Seismic Characterization of Naturally Fractured Reservoirs

P-wave seismic reflection data with variable offset and azimuth can be inverted for effective fracture compliances. The total effective compliance of a fractured rock, which is described using second- and fourth-rank fracture tensors, can be represented as a background compliance plus additional compliance due to fractures. Assuming monoclinic or orthorhombic symmetries (which take into account layering and multiple fracture sets), the components of the effective additional compliance tensor (second-and fourth-rank fracture tensors) can be used as attributes related to the characteristics of the fractured medium. Synthetic tests indicate that using a priori knowledge of the properties of the unfractured medium, the inversion can be effective on noisy data, with S/N on the order of 2. Monte Carlo simulation suggests that with Wide Azimuth (WAZ) and Narrow Azimuth (NAZ) reflection data, inversion of components of the second-rank fracture tensor alone has about 5 to 20% cumulative error (when uncertainties in the a priori information about elastic properties of unfractured rock vary from 0 to 40%) with Signal-to-noise ratios of 2 - 4. For the inversion of both second- and fourth-rank tensors (rotationally invariant fractures) cumulative error of about 30--50% was observed for the same uncertainty range, provided that synthetic data with S/N=2 - 4 is available.;Elastic properties of background media consisting of horizontal layers without fractures do not cause azimuthal changes in reflection coefficient variation with offset. Thus, due to the different nature of these properties compared to fracture tensor components (which cause azimuthal anomalies), simultaneous inversion for background isotropic properties and fracture tensor components requires additional constraints.;Lab measurements of interface (fracture) compliances on synthetic material, at low (90/120 kHz) and high (480 kHz) frequencies, show reasonable behavior for tangential and normal compliances of interfaces with pressure changes (compliance decreases as overburden pressure increases). At higher frequencies, synthetic fractures seem to be stiffer than at lower frequencies.;Singular Value Decomposition (SVD) and resolution matrix analysis can be used to predict fracture inversion efficacy before acquiring data. Thus, they can be used to determine optimal seismic survey design for inversion of fracture parameters.;In the formulation, equations for rotationally invariant fracture symmetries are generalized for rotationally varying (asymmetric) vertical fractures. This generalization introduces a new second-rank tensor, the magnitude of which is directly related to the asymmetry of the fractures. Thus, inversion results for this tensor can give clues about fracture shape and/or fracture dimensions in different directions.