Modeling the Omni-Directional Variogram
By default, this first plot is the omni-directional variogram (the directional tolerance is 90 degrees). Choose the model type, the sill, and the nugget effect based upon the omni-directional variogram.
5.1 Selecting the variogram model type
There are infinitely many possible variogram models. Surfer allows for the construction of thousands of different variogram models by selecting combinations of the ten available component types. When combined with a nugget effect, one of three models is adequate for most data sets: the linear, the exponential, and the spherical models. Examples of these three models are shown in Figure 5.1.
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Figure 5.1 Variogram Models |
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If the experimental variogram never levels out, then the linear model is usually appropriate. If the experimental variogram levels out, but is "curvy" all the way up, then the exponential model should be considered. If the experimental variogram starts out straight, then bends over sharply and levels out, the spherical model is a good first choice.
For the data in ExampleDataSetC.xls, a spherical model appears appropriate, though one could also try an exponential model. Click on the variogram plot and select the Model tab in the Properties window.
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Figure 5.2 The Model tab of the Variogram properties in the Properties window. |
To see the current model, click on the Nugget Effect next to Current component. You can see that there is also a Linear component to the default model. Next to Components, click the Remove button twice to remove the inappropriate default model. Then click the Add button. In the Add Component dialog, select the Spherical model and click OK.
5.2 Selecting the variogram model scale and length parameters
We must now set the Scale and the Length (A) parameters using an iterative approach (i.e. guess and check). The Scale is the height on the y-axis at which the variogram levels off. By simply looking at the plot, a value between 400 and 450 seems reasonable: enter 425. TheLength (A) for a spherical model is the lag distance at which the variogram levels off. Again, from the plot a value between 30 and 40 seems reasonable: enter 35. The new candidate variogram model is automatically drawn.
This is not a bad first guess, but upon examination of the redrawn curve, it appears that the Length (A) is a little bit too long since the model (blue line) lies to the right of the experimental variogram plot (black line and dots). Reset the Length (A) to 30. This is still a little bit too long. Try 29 for theLength (A) This is a good fit for a variogram.
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Figure 5.3 Variogram model with initial assumptions Left: Scale = 425, Length (A) = 35. Right: Scale =425. Length (A) = 29. |
5.3 Selecting the variogram nugget effect
If the experimental variogram appears to have a non-zero intercept on the vertical axis, then the model may need a nugget effect component. The variance of Delta Z in the Nearest Neighbor Statistics section of the Variogram Grid Report offers a quantitative upper bound for the nugget effect in most circumstances.
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Figure 5.4 Linear Variogram model with nugget effect for data set Demogrid.dat. |
In Surfer the nugget effect is partitioned into two sub-components: the error variance and the micro variance. Both of these sub-components are nonnegative,and the sum of these two sub-components should equal the apparent non-zero intercept.
The error variance measures the reproducibility of observations. This includes both sampling and assaying (analytical) errors. The error variance is best selected by computing the variance of differences between duplicate samples.
The micro variance is a substitute for the unknown variogram at separation distances of less than the typical sample spacing. This is best selected by taking the difference between the apparent non-zero intercept of the experimental variogram and the error variance.
The model for our example appears to intersect the vertical axis at 0, so we will not apply a nugget effect.
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