A new inverse distance model to calculate the percentage contribution of various Pb sources

Lead (Pb) isotopic composition analysis is a useful tool to accurately identify the origin of Pb in environmental media. The existing calculation method of the contribution of Pb sources from Pb isotope ratios greatly restricted the development of Pb contamination source apportionment. In the present study, a new distance model for calculating the mass proportion of Pb sources, which is based on the distance between the samples and the possible Pb sources in the Pb isotope ratios plot, was presented. The inverse distance model was applied to calculate the contribution proportion of two Pb sources in three previous studies. The average absolute differences between the proportions calculated by the conventional binary mixing equation and the inverse distance model were 0.21%, 1% and 1.9%, respectively, indicating that the new model agreeably calculated the contribution of two Pb sources. The anthropogenic sources proportion (52%) calculated by the inverse distance model of three Pb sources to park soil Pb in Shanghai was comparable to the result that was calculated by the conventional ternary mixing equation (53%), which showed the validity of the new model in calculating the contribution proportion of three Pb sources. Rational results were obtained by the inverse distance model in calculating the contribution of four Pb sources, illustrating that the new model has potential use in calculating the apportionment of four or more Pb sources. These results suggest that the inverse distance model is a simple and efficient approach for calculating the contribution proportion of various Pb contamination sources, and provides a prospective in the study of this field.