Reservoir Characterization With the Discrete Cosine Transform

Summary Inverse estimation (history matching) of permeability fields is commonly performed by replacing the original set of unknown spatially discretized reservoir properties with a smaller (lower-dimensional) 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), also known as principal component analysis, is a classical option for deriving low-dimensional parameterizations for history-matching applications. The KLT can provide an accurate characterization of complex-property 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 property covariance function and can give poor results when this function does not adequately describe the actual property 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 also 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.