Pressure-dependent dynamic elastic properties and wave velocities in saturated porous rocks with aligned fractures

SUMMARY Fractures are widely distributed in upper crustal rocks and significantly affect rock elasticity. Experiments and field studies indicate that pressure influences the rock's elastic properties. Therefore, it is critical to understand the pressure dependence of rock elastic properties. For this purpose, a theoretical model is developed that considers both pressure-dependent background elasticity and fracture deformation within the hyper-elasticity stage. Using the model, the dynamic (frequency-dependent) attenuation mechanisms of fracture-background wave-induced fluid flow (FB-WIFF), multishaped microcracks' squirt flows (MMSF), fracture elastic scattering and their coupling effects under different effective pressures are investigated. The results indicate effective pressure can greatly reduce fracture normal and shear compliances. The stiffness coefficients increase with the increasing effective pressure and the MMSF mechanism gradually disappears due to the almost completely closed microcracks. Effective pressure has a stronger effect on wave-induced fluid flow (WIFF) mechanisms (including FB-WIFF and MMSF) than the elastic scattering mechanism. The P-wave dynamic anisotropy is modulated by FB-WIFF, elastic scattering and their coupling effects, while the S-wave anisotropy is modulated only by elastic scattering. Compared to P-wave anisotropy, the S-wave anisotropy Thomsen coefficient ${\gamma _{\rm TH}}$ is almost independent of effective pressure. In addition, P-wave attenuation anisotropy is more sensitive to effective pressure than P-wave velocity anisotropy. The predicted velocities at ultrasonic frequencies were compared with previous laboratory ultrasonic velocity data under effective pressure loading to validate the model.