Ensemble-based data assimilation with curvelets regularization

This paper focuses on the use of the curvelet transform to reduce the noise from the posterior realizations after the assimilation of production data with ensemble-based methods. Curvelets provide an almost optimal sparse representation of objects with edges, making them well-suited for denoising estimated geologic facies distributions. The denoising of the updated model variables is implemented in the curvelet domain by minimizing an objective function which promotes the sparsity of curvelet coefficients. Because preservation of the data match is an important measure of the performance of the denoising method, the role of the approximation of the inverse posterior covariance is examined in the minimization. We demonstrate the application of curvelets to denoising with two examples. The results show that curvelets are useful for denoising in the problem concerned in this paper but lose data match unless the covariance is included. In that case, the data match remains relatively good, but not as good as achieved at the end of history matching.