Calculation Method of Dispersion and Attenuation in the Fractured Rock with Anisotropic Background

Fractures are widely distributed in virtually all kinds of rocks, and their characterization is of great meaning for improving the hydrocarbon production due to the fact that the presence of fractures can greatly improve the permeability of reservoirs. Seismic exploration is a useful tool to evaluate fractures because the wave induced fluid flow between the fractures and background pores will dramatically affect the seismic dispersion and attenuation. The quantitative characterization of fractures needs to establish the relations between the physical properties and seismic properties for fractured rocks according to the effects of fluid flow between the fractures and the background pores on the dispersion and attenuation. However, most relevant studies are based on the ideal case of isotropic background and are therefore inapplicable to the anisotropic formations that are commonly existing in nature. We presented a theoretical method to obtain the seismic dispersion and attenuation in a fractured rock with anisotropic background. In this method, we first assumed the anisotropic background of the fractured rock to be a layered background. Then, we developed theoretical methods to calculate the elastic coefficients in two specific middle frequencies that are determined by the fluid pressure distributions in the layered rock with fractures. After obtaining these elastic coefficients as well as those in the high- and low-frequency limits, the dispersion and attenuation were finally simulated by numerically determining the parameters in the relaxation function. We further compared the theoretical predictions with the experimental and numerical results, and the excellent agreements indicated the applicability of the proposed method in simulating the dispersion and attenuation of the fractured rocks with anisotropic background permeated by fractures of various orientations. Because of the universal presence of anisotropic background in fractured formations, the proposed method that considerer the effects of anisotropic background has a broad application range in the seismic exploration of fractured reservoirs.