Seismic Lithology 3: Rock Physics-Fractures Wednesday Morning, September 29th Limits to Crack Density: The State of Fractures in Crustal Rocks Stuart Crampin*, EAP & University of Edinburgh, Scotland; and Peter C. Leary, University of Edinburgh, Scotland SL3.1 SUMMARY Shear-wave splitting in sedimentary basins and above small earthquakes in a wide range of geological and tectonic domains typically displays evidence for azimuthal shear-wave velocity anisotropy of between 1% and 5%. Interpreted as the effects of parallel vertical fractures, microcracks, and preferentially oriented pore-space, these percentages of anisotropy are equivalent to crack densities of = 0.01 and 0.05 with normalized mean crack diameters of 0.43 and 0.74, respectively. The only exceptions are percentages of anisotropy exceeding 10% > 0.1) observed in near-surface rocks where there is pronounced jointing. It is suggested that the density of cracks in subsurface rocks is limited to shear-wave anisotropy of about 5% 0.05) because at a larger value of crack density, somewhere between = 0.05 and 0.10, which we call fracture-criticality, the rockmass is so thoroughly pervaded by cracks that the rock can no longer be considered as elastically intact. Any externally- or internally-induced deformation would tend to produce through going fractures in the critically fractured rockmass so that pore fluids would tend to disperse and the fractures collapse to a lower crack density. The range of normalized crack diameters, equivalent to the range from the smallest observed anisotropy (1%) to the largest (5%) is small, differs by a factor less than two. This means that the cracks within most rocks are comparatively close to the limit when the rock fragments. The implications of this critical state of fractures in crustal rocks are discussed. INTRODUCTION Shear-wave splitting in crustal rocks implying some form of azimuthal anisotropy was first identified above small earthquakes by Crampin et al. (1980a) and in sedimentary basins by Alford (1986) and Crampin et al. (1986). Since then, shear-wave splitting has been observed in a wide range of sedimentary, igneous, and metamorphic rocks on almost all occasions when shear-waves have been recorded on appropriate three-component instrumentation. Such shear-wave splitting typically displays differential shear-wave anisotropy of between 1% and 5% (Crampin and Lovell, 1991). Absence of azimuthal shear-wave anisotropy has not been reported. Shear-wave splitting in the crust implying azimuthal anisotropy is interpreted as the result of propagation through distributions of aligned cracks, microcracks, and preferentially oriented pore-space (Crampin and Lovell, 1991). Crack density is defined as = N , where N is the number of cracks of radius a in volume v. The radius a is much smaller than seismic wavelengths so that the long-wavelength approximation applies. It is convenient to put N = = 1 and refer to = a 3 as the normalized crack density where a is the radius of one crack in a unit cube. Figure 1 shows the numerical relationship between the normalized crack density and crack radius per unit cube. The relationship is reasonably well-behaved for values of crack density less than about = 0.05, radius a = 0.37, but larger values the crack density are very sensitive to small changes in radius. Crampin (1993) shows that the crack density is approximately the percentage of shear-wave anisotropy divided Figure 1. Plot of crack radius versus crack density. The arrows mark the range of commonly observed values in crustal rocks. Solid circles mark values illustrated in Figure 2. Table 1, Relative values of (approximate) differential shear-wave anisotropy (SWA), crack density (E), normalized crack radius (a), and normalized diameter (d = 2a) for Figure 2. by 100 when the Poisson’s ratio of the uncracked rock is 0.25. Percentages of anisotropy of 1% to 5% are thus approximately equivalent to crack densities of = 0.01 and 0.05. Table 1 shows the relationship between normalized crack density and crack radius for a few specific values. The box in Figure 1 outlines the values of shear-wave anisotropy that are commonly observed in subsurface rocks. Note that the lower limit is real in the sense that, although absence of azimuthal shear-wave anisotropy is sometimes claimed, there are no published examples of well-authentic cases of subsurface rock with much less than 1% shear-wave anisotropy. However, measures of anisotropy are usually averages over at least several tens of metres and small thicknesses of isotropic rock cannot be excluded. that neither cores nor well logs can necessarily provide much [The behaviour of fluid-filled voids is controlled by stress so direct information about the state of in situ microfractures. The rock in both cores and logs has been partially or wholly de- stressed, and some 20 direct or indirect stress-controlled phenomena (Crampin and Lovell, 1991) are likely to have modified the core, and the rock in the immediate vicinity of the well, in ways which may not be easy to estimate.] Such 1% to 5% values of shear-wave anisotropy have been found in km-length raypaths in a wide variety of sedimentary, metamorphic, and igneous rocks, and in mixed geological domains. This similarity of the observed anisotropy in a large range of rock types is remarkable. The only exceptions appear to be that occasionally large values of shear-wave anisotropy, implying large crack densities, have been found in the very near-surface, where they frequently indicate systems of bi- planar cracks. Crampin et al. (1980b) found P-wave anisotropy in a jointed limestone pavement equivalent to a bi-planar crack 758