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:
- determining the experimental semivariogram;
- adjusting to a semivariograms model family;
- 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
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