Block Simulation of Multiple Correlated Variables |
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Authors: | Alexandre Boucher Roussos Dimitrakopoulos |
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Institution: | (1) Department of Environmental Earth System Science, Stanford University, Stanford, CA 94305, USA;(2) COSMO—Stochastic Mine Planning Laboratory, Department of Mining, Metals and Materials Engineering, McGill University, Montreal, QC,, H3A 2A7, Canada |
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Abstract: | Numerical representations of multivariate natural phenomena, including characteristics of mineral deposits, petroleum reservoirs
and geo-environmental attributes, need to consider and reproduce the spatial relationships between correlated attributes of
interest. There are, however, only a few methods that can practically jointly simulate large size multivariate fields. This
paper presents a method for the conditional simulation of a non-Gaussian vector random field directly on block support. The
method is derived from the group sequential simulation paradigm and the direct block simulation algorithm which leads to the
efficient joint simulation of large multivariate datasets jointly and directly on the block support. This method is a multistage
process. First, a vector random function is orthogonalized with minimum/maximum autocorrelation factors (MAF). Blocks are
then simulated by performing LU simulation on their discretized points, which are later back-rotated and averaged to yield
the block value. The internal points are then discarded and only the block value is stored in memory to be used for further
conditioning through a joint LU, resulting in the reduction of memory requirements. The method is termed direct block simulation
with MAF or DBMAFSIM. A proof of the concept using an exhaustive data set demonstrates the intricacies and the performance
of the proposed approach. |
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Keywords: | Multivariate Min/Max autocorrelation factors Direct block simulation Joint simulation |
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