Efficient Permeability Parameterization With the Discrete Cosine Transform

摘要

The inverse estimation of permeability fields (history matching) is commonly performed by replacing the original set of unknown spatially discretized permeabilities with a smaller (lower dimensionality) group of unknowns that captures the most important features of the field. This makes the inverse problem better posed by reducing redundancy. The Karhunen-Loeve Transform (KLT) is a classical option for deriving low dimensional parameterizations for history matching applications. The KLT can provide an accurate characterization of complex permeability fields but it can be computationally demanding. In many respects this approach provides a benchmark that can be used to evaluate the performance of more computationally efficient alternatives. The KLT requires knowledge of the permeability covariance function and can give poor results when this matrix does not adequately describe the actual permeability field. By contrast, the Discrete Cosine Transform (DCT) provides a robust parameterization alternative that does not require specification of covariances or other statistics. It is computationally efficient and in many cases is almost as accurate as the KLT. The DCT is able to accommodate prior information, if desired. Here we describe the DCT approach and compare its performance to the KLT for a set of geologically relevant examples.