Concept

Variogram

Summary
In spatial statistics the theoretical variogram, denoted 2\gamma(\mathbf{s}_1,\mathbf{s}_2), is a function describing the degree of spatial dependence of a spatial random field or stochastic process Z(\mathbf{s}). The semivariogram \gamma(\mathbf{s}_1,\mathbf{s}_2) is half the variogram. In the case of a concrete example from the field of gold mining, a variogram will give a measure of how much two samples taken from the mining area will vary in gold percentage depending on the distance between those samples. Samples taken far apart will vary more than samples taken close to each other. Definition The semivariogram \gamma(h) was first defined by Matheron (1963) as half the average squared difference between the values at points (\mathbf{s}_1 and \mathbf{s}_2) separated at distance h. Formally :\gamma(h)=\frac{1}{2V}\iiint_V \left[f(M+h) - f(M) \right]^2dV, where
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