CCWSIM: An Efficient and Fast Wavelet-Based CCSIM for Categorical Characterization of Large-Scale

Over the last couple of decades, there has been a surge in various approaches to multiple-point statistics simulation, commonly referred to as MPS. These methods have aimed to improve several critical aspects of realism in the results, including spatial continuity, conditioning, stochasticity, and computational efficiency. Nevertheless, achieving a simultaneous enhancement of these crucial factors has presented challenges to researchers. In the approach that we propose, CCSIM is combined with the Discrete Wavelet Transform (DWT) to address some of these concerns. The primary step in the method involves the computation of the DWT for both the Training Image (TI) and a region shared with previously simulated grids at a specific level of wavelet decomposition. Then, the degree of similarity between the wavelet approximation coefficients is measured using a Cross-Correlation Function (CCF). These approximation coefficients offer a compressed representation of the pattern while capturing its primary variations and essential characteristics, thereby expediting the search for the best-matched pattern. Once the best-matched pattern in the wavelet approximation coefficients is identified, the original pattern can be perfectly reconstructed by integrating the DWT detail coefficients through an Inverse-DWT transformation. Experiments conducted across diverse categorical TIs demonstrate simulations comparable to multi-scale CCSIM (MS-CCSIM), accompanied by an enhancement in facies connectivity and pattern reproduction. The source code implementations are available at https://github.com/MBS1984/CCWSIM.