Conditioning reservoir models on rate data using ensemble smoothers

There are several issues to consider when we use ensemble smoothers to condition reservoir models on rate data. The values in a time series of rate data contain redundant information that may lead to poorly conditioned inversions and thereby influence the stability of the numerical computation of the update. A time series of rate data typically has correlated measurement errors in time, and negligence of the correlations leads to a too strong impact from conditioning on the rate data and possible ensemble collapse. The total number of rate data included in the smoother update will typically exceed the ensemble size, and special care needs to be taken to ensure numerically stable results. We force the reservoir model with production rate data derived from the observed production, and the further conditioning on the same rate data implies that we use the data twice. This paper discusses strategies for conditioning reservoir models on rate data using ensemble smoothers. In particular, a significant redundancy in the rate data makes it possible to subsample the rate data. The alternative to subsampling is to model the unknown measurement error correlations and specify the full measurement error covariance matrix. We demonstrate the proposed strategies using different ensemble smoothers with the Norne full-field reservoir model.     

Fast Hyperspectral Feature Reduction Using Piecewise Constant Function Approximations

The high number of spectral bands that are obtained from hyperspectral sensors, combined with the often limited ground truth, solicits some kind of feature reduction when attempting supervised classification. This letter demonstrates that an optimal constant function representation of hyperspectral signature curves in the mean square sense is capable of representing the data sufficiently to outperform, or match, other feature reduction methods such as principal components transform, sequential forward selection, and decision boundary feature extraction for classification purposes on all of the four hyperspectral data sets that we have tested. The simple averaging of spectral bands makes the resulting features directly interpretable in a physical sense. Using an efficient dynamic programming algorithm, the proposed method can be considered fast.