Improved P-Wave Equation in Partially Saturated Porous Media and Its Numerical Simulation

When seismic waves propagate through underground media, the multi-scale fluid flow in the porous media will cause attenuation and dispersion of seismic waves. However, the existing seismic wave equations rarely consider the influence of capillary pressure on fluid flow. We introduce the capillary pressure parameter into Johnson's formula for calculating the bulk modulus, and substitute the improved calculation method of the bulk modulus into the P-wave equation in the partially saturated porous medium. As a result, an improved P-wave equation in the partially saturated porous medium that considering capillary pressure is obtained. In order to better explore the propagation characteristics of the P-waves in the partially saturated porous media, we derive a high-order finite-difference scheme of the improved P-wave equation in the partially saturated porous media. We also conduct forward modeling, and obtain clear snapshots of the wavefield. Furthermore, we analyze the influence of capillary pressure on the velocity of fast P-wave. At the same time, it is proved that the seismic wave equation can describe the attenuation phenomenon of waves in the seismic frequency band, by means of the analysis of the seismic traces with and without oil in the thin layer and the thick layer models. It also shows that the higher the capillary pressure, the more significant amplitude attenuation in the seismic frequency band.