Elastic wave equations in modified patchy-saturated media and its numerical simulation

Huixing Zhang and Kristopher A. Innanen


Based on the modified patchy-saturated porous model, according to the method Biot used for the foundation of elastic wave equations in porous media, we established the stress-strain relations and obtained the dissipation function and kinetic energy in patchy-saturated porous media. By applying the Lagrange’s equations, we derived the elastic wave equations in modified patchy-saturated media. Through changing the equations to first-order stress-velocity equations, we deduced the 3D high-order finite difference schemes and numerically solved the equations in the complex domain. Numerical results show that there are two kinds of P-waves and one S-wave in patchy saturated media. The energy of the slow P-wave is very weak in the "solid" phase of the patchy saturated porous media and can hardly be seen, even though it is stronger in the fluid phase. The fast P-wave and S-wave are clear both in the solid phase and the fluid phase. The slow P-wave has a high dispersion. The velocities of the three waves are consistent with the theoretical results. All these results show that our numerical method is correct and effective.

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