MVarGOSIM: an MPS algorithm for characterizing complex structures with multiple variables

Creating a highly accurate geological model at a large scale presents a considerable challenge, primarily due to constraints imposed by sparse data availability. A promising strategy to mitigate these limitations involves the integration of multiple variables. Nevertheless, the effective incorporation and amalgamation of patterns derived from diverse variables during the simulation process remains a significant obstacle in pattern-based methodologies. This study presents a novel iterative multiple-point statistics (MPS) algorithm to construct complex geological structures by integrating co-located multiple variables in conjunction with fully connected deep artificial neural networks (FCNs). The algorithm operates under the assumption that profiles of different data types are co-located, allowing patterns from various variables to be converted into probabilities and combined using a cross-entropy-weighted pooling method. The proposed approach consists of three main components: generating geological subsurfaces using FCNs, creating an initial model incorporating multiple variables, and refining this initial model through an iterative process. The trained FCNs generate the top and bottom surfaces of a geological object, with a loss function defined by geological contact elevation. In the initial model construction, patterns from co-located data are integrated with pattern probabilities, using lithology cross-sections as the primary variable and velocity and density profiles as auxiliary variables. Geological constraints, such as stratigraphic sequences and the thickness of geological objects, are applied in a post-processing phase to adjust the relationships in the initial model. An expectation–maximization-like (EM-like) optimization technique is used to rectify artifacts present in the initial model. The efficacy of the proposed algorithm is demonstrated by reconstructing the overthrust model developed by SEG/EAGE. Comparative analyses between the reference model and the results obtained with and without multiple variables indicate that the proposed algorithm achieves a more accurate representation of geological objects while also better preserving their geometry and interrelationships.