Abstract
A new multiple-point statistics algorithm, SparseSim, is developed based on sparse approximation algorithm, which has wide applications for stochastic simulation in the field of geosciences and beyond. The current version is described in the context of reservoir characterization, which includes well and seismic data integration. In sparse approximation, a model image is represented as weighted linear combination of columns of the dictionary matrix. For this purpose, a parsimonious subset of the dictionary columns and their corresponding weights are selected using sparse coding methods. The dictionary is obtained by dictionary learning algorithms trained over and adapted for specific types of model images in the training set. Based on the sparse approximation algorithm, the approximated model image is generated by multiplication of the dictionary and the weight matrices. Intuitively, stochastic simulation of the coefficient (weight) matrix will lead to generation of new stochastic realizations. The SparseSim algorithm, as represented in this paper, works based on extracting the trend for nonzero elements in the significant rows of the weight matrix, and it is proposed under two general schemes: stochastically simulating the details of the training image or stochastically simulating both the details and the mean value of the training image. It is shown in this paper that under both schemes the generated realizations, while stochastically distinct, are similar to each other and to the training image. Different aspects of the SparseSim algorithm such as SparseSim in 3D, SparseSim in different scales, and data conditioning are also discussed.
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This research has not received any grant from any for-profit or non-for-profit institution or organization. This research is designed and performed by the author as part of a broader self-motivated and self-derived research study independently from any individual or organization and only consulting the references. I greatly appreciate the research works of other scientists cited in this article which have paved the way for further developments and discoveries.
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Hosseini, M. SparseSim: Stochastic Simulation and Modeling Based on Sparse Approximation and Dictionary Learning. Nat Resour Res 30, 3503–3532 (2021). https://doi.org/10.1007/s11053-021-09887-5
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DOI: https://doi.org/10.1007/s11053-021-09887-5