a b s t r a c tIn 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.

International audienceIn many domains, numerical models are initialized with inputs defined on irregular grids. In petroleum reservoir engineering, they consist of a great variety of grid cells of different size and shape to enable fine-scale modeling in the vicinity of the wells and coarse modeling in less important regions. Geostatistical simulation algorithms, which are used to populate the cells of unstructured grids, often have to address the problem of transition from the small-scale statistical data stemming from laboratory cores analysis and seismic processing to the multiple larger scale geological supports. The reasonable generalization of the above-mentioned problem is integrating the point-support data to simulations on irregular supports. Classical geostatistical simulation methods for generating realizations of a stationary Gaussian random function cannot be applied to unstructured grids directly, because of the uneven supports. This article provides a critical review of existing geostatistical simulation methodologies for unstructured grids, including fine-scale simulations with upscaling and direct sequential simulation algorithms, and presents two different generalizations of the discrete Gaussian model for this purpose, thereby discussing the theoretical assumptions and the accuracy when implementing these models

Although Boolean model simulation has been widely used during the last two decades to simulate sedimentary bodies (especially in fluvio-deltaic environments), a key issue has subsisted. One of the most important parameter for object model simulation, namely the (non stationary) intensity of the underlying object process, is not a parameter provided by the end user but must instead be computed from other input parameters, such as local proportions of lithofacies, erosion rule between objects of different types and interaction between objects. This paper revisits a birth and death algorithm for simulating conditional, non stationary, multitype objects models with interaction. It provides workable approximations for computing the local intensity of the underlying point process to respect proportion maps. Simulated examples show that this algorithm is able to reproduce the desired proportions. Important issues for implementing this algorithm are discussed.

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