Frequency-dependent elastic properties of fracture-induced VTI rocks in a fluid-saturated porous and microcracked background

Fractures are widely distributed underground. The stiffness matrix of fractured rocks has been extensively investigated in a fluid-saturated porous background medium. However, the existing stiffness models only incorporated the attenuation mechanism of wave-induced fluid flow (WIFF). For macroscopic fractures, the elastic scattering (ES) of fractures cannot be ignored. To alleviate this issue, a frequency-dependent stiffness matrix model was developed, including the mesoscopic wave-induced fluid flow between fractures and background (FB-WIFF), the microscopic squirt flow, and the macroscopic ES from the fractures. By combining the far-field scattered wavefields of normal incident P and SV waves with the linear slip theory, the dynamic full-stiffness matrices for fracture-induced effective VTI rocks in a fluid-saturated porous and microcracked background were derived. Then, the P, SV, and SH wave velocities and attenuation can be obtained through the Kelvin-Christoffel equation. The results indicate that the FB-WIFF mechanism significantly affects the velocities and attenuation of the P and SV waves, but has nearly no effect on the SH wave, while the squirt flow and ES mechanisms affect the velocities and attenuation of both the P, SV, and SH waves. For validation, the model was compared with existing models and previous experimental ultrasonic data.