Georges Matheron

Georges Matheron (1930 - 2000) is by some regarded as the father of Spatial Statistics (Geostatistics). In 1968 he created the "Centre de Géostatistique et de Morphologie Mathématique" at the Paris School of Mines in Fontainebleau. He is well known for his contributions on Kriging and Mathematical Morphology. His seminal work is posted for study and review with the Online Library of the Centre de Géostatistique, Fontainebleau, France. Matheron’s Formule des Minerais Connexes became his Note géostatistique No 1. In this paper of November 25, 1954, Matheron derived the degree of associative dependence between lead and silver grades of core samples. In his Rectificatif of January 13, 1955, he revised the arithmetic mean grades because of core samples of variable length. He did derive the length-weighted average lead and zinc grades but failed to derive the variances of those central values. Neither did he derive the degree of associative dependence between metal grades of ordered core samples as a measure for spatial dependence in his sample space. He did not disclose his primary data set and worked mostly with symbols. Matheron did not explain why his 1954 paper on Interprétations des corrélations entre variables aléatoires lognormales was marked Note statistisque No 2 rather than Note géostatistique No 2.

Matheron coined the eponym krigeage (Kriging) for the first time in his 1960 Krigeage d’un Panneau Rectangulaire par sa Périphérie. In this Note géostatistique No 28, Matheron derived k*, his estimateur and a precursor to the kriged estimate or kriged estimator. In mathematical statistics, Matheron’s k* is the length-weighted average grade of a single panneau in his set. What Matheron failed to derive was var(k*), the variance of his estimateur. So he did derive the length-weighted average grade of each block but did not derive the variance of this central value. In time, the length-weighted average grade for a three-dimensional sample space (Matheronian block grade) was replaced with the distance-weighted average grade for a zero-dimensional sample space (Matheronian point grade). As a result, each infinite set of Matheronian points fits in any Matheronian block. Matheronian block and point grades are unique because both are functionally dependent values without variances.