S U M M A R YIn this paper, the term 'upscaling' means the theoretical prediction of rock's elastic properties at lower frequency (seismic or cross-well data) using higher frequency logging data on sonic velocities (V P , V S 1 and V S 2 ), porosity and density. The mineral composition and water saturation derived from other logs are used. Due to the special treatment of sonic logging data provided by the dipole sonic probe, all the sonic velocities are obtained in the principal coordinate system of the rock's stiffness tensor. The upscaling procedure includes two steps. The first step involves the solution of an inverse problem on reconstruction of the parameters of the rock's microstructure from the logging data. The inversion is based on the effective medium theory. As a result of the inverse problem solution, the effective stiffness tensor is found for depths at which the sonic wave velocities are measured. At the second step, the velocities of waves at given lower frequencies are calculated as propagating in a layered medium. The number of layers in the medium depends on the given frequency and logging step. Each layer of the medium has the stiffness tensor found at the first step.This upscaling procedure has been applied to a wellbore for which the dipole sonic data are available. The rocks penetrated by the well are shales. In general, the resulting medium exhibits orthorhombic symmetry at sonic frequency. This symmetry results from the preferential orientation of clay platelets and grain-related cracks and vertical cracks. The existence of the latter is indicated by the dipole sonic tool. Depending on the microstructure parameters (orientation of clay platelets and cracks, pore/crack connectivity and shale mineralogical composition), the shales, at lower frequency, have either transversely isotropic symmetry (with the vertical axis of symmetry, a.k.a. VTI) or orthorhombic symmetry.

Clay minerals are important components in shales, controlling their elastic properties and anisotropy. The elasticity of crystalline clay minerals differs significantly from that of clay in situ because of the ability of clay particles to bind water. In the ma-jority of published works, only isotropic moduli for in situ clays are reported. However, anisotropy is inherent in the clay elas-ticity. We develop an inversion technique for determination of the stiffness tensor of in situ clay from the shale’s stiffness tensor. As an example, we obtain the stiffness tensor of a “water-clay” composite from the data on the water-saturated Greenhorn shale sample, whose clay composition consists of almost equal amounts of illite and smectite and comparable amounts of kaolinite and chlorite. The stiffness tensor of the water-clay composite is found for the Greenhorn shale with step-by-step inversion based upon an effective medium theory. The inversion usesa nonlinear optimization technique with bounds imposed on the estimated parameters. In the inversion, we apply different approaches of the effective medium theory using a published method referred to here as the generalized singular approxi-mation (GSA). The GSA method makes it possible to take into account the microstructure of shales. The resulting elasticity constants of the anisotropic (transversely isotropic) in situ clay composite are [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] (in GPa); and the density equals [Formula: see text]. The Thomsen parameters for the clay composite are [Formula: see text], [Formula: see text], and [Formula: see text]. The elasticity constants found for this clay composite can be used in the theoretical analysis of shales that have a similar composition of clay but with different mineral compositions. The inversion technique developed can be used for general shale water-clay composites when the mineral composition and orientation of the clay platelets are known.

Three-dimensional seismic volumes from the central Fort Worth Basin display roughly circular collapse chimneys that extend vertically about 800 m from the Ordovician Ellenburger Formation to the Atokan ͑middle Pennsylvanian͒ Caddo Limestone. Collapse chimneys in carbonates may be caused by subaerial karst, hydrothermal, or tectonic extensional processes. We use 3D multitrace geometric attributes including coherence, volumetric curvature, and energyweighted, coherent amplitude gradients to investigate details of the origin of these structures. The Ordovician Ellenburger surface resembles a subaerial karst landscape of cockpits, dolines, and frying-pan valleys, while resistivity-based wireline image logs record 50 m of karst breccia facies. However, images from coherence and long-wavelength most-positive and most-negative-curvature volumes show many of the 800-m collapse features are associated with basement faults or with subtle Pennsylvanian and younger tectonic features, rather than with intra-Ellenburger collapse. We hypothesize that although the Ellenburger surface does contain a subaerial karst overprint, the first-order control on the formation of the vertically extensive collapse chimneys is bottoms-up tectonic-induced extensional collapse. Although these collapse chimneys have been affected by burial fluid diagenesis, the main consequence of burial fluid flow may be limited to the documented cementation of macrofractures. The apparent dominance of tectonic extension processes over subaerial karst and hydrothermal processes has basinwide implications for distribution of fractures, late-stage cements, and reservoir development and compartmentalization.