About the precursor of increased seismicity in the area of transition of the mountainous territory to the plain
Abstract
The relevance of the paper lies in the need for further search for precursors of increased seismicity in areas where mountain ranges turn into plains. There are few rigorous mechanical and mathematical approaches to studying seismicity in such areas, due to the fact that they require solving some problems in the theory of integral equations. The aim of the research was to identify a zone of increased seismicity in the area of transition from a mountainous territory to the plain. Methods. The solution of the contact problem on the concentration of contact stresses in the transition zone of a mountain range to the plain area was used for the study. It is assumed that the mountain range towering above the plain is modeled by a deformable stamp, which, together with the bedrock, is located on an anisotropic half-space characteristic of the structure of the granite layer of the lithospheric plate. The paper takes into account tidal Moon impacts described by the time function. The task required constructing a solution to the two-dimensional Wiener-Hopf integral equation with an anisotropic symbol for the kernel of the integral equation. The authors of the study succeeded in establishing the general form of solutions of the two-dimensional Wiener-Hopf integral equation with an anisotropic symbol, and in proving its satisfaction to the integral equation. The case of a deformable stamp is considered for the first time in this paper. To describe a deformable stamp, the solution of the boundary value problem for a stamp of complex rheology is decomposed into solutions of boundary value problems for stamps of simplified rheology given by the Helmholtz equations. Results. In the process of study, a representation of the distribution of contact stresses under a deformable die was obtained. It is established that in the boundary zones of the deformable stamp, an increase in contact stresses occurs as it approaches the rectilinear boundary. The greatest increase in the concentration of contact stresses is observed when approaching the top of the angle of the deformable die. Functions describing the increase in stress concentrations are obtained.
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