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Lecture8

# Lecture8 - KRIGING KRIGING by Danny Dorsel Timothy La...

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KRIGING http://www.cee.vt.edu/ewr/environmental/teach/smprimer/kriging/kriging.html#TheoryEqns[3/30/2009 6:59:09 AM] KRIGING by Danny Dorsel & Timothy La Breche (These examples were created using statistical packages that utilize kriging.)

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KRIGING http://www.cee.vt.edu/ewr/environmental/teach/smprimer/kriging/kriging.html#TheoryEqns[3/30/2009 6:59:09 AM] Table of Contents 1) Geostatistics 2) Semivariograms 3) Kriging GEOSTATISTICS Geostatistics is a branch of applied statistics developed by George Matheron of the Centre de Morophologie Mathematicque in Fontainebleau, France. The original purpose of geostatistics centered on estimating changes in ore grade within a mine. However, the principles have been applied to a variety of areas in geology and other scientific disciplines. A unique aspect of geostatistics is the use of regionalized variables which are variables that fall between random variables and completely deterministic variables. Regionalized variables describe phenomena with geographical distribution (e.g. elevation of ground surface) The phenomenon exhibit spatial continuity; however, it is not always possible to sample every location. Therefore, unknown values must be estimated from data taken at specific locations that can be sampled. The size, shape, orientation, and spatial arrangement of the sample locations is termed the support and influences the capability to predict the unknown samples. If any of these characteristics change, then the unknown values will change. The sampling and estimating of regionalized variables are done so that a pattern of variation in the phenomenon under investigation can be mapped such as a contour map for a geographical region. SEMIVARIOGRAMS Semivariance is a measure of the degree of spatial dependence between samples. The magnitude of the semivariance between points depends on the distance between the points. A smaller distance yields a smaller semivariance and a larger distance results in a larger semivariance. The plot of the semivariances as a function of distance from a point is referred to as a semivariogram . The semivariance increases as the distance increases until at a certain distance away from a point the semivariance will equal the variance around the average value, and will therefore no longer increase, causing a flat region to occur on the semivariogram called a sill. From the point of interest to the distance where the flat region begins is termed the range or span of the regionalized variable. Within this range, locations are related to each other, and all known samples contained in this region, also referred to as the neighborhood , must be considered when estimating the unknown point of interest. Examples of possible semivariograms are provided in the drawing below.
KRIGING http://www.cee.vt.edu/ewr/environmental/teach/smprimer/kriging/kriging.html#TheoryEqns[3/30/2009 6:59:09 AM] The center of the neighborhood is usually the unknown value. In order to determine this value, all known values within the neighborhood are assigned weights using the semivariogram. These weights and known

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