Georges Matheron

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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 to the Online Library of the Centre de Géostatistique, Fontainebleau, France. Matheron’s Formule des Minerais Connexes became his Note Statistique 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 lead and silver grades because his core samples varied in length. He did derive the length-weighted average lead and silver 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 rather than measured values. Matheron's Interprétations des corrélations entre variables aléatoires lognormales of November 29, 1954, was marked Note statistisque No 2. In this paper, Matheron explored lognormal variables and set the stage for statistics by symbols. Primary data would have allowed him to assess whether or not lead and silver grades departed from the lognormal distribution, or displayed spatial dependence along his borehole.

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. Matheron presented his Stationary Random Function at the first colloquium on geostatistics in the USA. He called on Brownian motion to conjecture the continuity of his Riemann integral. He did not explain what Brownian motion and ore deposits have in common. Matheron, unlike John von Neumann in 1941 and Anders Hald in 1952, never worked with Riemann sums. It was not Professor Dr Georges Matheron but Dr Frederik P Agterberg who derived the distance-weighted average of a set of measured values determined in samples selected at positions with different coordinates in a sample space. What Agterberg did not do was derive the variance of this function.

Matheron did indeed derive length-weighted average grades of core samples and ore blocks but did not derive the variance of these functions. In time, the length-weighted average grade for Matheron's three-dimensional block was replaced with the distance-weighted average grade for Agterberg's zero-dimensional point. Both central values turned into honorific kriged estimates or estimators. An infinite set of Agterberg's zero dimensional points fits within any ore block, along any borehole, or inside any sampling unit or sample space. Matheron's block grades and Agterberg's point grades are unique because both are variance-deprived functions.

[edit] External links

• Obituary by Dominique Jeulin (Centre de Morphologie Mathématique Ecole des Mines de Paris, October 2000) probably from Image Analysis & Stereology.
• Georges Matheron - Founder of Spatial Statistics by Frederik P. Agterberg (Proceedings of the International Association for Mathematical Geology, 2003)
• A chronology of Matheron's seminal work
• Debunking Matheronian geostatistics