The Foundation of Geostatistics
The semivariogram is the cornerstone of geostatistical analysis. Introduced by Georges Matheron in the 1960s, it quantifies a deceptively simple observation: measurements taken close together tend to be more similar than measurements far apart. By plotting the average squared difference between paired observations against their separation distance, the variogram reveals the spatial structure hidden in scattered data — the range over which correlation exists, the total variance, and the amount of random noise.
Anatomy of the Variogram
Three parameters define a variogram model. The nugget C₀ is the y-intercept — variance that exists even at zero separation, caused by measurement error or micro-scale variation. The sill (C₀ + C) is the plateau the variogram reaches — equal to the total variance of the data. The range a is the distance at which the sill is reached — beyond this distance, measurements are essentially uncorrelated. The ratio of nugget to sill indicates how much of the total variation is spatially structured versus random.
Choosing the Right Model
This simulation lets you compare three standard authorized models. The spherical model is linear near the origin and reaches its sill at exactly distance a — it is the workhorse of mining geostatistics. The exponential model approaches the sill asymptotically, reaching 95% at distance 3a — suitable for phenomena that transition gradually. The Gaussian model is parabolic near the origin, indicating extreme short-range smoothness — useful for topographic surfaces and other very continuous fields, though it can cause numerical instability in kriging.
From Variogram to Prediction
Once a valid variogram model is fitted, it becomes the engine for kriging interpolation. The variogram determines exactly how much weight each nearby sample receives when estimating an unsampled location. Strong spatial dependence (low nugget ratio) means kriging can produce precise, smooth maps. Weak spatial dependence (high nugget ratio) means each sample influences only its immediate neighborhood. Variogram modeling is both science and art — automated fitting helps, but geological knowledge of the deposit is essential for choosing appropriate models and parameters.