Analysis and Assessment of Seismic Hazard for the Azov-Black Sea Recreation Area

One of the geological structures accountable for the implementation of seismic potential of the region is the largest vertical faults in the Earth’s interior, where earthquake foci are usually located. This article is aimed at developing a better method for calculation of stresses and strains that occur in such seismogenic areas. According to the results of the analysis of data collected during the expeditionary work, the geophysical medium is modeled by a block structure in the form of a half-space with a cut rectangular parallelepiped, which is divided into five block elements. The state of material in the geological medium is described in each block by motion equations for a homogeneous, isotropic elastic medium in the Lamé form. Following the block element method, the algorithm of the differential factorization method is implemented in each block. Based on the numerical analysis results, the main trends in contact stresses and dynamics of displacement amplitudes were determined depending on the mechanical property values of the block material and the geometric parameters of the structure.

On Simplifying Complex Equations by Applying Block Elements

There are several approaches aimed at simplifying complex partial differential equations or their systems involved in the formulation of boundary value problems by introducing simpler, but in a larger number of differential equations. Their solutions allow us to describe solutions to complex boundary value problems. However, to implement this approach, it is necessary to construct solutions of simplified boundary value problems for arbitrary boundary conditions in solvability spaces boundary value problem. In some cases, this can be done using the block element method. The block element method, which has a topological basis, reveals both global and local properties of solutions to boundary value problems for partial differential equations. At the same time, it can be used to study and solve more complex boundary value problems by applying relations that describe certain equations of the continuum by means of relatively simple equations, for example, Helmholtz. To do this, we need to construct solutions of the Helmholtz equations that satisfy boundary conditions that contain completely arbitrary values, rather than partial values, set at the boundary of functions. In relation to the Helmholtz equations, this is achieved using the block element method. Examples of constructing solutions to boundary value problems for Helmholtz equation for Dirichlet and Neumann problems and a comparative analysis of solutions are given in this article.

ASSESSMENT OF GEOECOLOGICAL CONSEQUENCES OF HYDROCARBON EXTRACTION ON THE SHELF

Time analysis of the level of seismicity in the territories of intensive hydrocarbon production shows a clear trend of increasing seismic activity. At the same time, the maximum magnitude of registered earthquakes is noted after the start of production activities. The paper presents methods for assessing the tension of the geological massif before the production process (natural tension), after the extraction of hydrocarbon raw materials from the reservoir and after pumping water into the reservoir. The study is carried out using the block element method, with the introduction of a block element in the form of a cut-out ball for reservoir modeling. Expressions for the functional and pseudo-differential equations and the integral representation of the solution are obtained. Model calculations were performed, and the main trends in tension changes were identified. The results obtained can be used in monitoring systems for assessing the geoecological consequences of mining activities to develop preventive measures that allow performing a prospective analysis of man-made stresses in the earth’s crust and assessing the risk of a seismic event before the start of the production process.