Simoulation of the seismic wave propagation in porous media described by three elastic parameters

An algorithm based on the spectral-difference method for numerical solution of the dynamic problem for porous media is proposed. We consider a linear two-dimensional problem in the form of dynamic equations in terms of displacement components described by three elastic parameters. The governing equations are based on conservation laws and consistent with the thermodynamics conditions. The medium is assumed to be isotropic and two-dimensional-inhomogeneous with respect to the spatial coordinates. To numerically solve the problem, we propose a method based on the joint use of the Laguerre integral transformation with respect to time and the finite difference approximation with respect to spatial coordinates. A description of the numerical implementation of the proposed method is given and its features are analyzed in the calculations. The efficiency of applying the Laguerre transformation and its difference from the Fourier transform for solving the direct dynamic seismic problems is discussed. Numerical results of the simulation of the seismic wave propagation fields for the test medium model are presented.