moveout inversion in azimuthally anisotropic media with lateral velocity variation : Theory and a case study
Reflection moveout recorded over an azimuthally anisotropic medium (e.g., caused by vertical or dipping fractures) varies with the azimuth of the source-receiver line. Normal-moveout (NMO) velocity, responsible for the reflection traveltimes on conventional-length spreads, forms an elliptical curve in the horizontal plane. While this result remains valid in the presence of arbitrary anisotropy and heterogeneity, the inversion of the NMO ellipse for the medium parameters has been discussed so far only for horizontally homogeneous models above a horizontal or dipping reflector. Here, we develop an analytic moveout correction for weak lateral velocity variation in horizontally layered azimuthally anisotropic media. The correction term is proportional to the curvature of the zero-offset traveltime surface at the common midpoint and, therefore, can be estimated from surface seismic data. After the influence of lateral velocity variation on the effective NMO ellipses has been stripped, the generalized Dix equation can be used to compute the interval ellipses and evaluate the magnitude of azimuthal anisotropy (measured by P-wave NMO velocity) within the layer of interest. This methodology was applied to a 3-D “wide-azimuth” data set acquired over a fractured reservoir in the Powder River Basin, Wyoming. The processing sequence included 3-D semblance analysis (based on the elliptical NMO equation) for a grid of common-midpoint “supergathers,” spatial smoothing of the effective NMO ellipses and zero-offset traveltimes, correction for lateral velocity variation, and generalized Dix differentiation. Our estimates of depth-varying fracture trends in the survey area, based on the interval P-wave NMO ellipses, are in good agreement with the results of outcrop and borehole measurements and the rotational analysis of fourcomponent S-wave data.
Using AVO for fracture detection: Analytic basis and practical solutions
Tight, low‐porosity reservoirs can produce significant amounts of hydrocarbons if fracture networks provide the necessary permeability. Characterization of naturally fractured reservoirs using surface seismic data is an important exploration problem that has attracted much attention in the literature. TLE, for example, had an entire issue (August 1996) on this subject. While the data and modeling in existing publications demonstrate that fracturing causes significant azimuthal variation in recorded seismic signatures, the problem is how to infer fracture parameters from these data.
The crystal structure of stilpnomelane. Part II. The full cell
Summary The structural formula of stilpnomelane averaged from 37 representative literature analyses and based on the determined structure is (Ca,Na,K)4(Ti0·1Al2·3Fe35·5Mn0·8Mg9·3)[Si63Al9](O,OH)216·nH2O. Ferrostilpnomelanes have up to 12 R 3+ cations in the octahedral sheet, ferristilpnomelanes commonly have between 24 and 30 R 3+ cations, rarely up to 37. The two groups can be distinguished by accurate X-ray powder diffraction, ferrostilpnomelanes having d 001 less and a greater than have ferristilpnomelanes. The unit cell is triclinic, a = b∼21·8 Å, γ = 120°, d 001∼12·2 Å, P . Hexagonal groups or ‘islands’ of 24 silicon-oxygen tetrahedra co-ordinate to the octahedral sheet, the centres of the ‘islands’ are displaced by 5a/12, 8b/12 on either side of the octahedral sheet as a result of warping of this sheet to permit articulation with the smaller tetrahedral sheet. The 24-tetrahedra ‘islands’ are linked laterally by 6-member rings of inverted tetrahedra, which in turn link at their apices to like rings connecting the next sheet of ‘islands’. Thus a single tetrahedral layer is 4 tetrahedra thick and has symmetry 6/m. The 6-member rings of tetrahedra act as hinges permitting up to 0·5 Å extension or contraction of the tetrahedral sheet to accommodate variations in the octahedral sheet dimensions with varying R 2+/R 3+ ratio.