On the Modeling of Slow Oscillations and Static Interaction of Lithospheric Units

The mechanical concept of assessing the regional seismicity involves determining stress concentration zones in lithospheric structures considered as indicative of areas with possible seismic events. This study is aimed at developing mechanical and mathematical models and methods to study the stress–strain state of geophysical structures subjected to static loads, as well as low-frequency harmonic loads. The article presents a method to solve problems related to static interaction of a system of coating plates and an elastic substrate. In this model, the equations for displacements of the front surface and contact stresses are based on the solutions to the matrix-function Wiener–Hopf equations to which the initial problem is reduced. A specific feature of the equations is unknown functionals of the solution and its derivative on their right-hand sides, which are determined from a system of linear algebraic equations. This approach makes it possible to determine all basic characteristics of the stress–strain state of a block structure formed by two contacting plates on a deformable base. In addition to the static problem arising in the study of factors affecting stress–strain properties of the geological structures, the article also considers the problem of long-period steady-state oscillations of the coating–substrate system. In relation to low frequencies, we propose to proceed to sequential solution of several static problems.