Crack-induced anisotropy in crustal rocks: Predicted dry and fluid-saturated Thomsen’s parameters

In upper crustal conditions, elastic anisotropy of rocks is mainly due to cracks, as long as the anisotropy of the background matrix remains low. Because, in general, rock anisotropy remains weak, in the sense that hexagonal symmetry may be sufficient to handle it, Thomsen suggested that a set of three parameters would be convenient to describe it. Using effective elasticity, we derive Thomsen’s parameters for the case of dry and fluid-saturated cracks, in a rock of isotropic background, in terms of crack density parameters and fluid compressibility. These results can be of interest for the interpretation of seismological and seismic data. They provide moreover a way to identify the fluid nature (gas or liquid) and to extract the crack density tensor from elastic wave data. Frequency effects are discussed when fluid is present so that frequency dependence can be accounted for.