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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S U M M A R YAnalysis of seismic data suggests that hydrocarbon deposits are often associated with higher than usual values of attenuation, but this is generally ignored during amplitude-versus-offset (AVO) analysis. The effect can be modelled with equivalent medium theory based on the squirt flow concept, but the excess attenuation is associated with strong velocity dispersion. Consequently, when we study reflections from the interface between such an equivalent medium and an elastic overburden we find that the reflection coefficient varies with frequency. The impact of this variation depends on the AVO behaviour at the interface; class I reflections tend to be shifted to higher frequency while class III reflections have their lower frequencies amplified. We calculate synthetic seismograms for typical models using the reflectivity method for materials with frequency dependent velocities and attenuations, and find that these effects are predicted to be detectable on stacked data. Two field data sets show frequency anomalies similar to those predicted by the analysis, and we suggest that our modelling provides a plausible explanation of the observations.

A B S T R A C TWe present laboratory ultrasonic measurements of shear-wave splitting from two synthetic silica cemented sandstones. The manufacturing process, which enabled silica cementation of quartz sand grains, was found to produce realistic sandstones of average porosity 29.7 ± 0.5% and average permeability 29.4 ± 11.3 mD. One sample was made with a regular distribution of aligned, penny-shaped voids to simulate meso-scale fractures in reservoir rocks, while the other was left blank. Ultrasonic shear waves were measured with a propagation direction of 90 • to the coincident bedding plane and fracture normal. In the water saturated blank sample, shearwave splitting, the percentage velocity difference between the fast and slow shear waves, of <0.5% was measured due to the bedding planes (or layering) introduced during sample preparation. In the fractured sample, shear-wave splitting (corrected for layering anisotropy) of 2.72 ± 0.58% for water, 2.80 ± 0.58% for air and 3.21 ± 0.58% for glycerin saturation at a net pressure of 40 MPa was measured. Analysis of X-ray CT scan images was used to determine a fracture density of 0.0298 ± 0.077 in the fractured sample. This supports theoretical predictions that shear-wave splitting (SWS) can be used as a good estimate for fracture density in porous rocks (i.e., SWS = 100ε f , where ε f is fracture density) regardless of pore fluid type, for wave propagation at 90 • to the fracture normal.

Elastic wave attenuation anisotropy in porous rocks with aligned fractures is of interest to seismic remote sensing of the Earth's structure and to hydrocarbon reservoir characterization in particular. We investigated the effect of partial water saturation on attenuation in fractured rocks in the laboratory by conducting ultrasonic pulse-echo measurements on synthetic, silica-cemented, sandstones with aligned penny-shaped voids (fracture density of 0.0298 ± 0.0077), chosen to simulate the effect of natural fractures in the Earth according to theoretical models. Our results show, for the first time, contrasting variations in the attenuation (Q−1) of P and S waves with water saturation in samples with and without fractures. The observed Qs/Qp ratios are indicative of saturation state and the presence or absence of fractures, offering an important new possibility for remote fluid detection and characterization.

Ultrasonic (500 kHz) P‐ and S‐wave velocity and attenuation anisotropy were measured in the laboratory on synthetic, octagonal‐shaped, silica‐cemented sandstone samples with aligned penny‐shaped voids as a function of pore fluid viscosity. One control (blank) sample was manufactured without fractures, another sample with a known fracture density ɛf=0.0314+0.0059 (measured from X‐ray CT images). Velocity and attenuation were measured in four directions relative to the bedding fabric (introduced during packing of successive layers of sand grains during sample construction) and the coincident penny‐shaped voids (fractures). Both samples were measured when saturated with air, water (viscosity 1 cP) and glycerin (100 cP) to reveal poro‐visco‐elastic effects on velocity and attenuation, and their anisotropy. The blank sample was used to estimate the background anisotropy of the host rock in the fractured sample; the bedding fabric was found to show transverse isotropy with shear wave splitting (SWS) of 1.45 ± 1.18% (i.e. for S‐wave propagation along the bedding planes). In the fractured rock, maximum velocity and minimum attenuation of P‐waves was seen at 90° to the fracture normal. After correction for the background anisotropy, the fractured sample velocity anisotropy was expressed in terms of Thomsen's weak anisotropy parameters ε, γ & δ. A theory of frequency‐dependent seismic anisotropy in porous, fractured, media was able to predict the observed effect of viscosity and bulk modulus on ε and δ in water‐ and glycerin‐saturated samples, and the higher ε and δ values in air‐saturated samples. Theoretical predictions of fluid independent γ are also in agreement with the laboratory observations. We also observed the predicted polarisation cross‐over in shear‐wave splitting for wave propagation at 45° to the fracture normal as fluid viscosity and bulk modulus increases.