LAUSR

The propagation of seismic waves in fractured rocks is greatly influenced by the fracture system and fluid content. Seismic anisotropy varies with frequency and fluid saturation. Previous theories on frequency-dependent anisotropy (FDA) are mostly limited to the assumption of single-phase fluid, whereas almost all reservoirs are usually partially or fully saturated with one or more fluids. The inelasticity, heterogeneity, and anisotropy exhibited by real earth media seriously challenge the traditional theory of uniform, fully elastic media. Therefore, based on the Chapman elastic theory, this paper considers the viscoelastic model, the relative mobility of saturated fluids, and the coupled effects of commonly independently considered squirt flow and patch effects on the frequency-dependent anisotropic seismic wave propagation in viscoelastic media. By calculating the frequency-dependent anisotropic elastic coefficients of two-phase immiscible fluid-saturated fractured rocks, a new viscoelastic Chapman extension model for FDA in partially saturated rocks, which includes the unified seismic wave propagation effects of squirt flow and patch effects, is constructed. The effect of relative permeability is significant, and compared to the case of complete saturation, the effective fluid mobility in partially saturated rocks may be lower, which may lead to nonmonotonic changes in elastic modulus and water saturation. Numerical experiments are conducted on the proposed viscoelastic Chapman extension model to discuss the coupling effects of squirt flow and patch effects on the FDA of viscoelastic media in cracked rocks with partially saturated reservoirs, under the conditions of no fractures and the existence of fractures. The simulation results of the P-wave modulus, P-wave velocity, and anisotropy parameters confirm the validity of the proposed method and model. This paper links the anisotropy of viscoelastic media with fluid flow parameters in fractures, which is conducive to improving the understanding of frequency-dependent seismic anisotropy in partially saturated rocks with fractures and the combination of seismology and reservoir engineering.