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.     

Distribution of Uranium in the crust of the northwestern canadian shield as shown by lake-sediment analysis

In 1972 a reconnaissance geochemical survey was carried out by the Geological Survey of Canada in the northwestern Canadian Shield. Samples of nearshore lake sediment were collected, by helicopter, from 36,000 sq. miles of the Bear and Slave Structural Provinces. Sample density was one per 10 miles. These samples have since been analyzed for 27 elements. This paper is concerned with the distribution of uranium in 1,241 samples from the western third of the survey area. This region mainly comprises the Bear Province, of Proterozoic age.The Bear Province, which is a metallogenic province for uranium, also appears to be a geochemical province for this element. Uranium is four times more abundant in lake sediments from this area (5.3 p.p.m. U) as compared to the eastern part of the Slave Province (1.3 p.p.m. U). The lake-sediment data are in agreement with analyses of composite rock samples from two parts of the survey area.Within the Bear Province the regional distribution of uranium is controlled mainly by the distribution of Proterozoic granitic rocks. Nearly all areas of 5 p.p.m. U or greater in lake sediments are underlain by Proterozoic granites, or are near to these rocks. Within the granite areas, uranium is distributed along two sets of regularly spaced linear trends. The highest contents in lake sediment, which include values up to 300 p.p.m. U, commonly occur near the intersections of the two trends. These trends correspond to a set of northeast and a set of northwest strike-slip faults and lineaments that were produced by east-west compression of the Bear Province during and after the Hudsonian Orogeny (1750 m.y.). Outside the western margin of the survey area, complex epigenetic mineralization is associated with northeasterly-trending faults. Uranium has been produced from veins of this type at Port Radium and at the Rayrock Mine. Since it is associated with faults, this type of mineralization tends to occur in topographic depressions, that often contain lakes and swamps. Lake-sediment analysis is believed to be an excellent means of detecting such mineralization, both within the survey area and possibly elsewhere in the Canadian Shield. The data obtained during 1972 provide a basis for more detailed prospecting in the region.