Theoretical modelling of seismic dispersion, attenuation and frequency-dependent anisotropy in a fluid-saturated porous rock with intersecting fractures

Detection of intersecting open fractures is an important task in many earth science domains. To quantify the seismic responses in the fluid-saturated porous rock with intersecting open fractures, we develop a theoretical model based on Biot's equations of dynamic poroelasticity. The seismic dispersion, attenuation and frequency-dependent anisotropy due to joint effects of fracture-background wave-induced fluid flow (FB-WIFF), and fracture-fracture wave-induced fluid flow (FF-WIFF), as well as elastic scattering are investigated. The numerical results on a fluid-saturated porous and fractured sandstone show that the characteristic frequency of FF-WIFF is controlled by fracture connectivity and fluid viscosity. Variations of fracture connectivity and fluid viscosity may result in the coupling of FF-WIFF with FB-WIFF or elastic scattering. When the fracture connectivity tends to zero, the FF-WIFF vanishes and FB-WIFF becomes most significant. Besides fracture connectivity and fluid viscosity, the fracture geometry and fluid bulk modulus also affect the magnitudes of these three mechanisms and their interplay. Due to effects of these three mechanisms, the P-wave anisotropy varies greatly with frequencies. Furthermore, the fracture intersection angle also influences the P-wave anisotropy significantly. Our model agrees well with previous models in the frequency limits and for the special case with parallel fractures. Since our model incorporates the effects of FF-WIFF, it has a great potential to be applied in the detection for effective fracture networks for fluid flow.