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.

翻译：在过去数十年间，多点统计模拟（MPS）方法层出不穷，旨在提升结果真实性的多个关键方面，包括空间连续性、条件性、随机性及计算效率。然而，同时增强这些关键因素对研究者而言仍具挑战。本文提出将CCSIM与离散小波变换（DWT）相结合以缓解上述问题。该方法的首要步骤是计算训练图像（TI）与特定小波分解层级上先前模拟网格共享区域的DWT，随后利用互相关函数（CCF）衡量小波近似系数之间的相似度。这些近似系数通过压缩模式表征的同时保留其主要变化与本质特征，从而加速最优匹配模式的搜索。一旦在小波近似系数中识别出最佳匹配模式，即可通过逆DWT变换整合DWT细节系数，完美重构原始模式。针对不同类别TI的实验表明，该方法的模拟结果与多尺度CCSIM（MS-CCSIM）相当，且改善了相连通性与模式复现能力。源代码实现见 https://github.com/MBS1984/CCWSIM。