Elastic anisotropy due to aligned cracks in porous rock¹

TLDR

Previous theory of elastic anisotropy in saturated aligned cracks was limited to stiff fluids, negligible equant porosity, and moderate frequencies, making it unsuitable for the upper crust where brine, substantial equant porosity, and sonic–seismic frequencies prevail. This study aims to eliminate those restrictions to broaden the applicability of crack‑anisotropy theory. In doing so, the authors identify a key dispersion mechanism arising from pressure equalization between pores and cracks. The generalized expressions show that at low frequencies the anisotropy depends only on crack density, not aspect ratio; shear‑wave splitting predictions remain valid, though conclusions on crack orientation or aspect ratio from P‑wave or critical‑angle data may need revision, and the theory is corroborated by Rathore et al.

Abstract

Abstract All theoretical expressions which relate the characteristics of saturated aligned cracks to the associated elastic anisotropy are restricted in some important way, for example to the case of stiff pore fluids, or of the absence of equant porosity, or of a moderately high frequency band. Because of these restrictions, previous theory is not suitable for application to the upper crust, where the pore fluid is brine (K f ≅ K 8 20) , the equant porosity is often substantial (φ p > 0.1), and the frequency band is sonic to seismic. This work removes these particular restrictions, recognizing in the process an important mechanism of dispersion. A notable feature of these more general expressions is their insensitivity, at low frequency, to the aspect ratio of the cracks; only the crack density is critical. An important conclusion of this more general model is that many insights previously achieved, concerning the shear‐wave splitting due to vertical aligned saturated cracks, are sustained. However, conclusions on crack orientation or crack aspect ratio, which were derived from P‐wave data or from shear‐wave‘critical angles’, may need to be reconsidered. Further, the non‐linear coupling between pores and cracks, due to pressure equalization effects, means that the (linear) Schoenberg‐Muir calculus may not be applied to such systems. The theory receives strong support from recent data by Rathore et al . on artificial samples with controlled crack geometry.