Permeability Parametrization Using Higher Order Singular Value Decomposition (HOSVD)

Abstract

Model reduction is of highly interest in many science and engineering fields where the order of original system is such high that makes it difficult to work with. In fact, model reduction or parametrization defined as reducing the dimensionality of original model to a lower one to make a costly efficient model. In addition, in all history matching problem, in order to reduce the ill-posed ness of the problem, it is necessary to de-correlate the parameters. Proper orthogonal decomposition (POD) as an optimal transformation is widely used in parameterization. To obtain the bases for POD, it is necessary to vectorize the original replicates. Therefore, the higher order statistical information is lost due to slicing the replicates. Another approach that deals with the replicates as they are, is high order singular value decomposition (HOSVD). In the present work permeability maps dimension is reduced using HOSVD image compression method. Unknown permeability maps are also estimated using HOSVD and results of both parts compared to those of SVD.