The potential of measuring fracture sizes with frequency-dependent shear-wave splitting.

Abstract

The success of seismic anisotropy is its ability to provide subsurface fracture orientations as derived from the polarization of the faster shear wave, and spatial distributions of fracture intensity inferred from time-delays between the faster and slower shear waves (Crampin 1985, Li 1997). However, the reservoir engineers’ reluctance to accept seismic anisotropy as a routine technique for fracture characterization is partly because of its failure to provide information about sizes of fractures. Although both grain scale micro-cracks and macro-scale fractures are considered to cause seismic anisotropy, reservoir engineers are more interested in the latter as permeability in many hydrocarbon reservoirs is believed to be dominated by formation-scale fluid units (in the order of meters). The interpretation of anisotropic measurements made from seismic data requires theoretical models that relate measurable seismic parameters to macroscopically determined rock properties. Based on the assumption that the scale length associated with fractures is considerably smaller than the seismic wavelength, a description of the average properties of the medium will be sufficient. The two most popular models for the average properties are the Thomsen equant porosity model (Thomsen, 1995) and Hudson’s model (Hudson, 1981). Thomsen’s model assumes perfect fluid pressure equalization between the cracks and the surrounding rock while Hudson’s model assumes that the cracks are isolated with respect to fluid flow. Both models predict frequency independent behaviour. In both models the magnitude of the anisotropy is related to the crack density, although the precise dependence is different in each case. This crack density is defined as ε=Na3 where N is the number of cracks per unit volume and a is the crack radius. Unfortunately, radically different fracture distributions few large cracks can give the same crack density as many smaller cracks. Figure 1 demonstrates this concept. Both cases have identical crack densities, but the fluid flow response would be expected to be markedly different in each case. If we are constrained to work within the conventional equivalent medium approach, then we can only obtain crack density and orientation from the seismic data. To obtain information on fracture size which can be useful for permeability prediction we require a different approach. In this study we investigate the possibility of using the frequency dependence of anisotropy to derive such information. We begin by reviewing a new theory which models frequency dependent anisotropy. The theory is then calibrated and tested against laboratory data, before we conclude with an application to field data.