Range, Sill, and Nugget

Three Numbers and a Shape

To use a variogram in modeling we fit it with a smooth model set by three parameters. The nugget is the jump at the origin: variability that appears even at near-zero lag, from measurement error and from structure finer than the sample spacing. The sill is the plateau, the total variance. The range is the lag where the model reaches the sill.

The Model Shapes

Three shapes cover most cases. The spherical model rises steadily and reaches the sill exactly at the range; it is the workhorse of reservoir modeling. The exponential model rises fastest near the origin and approaches the sill only asymptotically. The Gaussian model is flat near the origin and then rises steeply, describing a very smooth, continuous property; it is powerful but can make the kriging equations unstable unless a small nugget is added.

From Curve to Texture

These are not just curve-fitting knobs. The realization beneath the curve shows what each parameter does to the property itself: a large nugget makes neighboring values jump around like noise, a long range makes the field smooth and slowly varying, and the sill sets the amplitude of the swings. Choosing a variogram model is really choosing the texture the model will paint into every cell.