Simulation and analysis of elastic waves in partially saturated double-porosity media based on finite difference method

Abstract

Double-porosity poroelastic model takes into account the effect of mesoscopic flow induced by rock heterogeneity on dispersion and attenuation of elastic waves, and has obtained good application results in the quantitative explanation of seismic data in heterogeneous reservoirs. Wavefield simulation based on double-porosity model not only helps visualize the propagation characteristics of the elastic waves but also lays the foundation for seismic imaging. In this work, we perform wavefield simulation and analysis based on the Santos-Rayleigh model which incorporates mesoscopic and global flow in a partially-saturated double-porosity medium. Specifically, the mesoscopic flow mechanism is represented with a Zener viscoelastic model. The comparison shows that the Zener model can accurately capture the propagation characteristics of fast P-wave, but fails to describe the attenuation characteristics of slow P3 wave in the low-frequency band. It implies that Zener viscoelastic model and slow wave modes follow different mechanisms. Then the staggered grid finite-difference method is used to simulate wave propagation in a double-porosity medium, and the stiff problem is solved with a time-splitting algorithm, which can significantly improve computational efficiency. Based on the above methods, the correctness of our algorithm is verified with derived analytical solution for a P-wave source in a uniform partially saturated poroelastic medium. Analytical and numerical solutions are in good agreement and mean error is 0.33%. We provide some examples of wavefield snapshots and seismograms in homogeneous and layered heterogeneous media at seismic and ultrasonic frequencies. The simulation results demonstrate the strong attenuation of fast P-wave and no change of S-wave in the seismic band due to mesoscopic flow mechanism, which is consistent with the theoretical prediction of double-porosity model. Moreover, the energy of fast P-wave is concentrated in solid phase while slow waves are stronger in fluid phase. This work contributes to the understanding of broadband elastic wave propagation in a heterogeneous partially saturated porous medium and can be applied to the reservoir imaging with broadband geophysical data.