Patch‐based iterative conditional geostatistical simulation using graph cuts

Training image‐based geostatistical methods are increasingly popular in groundwater hydrology even if existing algorithms present limitations that often make real‐world applications difficult. These limitations include a computational cost that can be prohibitive for high‐resolution 3‐D applications, the presence of visual artifacts in the model realizations, and a low variability between model realizations due to the limited pool of patterns available in a finite‐size training image. In this paper, we address these issues by proposing an iterative patch‐based algorithm which adapts a graph cuts methodology that is widely used in computer graphics. Our adapted graph cuts method optimally cuts patches of pixel values borrowed from the training image and assembles them successively, each time accounting for the information of previously stitched patches. The initial simulation result might display artifacts, which are identified as regions of high cost. These artifacts are reduced by iteratively placing new patches in high‐cost regions. In contrast to most patch‐based algorithms, the proposed scheme can also efficiently address point conditioning. An advantage of the method is that the cut process results in the creation of new patterns that are not present in the training image, thereby increasing pattern variability. To quantify this effect, a new measure of variability is developed, the merging index, quantifies the pattern variability in the realizations with respect to the training image. A series of sensitivity analyses demonstrates the stability of the proposed graph cuts approach, which produces satisfying simulations for a wide range of parameters values. Applications to 2‐D and 3‐D cases are compared to state‐of‐the‐art multiple‐point methods. The results show that the proposed approach obtains significant speedups and increases variability between realizations. Connectivity functions applied to 2‐D models transport simulations in 3‐D models are used to demonstrate that pattern continuity is preserved. Key Points Increased flexibility in patch‐based simulation by using a graph cuts approach First time that geostatistical simulation is done by iterative replacement of patches Allows for more variability between realizations and CPU efficiency