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Spatial analysis of a conceptual geological model is the main purpose of any MPS algorithm. The method analyzes the spatial statistics of the geological model, called the training image, and generates realizations of the phenomena that honor those input multiple-point statistics.
Spatial statistics is a field of applied statistics dealing with spatial data. It involves stochastic processes ( random fields , point processes ), sampling , smoothing and interpolation , regional ( areal unit ) and lattice ( gridded ) data, point patterns , as well as image analysis and stereology .
Geostatistics is a branch of statistics focusing on spatial or spatiotemporal datasets.Developed originally to predict probability distributions of ore grades for mining operations, [1] it is currently applied in diverse disciplines including petroleum geology, hydrogeology, hydrology, meteorology, oceanography, geochemistry, geometallurgy, geography, forestry, environmental control, landscape ...
Chapter 6 concerns the types of data to be visualized, and the types of visualizations that can be made for them. Chapter 7 concerns spatial hierarchies and central place theory, while chapter 8 covers the analysis of spatial distributions in terms of their covariance. Finally, chapter 10 covers network and non-Euclidean data. [1] [3]
However, much of the life and interest of the subject, and indeed many of its original ideas, flow from a very wide range of applications, for example: astronomy, [6] spatially distributed telecommunications, [7] wireless network modeling and analysis, [8] modeling of channel fading, [9] [10] forestry, [11] the statistical theory of shape, [12 ...
In his widely cited book, Statistics for Spatial Data, [4] Cressie established a general spatial model that unified statistics for geostatistical data, regular and irregular lattice data, point patterns, and random sets, building on earlier research of his and many others on statistical theory, methodology, and applications for spatial data.
In geostatistical models, sampled data are interpreted as the result of a random process. The fact that these models incorporate uncertainty in their conceptualization doesn't mean that the phenomenon – the forest, the aquifer, the mineral deposit – has resulted from a random process, but rather it allows one to build a methodological basis for the spatial inference of quantities in ...
The need to use point processes to model these kinds of data lies in their inherent spatial structure. Accordingly, a first question of interest is often whether the given data exhibit complete spatial randomness (i.e. are a realization of a spatial Poisson process) as opposed to exhibiting either spatial aggregation or spatial inhibition.