2.5 Kriging & simulation - limited dataset
As mentioned in the previous section, the dense dataset is not realistic and one might even argue based on it that isotropic variograms are in fact good enough. To test this hypothesis, a subset made of 1/8th of points of the dense dataset has been randomly picked and kriging and simulation was run on it.
Firstly, kriging was run using an isotropic variogram. If we use the same small range than for the dense dataset, one gets an ocean of sand with a few patches of shale (Figure 1B). This is mathematically correct, but geologically implausible: it doesn’t look anything like the fluvial system we know we have. Kriging is assigning an average value – sand in this case – at all the locations too far from the input points for the variogram to include them. This is an example of problematic extrapolation that is up to us to spot and fix by changing the kriging parameters. Using a very range 10 times the size of the initial one fixes this problem (Figure 1A). Nevertheless, the model still doesn’t show any channel.
If we use the highly isotropic variogram, the model is showing some elongated geobodies that start looking like channels (Figure 2). But we are still far from the level of detail that we obtained with kriging the dense dataset (Figure 3).
On the other hand, the results of running simulation with this anisotropic variogram are very interesting (Figure 4 and Figure 5). The sand distribution in these two realizations is similar to the ones computed from the dense dataset (Figure 6 and Figure 7). It means that with a good variogram and simulation, even this limited dataset allows us to show possible geometries for the channels that our team knows must be present. Naturally, the local variations between these two realizations are much more important than with the two realizations of the dense dataset. For example, with this dataset (Figure 4 and Figure 5), the areas in rectangles 1 and 2 change from sand to shale drastically while with the two realizations ran on the dense dataset are very similar in these areas (Figure 6 and Figure 7).
This example shows that geostatistics have the potential to create realistic models even from a small dataset.