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When you have multiple datasets and you want to use cokriging, you need to develop models for cross-covariance.
Because you have multiple datasets, you keep track of the variables with subscripts, with Z_{k}(**s**_{j}) indicating a random variable for the *k*^{th} data type at location **s**_{i}.
The cross-covariance function between the *k*^{th} data type and the *m*^{th} data type is then defined to be

`C `_{km} (**s**_{i},**s**_{j}) = cov(Z_{k}(**s**_{i}), Z_{m}(**s**_{j}))

Here is a subtle and often confusing fact: C _{km} (**s**_{i} ,**s**_{j}) can be asymmetric:
C _{km} (**s**_{i} ,**s**_{j}) ≠ C _{mk} (**s**_{i} ,**s**_{j}) (notice the switch in the subscripts). To see why, look at the following example.
Suppose you have data arranged in one dimension, along a line, such as the following:

The variables for type 1 and 2 are regularly spaced along the line, with the thick red line indicating highest cross-covariance, the green line less cross-covariance, and the thin blue line the least cross-covariance, with no line indicating 0 cross-covariance.
This figure shows that Z_{1}(**s**_{i}) and Z_{2}(**s**_{j}) have the highest cross-covariance when **s**_{i} = **s**_{j},
and the cross-covariance decreases as **s**_{i} and **s**_{j} get farther apart. In this example, C _{km} (**s**_{i} ,**s**_{j} ) = C _{mk} (**s**_{i} ,**s**_{j} ).
However, the cross-covariance can be "shifted":

Notice that C_{12}(**s**_{2},**s**_{3}) now has the minimum cross-covariance (thin blue line)
while C_{21}(**s**_{2},**s**_{3}) has the maximum cross-covariance (thick red line), so here C_{km} (**s**_{i} ,**s**_{j}) ≠ C _{mk} (**s**_{i} ,**s**_{j}).
Relative to Z_{1}, the cross-covariances of Z_{2} have been shifted -1 unit. In two dimensions, Geostatistical Analyst will estimate any shift in the cross-covariance between the two datasets if you click the shift parameters.

The empirical cross-covariances are computed as follows:

Average [ (z_{1}(s_{i}) - _{1}) (z_{2}(s_{j}) - _{2})]

where Z_{k}(**s**_{i}) is the measured value for the *k*^{th} data set at
location **s**_{i} ,_{k} is the mean for the *k*^{th} dataset,
and the average is taken for all **s**_{i} and **s**_{j} separated by a certain distance and angle. As for the semivariograms, Geostatistical Analyst shows both the empirical and fitted models for cross-covariance.

Choosing different cross-covariance models, using compound cross-covariance models, and choosing anisotropy will all cause the theoretical model to change. You can make a preliminary choice of model by seeing how well it fits the empirical values. Changing the lag size and the number of lags and adding shifts will change the empirical cross-covariance surface, which will cause a corresponding change in the theoretical model. Geostatistical Analyst computes default values, but you should feel free to try different values and use validation and cross-validation to choose the best model.