Interpolation means estimating values for points not actually sampled, thereby producing a map or some other spatial model for an area that was not exhaustively sampled. There are many different interpolation techniques, ranging from simple linear techniques that average the values of nearby sampled points, to more complex techniques like kriging that use nearby points weighted by distance from the interpolate location plus the degree of autocorrelation for those distances.

GS+ provides three broad types of interpolation. All are nearest-neighbor techniques in which values at locations close to the interpolation point are used to estimate the interpolation point value. They differ in the way that nearby locations are weighted. The techniques are:

• Kriging, in which interpolation estimates are made based on values at neighboring locations plus knowledge about the underlying spatial relationships in a data set. Variograms provide knowledge about the underlying relationships. Kriging is usually superior to other means of interpolation because it provides an optimal interpolation estimate for a given coordinate location, as well as a variance estimate for the interpolation value.
• Inverse Distance Weighting (IDW) and Normal Distance Weighting (NDW), in which interpolation estimates are made based on values at nearby locations weighted only by distance from the interpolation location.
• Conditional Simulation, in which interpolation estimates are based on a form of stochastic simulation for which measured data values are honored at their locations. This allows one to map sharp spatial discontinuities such as contamination hotspots or fault lines. Punctual and block kriging as well as IDW will smooth out local details of spatial variation, especially as interpolated locations become more distant from measured locations.

Using carbon as a covariate to produce a cokriged map of uranium results in the below-right map, plotted next to the original map above. Note the substantial improvement in the definition of contour (isoline) differences, especially in the upper right quadrant of the map where the uranium was sampled most sparsely:

How do you perform cokriging? Prior to cokriging you must have

1. defined a covariate in the Field Assignment dialog, of the Data Worksheet;
2. performed semivariance analysis (including variogram modeling) for both the primary variate and the covariate; and
3. performed cross-semivariance analysis (including variogram modeling).

You will also have wanted to confirm that the covariate is in fact correlated with the primary variate by viewing the Regression Window in the Data Summary Window. Note that there is no advantage to cokriging (over ordinary kriging) if the sample density of your primary variate is the same as for the secondary variate, or if the variates are uncorrelated.

Once the three variograms are modeled, you can choose the Cokrig tab in the Interpolation window: