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. Within Surfer, Kriging can be either an exact or a smoothing interpolator depending on the user-specified parameters. It incorporates anisotropy and underlying trends in an efficient and natural manner.

 

Kriging Advanced Options Dialog

In the Grid Data dialog, specify Kriging as the Gridding Method and click the Advanced Options button to open the Kriging Advanced Options dialog.

 

Specify the variogram parameters, Kriging standard deviations file, Kriging type, and drift type in the Kriging Advanced Options dialog.

 

Variogram Model

An important component of the Kriging gridding method is the variogram. The default linear variogram provides a reasonable grid in most circumstances, as long as a nugget effect is not used. A variogram-modeling feature is included in Surfer to assist you in selecting the appropriate variogram model for your data. Do not change the variogram components without modeling the variogram first. If you do not understand variograms or variogram modeling, use the default linear variogram with no nugget effect. When in doubt, use the default linear variogram.

 

Add

Click the Add button to open the Variogram Components dialog where you can add additional variogram components. See variograms for more information on the variogram components.

 

Edit

Click the Edit button to display the Variogram Components dialog for the currently selected component. You can edit various parts of the variogram model from this dialog. Once you are finished editing the components, click OK to return to the Kriging Advanced Options dialog.

 

Remove

To remove a component from the variogram model, highlight the component in the Variogram Model group, and then click the Remove button.

 

Get Variogram

If you have modeled your data with Surfer's variogram modeling feature (Grids | New Grid | Variogram | New Variogram), click the Get Variogram button to use the variogram results. The Get Variogram button extracts the current variogram model from the variogram modeling subsystem and inserts it into the Kriging variogram model. You must have the variogram open in the current plot window to use the Get Variogram option.

 

Output Grid of Kriging Standard Deviations

Click the button to enter a file name into the Output Grid of Kriging Standard Deviations box to produce an estimation standard deviation grid. If this box 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.

 

The Kriging standard deviation grid is not allowed with the No Search option on the Search page.

 

Kriging Type

Choose Point or Block Kriging from the Kriging Type list box.

 

Surfer includes two Kriging types: Point Kriging (which is the only method supported by Surfer 6), and Block Kriging. A detailed discussion of the two methods can be found in Isaaks and Srivastava (1989, Chapters 12 and 13). Ordinary (no drift) and Universal Kriging (linear or quadratic drift) algorithms can be applied to both Kriging types.

 

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. In particular, Surfer uses Section 25.4.62 of Abramowitz and Stegun (1972).

 

Point Kriging is the default method.

 

 

In the diagram above, the crosses indicate a block of grid nodes and the filled circles indicate data points. If we were to interpolate the center grid node with Point Kriging, the data point closest to the center grid node would have the greatest weight in determining the value of the grid node. If we were to interpolate the center grid node with Block Kriging, all three data points within the block of grid nodes are averaged to interpolate the grid node value.

 

Drift Type

Select a Linear or Quadratic drift type. Drift type None is Ordinary Kriging, while Linear or Quadratic drift type is Universal Kriging.

 

If you use the Get Variogram command to apply a variogram model, be sure to set the Drift Type option to the same value as you used in the General page for Detrend when creating the variogram.

 

Search Page

The Search page allows you to specify search rules.

 

Breaklines Page

The Breaklines page is used to add breaklines to the gridding process. Faults are not supported with Kriging.

 

 

See Also

Grid Data

Using Variogram Results in Kriging

General Gridding Recommendations

Gridding Method Comparison

Kriging References