The Impact of Measurement Scale on the Univariate Statistics of K, Th, and U in the Earth Crust

The univariate statistics of Potassium (K), thorium (Th), and uranium (U) concentrations, in the Earth’s oceanic and continental crust are examined by different techniques. The frequency distributions of the concentrations of these elements in the oceanic crust are derived from a global catalog of mid-ocean ridge basalts. Their frequency distributions of concentrations in the continental crust are illustrated by the North Pilbara Craton, and the West Africa Craton. For these two cratons, the distributions of K, Th, and U derived from geochemical analyses of several thousand whole rock samples differ significantly from those derived from airborne radiometric surveys. The distributions from airborne surveys tends to be more symmetric with smaller standard deviations than the right-skewed distributions inferred from whole rock geochemical analyses. Hypothetic causes of these differences include (a) bias in rock sampling or in airborne surveys, (b) the differences between the chemistry of superficial material and rocks, and (c) the differences in scales of measurements. The scale factor, viewed as consequence of the central limit theorem applied to K, Th, and U concentrations, appears to account for most of the observed differences in the distributions of K, Th, and U. It suggests that the three scales of auto-correlation of K, Th, and U concentrations are of the same order of magnitude as the resolution of the airborne radiometric surveys (50–200 m). Concentrations of K, Th, and U are therefore generally heterogenous at smaller scales.