We propose an approach to the study of stress-strain state of lithospheric plates containing faults that is quite reliable, given the scale, and consists in modeling of their structures by two-dimensional plates on the three-dimensional elastic substrate. A method for studying the interactions of different types of lithospheric plates with rectilinear faults, which is a modification of the eigenfunction method using the method of block element is described. The method is considered on the example of the solution of the static problem and the problem of steady oscillations of extended plates on the surface of the elastic layer at a predetermined localized surface load. It's advantage lies in the possibility of its application to the study of stress-strain state of structures with faults, under the influence of vibration loads, and also in the process of slow or static interaction. The use of the proposed approach allows to draw conclusions about the impact of the type of fracture and physical-mechanical properties of the lithosphere structures on the character of the wave process in the geological environment, in particular the shape of the signal after passing through the fault, applicable for the study of the fault structure in the upper crust. Since experimental studies of the seismic signal transmission through the fault and features of the interaction of lithospheric structures at faults require significant material and time costs, the theoretical results obtained in this study will allow testing of fracture types of the lithospheric structures using vibroseismic sources while rationally defining the programs of experiments.

Предложен подход к исследованию напряженно-деформированного состояния литосферных плит, содержащих разломы, путем достаточно достоверного, с учетом масштабов, моделирования их структур двумерными пластинами на трехмерной упругой подложке. Описан метод моделирования взаимодействия разнотипных литосферных плит с прямолинейными разломами, представляющий собой модификацию метода собственных функций с использованием метода блочного элемента. Метод рассмотрен на примере статической задачи и задачи об установившихся колебаниях протяженных пластин на поверхности упругого слоя при заданной поверхностной нагрузке.