Semivariogram Generation - Surface Analysis
The Semivariogram Surface
It is a graphic, 2D, that gives a general view of the spatial variability of the
phenomenon being studied. It is used to detect the Anisotropy axis, that is, the directions of the
larger and smaller spatial continuity of the property being analyzed. It is also known as Semivariogram
Map, its calculus is based on the following formulation:
(1)
where:
- it is the semivariogram estimated;
- N(h) - it is the number of pairs of measured values, z(xi) and
z(xi+h), separated by a distance vector h;
- z(xi) and z(xi+h), - are values of the i-th
observation of the collected variables in the xi and xi+h points,
(i = 1, ..., n), separated by the h vector.
Initializing the Semivariogram Surface generation:
- activate in the "Control Panel" the IL, of the
numerical model, that has the samples of the POINTS type;
- In the Spring main window press on Analysis ->
Geoestatistics -> Semivariogram Generation...;
- the "Semivariogram Generation" window presents, on the top, the corresponding variable to the active IL; press on Analysis and
select the option: Surface;
- The Sample: Regular or Irregular type is automatically detected according to the data sample
geometry;
- If the Sample is of the Regular type, the Regular Sampling
Parameters: No. Columns, No. Line, Res. X and Res. Y are
informative, activated and filled, automatically, with the respective values of the data regular samples.
On the other hand, if the Sample is of the Irregular type these fields are disabled.
- Following, the fields related to the Surface Map Parameters:
No. LagX, No. LagY, No. Pairs, Tol.LagX and Tol.LagY, are filled with default values directly
influencing the final result.
- The No.LagX and No. LagY parameters define the
Semivariogram Surface dimension to be generated as shown in the Figure below.

- The valid values range for the No.LagX and No.LagY
parameters is: 0 < value £ 100. For No.LagX=
50 and No.LagY=50, means that it will be defining a Semivariogram Surface
with size 100 columns by 100 lines.
- It is important to mention that LagX and LagY are associated to metrical dimensions
of the studying area. For example, consider a studying area that has a width of 7Km (longitude) and has
a height of 10Km (latitude) if the No.LagX=50 and the No.LagY=50; means that
the first Lag in the X(+) or X(-) direction corresponds to 70 meters
(7km / (2*No.LagX)), and the first Lag in the
Y(+) or Y(-) direction corresponds to 100 meters (10km / (2*
No.LagY)). The second Lag in the X(+) or X(-) direction corresponds to 140 meters, and the
second Lag in the Y(+) or Y(-) direction corresponds to 200 meters, and so on, the twenty first Lag in the
X(+) or X(-) direction corresponds to 1470 meters (70*21), etc.
- parameter No. Pairs establish the minimum number of sample pairs
desired for Lag. In other words, this means that any cell will be estimated if the number of sample
pairs, satisfying the computation condition (Equation 1), is greater or equals to the specified
No. Pairs parameter.
- The Tol.LagX and Tol.LagY parameters are the established
tolerances in the X (East) and Y (North) directions, respectively. The Figure above shows an example. Notice
that the vector module h has not a unique value, but a range of values that consequently are
dependent on the specified tolerances . This makes the computation flexible, given by Equation (1), for each
of the cells compounding the semivariogram surface.
- Once all required parameters are established, press the Apply button. This
action opens a graphic window, which has the Semivariogram Surface, as presented below.

- In the graphic window above it is possible to visually detect the anisotropy axis.
It is possible to verify the corresponding directions (Angles) and Range associated to the continuity
larger and smaller axis. For this, just place the cursor over the graphic window, press the mouse left
button and drag it. The values for the Angle and Range are printed in the footnote interface, as shown
in the Figure above.
- At last, it is possible to save the result in an Information Layer. For this, activate
the Generate option, an Output Category (it has
to belong to the numerical category), and a name for the Output IL are defined. Note: the result is
an IL with the Grid type representation.
[ Procedures ] [ Concepts ] [
Exploratory Analysis
] [ Semivariogram Analysis ]
[ Semivariogram Models ] [ Model Validation
] [ Kriging ]
See also:
Spatial Analysis in the SPRING
Variogram
Semivariogram Generation - Unidirectional Analysis
Generation of a Cloudy Variogram
How to Execute ? - Exploratory Analysis
How to Execute ? - Semivariogram Modeling
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