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The Use of Frequency-Dependent Anisotropy for Improved Fracture Characterisation

Enru Liu (eliu@bgs.ac.uk) of the Geophysics and Marine Geoscience Division of the British Geological Survey discusses results from a project to use frequency-dependent anisotropy to improved fracture characterization.  This work is part of NERC's micro-to-Macro thematic programme discussed in the last newsletter (http://ior.rml.co.uk/issue2/rd/psfbs/psfb-2.htm) (Coauthors Mark Chapman, John A Hudson, Simon Tod, Serafeim Vlastos, Sonja Maultzsch, and Xiang Yang Li) (http://www.eap.bgs.ac.uk)

Traditional seismic methods of fracture detection measure two attributes of the fracture distribution: the average orientation and fracture intensity or density. These attributes, when mapped, aid in efforts to predict permeability anisotropy.

Nevertheless, real fracture systems are extremely complex, and the link to permeability anisotropy is far from straight forward. It is therefore of great interest to be able to determine more attributes of the fracture system from seismic data, in particular the fracture size. A research partnership between the British Geological Survey and Cambridge University, funded under the auspices of the NERC micro to Macro programme, has been set up to find innovative methods to extract such information from seismic data.

The techniques are based on developments of the basic theory of wave propagation in fractured rock. Existing methods make use of models, such as those of Hudson and Thomsen, which assume limiting values of the frequency. The newer models dispense with this assumption and allow the frequency response across the seismic frequency band to be computed. Our concept is to observe frequency-dependent anisotropy in seismic data and then to invert for the properties of the fracture distribution.

Two mechanisms can give rise to frequency-dependent anisotropy. These are scattering due to layering or large fractures and fluid effects associated with the concept of squirt flow.

A model has been developed (Chapman, 2002) which considers the effect of squirt flow on two scales: the grain scale and the fracture scale. The model reproduces the results of Hudson and Thomsen in the appropriate limits. Unlike those theories, however, the new model predicts substantial dependence on the fracture size, independently of fracture density. Figure 1 shows an example of the relationship between shear-wave splitting and frequency for various fracture sizes.

Conventionally, the mean crack shape has been assumed to be circular. Whilst this may seem a natural and indeed necessary assumption, fractures develop in layers of rock having different mechanical strengths. This can lead to the situation where fracture growth is limited in one direction and it becomes more appropriate to model fractures of ellipsoidal shape. Tod (2002) has investigated the effect of deviations from the circular shape. Although for many cases the deviation has little effect, under certain circumstances the crack shape can have an important effect. Figure 2 shows how velocity can vary with the shape of the crack.

The effect of fracture size and spacing on the scattering response has been investigated numerically using the pseudo-spectral method (Vlastos et. al, 2002). Sample snap-shots associated with various fracture geometries are shown in Figure 3. When the fractures are smaller than the wavelength each fracture is a single scatterer which results in a secondary wavefield which is independent of the distribution. If the fractures are larger than the wavelength then the wavefield depends on the statistics of the distribution. In the event of a near regular distribution the fractures are close to each other and form clusters which act as large interfaces, whereas for a random distribution the clustering is insignificant and the fractures act as individual scatterers once again.

Observations of shear-wave splitting from a VSP have been shown to be frequency dependent (Liu et. al, 2002). Maultzsch (2002) developed techniques to fully calibrate Chapman’s (2002) model from associated well-log and laboratory data. This permitted a joint inversion of fracture size and density. Figure 4 shows the results of the inversion. The inferred average fracture radius, 1.3 m, matches closely the evidence from cores and FMI logs. Such fractures, defined as flow units by reservoir engineers, have previously been considered as invisible to seismic techniques because they are too small to image directly. We now have the potential to construct maps of fracture size from surface seismic, and thus to greatly improve predictions of permeability anisotropy.

References

1. Chapman, M., 2002. Frequency dependent anisotropy due to meso-scale fractures in the presence of equant porosity. Submitted to Geophysical Prospecting.
2. Liu, E., Queen, J.H., Li, X-Y., Chapman, M., Lynn, H.B. and Chesnokov, E.M., 2002. Analysis of frequency dpenendent seismic anisotropy from a multicomponent VSP. Submitted to the Proceedings of the 10^th International Workshop on Seismic Anisotropy (J. Appl. Geophys.).
3. Maultzsch, S., 2002. Modelling of Frequency-dependent anisotropy. First year report, University of Edinburgh.
4. Tod, S.R., 2002. Bed limited cracks in effective medium theory. Submitted to Geophysical Journal International.
5. Vlastos, S., Liu, E., Main, I. And Li, X-Y., 2002, Numerical simulation of wave propagation in media with distributions of fractures: effects of fracture sizes and spatial distributions. Submitted to Geophysical Journal International.

Figure 1: Shear wave anisotropy as a function of frequency for a canonical 10% porosity water saturated sandstone for fractures of different sizes.
Figure 2: Variation in shear wavespeeds as a function of the larger aspect ratio for constant crack density.
Figure 3: Model geometries and snapshots of models when the fractures have a random distribution. In Figures (a) and (b) the size of the fractures , and in Figures (c) and (d) the size . We let λ denote the wavelength.
Figure 4: Results of the inversion for fracture radius and density.

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