The effect of oriented cracks on seismic velocities

Abstract

We have considered the problem of elastic wave velocities in a matrix containing aligned ellipsoidal fluid-filled cracks. This problem is relevant to a variety of geophysical applications, including crustal and mantle seismology and the behavior of stressed and dilatant rock. When the cracks are ellipsoids of revolution, the composite is transversely isotropic and is describable with five elastic constants. For aligned oblate spheroids the major reduction in velocity occurs along the axis of symmetry. The opening of new cracks, the widening of old cracks, or the reduction of pore pressure accompanying crustal dilatancy can be expected to cause a large decrease in compressional velocity and considerable compressional wave anisotropy.Laboratory experiments indicate that crack porosity significantly depresses the seismic velocities even in lowporosity igneous rocks [Birch, 1960]. Anderson and Spetzle•' [1970], using the Eshelby-Walsh theory, showed that flat cracks were much more effective in reducing the elastic constants than spherical pores were. Thus they were able to show that the properties of the low-velocity zone could be explained with a small amount of partial melting. Likewise, the low velocities in crystalline rocks at low pressures can be under- Most of the work to date on the properties of composites or solids containing cracks has assumed isotropy, i.e., random orientation of grains and cracks. Geophysical aggregates can be expected to be anisotropic even if the matrix is isotropic, due to preferred orientation of cracks. The crack fabric of rock can be caused by tectonic stress fields or temperature gradients. Layering, recrystallization, cooling, and tectonic deformation can all be expected to result in cracks with a preferred orientation, both on microscopic (intergranular cracks) and on macroscopic (preferred orientation of dikes, joints) scales. Nur [1971] has discussed the problem of stressinduced crack orientation and gives a general treatment for velocities in a matrix containing oriented dry cracks.In the case of crustal deformation the orientation of cracks is controlled by the orientation of the principal stresses. In particular, the occurrence of dilatancy should be associated with cracks aligned in a statistical sense. We shall investigate here the extreme case in which the cracks are parallel.The overall elastic symmetry of a material containing parallel penny-shaped cracks is axial or transversely isotropic. Only five elastic constants are then independent. The extreme case of a laminated medium has been examined by Postma Copyright ¸ 1974 by the American Geophysical Union. •11ipsoidal inhomogeneities. This theory has been used by Walsh [1969] to calculate the elastic constants of a solid containing penny-shaped fluid-filled cracks with random orientation. Such a material is isotropic in the large and is described by two elastic constants.We consider an isotropic matrix containing ellipsoidal fluidfilled zones where the axial ratios are a/b = a/c = a < 1. The Eshelby theory neglects i...

Seismic velocity anisotropy in a medium cotaining oriented cracks. Transversely isotropic case.

“…Effects of crack aspect ratio, fluid bulk modulus, and crack volume on velocity anisotropy were investigated. The present results showed smaller anisotropy than that given by ANDERSON et al (1974) for a medium containing oriented spheroidal cracks. The relation between velocity and crack density parameter (ratio of porosity to aspect ratio of cracks divided 1.…”

“…However, some theoretical work has been accomplished on elastic anisotropy caused by preferred crack orientations. ANDERSON et al (1974) presented numerical studies of seismic velocity anisotropy for an isotropic matrix containing circular cracks with their planes all in parallel. GRIGGS et al (1975) andHOENIG (1979) investigated the case of cracks with their normals randomly distributed.…”

The Physical State of the Upper Levels of Cretaceous Oceanic Crust from the Results of Logging, Laboratory Studies, and the Oblique Seismic Experiment at Deep Sea Drilling Project Sites 417 and 418

“…As can be seen in Table 6 (from Stephen et al, this volume), the mean north-south shear wave velocity (2.56 ±0.04 km/s) is not significantly different from the mean east-west velocity (2.66 ±0.14 km/s). In general, shear waves are well suited to the study of seismic anistropy since (a) the direct shear wave arrival plots as a straight line for about 3 km, whereas the direct compressional wave arrival falls on a curve; (b) shear wave amplitudes increase with range, in contrast to compressional wave amplitudes which decrease (Ergin, 1952); and (c) shear waves are theoretically more sensitive to the presence of water-filled cracks than compressional waves (Anderson et al, 1974). Since the present experiment was well suited to the detection of azimuthal anisotropy, it appears that large, oriented fissures are not present at Site 417.…”

Effective field method for seismic properties of cracked rocks

“…For homogeneous ellipsoidal inclusions and elliptical cracks this problem can be solved exactly, and therefore the exact solution of the homogenization problem may be easily constructed in these cases [Nur, 1971;Anderson et al, 1974;Hudson, 1981Hudson, , 1990Peacock and Hudson, 1990;Sayers and Kachanov, 1991;Kachanov, 1992Kachanov, , 1993Cheng, 1993;Thomsen, 1995;Xu, 1998;Schubnel and Gueguen, 2003]. For a high density of inhomogeneities when interactions between inclusions become essential, the homogenization problem is more complex because it is connected with the solution of the so-called many particle problem.…”