Spatial Statistics and Digital Image Analysis (1991) / Chapter Skim
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5. Geostatistical Analysis of Spatial Data
5. Geostatistical Analysis of Spatial Data
Pages 87-108
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From page 87... ...
are estimated from an initial analysis of the data. The prefix "geo" in geostatistics originally implied statistics pertaining to the earth (Matheron, 1963; see also Hart, 1954, who used the term difl:erently from Matheron, in a geographical context)
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From page 88... ...
S Gandin, independently developed a framework for inference that is virtually identical (Gandin, 1963~; he chose the term "objective analysis" instead of "geostatistics." Section 5.2 presents the basic ideas behind a geostatistical analysis, including a brief discussion of splines and conditional simulation.
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From page 89... ...
Variogram models that depend only on a few parameters ~ can be used as summaries of the spatial dependence and as an important component of optimal linear prediction (kriging)
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From page 90... ...
' the variogram is no longer purely a function of distance between two spatial locations. Anisotropies are caused by the underlying physical process evolving differentially in space.
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does not is a onedimensional standard Wiener process TWO: t > 0~.
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From page 92... ...
Minimizing mean-squared prediction error results from using [tZ(So)
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= Cost for s ~ D and [~) is a zer~mean, intrinsically stationary stochastic process with variers + h)
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Cressie (1989b) presents these two faces of spatial prediction along with 12 others, including disjunctive kriging and inverse-distance-squared weighting.
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From page 95... ...
, i = 1,...,n. That is, unconditional simulation of sample paths of V yields, through (5.22)
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. The strength of geostatistics over more classical statistical approaches is that it recognizes spatial variability at both the "large scale" and the "small scale," or in statistical parlance, it models both spatial trend and spatial correlation.
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From page 97... ...
The chemical reaction of salt and water would create hydrochloric acid that could slowly corrode the canisters. Eventually, the nuclear wastes could reach the aquifer and sometime later contaminate the drinking water.
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be a vali~ variogram, are 8~ > 0, 82 > 0, and 0 < 83 < 2. From the fitted variogram, kriging predictors {Z(so)
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99 Doo f Snatch Co. ~41 _ 31q2 2843 ~44 _ _ 946 616 '347 _ piezometric heat (fit)
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From page 100... ...
More fundamentally, such changes could also adversely affect most other aquatic organisms and plants, resulting in a disruption of the food chain. Acid deposition has also been closely connected with forest decline (Pitelka and Raynal, 1989)
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(1990~. Copyright ~ 1990 by Elsevier Science Publishers, Physical Sciences and Engineering Division.
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From page 102... ...
Optimal spatial prediction (ordinary kriging) can be implemented on the residual process b(~)
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From page 103... ...
Eleven potential sites (Minneapolis, Minnesota; Des Moines, Iowa; Jefferson City, Missouri; Madison, Wisconsin; Springfield, Illinois; Altoona, Pennsylvania; Charlottesville, Virginia; Charleston, West Virginia; Baltimore, Maryland; Trenton, New Jersey; and Knoxville, Tennessee) were chosen to improve geographic coverage of the existing network (of 19 sites)
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From page 104... ...
For temporal data, Rissanen (1984, 1987) takes such an approach; however, his being able to sequence the observations is important, since the accumulated prediction errors form an integral part of his method.
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473-493 in Proceedings of the Conference on Geostatistical, Sensitivity, and Uncertainty Methods for Groundwater Flow and Radionuclide Transport Modeling, B
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From page 106... ...
M Furr, Geostatistical Analysis of Potentiometric Data in the Wolfcamp Aquifer of the Palo Duro Basin, Texas, Technical report EMI/ONWI-587, Battelle Memorial Institute, Columbus, Ohio, 1986.
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From page 107... ...
N., The local structure of turbulence in an incompressible fluid at very large Reynolds numbers, Doklady Akademii Nauk SSSR 30 (1941)
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From page 108... ...
B Zimmerman, A Monte CarIo comparison of spatial semivariogram estimators and corresponding ordinary kriging predictors, Technometrics 33 (1991)
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