The impact of measurement scale on the univariate statistics of K, Th,
and U in the Earth crust
Abstract
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 (MORB). 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 (i)
bias in rock sampling or in airborne surveys, (ii) the differences in
the chemistry of superficial material, and (iii) 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) and
concentrations of K, Th, U are therefore generally heterogenous at
smaller scales.