(1)
The Cross Variogram operation, necessary to perform CoKriging, is an extension of the Spatial correlation operation. Distances, Average lags, Nr of Pairs and semi-variogram values are calculated in the same way as in Spatial correlation (algorithm).
Cross-variogram values are estimated directly from the sample data using the formula:
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(1) |
where:
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|
is the estimated cross-variogram value at distance h where h is ||h|| |
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n(h) |
is the number of data pairs of observations of the first variable ZA and the second variable ZB at locations xi and xj when the distance between xi and xj fits in a distance class h. |
Equation (1) resembles the manner in which experimental semi-variogram values are computed in the Spatial correlation operation with variable ZB replaced by ZA itself.
Cross-variogram values can increase or decrease with distance h depending on the correlation between variable A and variable B. Semi-variogram values on the other hand are by definition positive. When models are fitted to the experimental semi-and cross-variograms, the Cauchy-Schwartz relation (equation 2) must be checked to guarantee a correct CoKriging estimation variance in all circumstances (Deutsch and Journel 1992; Isaaks and Srivastava 1989).
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|gAB | <= Ö (gA * gB ) |
(2) |
for all values of distance 0 < h < limiting distance in the CoKriging operation.
where:
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gAB |
is a cross-variogram value, |
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gA |
is a semi-variogram value for variable A, |
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gB |
is a semi-variogram value for variable B. |
References:
See also:
