By Jeffrey M. Yarus, Richard L. Chambers
Stochastic Modeling and Geostatistics vol.1 (ISBN 0891817026)
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Extra info for Stochastic modeling and geostatistics: principles, methods, and case studies
Sample text
The inconvenience of this approach is the impossibility to directly detect anisotropies in the semivariogram. CROSS-VALIDATION Geostatistics has no tests of significance to guide the user’s decisions. Cross-validation is the only criterion available to measure the combined excellence for the selection of the kriging type, assumptions about the nature of the spatial variation of the mean, and 33 testing of isotropy and the semivariogram modeling, particularly when the fitting is done by eye. Crossvalidation is a procedure by which observations are dropped with replacement one at a time from a sample of size n, and for each discarded observation, an estimate is computed at the location of the discarded observation by using, at most, the remaining (n – 1) measurements.
The law, as paraphrased by Krumbine and Sloss (1963, Stratigraphy and Sedimentation, W. H. ” Taken commutatively, geologists have often attempted to predict the lateral variability of facies from a vertical sequence of stratigraphy. In the chapter Theory and Applications of Vertical Variability Measures from Markov Chain Analysis, J. H. Doveton presents an interesting alternative to the geostatistical simulation approach of reservoir facies. He points out that Markovian statistics of vertical variability are applicable to selected problems of lateral facies prediction and simulation.
Olea provides an excellent overview of semivariograms, the tool used in geostatistics to estimate and model spatial variability, in the chapter entitled Fundamentals of Semivariogram Estimation, Modeling, and Usage. The sample support is the area or volume over which a measurement is made. Understanding how one measurement relates to another in close proximity is critical because geostatistical methods are highly sensitive to the spatial controls on variability. This is particularly true with tensor variables like permeability, for which mathematical averaging over volumes of various dimensions tends to be a problem.