Introduction to Variography: Notions of Variability and Derivation

As emphasized throughout this book, the variogram is an important tool in the TOS toolbox. The origin of its use in sampling comes from Pierre Gy and his work on the TOS in the 1960s. At the time, his contemporary George Matheron was developing the foundations for what eventually became the field of geostatistics. In his work, Matheron made extensive use of the variogram to characterize variability in three dimensions for the purpose of estimating ore reserves. 28 Gy, borrowed the variogram from Matheron’s work, finding it to be an excellent tool to characterize variability in the single dimension of process streams. Gy specifically made use of what Matheron termed the experimental semi-variogram, an equation derived using the method of moments to provide a discrete estimator for the variogram. Geostatisticians have used this estimator to help them select from continuous variogram models (gaussian, spherical, exponential, etc.) to best represent the variability in targeted spatial volumes. It is important to note that there is no ideal equation for the variogram, and the estimator we use is just a model. As the statistician George Box famously put it, “All models are wrong, but some are useful …,” and for the purposes of the TOS, Matheron’s estimator for the variogram has proven to be very useful indeed. In this section we will lead the reader through a simple derivation of this estimator, something that is surprisingly lacking in most primers on the subject, yet important in achieving a fundamental understanding of the variogram and the information it is trying to convey.