Experimental variogram

In case you have chosen to use a variogram-based modeling method (SGS or Kriging), to each of the Volumes of Interest (VOIs) with such modeling method you must assign a variogram model. A variogram model defines the spatial continuity of the data (sometimes in specified directions) which is a pre-requisite for modeling with SGS or Kriging. A VOI with a variogram-based modeling method but with no variogram model assigned, will be blocked from running in the last step of the modeling workflow.

The Experimental Variogram form (model > Rock Properties > Experimental Variogram) is provided as an optional workflow step before assigning the variogram model in the next step of the workflow. The Experimental Variogram form, which works interactively with the Variogram View, helps you to find the parameters describing the variogram model (the curve). An option is provided to quickly generate variograms in 9 scanning directions to look for anisotropy (varying variability in your data along with spatial directions) in your data. In essence this is similar to generating a variogram map (although without a real map), see Variogram maps - general info. Input is the upscaled (and possibly transformed) grid property you have selected in the Assign Data step. In case you don't have enough data from your upscaled grid property, or already know the parameter values (Azimuth, Dip) of your variogram model, you can skip this step and go directly to the next form, Variogram model. In this case, uncheck the 'Create experimental variogram' checkbox at the top of the Experimental Variogram form, and click OK at the base.

Calculating one or more experimental variograms

With the Experimental Variogram form, you can calculate one or more experimental variograms (calculated from data points) on the basis of which you can then find the parameters describing the variogram model (curve fitted to the data). Note that only data points located within the VOI that you select on the form are used to build the experimental variogram(s). The intended workflow on the form is as follows:

  1. Upon opening the Experimental Variogram form, a dedicated Variogram View opens automatically.
  2. Select the Rock Property Model from the Model drop-down list at the top of the form.
    3. Using the context menu options Copy and Paste, you can copy-paste settings between the VOIs which have variogram-based modeling methods (i.e. Kriging, SGS). Once you have copied settings, you can select Paste Settings Options. This will open a separate form, which allows you to paste the settings to multiple VOIs at once. Note that checkbox selection can be done in bulk by holding down SHIFT while selecting a range of VOIs (they turn blue), then checking the box of one of them. All other VOIs in the selected range will get checked simultaneously.
  3. On the right side of the form, check the checkbox 'Create experimental variogram' to activate the 'Scanning Directions' and 'Scanning Direction Parameters' sections.
  4. Either add a single variogram with the green plus icon ( ) or add nine variograms at once with the Create 9 Directions button ( ). An experimental variogram will be calculated per direction. Choosing to create variograms in nine directions will automatically generate eight variograms laterally (one variogram for every 22.5° which this covers the full 360° as scanning directions are symmetrical) and one variogram vertically. Note that after you have created these variograms, you can edit or delete any rows from the table, as they are only generated this way to give you a starting point.
  5. You can use the toolbar () to add and delete variograms, or to change the other in which they are displayed in the Variogram View. For each variogram, you can adjust all entries.
    • Azimuth - Specify the azimuth (angle with Northing direction) of the direction. By default, the azimuth of the Major direction is 0°, and the azimuth of the Minor direction always perpendicular to it. The major direction is defined as the direction of the greatest spatial continuity (for general information about directions, see Variogram maps - general info).
    • Dip - Specify the dip angle. By default, the dip of the vertical direction is 90°.
    • Scanning Direction - Specify directions for which experimental variograms are calculated.
      • Lateral - This allows you to create a variogram in a lateral direction. Azimuth and dip are auto filled and both set to 0°.
      • Vertical - This allows you to create a variogram in the vertical direction, the dip angle is auto filled and set to 90°.
      • Lateral Omni-Directional - This allows you to create a directional/anisotropic variogram model with different ranges in two directions: a lateral direction, and a vertical direction. You cannot change the azimuth and dip when this option is selected. Use this option if there is a vertical trend in your data.
  6. In the Scanning Direction Parameters section, fill in values for the following parameters:
    • Lag separation - This is the 'step size' of the total lag distance, the maximum separation distance to be considered. It represents the bin within which data pairs are grouped.
    • Lag tolerance - This control specifies the tolerance used for each lag when calculating the variogram. Lag tolerance is part of the total lag distance. Hereby, the value 0.5 (50%) means that all data points between neighboring lags will be taken into account during variogram calculation; a value less than 0.5 means that some data may not be considered. This parameter cannot be greater than 0.5, to prevent the double-counting of points.
    • Number of lags - The total number of lags, which is equivalent to the Total length divided by the Lag size.
    • Total lag distance - This is the largest overall distance within which you want data points to be included in the calculation of the variogram. The total lag distance is equal to the product of the number of lags and the lag size.
    • Horizontal bandwidth - This is the horizontal bandwidth (perpendicular distance cutoff) that is used when calculating the variogram.
    • Vertical bandwidth - This is the vertical bandwidth (perpendicular distance cutoff) that is used when calculating the variogram.
    • Angle tolerance - This control specifies the angle tolerance when calculating the variogram.

    Alternatively you can use the Autofill button and let the application calculate these values for you.

    For lateral/lateral omni-directional scanning directions, Autofill will default to:

    • Lag separation distance: Total lag distance / Number of lags (where total lag distance = 0.5 (max. total (simbox) grid size in either I or J direction) (the greatest is used) ).
    • Lag tolerance: 50 %
    • Number of lags: 20
    • Horizontal bandwidth: 2 * Lag separation distance
    • Vertical bandwidth: 0.5 * Lag separation distance.
    • Angle tolerance: 10 degrees

    For vertical scanning direction, Autofill will default to:

    • Lag separation distance: Average layer thickness (calculated from top to bottom of the 3D grid)
    • Lag tolerance: 50 %
    • Number of lags: Total lag distance / lag separation distance (rounded) (where total lag distance =0.5 (total (simbox) grid size K direction) )
    • Horizontal bandwidth: 0.5 * Lag separation distance
    • Angle tolerance: 2 degrees
  7. Click Apply or OK at the bottom-right of the form to save the experimental variogram(s) to the selected VOI, and go to the next form, Variogram Model.