Semivariogram Generation - Unidirectional Analysis

In the geostatistics, the semivariogram analysis is an important step, because the selected variogram model is the interpretation of the spatial correlation structure to be used in the kriging inference procedures. The semivariogram complete analysis has the following steps:

  1. determining the experimental semivariogram;
  2. adjusting to a semivariograms model family;
  3. module validation for the kriging procedures.

NOTE: This page presents the item 1 above. The other (2 and 3) items are presented in the following pages.

The kind of analysis presented here is the Unidirectional. See also the Surface and Cloud analysis.



Initializing Semivariogram Spatial Analysis :


 Unidirectional Analysis

The Unidirectional option considers two statistics types: Univariate and Bivariate. The Univariate statistics available are: Semivariogram, Covariance, Correlogram, General Relative Semivariogram, Pairwise Relative Semivariogram, Semivariogram of Logarithms, Semimadogram, Semivariogram by Indication (Continuous and Categorical). The Bivariate option corresponds to the Crossed Semivariogram. More detailed information about these statistics can be found in Deutsch and Journel (1992).

Unidirectional Analysis over Irregular Samples

  • after selecting the Unidirectional Analysis type, press on Sampling and select Irregular;
  • notice that the "Semivariogram Generation" window presents some filled fields such as:Lag Parameters (Lag's No , Tolerance Increment) and Directions Parameters (Diri , Toli and Bwi , where i=1,2,3 and 4) which are initialized by default values. However, in many cases, depending on the sample geometry, it is necessary to review these parameter values such that we get a better experimental semivariogram. To better understand these fields see Deutsch and Journel (1992);
  • press on Options and select among Semivariogram, Crossed Semivariogram, Covariance, Correlogram, General Relative Semivariogram, Paired Relative Semivariogram, Logarithms Semivariogram , Semimadogram, Continuous Indicator Semivariogram and Categorical Indicator Semivariogram. See each of these options next.
  • if the selection was Crossed Semivariogram, press on Crossing IL... . The "Categories and Infolayers" window is presented; notice that only categories of the numerical models are presented. Select the corresponding IL and press on Apply;
  • if the selection was Continuous Indicator Semivariogram or Categorical Indicator Semivariogram, it is required to define a Threshold value.
  • in Directions Parameters select the desired direction or all. The colors presented around each of the four options corresponds to the colors to be used in the graph;
  • if the selection was Semivariogram, it is possible to use the Standardize option (by the data variation) or not. This option will standardize the values to be used in the graph;
  • press the Apply button. Notice that the window in the Figure below is presented


Configure your Chart

NOTE: The result presented in the Figure above shows four semivariograms. The red semivariogram is related to the first direction, 0o, the green one to the second direction, 45o, the blue one to the third direction, 90o, and the black one to the 135o direction.

Besides the graphs it is possible to verify the numerical results for the four generated semivariograms. See next.


Showing the Unidirectional Numerical Analysis Results over the Irregular Samples:

  • after pressing on the Apply button, notice that the Numerical Results... button is enabled;
  • press the Numerical Results... button and an associated window will be displayed.


Unidirectional Analysis over Regular Samples

The parameters defining the sample regular grid are: number of columns, number of lines, X resolution and Y resolution as presented in the Figure below.


Executing Unidirectional Analysis over Regular Samples

  • after selecting the Unidirectional Analysis, press on Sample and select Regular;
  • press on Options and select among Semivariogram, Crossed Semivariogram, Covariance, Correlogram, General Relative Semivariogram, Paired Relative Semivariogram, Logarithms Semivariogram , Semimadogram, Continuous Indicator Semivariogram and Categorical Indicator Semivariogram.
  • if the selection was Crossed Semivariogram, press on Crossing IL... . The "Categories and Infolayers" window is presented; notice that only categories of the numerical models are presented. Select the corresponding IL and press on Apply;
  • if the selection was Continuous Indicator Semivariogram or Categorical Indicator Semivariogram, press the Crossing IL... button.
  • notice that the fields related to Regular Sample Parameters are automatically filled and they are just for information purpose. The parameters defining the sample regular grid are: number of columns, number of lines, X and Y resolutions.
  • in Directions Parameters select the desired direction or all. The colors presented around each of the four options corresponds to the colors to be used in the graph;
  • if the selection was Semivariogram, it is possible to use the Standardize option (by the data variation) or not. This option will standardize the values to be used in the graph;
  • press the Apply button.

NOTE: The result is illustrated in a graphical window, which presents up to four variograms, similar to the ones presented previously.

The numerical result is visualized as described in the semivariogram generation for Irregular samples.

The semivariogram generated, for both Irregular and Regular samples, are stored in files used in the adjusting or modeling phase.

[Procedures] [Concepts] [Exploratory Analysis] [ Semivariogram Analysis ]
[Semivariogram Modeling] [Model Validation ] [Kriging]

See also:
SPRING - Spatial Analysis
Variogram
The Semivariogram Surface Generation
How to Execute? - Exploratory Analysis
How to Execute? - Semivariogram Modeling