Characteristics of anisotropy and dispersion in cracked medium

In upper crustal conditions, where effective pressure is not high enough to close them, all rocks contain cracks. Understanding the effect of cracks on both the elastic anisotropy and the elastic waves frequency dependence (dispersion) is of major interest to Underground Storage Monitoring, Reservoir Monitoring, and Fault Mechanics. The challenge is to extract from geophysical data the maximum information with a minimal number of assumptions and model parameters. This is possible if reference data exist at the laboratory scale and if extrapolation from laboratory to field scale is not biased. In order to check that, investigating few basic idealized cases can provide useful guidelines. Let us consider an isotropic rock matrix and assume that dispersion is the result of squirt-flow. In this paper we will not consider crack-to-pore but rather focus on crack-to-crack squirt-flow. Three basic cracks configurations are quantitatively investigated, for which the elastic symmetry is transverse isotropy (TI). Our aim is to check if - from first principles - high frequency laboratory data can be used for field data interpretation in these three cases. The first case is that of identical cracks aligned in the same direction. A sufficiently strong deviatoric stress field in a given plane is expected to induce such a distribution at the field scale (sigma(1) = sigma(2) >> sigma(3)). We show that it results in a maximum anisotropy but with virtually no dispersion. Because there is no dispersion, high frequency data obtained in the laboratory (MHz ultrasonic range) are directly applicable to field data (Hz to kHz range) interpretation. Thomsen parameters provide then a direct proxy for crack density. A second case is that of identical cracks with random orientations (isotropic distribution). Such a situation could exist at the field scale if cracks result from the superposition of several independent tectonic episodes associated with different directions of principal stresses. In that case sigma(1) = sigma(2) = sigma(3). This configuration could also result from thermal cracking in an initially isotropic metamorphic rock. Obviously, there is no overall anisotropy then, but we show that dispersion may be large. Due to dispersion, ultrasonic laboratory data are not directly applicable to field data interpretation (unless the medium is dry). A third, intermediate case, is that of cracks randomly distributed in zone with a given axis. The corresponding symmetry is that of a so-called axi-symmetric triaxial test (which in fact is biaxial). It is of interest because it represents a classical laboratory experiment situation. It can also exist at the field scale if one principal stress is much larger than both others (sigma(1) =sigma(2) << sigma(3)). This case provides a simple example where both anisotropy and dispersion exist. Extrapolation of laboratory data to field scale is therefore not straightforward. Some quantitative microstructural information can however be derived from anisotropy quantification. (C) 2010 Elsevier B.V. All rights reserved.