Geostatistics has become a preferred tool for the identification of lithofacies from sparse data, such as measurements of hydraulic conductivity and porosity. Recently we demonstrated that the support vector machine (SVM), a tool from machine learning, can be readily adapted for this task, and offers significant advantages. On the conceptual side, the SVM avoids the use of untestable assumption...

Geostatistical techniques have gained widespread use in ecology and environmental science. Variograms are commonly used to describe and examine spatial autocorrelation, and kriging has become the method of choice for interpolating spatially-autocorrelated variables. To date, most applications of geostatistics have defined the separation between sample points using simple Euclidean distance. In ...

The modeling of the spatial distribution of image properties is important for many pattern recognition problems in science and engineering. Mathematical methods are needed to quantify the variability of this spatial distribution based on which a decision of classification can be made in an optimal sense. However, image properties are often subject to uncertainty due to both incomplete and impre...

Temporal and Spatial Modeling of Groundwater Level in Bushehr Plain using Artificial Intelligence Geostatistics

With the growing capabilities of Geographic Information Systems (GIS) and user-friendly software, statisticians today routinely encounter geographically referenced data containing observations from a large number of spatial locations and time points. Over the last decade, hierarchical spatiotemporal process models have become widely deployed statistical tools for researchers to better understan...

Spatially correlated functional data is present in a wide range of environmental disciplines and, in this context, efficient prediction of curves is a key issue. We present an approach for spatial prediction based on the functional linear point-wise model adapted to the case of spatially correlated curves. First, a smoothing process is applied to the curves by expanding the curves and the funct...

Two geostatistical methods for history matching are presented. Both rely on the sequential simulation principle for generating geologically sound realizations. The first method relies on perturbing the sequential simulation through the perturbation of the conditional distribution models; the second method relies on the perturbation of random numbers. We show that both approaches are general in ...