Modeling Spatial Correlation

Experimental variography provides estimated values of the correlation structure for a finite number of distances. When performing ordinary kriging or indicator kriging, semivariogram values for any distance may be required. Therefore, a model must be fit to the semivariogram values to provide a semivariogram value for any distance.

Explanation of valid semivariogram models and how to use them are beyond the scope of this manual. It is assumed that the user is familiar with fitting correlation models. For a detailed explanation of these models see GSLIB Geostatistical Software Library and User’s Guide by Deutsch and Journel (1992).

SADA provides three standard models for this purpose: Spherical, Exponential, and Gaussian. In addition to these three models, a nugget effect is also available. Furthermore, SADA allows two nested correlation structures. To fit a correlation model to the semivariogram results, enter the appropriate values in the second table on the Cov tab of the Control Panel.

The nugget effect is required and is found at the bottom right hand corner. The models are located in the drop down boxes next to Model; there are two available for nested structures. Below each model are the parameters for fitting the semivariogram values.

Anisotropy in space is characterized by an ellipsoid model. This model is exactly the same as defining a neighborhood, which characterizes how points are estimated in space and is described by the following parameters.

Major Range – correlation length along the major anisotropic axis.

Minor Range – correlation length along the minor anisotropic axis.

Angle – The angle of anisotropy in the XY plane (equal to the major axis angle in experimental variography).

Contribution – The model’s contribution to the sill (maximal model value).

Z Angle – The angle of anisotropy in the Z plane (equal to the Dip parameter in experimental variography).

Z Range – A value describing how anisotropy behaves in the z minor direction, relative to major axis.

Rotation – How the anisotropic ellipsoid is rotated about its major axis.

To visualize how these parameters effect the ellipsoid, see defining a neighborhood. For more sophisticated modeling, the Angle and Z angle do not need to equal their experimental variography counter parts, Angle and Dip. Note: this level of detail in fitting semivariogram models is not usually necessary.

Press the Variography button on the main toolbar to view the results in the graphics window.