A New High-Order, Nonstationary, and Transformation Invariant Spatial Simulation Approach
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This paper presents a new high-order, nonstationary sequential simulation approach, aiming to deal with the typically complex, curvilinear structures and high-order spatial connectivity of the attributes of natural phenomena. Similar to multipoint methods, the proposed approach employs spatial templates and a group of training images (TI). A coarse template with a fixed number of data points and a missing value in the middle is used, where the missing value is simulated conditional to a data event found in the neighborhood of the middle point of the template, under a Markovian assumption. Sliding the template over the TI, a pattern database is extracted. The parameters of the conditional distributions needed for the sequential simulation are inferred from the pattern database considering a set of weights of contribution given for the patterns in the database. Weights are calculated based on the similarity of the high-order statistics of the data event of the hard data compared to those of the training image. The high-order similarity measure introduced herein is effectively invariant under all linear spatial transformations.
Following the sequential simulation paradigm, the template chosen is sequentially moved on a raster path until all missing points/nodes are simulated. The high-order similarity measure allows the approach to be fast as well as robust to all possible linear transformations of a training image. The approach respects the hard data and its spatial statistics, because it only considers TI replicate data events with similar high-order statistics. Results are promising.
KeywordsTraining Image Data Event Hard Data Sequential Simulation Conditioning Data
Funding was provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant 239019 and mining industry partners of the COSMO Laboratory (AngloGold Ashanti, Barrick Gold, BHP Billiton, De Beers Canada, Kinross Gold, Newmont Mining, and Vale) and the Group for Research in Decision Analysis (GERAD). Thanks are given to Prasun Lala for his assistance.
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