Multi-scale stochastic simulation with a wavelet-based approach

Conditional simulation of random fields based on integrating multi-scale spatial data using wavelets is detailed herein. Course scale data are first simulated using sequential Gaussian co-simulation. For all finer scales, wavelet coefficients are simulated by using a template matching algorithm borrowing information from a training image. Spatial up-scaling is performed through the inverse wavelet transformation. Examples using an exhaustive dataset show that the proposed method works well and is robust when changing the amount of hard data and resolution of secondary data. Sensitivity analysis shows that the selection of a suitable template size can improve the performance of the proposed method. A comparative study shows that the proposed algorithm is computationally faster than the well-known simpat and filtersim algorithms, as well as reasonably accurate in terms of reproduction of continuity in complex geologic environments.