## 4 Results and Discussion  
### Direct Comparison of Spectra and Semi-Quantitative Results  
The first step through the validation of our methodology is a qualitative evaluation to check if any inconsistency with literature data (see Section 2.2) is present. Differences between geological provenances for our samples were thus at first studied from the qualitative comparison of XRF spectra; this procedure allows the identification of sixteen elements on which to base chemometric elaboration. As reported in Section 2, the chosen elements are K, Ca, Ti, Mn, Fe, Cu, Zn, Rb, Sr, Y, Zr, Nb, La, Ce, Pb, and Th. A few elements with energy emissions lower that K, such as Si, were also detected; regardless, the evaluation of their peak areas was affected by a relatively high error, and they were considered not suitable for MV elaboration as they could have added some statistical noise. Figure 2 reports one typical spectrum for each provenance using the same color code as in Figure 1. Spectra obviously appear to be normalized to the Rayleigh diffusion peak (Rh R in Figure 2) without any data elaboration as all spectra have been acquired in the same irradiating and geometrical conditions. Only more evident elements have been indicated in the spectra reported in Figure 2; please note that the Fe K\(\alpha\) peak in Pantelleria spectrum is cut due to the vertical scale to allow the comparison of less-present elements from the various provenance. Differences were then investigated using direct comparison and bivariate analyses to check correspondence with literature data: for each detected element, peak area of the principal line of the K or L series was evaluated by spectra fitting using the AXIL-QXAS 3.6 software developed by IAEA considering the background and the possible superimposition between different elements. Semi-quantitative values [52] were obtained considering the intensity of emission in cps (count per second) for each element normalized to the relative sensitivity for the specific element [48]; in the following, we will refer to the semi-quantitative values obtained as to \"relative concentration\" for the sake of brevity. From comparison between the XRF spectra obtained for considered geological regions and literature data, it is clear that Pantelleria is the easiest to recognize; indeed, Pantelleria obsidian shows much higher Fe, Zr, and Mn contents, as evident from the bar chart reported in Figure 3.  
Considering the average semi-quantitative values obtained for Fe in the different groups (named in Figure 3 and in the following as PNTav, PAav, MNav, PMav, and LPav), we can calculate a content 3 to 4 times higher in Pantelleria samples [28]. The same applies to other elements, such as Ti, Nb, and Zn. These details about minor elements are coherent with literature data, even though high relative errors are present within the same provenance, depending also on the exploited technique [27; 31], as stressed in Section 2.2. In the Pantelleria sample spectra, we also detected some elements that are under the minimum detection limit of our spectrometer [16] in the obsidian samples from the other considered sources. This is the case of La and Ce [5; 28]. It is worth noting that the detection of these elements is performed on the L series (4.6 and 5, and 4.8 and 5.3 keV respectively), which partially was superimposed to the K series of Ti (4.5 and 4.9 keV). The identification has been based on the K\(\alpha\)/K\(\beta\) and L\(\alpha\)/L\(\beta\) ratios via AXIL deconvolution subroutine, but the quantification of peak areas can be subject to larger errors. Regardless, La and Ce were not considered when performing statistical elaborations as they have been detected only in Pantelleria obsidians. Figure 2: Comparison between representative XRF spectra for the five obsidian sources considered in the present paper: Pantelleria (PNT), Palmarola (PA), Sardinia-Monte Arci (MN), Lipari (LP), and Milos Island (PM). Only the main elements are reported.