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Understanding disjunctive kriging

Available with Geostatistical Analyst license.

Disjunctive kriging assumes the model

f(Z(s)) = µ1 + ε(s),

where µ1 is an unknown constant and f(Z(s)) is an arbitrary function of Z(s). Notice that you can write f(Z(s)) = I(Z(s) > ct), so indicator kriging is a special case of disjunctive kriging. In Geostatistical Analyst, you can predict either the value itself or an indicator with disjunctive kriging.

In Geostatistical Analyst, the functions g(Z(s0)) available are simply Z(s0) itself and I(Z(s0) > ct). In general, disjunctive kriging tries to do more than ordinary kriging. While the rewards may be greater, so are the costs. Disjunctive kriging requires the bivariate normality assumption and approximations to the functions fi(Z(si)); the assumptions are difficult to verify, and the solutions are mathematically and computationally complicated.

Disjunctive kriging can use either semivariograms or covariances (the mathematical forms used to express autocorrelation) and transformations, but it cannot allow for measurement error.