Dynamics anisotropy in a porous solid with aligned slit fractures

Abstract

Crustal rocks are commonly permeated by aligned fractures which may control the wave anisotropy and permeability pattern. In the presence of pore fluid the mechanical and hydraulic features of such rocks become more complex. Understanding the dynamic anisotropy in fluid-saturated fractured rocks is important for detecting and characterizing fractured reservoirs and fault zones with applications in geomechanics, hydrogeology, exploration geophysics and reservoir engineering. For waves propagating normal to the fractures, the effects of wave-induced fluid flow (WIFF) due to the presence of permeable fractures on seismic dispersion and attenuation are significant and have been quantified in earlier studies. But previous literatures are restricted to low frequency range within which the fracture size is much smaller than the incident wavelength. In this paper, we extend low-frequency normal incidence results to full-frequency oblique incidence. We first derive exact solutions of the scattering problem of obliquely incident plane waves by a single slit fracture in a poroelastic solid. Based on previous analysis, for ideal fractures with infinitesimal thickness, the fracture fluid can be modelled as an incompressible one. Then, based on the solutions and Foldy's scattering theorem we develop a dynamic-effective-medium model to estimate frequency-dependent anisotropy of wave propagation in a fluid-saturated poroelastic rock with a sparse set of aligned fractures. We find that for the oblique incidence problem apart from WIFF there exist another two important attenuation mechanisms, i.e., the elastic scattering (scattering into fast P and S waves via mode conversion at the fracture faces) and Biot's global flow, in causing velocity dispersion and attenuation. The mixed-boundary problem reveals that the WIFF is controlled by the normal displacement discontinuity that is determined by effective normal stress applied on the fracture faces, while the scattering effects by the tangential displacement discontinuity that is determined by effective shear stress. Because the effective normal and shear stresses depends on incident angles and frequency, the dispersion and attenuation of both P and S waves are anisotropic and frequency-dependent. In contrast, Biot's global flow is an intrinsic energy loss mechanism that can play a role in causing velocity dispersion and attenuation at higher frequency range but it is independent of the presence of fractures or incident angle.