Oil and Gas Exploration, Statistical Decision Criteria: Applications of Discriminant Analysis in the Petroleum Industry
Authors: Wignall Thomas Kenneth 
Published: December 2007

American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc.
This paper was prepared for the 43rd Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in Houston, Tex., Sept. 29-Oct. 2, 1968. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made. provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines.

Abstract
Discriminant functions are defined, based on well data and field data. The field studies [in the U.S. and Canada] confirm that these functions are invaluable in discriminating between target wells and non-target wells; thus, the mappings they yield provide valuable exploration tools.
Discriminant functions are very useful in several other ways:
in decisions concerning well completions; in selecting fields suitable for secondary recovery production; and 131 in general classification problems, such as assigning wells to g groups based on the composition of the fluids they yield, and for classification in paleontological problems.

Introduction
Experience has shown that there is often a high correlation between the electric logs, geological strata, formation tops, etc., among producing wells in the same field or basin. producing wells in the same field or basin. If we can define such a set of relevant parameters that correlate in producing wells and that differ in noncommercial wells, then we can formulate a discriminant function based on these parameters. Discriminant functions are parameters. Discriminant functions are essentially functions that maximize the difference between the parameter mean vector of target wells from that of non-target wells. When the discriminant function has been established, we may evaluate it at each control point to find the discriminant score for each location. These scores are then probability indices for the locations, and when contoured, yield a mapping that designates target areas and non-target areas. The purpose of this paper is to demonstrate the applications of this process in three field studies. A more detailed account of the process is presented in Chap. III of "Oil and Gas Exploration: Statistical Decision Criteria".

DISCRIMINANT FUNCTIONS
Discriminant functions are decision functions defined on two sets of relevant parameters: one set is based on target wells parameters: one set is based on target wells and the other on non-target wells. If a well is drilled in any particular location, there are two possibilities: the well will yield petroleum in commercial quantities, thus petroleum in commercial quantities, thus belonging to population, the population of target wells; or the well will not yield petroleum, thus belonging to population, the petroleum, thus belonging to population, the population of non-target wells. population of non-target wells.