Numerical modeling of the seismic waves propagation in a porous medium from singular sources

A linear two-dimensional problem in the form of dynamic equations of porous media for the components of velocities, stresses and pressure is considered. The dynamic equations are based on conservation laws and consistent with the thermodynamics conditions. The medium is considered to be ideal (there is no energy loss in the system)isotropic and two-dimensional inhomogeneous with respect to space. For the numerical solution of the problem posed, the method of integrating the integral Laguerre transform with respect to time with finite-difference approximation in spatial coordinates is used. The solution algorithm employed makes it possible to efficiently carry out simulations in a complex porous medium and to study the wave effects arising in such media.