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.

Summary: Geophysical logging is widely used in lithofacies identification, reservoir parameter prediction, and geological modeling. However, it is common to have well-log sections with low-quality and/or missing segments. Repeating the well-log measurements is not only expensive but might also be impossible depending on the condition of the borehole walls. In these situations, reliable and accurate well-log prediction is, therefore, necessary in different stages of the geomodeling workflow. In this study, we propose a time series regression model to predict missing well-log data, incorporating facies information as an additional geological input and using discrete wavelet transform (DWT) to denoise the input data set. The main contributions of this work are threefold: (i) We jointly use facies information with well logs as the input data set; (ii) we use DWT to denoise the input data and consequently improve the signal-to-noise ratio of the input data; and (iii) we regard the depth domain as the time domain and use a time series regression algorithm for log reconstruction modeling. We show a real application example in two distinct scenarios. In the first, we predict missing well-log intervals. In the second, we predict complete well logs. The experimental results show the ability of the proposed prediction model to recover missing well-log data with high accuracy levels.