## 3 Materials and Methods
### X-ray Fluorescence Analysis  
Energy-dispersive X-ray fluorescence (EDXRF) analysis was performed on thick samples using the FUXYA2020 spectrometer [47], a homemade portable EDXRF spectrometer equipped with a MINI-X2 X-ray tube (Amptek, Bedford, MA, USA) with a maximum power of 4 W (50 kV, 0.2 mA) and a transmission rhodium anode. The X-ray detector used is XGL-SPCM-DANTE25, a complete SDD spectrometer from XGLAB Bruker Nano Analytics Division (Milan, Italy) with 17 mm\({}^{2}\) active area, 500 \(\upmu\)m thickness, and 12.5 \(\upmu\)m Be window. FUXYA2020 has a typical 45\({}^{\circ}\)-45\({}^{\circ}\) geometric configuration: the angle between the X-ray tube and the detector is set at 90\({}^{\circ}\)[47]. No filters were mounted on the exit window of the X-ray tube, so we used unfiltered continuous radiation emitted from the device: the continuous energy distribution allowed to have a better excitation for low Z elements. Regardless, energies below 2 keV were poorly detected, as detector efficiency is limited in this region due to the thickness of its entrance Be window. For instance, Si K lines (1.7 and 1.8 keV for K\(\upalpha\) and K\(\upbeta\), respectively) were detected, but the evaluation of their area was affected by a relatively high error due to the background to peak ratio; for this reason, elements under K (3.3 keV for K\(\upalpha\) line) were not considered for MV elaboration. The radiation produced by the X-ray tube was collimated by a 2 mm diameter pinhole; the irradiated surface on the sample was therefore about 30 mm\({}^{2}\), so as to investigate a representative area of each sample. Thick obsidian blocks were measured without any preparation on flat surface areas. More than one point was considered on each of the 33 fragments under investigation to achieve a better statistic.  
The working conditions were 40 kV and 0.6 mA with a 300 s acquisition time. Spectra deconvolution and area calculation were performed using the AXIL-QXAS 3.6 (Quantitative  
Figure 1: Geographical location of considered obsidian sources in the Mediterranean basin.  
X-ray Analysis System) software developed by IAEA, subtracting the background signals for each considered peak; in this way, a good discrimination between K and L series can be also be performed in case of very close energy values. Sixteen elements were detected and considered, namely K, Ca, Ti, Mn, Fe, Cu, Zn, Rb, Sr, Y, Zr, Nb, La, Ce, Pb, and Th; their areas were normalized to the Rayleigh scattering peak of rhodium (20.2 keV for K\(\alpha\) line) to eliminate eventual differences deriving from geometrical issues. Indeed, even when considering trace elements, the probability that obsidian from two different sources will have the same concentration of a few given elements within the experimental errors must not be overlooked. To reduce the probability of coincidental similarity it is useful to consider as many elements as possible, and MV analysis is the best way to handle such a huge amount of data. Multivariate analyses were performed considering semi-quantitative data [48] without calculating concentration values for the detected chemical elements. This approach already proved to be useful for glass classification on the bases of chromophore elements detected by XRF [49].