  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.
