Abstract. Accurate and detailed models of the seismic velocity structure of gas hydrate-bearing sediments may be determined by careful analysis of controlled source seismic data. However, interpretation of these velocities in terms of hydrate saturation of the pore space has hitherto relied on semiempirical formulae and/or simple effective medium theory. We develop a rigorous theoretical scheme to relate the seismic properties of a clay-rich hydrate-bearing sediment to its porosity, mineralogy, microstructural features and hydrate saturation. We consider separately the two possible end-members for the distribution of hydrate in the pore space: (1) hydrates are unconnected and located in the pore voids without appreciable grain contact and (2) connected hydrates are forming cement binding around the grains.The scheme is transversely isotropic, to allow for anisotropy due to alignment of clay platelets, and is based on a combination of a self-consistent approximation, a differential effective medium theory, and a method of smoothing for crystalline aggregates. We have applied the scheme to lithological and seismic velocity data from Ocean Drilling Program Site 995 on the Blake Ridge (southeastern U.S. continental margin) to make estimates of the hydrate saturation. It was found that the hydrates are probably unconnected, and their volume concentration varies between -• 0% at 100 m below the seabed and -• 9% at 400 m depth, just above the "bottom simulating reflector", if the clay platelet orientation distribution resembles the function we have used.

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SUMMARY The T‐matrix approach of quantum scattering theory is used here to place many long‐wavelength equivalent‐medium approximations for porous composites, polycrystals and cracked media on a common footing and to indicate their limitations, but also to derive some new results based on two‐point statistics. In this way, we have obtained an insight into the difficult problem of elastic inclusions at finite concentrations, which is of foremost relevance when estimating the effective material parameters of porous/cracked shales, involving stacks of more or less horizontally aligned clay platelets, mixed together with more rounded silt minerals, and with fluid filling the spaces. A rather involved perturbative analysis of the effects of interactions between (or structural correlations among) the various inclusions (minerals and cavities) making up a real shale of hexagonal symmetry was performed in an attempt to obtain a better match between theoretical predictions (based on a combination of coherent and optical potential approximations) and experimental results (recovered from ultrasonic wave speeds) for the effective elastic stiffness tensor. For the particular data set considered in this study, the T‐matrix approach was able to match the data better than the approach of Hornby et al., but the match was not completely satisfactory. Further progress in theoretical shale modelling may come from a better knowledge of the elastic properties of pure clay minerals, a more detailed knowledge of the microstructure of shales, the incorporation of constraints obtained from comparisons between theoretical predictions and experimental results, as well as a continuing development of the T‐matrix approach. Numerical results (also for the effect of bedding parallel microcracks on the elasticity of such a real shale) have value in illustrating the importance of taking into account the effects of spatial distribution when trying to deal with non‐dilute mixtures of highly contrasting material properties.

This work evaluates and improves upon existing effective medium methods for permeability upscaling in fractured media. Specifically, we are concerned with the asymmetric self-consistent, symmetric self-consistent and differential methods. In effective medium theory, inhomogeneity is modeled as ellipsoidal inclusions embedded in the rock matrix. Fractured media correspond to the limiting case of flat ellipsoids, for which we derive a novel set of simplified formulas. The new formulas have improved numerical stability properties, and require a smaller number of input parameters. To assess their accuracy, we compare the analytical permeability predictions with accurate, three-dimensional finite-element simulations. We also compare the results with a semi-analytical method based on percolation theory and curve fitting, which represents an alternative upscaling approach. A large number of cases is considered, with varying fracture aperture, density, matrix/fracture permeability contrast, orientation, shape and number of fracture sets. The differential method is seen to be the best choice for sealed fractures and thin open fractures. For high-permeable, connected fractures, the semi-analytical method provide the best fit to the numerical data, whereas the differential method breaks down. The two self-consistent methods can be used for both unconnected and connected fractures, although the asymmetric method is somewhat unreliable for sealed fractures. For open fractures, the symmetric method is generally the more accurate for moderate fracture densities, but only the asymmetric method is seen to have correct asymptotic behaviour. The asymmetric method is also surprisingly accurate at predicting percolation thresholds.

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