Horizontal layered formation with a suite of vertical or near-vertical fractures can usually be assumed to be approximate orthotropic medium and it is more suitable for the estimation of the fracture properties with wide-azimuth pre-stack seismic data in shale reservoirs. However, the small contribution of anisotropic parameters to the reflection coefficients highly reduces the stability of the estimation of the anisotropic parameters by utilizing seismic inversion approaches. Therefore, a novel model parameterization approach for the reflectivity and a pragmatic inversion method are proposed to enhance the stability of the inversion for orthotropic media. Previous attempts to characterize the properties of orthotropic media required by the inversion using four or ??ve independent parameters and we derive a novel formulation which reduces the number of parameters to three. The inversion process is better conditioned with fewer degrees of freedom. The result of accuracy comparison between our formulation and the previous ones indicates that our approach has suf??cient precision for reasonable parameters estimation. Furthermore, a Bayesian inversion method is developed that utilizes the amplitude variation with angle and azimuth (AVAZ) of the seismic data. Smooth background constraints reduce the similarity between the inversion result and the initial model, thereby reducing the sensitivity of the inversion result to the initial model. Cauchy and Gaussian probability distributions are utilized as prior constraints on the model parameters and the likelihood function, respectively. These ensure that the results are within the range of plausibility. The synthetic examples demonstrate that the proposed orthotropic AVAZ inversion method is feasible to estimate the anisotropic parameters even with moderate noise. The ??eld data example illustrates the inversion robustness and stability of the proposed method in a fractured reservoir with a single well control.
The classification of shale gas facies from seismic properties is critical for shale gas reservoir characterization. Shale gas facies are affected by many petrophysical properties. Therefore, the characterization of shale facies should be carried out by multiple parameters, which is more reasonable and accurate. However, multi-parameter inversion often leads to unstable results, and coupled properties are generally a way of solving this problem. A Fisher-Bayesian inversion method for estimating shale gas facies is developed in this paper by combining the Fisher projection and Bayesian inversion method. The mathematical method adopted for the inversion is the Bayesian framework. The link between different facies and coupled properties is given by a joint prior distribution. We derive the analytical formulation of the Bayesian inversion under the Gaussian mixture assumption for coupled attributes and different shale gas facies. The proposed approach realizes the fusion of multi-dimensional petrophysical parameters and establishes a shale gas facies prediction method based on coupled properties. The application to real data sets delivers accurate and stable results, where shale gas facies and coupled attributes are accurately predicted and inversed.
The rock permeated by tilted aligned fractures, which is common in the earth, can be considered as the tilted transversely isotropic (TTI) medium under the assumption of the long wavelength. We developed a feasible method to predict fracture parameters (namely weakness parameters and dip angle) and fluid type in the TTI rock using azimuthal seismic data. Based on an approximate stiffness matrix, we first deduced a linear reflection coefficient of the gas-bearing TTI medium in terms of the new fluid indicator and fracture parameters. The reflection coefficient was then rewritten in the form of the Fourier series to decouple the fracture and skeleton-fluid information. Whereupon the sequential Bayesian inversion method was proposed, which consists of three steps. The first two steps conquer inversion instability owing to coupling of the fracture parameters by constructing the linear relationship between the second-order and fourth-order Fourier coefficients. The last step aims at estimating the skeleton-fluid parameters. The sequential Bayesian inversion method alleviates the ill posedness of the multi-parameter simultaneous inversion caused by large differences between contributions of the fracture and skeleton-fluid parameters to the reflectivity. Synthetic and field cases proved the proposed method stable and rational in fracture and fluid detections. Finally, we draw some conclusions from numerical experiments that the approximate stiffness coefficients and derived reflection coefficient are of satisfactory accuracy for the gas-bearing reservoir with low fracture density; The new fluid indicator is sensitive to the fluid type but very weakly dependent on the mineral composition and porosity; Deconvolution processing can improve accuracies of different seismic components calculated using the discrete Fourier transformation.
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