Variography in Micromine 2014 – Part 3: Modelling directional variograms

In Part 1 of this series I showed you how to set up a variogram map, and in Part 2 you learned to use and interpret it. In Four tips for using the variogram map I introduced some data effects that can produce misleading maps. The final step was to create a variogram control file containing your measured orientations:

The new workflow

In this post I’ll conclude the series by showing you how to model three-axis directional variograms. I’ll concentrate on the new workflow, relying on the variogram control file to provide the orientation information.

Some parts of the old workflow haven’t changed. You still model a downhole variogram to determine the nugget effect, and for now you must also experiment with omnidirectional variograms to estimate the optimum lag interval. (We’ll add interactive lag sliders in a future update.) In this article I’ll assume these parameters have already been determined:


A sequence of omnidirectional variograms at different lag intervals. Stepping through individual variograms will reveal candidates for the lag interval

Moreover, you can still create variogram fans if you’d rather keep using the old workflow. The biggest disadvantage of working this way is losing access to the variogram control file and its associated benefits.

The variogram control file

The variogram control file does more than just store axis directions defined in a variogram map. In a 3-D setting it also synchronises the nugget and the number of components along with their types and partial sills across the three axes. In other words it enforces geometric anisotropy so you can concentrate on fitting the theoretical model without worrying about the numbers.

Even better, once you’ve created a three-axis model you can save it to a new variogram control file, which then includes the original orientations along with the properties of the experimental variograms. (Although it is possible to overwrite the original file we recommend always saving a new file. Not only does this protect your original orientations, it also provides a simple way to create alternative scenarios by saving a different file each time.)

Displaying experimental directional variograms

To display the experimental directional variograms, select Stats | Semi Variograms from the main menu and then set the Input to Calculate, the Direction to Directional and the Type to Variogram. Next, use the Raw Data and Data Values options to configure the input data and any transformations. It’s a good idea to enable Show Variance so that you can compare the variograms with the global variance of the data.

Click the Semi Variogram Directions button to display the corresponding dialog. But don’t go setting up the directions just yet. Instead, go to the bottom of the form, click the browse button in the Variogram control file response and choose the file you created in the variogram map:




The variogram control file will automatically add the three axes and adjust their angles to the ones you measured on the variogram map, always ensuring they are at right-angles to each other. Now you can set up the rest of the directions list.

For numbers that remain constant (pretty much everything except the angles), enter the value in any cell in that column and then right-click it and choose Replicate from the pop-up menu. The Display options work the same way: to apply the same option to all vario­grams, right-click that cell and choose Replicate. Lastly, right-click any cell in the Colour column and choose Fill With Random Colours:




You’re now ready begin modelling.

Fitting three-axis theoretical variograms

To fit models to the variograms:

1. Ensure Show Together is enabled, by selecting Show semi variograms together on the Directions dialog or by toggling the Show Together button on the chart toolbar.

2. Click the Chart Control Pane button to show the Chart Controls.

Micromine will fit linear variograms to the three axes using estimated parameters, but because the variograms are identical they appear as one. However, the visible handles only apply to the selected variogram direction, which is usually the first one in the list.

3. Change Component 1’s Type to something more suited to your data; perhaps SPHERICAL or EXPONENTIAL.

4. Drag the Component 1 handle until the model roughly fits all three axes. (You should not need to adjust the nugget here.)


An initial three-axis fit using a nugget and one component

Sill or nugget (i.e. vertical) adjustments apply to all three axes, but changes to the range only apply to the selected axis. Micromine quietly takes care of geometric anisotropy when you use a variogram control file.

5. If necessary change the component type or add extra components to get a reasonable fit with all three axes. Now the real work begins.

6. Toggle the Show Together button to show only the first variogram, and use the handles to make small adjustments to the fitted curve.

When you use a variogram control file any vertical adjustments (nugget or partial sill) also affect the directions you can’t see.

7. Click the Next or Previous buttons (or press Page Up or Page Down) to switch between individual variograms, adjusting each one in turn.

8. For fine control, click into a Range or Partial Sill edit box in the Chart Controls window and adjust the value by rolling the mouse wheel, adding or removing decimals to change its sensitivity.

As you update the axes you should find that you are making smaller and smaller adjustments.

9. Periodically toggle the Show Together button to visually validate all three variograms.


The final fitted model for Axis 1, incorporating two components. The other axes use the same two components with different ranges

Locking axis components

It can be hard to keep track of everything when you’re fitting a multi-component three-dimensional model, and to make it easier Micromine includes a handy Lock Axes option. It’s easy to use: once you’re satisfied with the partial sill of a component, just enable its Lock Axes button. This frees you to adjust its range without making accidental changes to its partial sill. Lock Axes also works without a variogram control file; however it is not as strict without a control file because it allows independent changes to the nugget.

Saving and using the resulting model

To save the model, simply click the Create Variogram Control File button at the end of the chart toolbar and enter a new filename.

You may use the resulting model in many different ways. To permanently associate it with the original experimental semi variograms, just replace the original variogram control file on the Directions dialog with the new one. If you then save the main Semi Variograms dialog as a form set in Display existing mode you can instantly revisit your combined experimental variograms and theoretical models at any time. This is great for audits or long-term projects.

Similarly, you can use a variogram control file containing a fitted model wherever a Model Parameters form set is used, in particular cross-validation (Stats | Cross Validation) and, of course, the kriging interpolators.




Another nice technique is to import the orientations into a Data Search form set, with or without a fitted model. Just open the Data Search dialog from within the Vizex Search Ellipsoid or an interpolator on the Modelling menu and click the Import button at right of the dialog. Micromine will apply the orientations; you must manually define the radius and factors.

Conclusion

Variography is a major addition to Micromine’s geostatistical toolkit, and we’ve put a lot of effort into ensuring the new workflow is as fluid as possible. It’s much easier than the old workflow whilst providing greater control over the modelling process and its parameters. And we haven’t forgotten the old workflow for those who prefer to work that way.

Starting with a variogram map doesn’t just give you a better way to visualise the anisotropy in your project area, it also simplifies the way you create the resulting directional model. I hope this series has given you a better understanding of this workflow. But, as always, please feel free to post any questions to the forum.