Continuum Model and Method of Calculating for Dynamics of Inelastic Layered Medium

Abstract

Mathematical modeling of the processes of wave propagation in a layered medium with viscoplastic slip conditions at contact boundaries was carried out, also as passing of waves through a fluid-containing layered massif. An improved model of a layered medium with nonlinear viscoplastic slip conditions at interlayer boundaries was constructed. A numerical solution method for the equations of a layered medium with viscoplastic interlayers for a power slip condition was developed. An example was given of a numerical calculation of the passing of a transverse elastic wave through a layered massif possessing effective anisotropic viscoplastic properties. A two-dimensional problem of the reflection from the buried layered massif was numerically solved for a system of waves excited by a nonstationary surface source. A comparison was made between the dynamics of the surface points for the elastic solution and the solution, taking into account the influence of the buried layered massif, as well as the effect of the thickness of the layers. The proposed models can be useful in solving of the dynamic problems of seismic survey and interpretation of wave patterns obtained in its course.