Characteristics of elastic wave dispersion and attenuation induced by microcracks in complex anisotropic media

Abstract

Abstract The mechanism of dispersion and attenuation induced by fluid flow among pores and microcracks in rocks is an important research topic in geophysical domain. A generalised frequency-dependent fourth-rank tensor is proposed and derived herein by combining Sayers's discontinuity tensor formula and Gurevich's squirt flow model. Furthermore, a proposed method for establishing a cracked model with cracks embedded in a transversely isotropic (TI) background medium is developed. Based on the new formulation, we investigate the characteristics of dispersion, attenuation and azimuthal anisotropy of three commonly encountered vertical crack distributions, including aligned cracks, monoclinic cracks and cracks with partial random orientations. We validate the developed model by comparing its predictions with those of the classic anisotropic squirt flow model for an aligned crack. The numerical analyses indicate that the azimuth is independent of frequency when the maximum attenuation is observed for all three crack distributions. In a low-frequency range in the case of an anisotropic background, the attenuation of the qP-wave is inversely proportional to velocity, whereas the attenuation of the qSV-wave is proportional to velocity. In addition, the inherent anisotropy of the rock does not significantly affect the dispersion and attenuation owing to squirt flow. Finally, to investigate the applicability of the theory, we model laboratory data of a synthetic porous sandstone with aligned cracks. Overall, the models agree well with laboratory data. The complex characteristics determined through this study may be useful for the seismic characterisation of fractured reservoirs.