The univariate statistics of potassium (K) and thorium (Th) concentrations in the oceanic and continental crust of the Earth has been recently investigated from geochemical databases and airborne radiometric surveys [1]. This study demonstrates that the frequency distributions of these elements are scale-dependent. There are right-skewed for small-scale samples (typical volume of rocks analyzed for an individual sample in a dataset) but tend to be more symmetric for large-scale samples. The right-skewed behavior of K and Th is attributed to their incompatible behavior during partial melting or fractional crystallization. The scale-dependence and evolution toward normal distributions are a direct consequence of the central limit theorem applied to K and Th concentrations. The results of the results of this study may be applied to Mars, using the Mars Odyssey global maps of K and Th concentrations [2]. In light of available K, Th concentrations at the rock-scale (in-situ samples and martian meteorites), we infer that each “pixel” of these maps reflect a right-skewed distribution of K and Th concentrations at smaller-scales, where K and Th-poor rocks, such as basalts, are spatially dominant. In turn, K, and Th-rich rocks, such as those found by Curiosity at Gale crater [3], may occur globally, though their spatial extension must be limited to account for the values reported by Mars Odyssey. The global, but sparse occurrence of K, Th-rich rocks at the surface is consistent with a buried felsic crust, outcropping at the favor of tectonic or impact events. These conclusions will be discussed in the context of the inferred constraints about the structure of the martian crust from Insight data [4]. [1] Baratoux, et al., Earth and Space Science, in press. [2] Boynton et al. JRGP, doi:10.1029/2007JE002887. [3] Sautter et al. doi:10.1038/NGEO2474. [4] Knapmeyer-Endrun et al., Science, doi: 10.1126/science.abf8966

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.