SOLVING OF ELASTIC DYNAMICAL PROBLEM IN A POROUS FLUID-SATURATED PIECEWISE-HOMOGENEOUS HALF-SPACE BY THE INDIRECT METHOD OF NEAR-BOUNDARY ELEMENTS

Abstract

Context. Solving the different applied problems of engineering and petroleum geology, geophysics and geodynamics, researchers often use methods based on phenomenon seismic-electrical effect of the second kind, since the electromagnetic field of electrical-kinetic origin is much more informative than the seismic one that generated it, and from it they can determine important petrophysical parameters (for example, porosity and fluid permeability) geological environment. At the first stage of investigation of this effect, the need of solving an elastic-dynamic problem arises, when the object of investigation is the processes of propagation of elastic waves in porous, fluid-saturated piecewise homogeneous media. This task also has an independent meaning for monitoring ecologically dangerous phenomena in the study of deformation processes in soil massifs, especially in mountainous areas, associated with their subsidence due to caverns, earthquakes, filtration of precipitation on the slopes and other phenomena.Objective. Construction of a mathematical model for the propagation of elastic waves in piecewise homogeneous media; creation of software for its numerical implementation and testing of its effectiveness; carrying out numerical investigations of the dependence on the parameters of the medium on the distribution of the displacement components at the boundary of the half-space.Method. We used the Bio theory to create a mathematical model of the problem and the indirect method of near-boundary elements to construct its numerical-analytical solution, last one is based on the theory of methods of boundary integral equations.Results. The software that implements the near-boundary elements method for numerical and analytical modeling of the elastic-dynamic problem has been developed. Computational experiments were carried out to estimate errors of discretization of the near-boundary region and of approximation of the mathematical model.Conclusions. The effect of change of the characteristics of an inclusion (in a form of a parallelepiped), in particular its fluid permeability and porosity, on the distribution of displacement components on the half-space boundary has been investigated. The practical recommendations of the recognition of inclusions have been done.