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Variogram Modeling (Advanced Topic)

Some really powerful packages offer additional functionality such as variogram modeling, particularly useful for selecting an appropriate variogram model when gridding with the kriging algorithm.

The variogram is a measure of how quickly things change on the average. The underlying principle is that, on the average, two observations closer together are more similar than two observations farther apart. Because the underlying processes of the data often have preferred orientations, values may change more quickly in one direction than another. As such, the variogram is a function of direction.

Since the variogram is a three dimensional function, plotting it can be difficult (the difficulty comes in fitting a three dimensional model to a three-dimensional surface). An effective representation is to plot a radial slice (like a piece of pie) from the variogram grid, which can be thought of as a "funnel shaped" surface.  By taking slices, it is possible to draw and work with the directional experimental variogram in a familiar form - an XY plot.

Remember that a particular directional experimental variogram is associated with a direction. The ultimate variogram model must be applicable to all directions. When fitting the model, the user starts with numerous slices, but must ultimately mentally integrate the slices into a final 3D model.

Variogram modeling is not an easy or straightforward task. The development of an appropriate variogram model for a data set requires the understanding and application of advanced statistical concepts and tools. In addition, the development of an appropriate variogram model for a data set requires knowledge of the tricks, traps, pitfalls, and approximations inherent in fitting a theoretical model to real world data: this is the art of variogram modeling. Skill with the science and the art are both necessary for success.

The development of an appropriate variogram model requires numerous correct decisions. These decisions can only be properly addressed with an intimate knowledge of the data at hand, and a competent understanding of the data genesis (i.e. the underlying processes from which the data are drawn). The cardinal rule when modeling variograms is know your data. 

(As an aside, the HELP file supplied with Surfer has an excellent section detailing variogram modeling and includes sections on lag parameters, anisotropy, nugget effects, and references for further reading - I highly recommend it!)