About One Method of Investigation of Lithospheric Plates of Non-Classical Shape and Complex Rheology

The paper studies the possibility of assessing the behavior of lithospheric plates of non-classical shape, located on a multilayer base. The study is driven by the need to survey the dynamic properties of such lithospheric plates due to the discovery of the possibility of their resonances. Resonances can affect the seismic state of the territory of the lithospheric plate and provoke earthquakes. As a lithospheric plate, a wedge-shaped plate in the form of a quarter of a plane is being studied. The solution of the problem under consideration is based on the possibility of solving the contact problem in a wedge-shaped region in which a deformable stamp acts. Solutions to boundary value problems for complex rheology dies are then a combination of solutions to boundary value problems for simple rheology dies. In this article, a previously developed new mathematical tool based on the fractal properties of block elements is used to analyze the problem under consideration. Given the practice of applying this approach, it is possible to achieve certain results. In earlier works, to obtain all the parameters describing the behavior of lithospheric plates in a quadrant, it was necessary to study three equations. In this paper, we construct one equation of the second kind with a completely continuous operator, which makes it possible to cover all the necessary parameters. It allows this equation to be approximated by a finite system of algebraic equations and it is rather simple to obtain a dispersion equation. The issues of consideration of lithospheric plates of complex rheologies are discussed.

contact problem, block element, deformable punch, Wiener-Hopf integral equation