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.

中文翻译：

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一种新的反距离模型，用于计算各种铅源的百分比贡献。

铅（Pb）同位素组成分析是准确识别环境介质中Pb起源的有用工具。现有的基于铅同位素比的铅源贡献的计算方法极大地限制了铅污染源分配的发展。在本研究中，提出了一种新的距离模型，用于计算铅源的质量比例，该模型基于样品与铅同位素比图中的可能铅源之间的距离。在先前的三项研究中，采用了反距离模型来计算两个铅源的贡献比例。由常规二元混合方程和反距离模型计算的比例之间的平均绝对差分别为0.21％，1％和1.9％，表明新模型可以很好地计算出两个铅源的贡献。用三种铅源的反距离模型计算的上海人为土壤铅含量的人为源比例（52％）与常规三元混合方程式计算的结果（53％）相当，表明了新方法的有效性。模型计算三个铅源的贡献比例。反距离模型在计算四个铅源的贡献中获得了合理的结果，说明新模型在计算四个或更多铅源的分配中具有潜在的用途。这些结果表明，逆距离模型是一种用于计算各种Pb污染源贡献比例的简单有效方法，