Experimental variogram

In case you have chosen to use a variogram-based modeling method (SIS or TGS), 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 facies (sometimes in a specified direction) which is a pre-requisite for modeling with SIS or TGS. 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 > Facies > 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 (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 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. When you are using SIS, one variogram model per indicator (discrete property class) needs to be created; for TGS you only need one variogram model.

Calculating an experimental variogram

The experimental variograms are calculated from data points. Based on the experimental variograms, you can then determine the parameter values 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 Facies 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 experimental variogram settings between the VOIs which have variogram-based modeling methods (i.e. SIS, TGS). 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, select '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 nine directions will automatically generate a variogram for every 22.5° (this covers the full 360° as scanning directions are symmetrical).
  5. You can use the toolbar ( ) to add and delete variograms, or to change the order in which they are displayed in the Facies Variogram View.
    • 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.
    • 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-Drirectional - This allows you to create a directional/anisotropic variogram 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(s), and go to the next form, Variogram model.