Advanced Estimation

Creating experimental variograms

Advanced Estimation - Create Variograms

To access this dialog:

Using the Advanced Estimation dialog, select the Create Variograms menu item.

This panel, part of the Advanced Estimation dialog, is used to create one or more experimental variograms. Variograms are calculated for each zone if a ZONE field has been defined previously on the Select Samples panel.

This panel is only visible if Supervisor data is not being imported. You decide this using the Scenario Setup screen.

You can also use this panel to create cross-variograms for multivariate analysis. Once you have selected your parameters for variogram creation (see below) click Calculate Variograms to generate the variogram file.

Note that if you create experimental variograms on this panel, they will be automatically loaded into the Fit Models panel when it is opened. You will also be able to use the Fit Models panel to load any previously generated variogram file, regardless of the scenario in which it was created.

Experimental variogram files generated by the Advanced Estimation dialog are compatible with the VCONTOUR process

Note: Advanced Estimation is part of the Studio RM toolset. Additional licensing modules aren't required.

Normal Score Variograms

The NSCORE process can be used to create a normal score transformation for grade values prior to calculating the variograms. The process is available from the Estimate ribbon (Conditional Simulation command group). The normal score values can then be treated as Gaussian equivalent grades for variogram calculation purposes.

For grade values where the distribution is highly skewed or log normal, modelling a variogram of the untransformed values may be difficult. Modelling the normal score of the variogram and back transforming the variogram can give a variogram with a better shape.

Output

Depending on the complexity of the input sample set, it can take time to generate all of the experimental variograms required for your scenario. Progress information is written to theCommandwindow.

On completion the experimental variograms are written to the file defined at the top of the panel. This can be viewed in theTable Editorand the variograms can be displayed graphically in theFit Modelspanel.

Example - Create Variograms

In this example, experimental variograms are calculated for zone ROCK 1, both downhole and directional. The variograms are calculated relative to a rotated plane that dips at 17o in the direction N30 degrees E. The directional variograms are every 22.5 degrees (180 / 8) in the rotated plane. Only two vertical directions are selected, with an increment of 90 degrees (180 / 2); the two dip values are 0 degrees (in the rotated plane) and 90 degrees (perpendicular to the rotated plane). The output experimental variogram file name is vgrams_holes_1w.

The following progress information is written to the Command window:

################################################################################

# Variography

# ===========

# Experimental Variogram Calculations started.

Calculating variograms for zone 1...

RETRIEVAL FIELDS

================

>>> CURRENTLY ESTABLISHED RETRIEVAL CRITERIA

ROCK = 1.0

Variogram Calculation - Input Summary

-------------------------------------

Variogram calculation for 3 field(s) as follows:

AG AU CU

Variograms will be calculated for the directions and dips shown below.

In addition a variogram independent of direction and dip will be calculated.

Initial direction: 0.00 + or - 5.00 degrees

Initial dip: 0.00 + or - 5.00 degrees

Increment between successive directions: 10.00 degrees

Increment between successive dips: 10.00 degrees

Number of directions: 18

Number of dips: 18

The cylindrical search constraint is not used.

Lag intervals are defined as follows:

Number of lags: 1000

Lag distance: 0.98

Lag tolerance: 0.49

>>> 53358 sample pairs, 0.5% completed. Time: 9:18:28 <<<

>>> Time remaining: 0 hrs 1 mins 33 secs. Finish time: 9:20:12 <<<

>>> 2057712 sample pairs, 20.8% completed. Time: 9:18:50 <<<

>>> Time remaining: 0 hrs 0 mins 30 secs. Finish time: 9:20:15 <<<

>>> 8085462 sample pairs, 81.6% completed. Time: 9:19:56 <<<

>>> Time remaining: 0 hrs 0 mins 9 secs. Finish time: 9:20:16 <<<

>>> 9912378 sample pairs, 100.0% completed. Time: 9:20:17 <<<

>>> 285907 Records in File C:\Database\Adv_Est\vgramout_tmp.dm <<<

>>> VGRAM Complete <<<

RETRIEVAL FIELDS

================

>>> CURRENTLY ESTABLISHED RETRIEVAL CRITERIA

ROCK = 1.0

Variogram Calculation - Input Summary

-------------------------------------

Variogram calculation for 3 field(s) as follows:

AG AU CU

Variograms will be calculated for each value of key field: BHID

Only the average variogram(s) over all key field values will be reported.

Variograms will be calculated for the directions and dips shown below.

In addition a variogram independent of direction and dip will be calculated.

Initial direction: 0.00 + or - 5.00 degrees

Initial dip: 0.00 + or - 5.00 degrees

Increment between successive directions: 10.00 degrees

Increment between successive dips: 10.00 degrees

Number of directions: 18

Number of dips: 18

The cylindrical search constraint is not used.

Lag intervals are defined as follows:

Number of lags: 1000

Lag distance: 0.98

Lag tolerance: 0.49

>>> 50022 sample pairs, 63.4% completed. Time: 9:21:32 <<<

>>> 78862 sample pairs, 100.0% completed. Time: 9:21:32 <<<

>>> 1926 Records in File C:\Database\Adv_Est\vgramout_tmp.dm <<<

>>> VGRAM Complete <<<

# Variography

# ===========

# Experimental Variogram Calculations succeeded.

# vgrams_holes_eg1a

################################################################################

Field Details:

This panel contains the following fields:

Input Parameters for Variogram Creation

Experimental variogram file: enter the name of the experimental variogram data file you wish to create (or accept the default).

Select variables for variogram: select variables (grades) for variogram creation.

Transform: choose if you wish to create variograms of the normal scores. The Normal score transformation (NST) is designed to transform your dataset so that it closely resembles a standard normal distribution. You can transform one or more grade fields to a normal (gaussian) distribution and calculate the experimental variograms for the nscore values using the Normal score check box.

If this option is selected:

all selected grades will be transformed.
both untransformed and transformed variograms will be calculated.
you can back transform the variogram model parameters so that the back transformed model can be used for kriging untransformed values later on, if required.

You can view transformed and untransformed variograms on the Fit Models panel.

Grades will be transformed within each domain, if you have specified one or more domains/zones.

Type: select the type of variograms to be created:

Downhole: tick the box to create downhole variograms and cross-variograms.
Cross: if you select more than one grade and tick the Calculate cross-variograms box then cross-variograms will be calculated for all possible pairs of grades.
Directional: if this is not ticked only omnidirectional variograms (and cross-variograms if selected) will be calculated. If this box and the downhole variograms box are ticked then directional variograms will be calculated for both the all-samples variograms and the downhole variograms

If none of the three variogram options above (downhole, cross, directional) are selected then only omni-directional variograms will be calculated.

Select zones: select the zone(s) for which variograms and cross-variograms are required. Absent data (-) qualifies as an independent zone.

Maximum distance for variogram calculation...: by default, this will be capped to the maximum sample spacing. You can see this value on the Select Samples panel (Max Dist) = the maximum distance between any two samples. Reducing this value can reduce the amount of time taken to process variograms, but potentially at the expense of accommodating a sufficient data sample set.

Reference Plane Rotation

You can use this area to set a reference plane and the variograms will then be created relative to this plane. By default all three angles are set to zero so the reference plane is horizontal. If you have used the Investigate Anisotropy option then you can read the current rotations directly from the Variogram Window by clicking theReadfrom3Dmapwindowbutton.

If you prefer you can set the rotation angles yourself by entering the rotations in the Angle boxes. You can also also set the order of the axes.

If you want to reset the values back to zero, clickReset to horizontal.

The default sequence of axes is Z, then X, then Y. In the above example the first rotation is by 75.7^o around the Z axis, then 15.3^o around X, and finally 39^o around Y.

The rotation angle convention shown on this panel will be the same as that shown on the 3D Variogram ribbon. This is automatically updated when you select Read from 3D map window.

All variograms and cross-variograms will be calculated relative to the rotation plane. This means that a direction along the Y axis of the rotation plane will have DIP and AZI angles of zero. The perpendicular direction in the rotation plane, the X axis, will have a DIP of zero and an AZI of 90 degrees. The DIP and AZI angle for each experimental variogram is reported in the Fit Models panel together with the WDIP and WAZI values. These are the directions of the variograms in the World coordinate system ie relative to a horizontal plane.

In the descriptions below for Horizontal and Vertical directions the definition for horizontal and vertical applies to the reference plane after it has been rotated. This means that after rotation the reference plane becomes the horizontal plane.

Horizontal Directions

This option is enabled if Directional variograms are being created for 2D or 3D data (see above).

No. of directions: this defines the number of directions for which variograms and cross-variograms are calculated. The directions all lie in the reference plane with the default reference plane being horizontal.

The incremental angle, in degrees, between adjacent directions is calculated as the Range angle (default 180 degrees) divided by the number of directions. For example if the number of directions is specified as 8 then the incremental angle between adjacent directions will be 22.5 degrees (180/8).

Horizontal and VerticalDirections are set independently. The Horizontal Directions represent the localazimuth (with 0 pointing up, 90 to the right, and 180 pointing down). The Vertical Directions represent local dip (with 0 to the right, 90, pointing down, and 180 pointing left)

If the number of directions is an even number then the set of directions will always include pairs of orthogonal directions. Although this is not essential it is often useful to make it even so that if the fitted variogram model includes two directions in the reference plane there will always be an experimental variogram for at least two directions of anisotropy. This will make it easier to validate the fitted model visually.

The Tolerance angle is measured in the horizontal plane either side of variogram direction and defines an arc within which the vector connecting a pair of samples must lie in order to be assigned to that direction. The default Tolerance angle is half the incremental angle. In the example graphic this is calculated as 11.25o. This means that if the vector connecting two samples has a horizontal angle (azimuth) within the interval 0 degrees ± 11.25 then the grades will contribute to the variogram with a 0 degrees azimuth.

Although the default Tolerance angle is half the incremental angle, the user can reset it if required. Making the angle greater than the default means that there will be an overlap between adjacent Tolerance areas. Pairs of samples lying in the overlap area will then contribute to the variogram directions on either side. This means there will be some degree of averaging between adjacent directions which can sometimes be helpful in smoothing the variograms and making it easier to identify anisotropies particularly if there is a limited amount of data. Making the Tolerance angle less than half the incremental angle will reduce the number of pairs of samples and in general will make it more difficult to interpret any anisotropy.

Vertical Directions

For 2D data "Vertical Directions" is disabled. This function is only available if 3D sample data is specified.

No. of directions: this defines the number of dips for which variograms and cross-variograms are calculated. The dips are measured relative to the reference plane with the default reference plane being horizontal.

Other parameters for the vertical directions are identical to those described above for the horizontal direction except that the angles are measured in the vertical plane.

Options

Maximum Distance: the maximum lag distance for the loaded samples (or 0.1 default if none are loaded). This distance is calculated as 50 % of the maximum sample separation found but can be edited anywhere within the range zero to the maximum sample separation.

Minimum Lag: define a minimum permissible lag distance for the sample set. The default value of Minimum lag is the largest of 5 or the maximum separation of any two samples / 1000.

Minimum Lag (downhole): only available if the Downhole Type check box has been enabled, this lets you set the minimum lag distance down the hole. By default, this is the average length of non-absent intervals (i.e. the length of samples that contain one or more of the selected grade values), rounded to the nearest 0.1.

Cylinder Radius: if enabled, this option allows you to define the radius of a cylinder to represent the search scope, centred on the variogram direction. As such, this option only applies to directional variograms.

The search radius will only have an effect on samples which are within it. Choosing a value which is larger than a certain threshold will produce no change in the results.

	Related Topics
	Advanced Estimation Introduction Advanced Estimation - Select Samples Advanced Estimation - Fit Models