Résultat de la recherche
Multiple-point statistics using multi-resolution images
Multiple-point statistics (MPS) is a simulation technique allowing to generate images that reproduce the spatial features present in a training image (TI). MPS algorithms consist in sequentially filling a simulation grid such that patterns around the simulated values come from the TI. Following this principle, joint simulations of multiple variables can be handled and complex heterogeneous fields can be generated. However, inconsistent patterns are often found in the results and some spatial features can be difficult to reproduce. In this paper, a new MPS algorithm based on a multi-resolution representation of the TI is proposed to enhance the quality of the realizations. The method consists in first building a pyramid of images from the TI by successive convolution using Gaussian-like kernels. Secondly, a MPS simulation is done at the lowest resolution level. Then, the result is expanded to the next level of resolution (one rank higher) and used as a conditioning variable for a joint MPS simulation at that level. This last step is repeated up to the initial resolution, where the final simulation is retrieved. The method is implemented in the DeeSse code based on the direct sampling algorithm. Most of the features provided by the direct sampling (conditioning to hard data, uni- or multi-variate simulation of categorical and continuous variables, scaling and rotation of the training structures) are compatible with the proposed method and the usability is maintained. Finally, various examples show that in most of the situations, combining Gaussian pyramids with MPS allows to get results of better quality and in less time compared to direct MPS simulations.
Constraining distance-based multipoint simulations to proportions and trends
In the last years, the use of training images to represent spatial variability has emerged as a viable concept. Among the possible algorithms dealing with training images, those using distances between patterns have been successful for applications to subsurface modeling and earth surface observation. However, one limitation of these algorithms is that they do not provide a precise control on the local proportion of each category in the output simulations. We present a distance perturbation strategy that addresses this issue. During the simulation, the distance to a candidate value is penalized if it does not result in proportions that tend to a target given by the user. The method is illustrated on applications to remote sensing and pore-scale modeling. These examples show that the approach offers increased user control on the simulation by allowing to easily impose trends or proportions that differ from the proportions in the training image.