Variograms - Model Fitting

Fitting models to experimental variograms

Varograms - Model Fitting

To access this dialog:

In the Variogram dialog, select the Model Fitting tab.

The Model Fitting tab is used to fit a model to the current variogram chart.

The icons at the top of the dialog represent the following commands:

Field Details:

: browse and select a variogram model file (optional).

: save the current model to the variogram model file. This will open the Save Model As dialog shown below:

: load a variogram model from the file defined in Current Model File field.

Parameters:

Current Model File: the current variogram model file; this is either an existing file which was selected above or, can be a new file (name typed in to this box).

Direction: two options are available:

Isotropic: select this option if the new model is to be isotropic i.e. the same in all directions.

Anisotropic: select this option if the new model is to be anisotropic i.e. the model is to be different in at least two of the three orthogonal axes.

Display in Split Window : In the case of an anisotropic model, select this option to display each of the three orthogonal variograms in a separate split preview panes. Each of the three variogram charts will a separate pane and corresponding thumbnail. Double-clicking on a chart thumbnail in the lower part of the preview window will display the full chart in the upper pane.

Display Omni-directional variogram : display the omni-directional variogram for visual reference purposes. This will not have an effect on the any variogram model axes or parameters.

Rotation Angles and Axes:

Axis rotation angles are calculated when an anisotropic variogram model is applied using the Apply button. The angles are calculated from the azimuth and dip of the experimental variograms and are based on a fixed sequence of rotations – the first about Z, the second around the Y axis and the third around the X axis.

Positive rotation angles indicate a clockwise rotation looking down the corresponding axis (i.e. in the direction of the axis origin); negative rotation angles are anticlockwise. Axes are orientated using the Left Hand Rule where, held orthogonal to one another, the thumb points in the positive Z coordinate direction, the index finger points in the positive Y coordinate direction and the second finger in the positive X coordinate direction.

These parameters cannot be edited, as the XYZ axes correspond to the first, second and third axes selected in the Data Selection tab, Variograms list.

First: the first rotation angle about the Z axis.

Second: the second rotation angle about Y.

Third: the third rotation angle about X.

Model Definition: model structures can be added and removed using the Add and Delete buttons shown below

Nugget Variance: define a value for the variogram model nugget.

: click this button to add a new structure to the list of model parameters.

: delete the currently listed model i.e. all structures.

Model Parameters: the following model parameters, for each structure, are listed in the pane

No: variogram model structure number.

Type: using the drop-down, select the variogram model type i.e. [Spherical], [Exponential] or [Gaussian].

By default a spherical model will be selected for a new structure. This can be changed using the drop-down list.

Spatial Variance: define a spatial variance by typing in a value or using the cursor to drag the corresponding point in the preview pane.

Range: define a range by typing in a value or using the cursor to drag the corresponding point in the preview pane.

Options: The variogram model parameter values can be restricted using the following controls:

The variogram model's nugget, spatial variance(s) and range parameters can also be interactively positioned in the preview pane once the model's structure(s) has been added to the model parameter pane with the Add New Structure button. More...

Display Model: allows the model display to be switched on and off.
Lock Sill Value: select this to fix the upper sill of the model at its current level. Moving the control point for the highest structure will then only change the range. Moving control points for other structures (if any) will change the spatial variances (Ci values).
Lock all C Values: select this option to lock all variance value. Moving control points will then only change the ranges.
Lock Range Value: select this to keep the current range values. Moving control points will then only change the spatial variances.
Display Model Parameters: select this option to display the model parameters on the chart.
Decimals for Variances: the number of decimal places to be used for displayed variance values (default '3').
Decimals for Ranges: the number of decimal places to be used for displayed range values (default '0').
Reset Sill to Variance: initially the sill will be set equal to the variance. If the sill has been changed then it can be reset to the variance.

3D Ellipsoid: these controls are used to create a wireframe ellipsoid of the variogram model:

Wireframe: define a name for the ellipsoid wireframe. This base name will be used when creating both the triangle and points files; the suffixes '_tr' and '_pt' are added to the base name to create these two files respectively.

X Centre: type or pick the X coordiinate for the ellipsoid centre.

Y Centre: type or pick the Y coordiinate for the ellipsoid centre.

Z Centre: type or pick the Z coordiinate for the ellipsoid centre.

: use this button to pick an ellipsoid centre point in the Design or VR window.

Typically placed at a suitable location within the extents of the sample data which was used to generate the experimental variogram(s).

Create Ellipsoid : click this button to create the ellipsoid wireframe, load it and view it in the VR Window.

The ellipsoid size and orientation correspond to the maximum ranges (for multiple structure models) and orientation of model. After it is created, it is automatically loaded into memory so that it is displayed the Design or VR window. The ellipsoid wireframe can be repositioned using the move-wireframe command.

When the required number of structures has been selected the Apply button must be clicked. The model based on a default set of parameters will then be displayed in the Chart window. The headings for the three ranges will change from X, Y, Z to show the actual Azimuth/Dip of each variogram axis.

Creating a New Anisotropic Variogram Model

In the Data Selection tab, select (tick) two or more orthogonal experimental variograms in the Variograms list.

The order in which the variograms are selected in the Variograms list is the order:

in which they will be drawn in the Preview pane and the legend
which is used to defining the variogram model XYZ axes.

In the Model Fitting tab, Parameters group, define the current variogram model file.
In the Direction group, select the Anisotropic option.
Optionally select Display in Split Windows.
Define a Nugget Variance value.
Click Add New Structure, check that a new model has been added to the varoigram model list as shown below:
In the Variogram Model list, for this new model, select a model Type from the drop-down.

Define the corresponding model parameters e.g. Spatial Variance, Range X, Range Y and Range Z.

When Add New Structure is clicked, the displayed experimental variogram data is used to calculate estimates for the new variogram model's parameters. These can be edited by clicking in each field and typing in a different value.

Click Apply.
Check the Rotation Angle parameters and corresponding Dip Direction/Dip model parameters for the XYZ axes of the selected experimental variograms i.e. those selected in step 1.
In the Preview pane, check that displayed variogram model for each of the XYZ axes.
If required, adjust the Nugget, Spatial Variance and Range parameters interactively using the mouse cursor by click-and-dragging the relevant synbol left, right, up or down:

The selected Lock options in the Options group will control which parameters can be interactively adjusted.

Click Save Variogram Model to File.
Repeat steps 6. to 13 for each variogram model structure.

This applies when a spherical variogram model type is used to model a variogram and which contains more than one structure e.g. a 2 structure spherical model.

	Related Topics
	Introduction Data Selection Format Charts Data