Wave field simulation for heterogeneous transversely isotropic porous media with the JKD dynamic permeability

Abstract

Poroelastic wave field in a 2D heterogeneous transversely isotropic porous medium is calculated. The Johnson-Koplik-Dashen (JKD) dynamic permeability is assumed with two scalar JKD permeability operators for vertical and horizontal direction, respectively. The time domain expression of drag force in the JKD model is expressed in terms of the shifted fractional derivative of the relative fluid velocity. A method for calculating the shifted fractional derivative without storing and integrating of the entire velocity histories is developed. By using the new method for calculating the shifted fractional derivative, the governing equations for the 2D transversely isotropic porous medium are reduced to a system of first-order differential equations for velocities, stresses, pore pressure and the quadrature variables associated with the drag forces. The spatial derivatives involved in the first-order differential equation system are calculated by the Fourier pseudospectral method, while the time derivatives of the system are discretized by a predictor-corrector method. For the demonstration of our method, some numerical results are given in the paper.