1994 Jackling Lecture - Mining Geostatistics - Forty Years Passed. What Lies Ahead?

That you are giving the Daniel C. Jackling award to me is a great personal honor. But more significantly, it is a recognition that geostatistics has come of age. And since I am considered by many as belonging to an older generation of geostatisticians, I thought that it would be fitting that I reflect on where geostatistics came from and where it might be going. First, though, let me propose a definition of geostatistics. Etymologically, paraphrasing Webster's definitions of "geo" and "statistics," it is "a branch of mathematics dealing with the collection, analysis, interpretation and presentation of masses of numerical data taken from the earth." This definition is most appropriate in the context of mining geostatistics. It includes both classical and spatial statistics. It emphasizes the earth aspect, or the analysis of geologic features. And it should remind the practitioner that geologic input is a critical part of all geostatistical applications. In the 1910s, statistical methods were already used to analyze geological data. However, the origin of geostatistics, as we know it today, is best set in the late 1940s, when H.S. Sichel recognized the lognormal distribution of sample values in the South African gold mines. In 1951, Daniel Krige observed that "it can be expected that the gold values in a whole mine will be subject to a larger relative variation than those in a portion of the mine." In other words, samples taken close to each other are more likely to have similar values than if taken farther apart. This observation is the foundation on which spatial statistics, which characterizes values defined in a multidimensional space, is built. However, the 1950s were marked by studies based on classical, as opposed to spatial, statistics. It was only in the 1960s that the need was recognized to model the similarity between sample values as a function of the distance between samples and that the semivariogram was defined. A theoretical framework was developed by Matheron that supplied an elegant mathematical explanation to the empirical observations made by Krige. Matheron coined the term "kriging" in recognition of Krige's pioneering work on the geostatistical evaluation of mineral deposits. As soon as this theoretical framework was developed, it was possible to bring geostatistics to the academic world. The "Centre de Geostatistiques" was founded in Fontainebleau. Numerous students were trained there, disciples eager not only to improve the theory and develop more sophisticated mathematical tools, but also to spread the new faith throughout the world. Expansion of geostatistics exploded in the 1970s, arguably the most fertile decade if it is judged by the frequency of theoretical breakthroughs, the number of original publica-