变差函数Variogram

In spatial statistics the theoretical variogram is a function describing the degree of spatial dependence of a spatial random field or stochastic process . It is defined as the variance of the difference between field values at two locations ( and ) across realizations of the field (Cressie 1993):
 
                
                
If the spatial random field has constant mean , this is equivalent to the expectation for the squared increment of the values between locations x and y (Wackernagel 2003) (where x and y are not coordinates but points in space):
 
                
                
where itself is called the semivariogram. In the case of a stationary process, the variogram and semivariogram can be represented as a function of the difference between locations only, by the following relation (Cressie 1993):
 
                
                
If the process is furthermore isotropic, then the variogram and semivariogram can be represented by a function of the distance only (Cressie 1993):
 
                
                
The indexes or are typically not written. The terms are used for all three forms of the function. Moreover, the term "variogram" is sometimes used to denote the semivariogram, and the symbol is sometimes used for the variogram, which brings some confusion.
http://en.wikipedia.org/wiki/Variogram