- Copyright © 2000 Society of Exploration Geophysicists
Editor's Note: The Geologic Column, which appears monthly in TLE, is (1) produced cooperatively by the SEG Interpretation Committee and the AAPG Geophysical Integration Committee and (2) coordinated by M. Ray Thomasson and Lee Lawyer.
This is the first of two articles intended to describe petroleum geostatistics for the nongeostatistician. There are many misconceptions about geostatistics, what it is, and what it can or can't do for the petroleum industry.
The first article defines geostatistics, examines its origins, and reviews the spatial model and the kriging interpolation algorithm. The second article describes geostatistical conditional simulation and its use for uncertainty (risk) analysis.
Earth science data exhibit spatial correlation to greater or lesser degrees. As the distance between two data points increases, the similarity between the two measurements decreases. Geostatistics is a rapidly evolving branch of applied statistics and mathematics that offers a collection of tools which quantify and model spatial variability. Spatial variability includes scales of variability (heterogeneity) and directionality within data sets.
Origins of geostatistics
The origins of geostatistics are found exclusively in the mining industry. D. G. Krige, a South African mining engineer, and H. S. Sichel, a statistician, developed a new estimation method in the early 1950s when “classical” statistics was found unsuitable for estimating disseminated ore reserves.
Georges Matheron, a French engineer, developed Krige's innovative concepts and formalized them within a single framework with his Theory of Regionalized Variables. Matheron, at the Centre de Geostatistique, pioneered the use of mining geostatistics in the early 1960s. The word kriging was coined in recognition of D. G. Krige.
It is interesting that geostatistics was not originally developed to solve interpolation problems (kriging) but to address what is called the support effect. In ore mining, this refers to the difference between the variance of average values measured from large samples …