Prestack seismic inversion is an ill-posed problem and must be regularized to stabilize the inverted results. In particular, edge-preserving regularization with prior constraints based on Markov random field (MRF) has proved to be an effective technique for reconstructing subsurface models. However, regularized seismic inversion, based on the standard MRF scheme, typically makes use of isotropic MRF neighborhoods, in which the weighting coefficients of the model gradients are equivalent in all directions. Considering real geological conditions, subsurface formations are expected to be laterally continuous and vertically stratified. Therefore, the anisotropic effects caused by model gradients which vary along different directions should not be ignored. In this paper, we proposed a new prestack seismic inversion method based on anisotropic MRF (AMRF). In this method, AMRF coefficients are incorporated into the standard MRF scheme. These coefficients demonstrate directional variations and gradient dependencies, intended to directly correct the errors caused by the anisotropic model gradients on the prior constraints. In particular, we introduced the anisotropic diffusion method to calculate the AMRF coefficients. The proposed inversion method can effectively remove the anisotropic features of the model gradients and significantly improve the inversion results, especially for geologically layered formations. We demonstrated the effectiveness of the inversion method by both 2-D synthetic test and field data example, which presented encouraging results.

Regularization is effective in mitigating the ill-condition existing in inverse problems. With respect to the ill-conditioned prestack seismic inversion, regularization aims to stabilize the multiple inverted results and, essentially, reconstruct structural features of subsurface parameter (model) as realistic as possible. Among variants of regularization method, Markov random field (MRF) is an effective approach in formulating prior constraint. However, standard MRF-based or other methods often require prior knowledge of the structural features of desired models, e.g., smoothness, blockiness, and sparsity, after which the prior constraint is formulated. Therefore, such a model-driven regularization method lacks applicability to the cases with geological complexity or limited prior knowledge. In this article, we propose a data-driven regularization scheme for prestack seismic inversion. The MRF-based constraints formulated by multiple orders are quantitatively integrated into the inversion procedure driven by seismic data. In order to endow the method with high adaptation to geological complexity, we iteratively adjust the regularization parameters of multiple orders via the maximum likelihood estimator. Besides, we incorporate the multivariate Gaussian distribution among elastic parameters into the model update/perturbation in fast simulated annealing, by which the objective function is optimized while the multiple results are correlated and stabilized. Synthetic tests indicate that the proposed method is capable of revealing structural details and achieving multiple results with less uncertainty. Field application provides further validation, wherein the results distinctly reveal structural details within the target formation.

Rock-physics amplitude-variation-with-offset (AVO) inversion aims at directly predicting reservoir properties from prestack seismic data. However, carbonate reservoir rocks often develop complex pore structures, which limits the application of conventional inversion methods with fixed pore-geometry parameters. We derive a PP-wave reflectivity equation in terms of porosity, water saturation, and pore-aspect ratio and we develop a rock-physics AVO inversion method to jointly estimate the petrophysical and pore-geometry parameters in carbonates. The reflectivity equation is obtained by linearizing the rock-physics model based on the differential effective medium model and Gassmann’s equation using Taylor series approximation, and we combine the linearization with the Aki-Richards equation. Thanks to the linearized model, the analytical solution to the inverse problem is derived using Bayesian linear theory. Our solution combines simulated annealing to estimate the prior information of the pore geometry and the iterative Bayesian inversion to update the posterior model. The method is tested on a benchmark data set and compared with conventional methods with a fixed aspect ratio. The results show that our method improves the petrophysical results. The method is also compared with two-step and nonlinear inversion methods to demonstrate its advantages. The method is applied to a field seismic section from a carbonate reservoir with a complex pore structure to demonstrate its advantages in terms of prediction accuracy.

The estimation of reservoir parameters from seismic observations is one of the main objectives in reservoir characterization. However, the forward model relating the petrophysical properties of rocks to observed seismic data is highly nonlinear, and solving the relevant inverse problem is a challenging task. We have developed a novel inversion method for jointly estimating the elastic and petrophysical parameters of rocks from prestack seismic data. We combine a full rock-physics model and the exact Zoeppritz equation as the forward model. To overcome the ill conditioning of the inverse problem and address the complex prior distribution of model parameters given lithofacies variations, we have developed a regularization term based on the prior Gaussian mixture model under a Bayesian framework. The objective function is optimized by the fast simulated annealing algorithm, during which the Gaussian mixture-based regularization terms are adaptively and iteratively adjusted by the maximum likelihood estimator, allowing the posterior distribution to be more consistent with the observed seismic data. The adaptive regularization method improves the accuracy of petrophysical parameters compared with sequential inversion and nonadaptive regularization methods, and the inversion result can be used for indicating gas-saturated areas when applied to field data.

Petrophysical inversion quantitatively extracts reservoir properties from seismic data/attributes, which has gained increasing attention in assisting hydrocarbon reservoir exploration and evaluation. However, given complex reservoirs, its application is limited either due to the adopted rock-physics model or due to the computational demand. We have developed a semianalytic seismic petrophysical inversion method intended for complex reservoirs. The method incorporates the double-porosity Biot-Rayleigh (BR) model into the petrophysical forward operator, to take into account the heterogeneities within reservoir rocks. The inversion process combines statistical rock-physics modeling and Bayesian Gaussian mixture estimation, by which the analytical expression of the results can be achieved with limited computational cost. To better describe pore structure complexities, the inclusion content that constitutes a double-porosity medium of the BR model is considered an unknown variable, which favors the spatial variation of pore structures under complex lithofacies conditions. In addition, the method uses simulated annealing to estimate the inclusion content at a well location to obtain its prior information and takes advantage of the Monte Carlo simulation in rock-physics modeling to stabilize the inversion results. The method is tested and applied to the field data from a carbonate reservoir in southern China, the results of which show that the accuracy of the petrophysical parameters in terms of root-mean-square error are increased by as much as 12% compared with the method based on the Gassmann model.