PROPAGATION OF SURFACE WAVES IN PORROSSY ANISOTROPIC MEDIUMS AND ITS MATHEMATICAL MODELS

Abstract

In this paper, mathematical–physical foundations and stable numerical approaches are proposed for modeling the propagation of surface waves in a porous–anisotropic medium. Starting from the fully anisotropic form of Biot’s theory, an energy-stable and symmetric weak formulation is derived for a mixed-scale setting. For free surfaces and interlayer interfaces, the SAT (Simultaneous Approximation Terms) stabilization mechanism is employed. Discretizations based on SBP–SAT (Summation-By-Parts and Simultaneous Approximation Terms) high-order finite differences and the HDG (Hybridizable Discontinuous Galerkin) method are developed, providing consistent energy estimates and observable dispersion errors. Through nondimensionalization, the governing dimensionless groups (filtration viscosity, Biot modulus, effective stress coefficient, dynamic tortuosity, and degree of anisotropy) are identified, and for a TI (transversely isotropic) half-space, the secular equation and Fréchet sensitivity integral operators of the Rayleigh phase velocity are obtained. Numerical experiments demonstrate the strong influence of azimuthal dispersion, permeability, and surface conditions (drained/undrained). The proposed approach has practical significance for problems in seismics, geotechnics, and reservoir monitoring.