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变差函数(Variogram)又称半变差函数(Semivariogram),是研究区域化变量的基本工具,记Z(x)为所研究的区域化变量(如矿石品位),γ_z为其变差函数,则变差函数的数学定义为γ_z(x,h)=1/2E{[Z(x+h)-Z(x)]~2}(1)(1)式又称为理论变差函数.按一般的统计学观点,应由下列统计基来估计γ_z,即γ_2(x,h)=1/2N sum from i=1 to N′(i/1)[Z_i(x+h)-Z_i(x)]~2(2)但是在地质问题的应用中,通常是不可能由(2)式来估计γ_z的.因为,在确定的空间位置点X_0上只能有Z(X)的一次观测值,即Z(X_0).因而,只得利用下式来估计γ_z(但这样做仍是有一定条件的).
Variogram, also known as Semivariogram, is the basic tool for studying regionalized variables. Let Z (x) be the regionalized variable (such as ore grade) under study and γ_z be its variogram, Then the mathematical function of variogram is γ_z (x, h) = 1 / 2E {[Z (x + h) -Z (x)] ~ 2} (1) The equation is also called the theoretical variogram. From a general statistical point of view, γ_z should be estimated from the following statistics: γ_2 (x, h) = ½N sum from i = 1 to N ’(i / 1) [Z_i (x + h) However, in the application of geological problems, it is usually impossible to estimate γ_z from equation (2) because only one observation of Z (X) can be made at the determined spatial location point X_0 Therefore, we have to use the following formula to estimate γ_z (but this is still a certain condition).