Frequency‐Dependent <i>P</i> Wave Anisotropy Due to Wave‐Induced Fluid Flow and Elastic Scattering in a Fluid‐Saturated Porous Medium With Aligned Fractures
Junxin Guo, Boris Gurevich
Abstract
Abstract Seismic anisotropy is an important attribute for fracture detection and characterization. If fracture size is comparable to the wavelength or fluid diffusion length, the P wave anisotropy is frequency dependent. By solving the Biot's equations of dynamic poroelasticity and using the Foldy approximation, we investigate the frequency‐dependent P wave anisotropy in a fluid‐saturated porous rock with a set of aligned penny‐shaped fractures. This approach includes the effects of both wave‐induced fluid flow (WIFF) and elastic scattering on P wave anisotropy. The results show that the velocity and attenuation anisotropy in the WIFF and elastic scattering regimes have quite different features and are affected by various factors. In particular, the background permeability and fluid viscosity primarily affect the frequency‐dependent anisotropy caused by WIFF. The fracture geometry (radius and thickness) and fracture density have significant effects on both WIFF and elastic scattering‐induced frequency‐dependent anisotropy. The fluid bulk modulus also affects the frequency‐dependent anisotropy. With the vanishing fluid bulk modulus, the frequency dependency vanishes in the WIFF regime but is the largest in the elastic scattering regime. Predictions of the model agree with previous models in all known limiting cases. Comparison with experimental data shows that WIFF and elastic scattering are important causes for frequency‐dependent P wave anisotropy, and our model is capable to account for these effects.