2.5-D Poro-viscoseismic wave modeling in a double porosity medium

Abstract

For the double porosity Biot model, the local flow energy dissipation mechanism can be approximated by a single Zener visco-acoustic element. This replaces the convolution integrals of the governing equations with the memory equations for the memory variables. From the 3-D governing equations for poro-viscoseismic wave propagation, the 2.5-D governing equations are obtained by taking a Fourier transform in the medium-invariant (strike) y-direction and trasnforming to the wavenumber domain. For a heterogeneous, double porosity 2.5 D medium, we obtain numerical transient solutions for a point source by solving the poro-viscoseismic modelling using a time splitting method for the non-stiff parts and an explicit 4th-order Runge-Kutta method for the time integration and a Fourier pseudospectral staggered-grid for handling the spatial derivative terms. Since the 2.5-D scheme can be used to calculate the 3-D wavefields, it is clearly more realistic than 2-D (line source) modelling. By this method, the stress, particle velocity and pore pressure can be calculated simultaneously. Comparison with the analytical solution for a homogeneous model shows the correctness of this approach. © 2010, European Association of Geoscientists and Engineers.