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The increase in the semivariogram values with increasing lags seen in Figure 6‑39 diminishes with distance and levels off, in this example at around 1100 meters. This distance is known as the range or active lag distance, and is the approximate distance at which spatial autocorrelation between data point pairs ceases or becomes much more variable. At this range a plateau or sill in the semivariance values has been reached (Figure 6‑40). Such variograms are called transitive. Non-transitive variograms are ones in which the sill is not reached within the region of interest. The term practical range is sometimes used and defined as the distance at which 95% of the sill is reached for an asymptotic variogram model (as in Figure 6‑40), or for which variation around the sill is <5% for a wave/hole-effect model (see further, Figure 6‑44K). When a curve is fitted to the set of points that lie within this range and sill the model used may have a zero or non-zero intercept with the y-axis. In Figure 6‑40 a non-zero intercept is shown, which is known as the nugget or nugget variance, C0, referring back to the original application of such methods to mineral exploration. The nugget is usually assumed to be non-spatial variation due to measurement error and variations in the data that relate to shorter ranges than the minimum sampled data spacing. The sill minus the nugget is sometimes known as the partial sill or structural variance, C. The values C and C0 often appear as parameters in fitted models.

Figure 6‑40 Sill, range and nugget

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