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