Stochastic simulation of patterns using distance-based pattern modeling [electronic resource]
Keywords: Energy Resources Engineering

The advent of multiple-point geostatistics (MPS) gave rise to the integration of complex subsurface geological structures and features into the model by the concept of training images. Initial algorithms generate geologically realistic realizations by using these training images to obtain conditional probabilities needed in a stochastic simulation framework. More recent pattern-based geostatistical algorithms attempt to improve the accuracy of the training image pattern reproduction. In these approaches, the training image is used to construct a pattern database. Consequently, sequential simulation will be carried out by selecting a pattern from the database and pasting it onto the simulation grid. One of the shortcomings of the present algorithms is the lack of a unifying framework for classifying and modeling the patterns from the training image. In this thesis an entirely different approach will be taken towards geostatistical modeling. A novel, principled and unified technique for pattern analysis and generation that ensures computational efficiency and enables a straightforward incorporation of domain knowledge will be presented. In the developed methodology (called DisPAT), patterns scanned from the training image are represented as points in a Cartesian space using multi-dimensional scaling. The idea behind this mapping is to use distance functions as a tool for analyzing variability between all the patterns in a training image. These distance functions can be tailored to the application at hand. Next, by significantly reducing the dimensionality of the problem and using kernel space mapping, an improved pattern classification algorithm is obtained. Additionally, a multi-resolution approach is presented for modeling the patterns of the training image at various scales. The proposed distance-based pattern-modeling techniques are inspired by biology and the human visual system. Several examples are presented and a qualitative comparison is made with previous methods to demonstrate the capabilities of this simple, yet powerful system. We show how the proposed methodology is much less sensitive to the user-provided parameters, and at the same time has the potential to reduce computational time significantly. Another aspect of present MPS algorithms is their strong dependence on the algorithmic parameters that the practitioner specifies. This, not only entails tedious trial-and-error computations for tuning the parameters, but also triggers potential subjectivity in modeler's decisions. In order to obtain a systematic pattern-based approach, new techniques on learning the optimal set of parameters are introduced. A series of examples is provided to verify the competency of these approaches in, not only facilitating the modeling process, but also ensuring a rigorous simulation framework. Furthermore, better data conditioning algorithms for both the hard data and the soft data are proposed. An improved pattern continuity and data-conditioning capability is observed in the generated realizations for both continuous and categorical variables. Some improvements in multi-scale data conditioning are also described. Overall, we demonstrate the higher conditioning capability of the proposed method in comparison with the traditional algorithms. Finally, novel techniques on modeling non-stationary phenomena are introduced. The traditional approaches rely mainly on auxiliary variables to force the MPS algorithm into generating the desired spatial behavior; such as defining regions, constraining the facies proportions, or specifying the rotation/scaling of the features spatially. Rather in this thesis, the original MPS modeling paradigm, where a training image is the sole prerequisite for simulation, is re-established. The proposed framework conceptually embeds the spatial components of the patterns into geostatistical modeling. Various training images are used to demonstrate the capabilities of proposed approaches for modeling non-stationarity.