## 3 Materials and Methods
### High-Purity Germanium (HPGe) Gamma Spectrometry  
For HPGe analysis, 5 cube-shaped aliquots (approx. 5 \(\times\) 5 \(\times\) 5 cm\({}^{3}\)) were prepared from each rock by cutting the larger stone fragments using a circular saw, each treated in the laboratory as reported in [46; 47]. A live time of 70,000 s was employed, and the activity concentrations were evaluated as follows:  
(i) \({}^{226}\)Ra: based on the 295.21 and 351.92 keV (\({}^{214}\)Pb) and 1120.29 keV (\({}^{214}\)Bi) gamma-ray lines;  
(ii) \({}^{232}\)Th: using the 911.21 and 968.97 keV (\({}^{228}\)Ac) gamma-ray lines;  
(iii) \({}^{40}\)K: evaluated from its 1460.8 keV gamma-ray line [48]. Gamma spectrometry analysis was performed using an electrically cooled Ortec HPGe detector housed within lead wells to minimize background radiation, i.e., a direct biased semiconductor with 1.85 keV FWHM resolution, 40% relative efficiency, 64:1 peak-to-Compton ratio, bias voltage of 4000 V, and an energy range of 50 keV-2 MeV. The Eckert and Zigler Nuclitec GmgH (Braunschweig, Germany) traceable multinuclide radioactive standard, number BC4464, covering the energy range 59.54 keV-1836.09 keV, was employed to perform efficiency and energy calibrations [49]. The precise geometry of the sample was replicated by this calibration standard in an epoxy resin matrix water equivalent. Data collection and analysis were performed using Ortec Gamma Vision software (ver. 8). The activity concentration (Bq kg\({}^{-1}\) dry weight, d.w.) of each radioisotope was quantified as follows:  
\[\mathrm{C(Bqkg^{-1}d.w.)}=\frac{\mathrm{N_{E}}}{\epsilon_{E}\mathrm{t}\gamma _{d}\mathrm{M}}\, \tag{1}\]  
with \(\mathrm{N_{E}},\epsilon_{E},\gamma_{d},\mathrm{M},\mathrm{and}\) t representing the net area, efficiency for energy E, decay probability of the gamma photon, dry mass of the sample (kg), and acquisition time (s), respectively. For the assessment of the combined standard measurement uncertainty at coverage factor k = 2, the counting statistics, nuclear data library, calibration efficiency, sample quantity, and self-absorption correction were addressed [50]. The detection limit evaluation was accomplished through the RISO method [50]. Moreover, in order to take into account self-absorption (SA) processes, it is important to underline that, for photons with energy greater than 100 keV, SA depends almost exclusively on the density of the sample, while for photons characterized by energy less than 100 keV, it is also necessary to consider the effect of the chemical composition of the investigated matrix. Accordingly, the sample's bulk density must be quantified to check whether it is within the range of acceptability defined by the laboratory [50]. In cases where it is also necessary to consider the effect of the chemical composition of the sample, the same should be estimated at least approximately (also using the literature data), and it should be verified that it is compatible with the chemical composition of the matrix used for calibration or used as input data in the application of numerical correction methods. In our case, SA corrections were carried out using Gamma Vision software (ver. 8) [51]. Finally, the elevated quality of HPGe analysis outcomes was formally certified by the Italian Accreditation Body (ACCREDIA) [52], which implies the continuous verification (with an annual periodicity) of the maintenance of the performance characteristics of the gamma spectrometry method. In particular, the repeatability of the results was verified over time using the double test method. A certified reference material (also containing the radionuclides \({}^{40}\)K and \({}^{137}\)Cs) as analyzed twice, with the active concentration of the radionuclide of interest being defined as \(x_{1}\) (first measurement) and \(x_{2}\) (second measurement). The probability level p = 0.95 was considered.