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A non-destructive analytical method using wavelength-dispersive X-ray fluorescence (WDXRF) that allows the establishment of the provenance of archaeological obsidians was developed and a comparison with the classical XRF method on powders is discussed. Representative obsidian samples of all the geological outcrops of archaeological interest of the Mediterranean area (Lipari, Pantelleria, Sardinia, Palmarola and the Greek islands of Melos and Gyali), were analysed with the normal procedures used in rock analysis by XRF (crushing, powdering and pelletizing). The non-destructive XRF analysis was instead conducted on splinters taken from the original geological pieces, with the shape deliberately worked to be similar to the refuse usually found at archaeological sites. Since the analysis was conducted on the raw geological fragment, intensity ratios of the suitably selected chemical elements were used, instead of their absolute concentrations, to avoid surface effects due to the irregular shape. The comparison between concentration ratios (obtained by traditional XRF methods) and the intensity ratios of the selected trace elements (obtained from the non-destructive methodology) show that the different domains of the chemical composition, corresponding to the geological obsidians of the source areas, are perfectly equivalent. In the same way, together with the geological splinters, complete archaeological obsidians, from Neolithic sites, may be analysed and their provenance may be determined. The proposed non-destructive method uses the XRF method. Due to its sensitivity, low cost and high speed, it is surely an extremely valid instrument for the attribution of the provenance of the archaeological obsidian from Neolithic sites. [ABSTRACT FROM AUTHOR]