Kriging is a regression technique used in geostatistics to interpolate data. The theory of Kriging was developed by Daniel G. Krige and further developed by Georges Matheron. It is also known as Gaussian process regression and from the geological point of view, Kriging uses prior knowledge about the spatial distribution of how minerals occur in space. Then, given a series of measurements of mineral concentrations at known points, Kriging predicts mineral concentrations at grid nodes or 3-D blocks.

Kriging is a family of linear least squares estimation algorithms. This methodology attempts to minimize the error variance when the optimal criterion is based on least squares residuals. The Kriging estimate is a weighted linear combination of the data with weights that are assigned to each known datum as determined by the solution of a system of linear equations. 

One of the assumptions made in kriging is that the data being estimated are stationary. That is, as you move from one region to the next in the data set, the average value of the data points is relatively constant. Whenever there is a significant trend in the data values, this assumption is violated. In such cases, the stationary condition can be temporarily imposed on the data by use of a drift term. The drift is a simple polynomial function that models the average value of the scatter points. The residual is the difference between the drift and the actual values of the scatter points. Since the residuals should be stationary, kriging is performed on the residuals and the interpolated residuals are added to the drift to compute the estimated values.

The kriging algorithm is not one that is easily calculated (much less understood!) and its application is almost completely restricted to specialized computer programs. Like all “black box” approaches, however, care must be taken with the use of Kriging to ensure that the computer results match the expected results. It is important to do a number of “sanity” checks before accepting the results.