Algebraic dispersion fields on ternary diagrams

Previously published dispersion fields on ternary diagrams have been constructed variously, and their derivations have not been well-specified. Here an explanation of their bases is provided through an algebraic method for calculating two related forms, designated thesilhouette dispersion field and thegirth dispersion field. Such dispersion estimates can be made more precise by specifying the percentage of samples that fall within the field. Because such fields represent a mechanistic rather than a probabilistic approach, their use in comparison of sample sets must be viewed with caution.     

Trend-surface analysis

This paper is largely an exposition of the work of the French geostatistian G. Matheron and his school in English and at a simpler mathematical level. The probability theory on which it is based is essentially all contained in the references cited, most of which will be unfamiliar to mathematical geologists. The important method of universal kriging is explained intuitively. The genuine statistical problems, which have yet to be overcome, are pointed out.Research supported by the Office of Naval Research under contract NONR 4010(09) awarded to the Department of Statistics, The Johns Hopkins University. This paper in whole or in part may be reproduced for any purpose of the United States Government.     

Stochastic geometry in petroleum geology

Many aspects of the generation, migration, trapping, and discovery of petroleum, as well as its primary and enhanced recovery, depend upon geometry. The scale of the relevant geometric features varies all the way from that of continental margins and basins down to the pores and fissures in reservoir rocks. Because the spatial complexity is so great for each of these processes, it is reasonable to describe them statistically. The primary purpose of this paper is to survey possible ways in which statistical or stochastic geometry enters and might be used in petroleum geology and engineering. While it offers some new theory, this paper does not directly suggest any specific new methods for the estimation of hydrocarbon resources or reserves. This deficiency is mainly due to the current lack of relevant data. When data are available the point of view explained herein will be fruitful. The survey ties together many topics in a novel way.