The Laguerre spectral method as applied to numerical solution of a two−dimensional linear dynamic seismic problem for porous media

The initial boundary value problem of the dynamics of fluid saturated porous media, described by three elastic parameters in the reversible hydrodynamic approximation, is numerically solved. A linear two-dimensional problem as dynamic equations of porous media for components of velocities, stresses and pore pressure is considered. The equations of motion are based on conservation laws and are consistent with thermodynamic conditions. In this case, a medium is considered to be ideally isotropic (in the absence of energy dissipation) and twodimensional heterogeneous with respect to space. For a numerical solution of the dynamic problem of poroelasticity we use the Laguerre transform with respect to time and the finite difference technique with respect to spatial coordinates on the staggered grids with fourth order of accuracy. The description of numerical implementation of the algorithm offered is presented, and its characteristics are analyzed. Numerical results of the simulation of seismic wave fields for the test layered models have been obtained on the multiprocessor computer.