Frequency-dependent anisotropy of porous rocks with aligned fractures

Abstract

Naturally fractured reservoirs are becoming increasingly important for oil and gas exploration in many areas of the world. Because fractures may control the permeability of a reservoir, it is important to be able to find and characterize fractured zones. In fractured reservoirs, the wave-induced fluid flow between pores and fractures can cause significant dispersion and attenuation of seismic waves. For waves propagating normal to the fractures, this effect has been quantified in earlier studies. Here we extend normal incidence results to oblique incidence using known expressions for the stiffness tensors in the low- and high-frequency limits. This allows us to quantify frequency-dependent anisotropy due to the wave-induced flow between pores and fractures and gives a simple recipe for computing phase velocities and attenuation factors of quasi-P and SV waves as functions of frequency and angle. These frequency and angle dependencies are concisely expressed through dimensionless velocity anisotropy and attenuation anisotropy parameters. It is found that, although at low frequencies, the medium is close to elliptical (which is to be expected as a dry medium containing a distribution of penny-shaped cracks is known to be close to elliptical); at high frequencies, the coupling between P-wave and SV-wave results in anisotropy due to the non-vanishing excess tangential compliance.