The Impact of Measurement Scale on the Univariate Statistics of K, Th, and U in the Earth Crust. Issue 9 (8th September 2021)

• Record Type: Journal Article
• Authors: Baratoux, D.; Fall, M.; Meslin, P.‐Y.; Jessell, M. W.; Vanderhaeghe, O.; Moyen, J.‐F.; Ndiaye, P. M.; Boamah, K.; Baratoux, L.; André‐Mayer, A.‐S.
• Is Part Of: Earth and space science. Volume 8:Issue 9(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-09-08
• Subjects: potassium -- uranium -- thorium -- geostatistics -- radiometrics; Space sciences -- Periodicals; Geophysics -- Periodicals; 500.5
• DOI: 10.1029/2021EA001786
• Languages: English
• ISSNs: 2333-5084

Abstract

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. 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. Plain Language Summary: Potassium (K), thorium (Th), and uranium (U), termed together heat‐producing elements (HPE) are commonly analyzed in Earth sciences, owing to their faculty to trace various geological processes. The concentrations of these elements may be analyzed in rock samples, or mapped by airborne radiometric surveys (mapping of gamma ray emitted by 40 K, 232 Th, and 238 U), which are very different techniques. Here, we reveal that frequency distributions of HPE concentrations estimated from data sets build from these different techniques are different. The possible causes of these differences, including possible biases in the data, and the large differences between measurement scales are investigated. We conclude the scale factor and the heterogeneity of HPE at scales that are typically lower than the footprint of airborne radiometric surveys is the main factor controlling the shapes of the frequency distributions. The evolution of asymmetric (right‐skewed) frequency distributions toward normal distributions as a function of the sample size is a natural consequence of the Central Limit Theorem. Key Points: Frequency distributions of Potassium (K), thorium (Th), and uranium (U) concentrations from airborne radiometric surveys and geochemical databases are compared Frequency distributions of K, Th, and U concentrations are scale‐dependent Concentrations of K, Th, and U are heterogeneous at the sub‐pixel scale of gridded airborne radiometric maps