16 



UNITED STATES MINERAL RESOURCES 



favorable pre-ore surface adequately explored by 

 drilling, and Armstrong (1970) has similarly esti- 

 mated undiscovered uranium reserves in the Gas 

 Hills area of Wyoming on the basis of the ratios 

 between explored and unexplored favorable areas. 



I have suggested another variant of the areal 

 method for estimating reserves of nonfuel minerals 

 which is based on the fact that the tonnage of 

 minable reserves of the well-explored elements in 

 the United States is roughly equal to their crustal 

 abundance in percent times a billion or 10 billion 

 (fig. 5). Obviously this relation is influenced by the 



10" 



10" 



10" 



ABUNDANCE (A) IN EARTH'S CRUST, IN PERCENT 



Figure 5. — Domestic reserves of elements compared to their 

 abundance in the earth's crust. Tonnage of ore minable 

 now is shown by a dot; tonnage of lowergrade ores whose 

 exploitation depends upon future technological advances 

 or higher prices is shown by a bar. 



extent of exploration, for it is only reserves of the 

 long-sought and well-explored minerals that display 

 the relation to abundance. But it is this feature 

 that gives the method its greatest usefulness, for 

 it makes it possible to estimate potential resources 

 of elements, such as uranium and thorium, that 

 have been prospected for only a short period. Sekine 

 (1963) tested this method for Japan and found it 

 applicable there, which surprised me a little, for I 

 would not have thought Japan to be a large enough 

 sample of the continental crust to bring out this 

 relationship. 



The relation between reserves and abundance, of 

 course, can at best be only an approximate one, use- 

 ful mainly in order-of-magnitude estimates, for 

 obviously crustal abundance of an element is only 



one of its properties that lead to its concentration. 

 That it is an important factor, however, may be 

 seen not only in its influence on the magnitude of 

 reserves but also in other expressions of its influence 

 on the concentrations of the elements. For example, 

 of the 18 or so elements with crustal abundances 

 greater than about 200 parts per million, all but 

 fluorine and strontium are rock forming in the 

 sense that some extensive rocks are composed chiefly 

 of minerals of which each of these elements is a 

 major constituent. Of the less abundant elements, 

 only chromium, nitrogen, and boron have this dis- 

 tinction. Only a few other elements, such as copper, 

 lead, and zinc, even form ore bodies composed 

 mainly of minerals of which the valuable element 

 is a major constituent, and in a general way the 

 grade of minable ores decreases with decreasing 

 crustal abundance. A similar gross correlation exists 

 between abundance of the elements and the number 

 of minerals in which they are a significant con- 

 stituent. 



Members of a committee of the Geology and the 

 Conservation of Mineral Resources Board of the 

 Soviet Union have described a somewhat similar 

 method for the quantitative evaluation of what they 

 call predicted reserves of oil and gas, based on esti- 

 mates of the total amount of hydrocarbons in the 

 source rock and of the fraction that has migrated 

 into commercial reservoirs — estimates that would 

 be much more difficult to obtain for petroleum than 

 for the elements. Probably for this reason not much 

 use has been made of this method, but it seems 

 likely that quantitative studies of the effects of the 

 natural fractionation of the elements might be of 

 some value in estimating total resources in various 

 size and grade categories. 



Some studies of the grade-frequency distribution 

 of the elements have, in fact, been undertaken by 

 geochemists in the last couple of decades, and, 

 taking off from Nolan's work, several investigators 

 have studied the areal and size-frequency distribu- 

 tion of mineral deposits in conjunction with at- 

 tempts to apply the methods of operations research 

 to exploration (for example, Allais, 1957; Slichter, 

 1960; Grifl^ths, 1964; DeGeoffroy and Wu, 1970, 

 and Harris and Euresty, 1969). None of these stud- 

 ies has been concerned with the estimation of un- 

 discovered reserves, but they have identified two 

 features about the distribution of mineral deposits 

 that may be applicable to the problem. 



One is that the size distribution of both metal- 

 liferous deposits, expressed in dollar value of pro- 

 duction, and of oil and gas, expressed in volumetric 

 units, has been found to be log normal, which means 



