пространственной и плоской постановках, основанный на преобразовании дифференциального оператора. Предложенный подход позволяет провести анализ полученных смещений поверхности в условиях вибрационных воздействий для различных условий контакта в области разлома. Использование описанного метода позволит сделать применимые для изучения структуры разломов в верхней части земной коры выводы о влиянии типа разлома и физико-механических свойств литосферных структур на характер волнового процесса в геологической среде.