A B S T R A C TFractured rock is often modelled under the assumption of perfect fluid pressure equalization between the fractures and equant porosity. This is consistent with laboratory estimates of the characteristic squirt-flow frequency. However, these laboratory measurements are carried out on rock samples which do not contain large fractures. We consider coupled fluid motion on two scales: the grain scale which controls behaviour in laboratory experiments and the fracture scale. Our approach reproduces generally accepted results in the low-and high-frequency limits. Even under the assumption of a high squirt-flow frequency, we find that frequency-dependent anisotropy can occur in the seismic frequency band when larger fractures are present. Shear-wave splitting becomes dependent on frequency, with the size of the fractures playing a controlling role in the relationship. Strong anisotropic attenuation can occur in the seismic frequency band. The magnitude of the frequency dependence is influenced strongly by the extent of equant porosity. With these results, it becomes possible in principle to distinguish between fracture-and microcrack-induced anisotropy, or more ambitiously to measure a characteristic fracture length from seismic data.

Summary The standard description of wave propagation in fluid‐saturated porous media is given by the Biot–Gassmann theory of poroelasticity. The theory enjoys strong experimental support, except for specific and systematic failings. These failings may be addressed by the introduction of the concept of squirt flow. A wide range of squirt flow models exist, but the predictions of these models contradict each other and those of poroelasticity. We argue that a valid squirt flow model should be consistent with the evidence in favour of poroelasticity and with the rigorous results of effective medium theory. We then proceed to derive such a model for a simple pore space consisting of a randomly oriented collection of small aspect ratio cracks and spherical pores. However, compliance with our constraints is not a sufficient condition for the model to be a valid representation of rock. We build confidence in the approach by showing that a range of geometries can be handled without complicating the mathematical form of the model. Indeed, the model can be expressed through macroscopic parameters having physical interpretations that are independent of the specific microstructural geometry. We estimate these parameters for a typical sandstone and demonstrate the predictions of the model.

A B S T R A C TMeasurements of seismic anisotropy in fractured rock are used at present to deduce information about the fracture orientation and the spatial distribution of fracture intensity. Analysis of the data is based upon equivalent-medium theories that describe the elastic response of a rock containing cracks or fractures in the long-wavelength limit. Conventional models assume frequency independence and cannot distinguish between microcracks and macrofractures. The latter, however, control the fluid flow in many subsurface reservoirs. Therefore, the fracture size is essential information for reservoir engineers. In this study we apply a new equivalent-medium theory that models frequency-dependent anisotropy and is sensitive to the length scale of fractures. The model considers velocity dispersion and attenuation due to a squirt-flow mechanism at two different scales: the grain scale (microcracks and equant matrix porosity) and formation-scale fractures. The theory is first tested and calibrated against published laboratory data. Then we present the analysis and modelling of frequency-dependent shear-wave splitting in multicomponent VSP data from a tight gas reservoir. We invert for fracture density and fracture size from the frequency dependence of the time delay between split shear waves. The derived fracture length matches independent observations from borehole data.

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