Kriging

Kriging is a geostatistical gridding method that has proven useful and popular in many fields. This method produces visually appealing maps from irregularly spaced data. Kriging attempts to express trends suggested in your data, so that, for example, high points might be connected along a ridge rather than isolated by bull's-eye type contours.
Kriging is a very flexible gridding method. You can accept the Kriging defaults to produce an accurate grid of your data, or Kriging can be custom-fit to a data set by specifying the appropriate variogram model.

Kriging Standard Deviations
Enter a path and file name into the Output Grid of Kriging Standard Deviations field in the Kriging Advanced Options dialog to produce an estimation standard deviation grid. If this edit control is empty then the estimation standard deviation grid is not created.
The Kriging standard deviation grid output option greatly slows the Kriging process. This is contrary to what you may expect since the Kriging variances are usually a by-product of the Kriging calculations. However, Surfer uses a highly optimized algorithm for calculating the node values. When the variances are requested, a more traditional method must be used, which takes much longer.
There are several cases where a standard deviation grid is incorrect or meaningless. If the variogram model is not truly representative of the data, the standard deviation grid is not helpful to your data analysis. Also, the Kriging standard deviation grid generated when using a variogram model estimated with the Standardized Variogram estimator or the Autocorrelation estimator is not correct. These two variogram estimators generate dimensionless variograms, so the Kriging standard deviation grids are incorrectly scaled. Similarly, while the default linear variogram model will generate useful contour plots of the data, the associated Kriging standard deviation grid is incorrectly scaled and should not be used. The default linear model slope is one, and since the Kriging standard deviation grid is a function of slope, the resulting grid is meaningless.

Kriging Type

There are two most common Kriging types: Point Kriging  and Block Kriging. Both Point Kriging and Block Kriging generate an interpolated grid. Point Kriging estimates the values of the points at the grid nodes. Block Kriging estimates the average value of the rectangular blocks centered on the grid nodes. The blocks are the size and shape of a grid cell. Since Block Kriging is estimating the average value of a block, it generates smoother contours (block averaging smooths). Furthermore, since Block Kriging is not estimating the value at a point, Block Kriging is not a perfect interpolator. That is even if an observation falls exactly on a grid node, the Block Kriging estimate for that node does not exactly reproduce the observed value.
When a Kriging standard deviation grid is generated with Block Kriging, the generated grid contains the Block Kriging standard deviations and not the Point Kriging standard deviations.
The numerical integration required for point-to-block variogram calculations necessary for Block Kriging are carried out using a 3x3, two-dimensional Gaussian-Quadrature.

Kriging References

For a detailed derivation and discussion of Kriging see Cressie (1991) or Journel and Huijbregts (1978). Journel (1989) is, in particular, a concise presentation of geostatistics (and Kriging). Isaaks and Srivastava (1989) offer a clear introduction to the topic, though it does not cover some of the more advanced details. For those who need to see computer code to really understand an algorithm, Deutsch and Journel (1992) includes a complete, well-written, and well-documented source code library of geostatistics computer programs (in FORTRAN). Finally, a well-researched account of the history and origins of Kriging can be found in Cressie (1990).
Abramowitz, M., and Stegun, I. (1972), Handbook of Mathematical Functions, Dover Publications, New York.
Cressie, N. A. C. (1990), The Origins of Kriging, Mathematical Geology, v. 22, p. 239-252.
Cressie, N. A. C. (1991), Statistics for Spatial Data, John Wiley and Sons, Inc., New York, 900 pp.
Deutsch, C.V., and Journel, A. G. (1992), GSLIB - Geostatistical Software Library and User's Guide, Oxford University Press, New York, 338 pp.
Isaaks, E. H., and Srivastava, R. M. (1989), An Introduction to Applied Geostatistics, Oxford University Press, New York, 561 pp.
Journel, A.G., and Huijbregts, C. (1978), Mining Geostatistics, Academic Press, 600 pp.
Journel, A.G. (1989), Fundamentals of Geostatistics in Five Lessons, American Geophysical Union, Washington D.C.