Patch‐based iterative conditional geostatistical simulation using graph cuts

Abstract

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.

Training‐Image Based Geostatistical Inversion Using a Spatial Generative Adversarial Neural Network

“…Producing 10 2 and 10 3 realizations with our SGAN thus requires 6.0 h, and 6.0 h as well. In contrast, producing 10 2 and 10 3 realizations with DS necessitates 32.8 h and 327.8 h. Faster MPS algorithms than DS are however available (e.g., Li et al, ; Tahmasebi & Sahimi, ). Since training time is expected to reduce a lot in the near future (and already has at the time of writing) owing to the quick evolution of deep learning software, this warrants further investigations.…”

“…Subsurface flow and transport modeling studies often rely on inversion methodologies to derive subsurface structures that are consistent with both available prior information and indirect measurements of one or more state variables, such as hydraulic head or concentration. When it is unrealistic to assume that the subsurface is multi‐Gaussian (e.g., Gómez‐Hernández & Wen, ; Journel & Zhang, ), one popular solution is to resort to multiple‐point statistics (MPS) simulation (e.g., Li et al, ; Mariethoz et al, ; Strebelle, ; Tahmasebi, ; Tahmasebi & Sahimi, ). MPS techniques generate model realizations that honor a prior model which is determined by a training image (TI).…”

Inversion using a new low-dimensional representation of complex binary geological media based on a deep neural network

“…We now turn our attention to the generation of 3D model realizations. Li et al (2016). Running 8 different GC instances simultaneously, this took approximately 6 hours.…”

Generative Modeling of InSAR Interferograms

“…Sentinel-1 can provide many training images of noise and processing errors when using a small temporal baseline to exclude deformations. One solution stands out: simulating patches of cells instead of a single cell at a time (e.g., Hoffimann et al, 2017;Li et al, 2016;Tahmasebi & Sahimi, 2016). However, the DS runs slowly compared to its covariance-based counterpart (Figure 3).…”

“…Fortunately, many studies over the recent years have focused on decreasing the computing cost while improving the quality of the realizations. One solution stands out: simulating patches of cells instead of a single cell at a time (e.g., Hoffimann et al, 2017;Li et al, 2016;Tahmasebi & Sahimi, 2016). It also shows promising applications in a Monte Carlo setting (Pirot et al, 2017;Zahner et al, 2015).…”