P‐wave seismic reflection data, with variable offset and azimuth, acquired over a fractured reservoir can theoretically be inverted for the effective compliance of the fractures. The total effective compliance of a fractured rock, which is described using second‐ and fourth‐rank fracture tensors, can be represented as background compliance plus additional compliance due to fractures. Assuming monoclinic or orthotropic symmetry (which take into account layering and multiple fracture sets), the components of the effective second‐ and fourth‐rank fracture compliance 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 was used to test the effect of uncertainties in the a priori information about elastic properties of unfractured rock. Two cases were considered with Wide Azimuth (WAZ) and Narrow Azimuth (NAZ) reflection data and assuming that the fractures have rotationally invariant shear compliance. The relative errors in determination of the components of the fourth‐rank tensor are substantially larger compared to the second‐rank tensor, under the same assumptions. Elastic properties of background media, consisting in horizontal layers without fractures, do not cause azimuthal changes in the 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. Singular value decomposition (SVD) and resolution matrix analysis can be used to predict fracture inversion efficacy before acquiring data. Therefore, they can be used to determine the optimal seismic survey design for inversion of fracture parameters. However, results of synthetic inversion in some cases are not consistent with resolution matrix results and resolution matrix results are reliable only after one can see a consistent and robust behaviour in inversion of synthetics with different noise levels.

Variations of reflection amplitude with offset and azimuth are sensitive to the presence of natural and induced fractures. We tested inversion for fracture compliance matrix components from wide azimuth noisy synthetic PP-reflection data. The model was a fractured reservoir with monoclinic symmetry, formed by two sets of vertical asymmetric fractures embedded in a VTI background. The fractures (joints) were assumed to be vertical, with noncircular shape and/or with asymmetric shear compliance. Results of synthetic inversion showed that an incorrect assumption about fracture shear symmetry (e.g., treating asymmetric fractures as rotationally invariant fractures) can cause considerable error in estimation of the fracture compliance matrix. Components of effective second- and fourth-rank fracture compliance matrices for a medium with monoclinic symmetry (which takes into account layering and multiple fracture sets) can be used as attributes related to the characteristics of the fractured medium. Monte Carlo simulation was used to test the effect of uncertainties in the a priori information (about background VTI parameters of unfractured rock), as they affect inversion for these attributes. According to this analysis, the direction of fast shear-wave polarization was inverted robustly in the Monte Carlo simulation. Although the average values of the components of fracture compliance matrices obtained from Monte Carlo simulation were in agreement with the actual values used for forward modeling, individual values obtained in Monte Carlo simulation were sensitive to uncertainties in the background properties in general. Because the elastic properties of background VTI media without fractures (or other azimuthally variable features) do not cause azimuthal changes in reflection coefficient variation with offset, simultaneous inversion for background properties and fracture tensor components require additional constraints.

No abstract

No abstract

No abstract

We inverted P-wave amplitude variation with offset and azimuth (AVOAz) data from the Marcellus Shale to obtain fracture parameters that can fully describe the elastic behavior of fractured rocks with overall symmetry of orthorhombic or monoclinic. AVOAz data from two interfaces, (1) the upper interface between top Marcellus and Stafford limestone and (2) the lower interface between base Marcellus and Onondaga limestone, were used for inversion. To check the validity of our inversion results, fracture parameters for the Marcellus Shale were inverted for each interface using Monte Carlo simulation to include uncertainty in our a priori information, i.e., elastic properties of unfractured rocks that are assumed to be known from well logs. Inversion results appeared robust with respect to uncertainties and converge to the same values for the two inversions. Our results were also consistent with singular value decomposition analysis (resolution matrix).

A B S T R A C TWe present a method for inversion of fracture compliance matrix components from wide-azimuth noisy synthetic PS reflection data and quantitatively show that reflection amplitude variations with offset and azimuth for converted PS-waves are more informative than P-waves for fracture characterization. We consider monoclinic symmetry for fractured reservoir (parameters chosen from Woodford Shale), which can be formed by two or more sets of vertical fractures embedded in a vertically transverse isotropic background. Components of effective fracture compliance matrices for a medium with monoclinic symmetry are related to the characteristics of the fractured medium. Monte Carlo simulation results show that inversion of PS reflection data is more robust than that of PP reflection data to uncertainties in our a priori knowledge (vertically transverse isotropic parameters of unfractured rock) than PP reflection data. We also show that, while inversion of PP reflections is sensitive to contrasts in elastic properties of upper and lower media, inversion of PS reflections is robust with respect to such contrasts.

This paper compares rock physics trends in the Vp-vs.-Vs crossplot and the Vp/Vs-vs.-compressional slowness crossplot. Trend uncertainties are presented with laboratory data from the Bakken, Bazhenov, Monterey, and Niobrara shales; departures from expected trends attributed to kerogen, hydrocarbon, anisotropy, and well deviation are discussed. Anisotropy models, such as ANNIE (Schoenberg et al.1996), are presented for computing Thomsen parameters and stiffness coefficients. Castagna mudrock line (Castagna et al. 1993) derived from in-situ sonic and seismic measurements provided an average linear relationship between compressional and shear-wave velocities. Brie (1995) extended previous work to include predicting gas saturation from a Vp/Vs-vs.-compressional slowness crossplot. Projecting the Castagna mudrock line onto a shear-vs.-compressional slowness crossplot proved useful for interpreting sonic data. Classical-rock physics equations were used to model compressional and shear velocities as a function of well deviation. Laboratory anisotropy models allowed for characterizing the effects of dispersion, anisotropy, and well deviation. Anisotropic-rock physics models for the Bakken, Bazhenov, Monterey, and Niobrara organic shales are presented and compared in terms of the Thomsen parameters, ε, γ, and δ, and stiffness coefficients, Cij. These models are first transposed to trend curves in Vp-vs.-Vs, Vp/Vs-vs.-compressional slowness, and shear-vs.-compressional slowness crossplots and then compared to the Castagna mudrock trend curve. The anisotropy models are then applied to characterize the effect of well deviation on these trend curves. Results are also presented for well log data from the Eagle Ford, Haynesville, and Bakken formations in the context of the discussed crossplots and then compared with the expected trend curves. The Eagle Ford data satisfies the carbonate Vp-vs.-Vs trend predicted in previous literature by Castagna et al. (1993), and the Haynesville data clearly satisfies the gas effect predicted by the Brie Vp/Vs-vs.-compressional slowness crossplot discussed. In theory, the models describing anisotropy with the Thomsen parameters or stiffness coefficients are equivalent. In practice, not all the parameters for either model can be measured from log data. Preferentially, anisotropic models should be derived by combining log data from multiple vertical, deviated, and horizontal wells for each shale reservoir.