GREENBERG, M.L. and CASTAGNA, J.P. 1992. Shear-wave velocity estimation in porous rocks : theoretical formulation, preliminary verification and applications. Geophysical Prospecting 40, Shear-wave velocity logs are useful for various seismic interpretation applications, including bright spot analyses, amplitude-versus-offset analyses and multicomponent seismic interpretations. Measured shear-wave velocity logs are, however, often unavailable.We developed a general method to predict shear-wave velocity in porous rocks. If reliable compressional-wave velocity, lithology, porosity and water saturation data are available, the precision and accuracy of shear-wave velocity prediction are 9% and 3%, respectively. The success of our method depends on: (1) robust relationships between compressional-and shear-wave velocities for water-saturated, pure, porous lithologies; (2) nearly linear mixing laws for solid rock constituents; (3) first-order applicability of the Biot-Gassmann theory to real rocks.We verified these concepts with laboratory measurements and full waveform sonic logs. Shear-wave velocities estimated by our method can improve formation evaluation. Our method has been successfully tested with data from several locations. 195-209. and rock composition, these have necessarily had limited success, because velocity also depends on effective stress, porous rock structure (pore shape distribution) and degree of lithification. An alternative approach to shear-wave velocity prediction exists, because these factors affect compressional-and shear-wave velocity in a similar way and because compressional-wave velocity data are widely available. We have investigated the use of measured compressional-wave velocity, with porosity and lithology data, to predict shear-wave velocity.Relationships between compressional-and shear-wave velocities are well-known for brine-saturated, pure lithologies (Pickett 1963). These relations are readily applied to mixed lithologies because, as predicted from Hashin and Shtrikman (1963) bounds, the solid rock constituents combine almost linearly.A general method for shear-wave velocity prediction must account for rocks which are not brine saturated. Biot's (1956) theoretical work on elastic-wave propagation in porous media, once coupled to measurable elastic parameters by Geertsma and Smit (1961), showed that Gassmann's (1951) equations are generally applicable to statistically isotropic, porous rocks in the limit of zero-frequency wave propagation. When applied to real rocks, Gassmann's equations yield a first-order prediction for the dependence of elastic velocities on the properties of pore-filling fluids (e.g. Castagna, Batzle and Eastwood 1985).We developed a method for predicting shear-wave velocity in porous, sedimentary rocks which couples empirical relations between shear-and compressionalwave velocities with Gassmann's equations. Mixed lithologies and fluids are accounted for. Laboratory measurements are used for method verification. We find that the mean predicted shear-wave velo...

Numerical simulation can be a useful tool for studying composite media. It is not limited by weak or single scattering assumptions, and it requires only constituent properties and an arrangement of constituents as input. For solid/solid media with octagonal cylindrical inclusions and for typical values of constituent moduli, composite moduli are accurately predicted by two‐dimensional (2-D) analogs of Kuster‐Toksöz formulas. For solid/solid media there is a small but discernable difference between responses of square and those of octagonal inclusions. Coherent reflections are produced by a coherent wave incident at a change in concentration of inclusions, if the contrast between material properties of the matrix and those of the inclusions is sufficient to produce significant scattering, and if the size of scatterers is sufficiently small and their concentration sufficiently large so there is constructive interference between waves originating at adjacent scatterers.

No abstract

Numerical simulation can be a useful tool for studying composite media. It is not limited by weak or single scattering assumptions, and it requires only constituent properties and an arrangement of constituents as input. For solid/solid media with octagonal cylindrical inclusions and for typical values of constituent moduli, composite moduli are accurately predicted by twodimensional (2-D) analogs of Kuster-Toksoz formulas. For solid/solid media there is a small but discernable difference between responses of square and those of octagonal inclusions. Coherent reflections are produced by a coherent wave incident at a change in concentration of inclusions, if the contrast between material properties of the matrix and those of the inclusions is sufficient to produce significant scattering, and if the size of scatterers is sufficiently small and their concentration sufficiently large so there is constructive interference between waves originating at adjacent scatterers.

No abstract