Multi-Scale Feature Analysis Method for Soil Heavy Metal Based on Two-Dimensional Empirical Mode Decomposition: An Example of Arsenic

The spatial distribution of soil heavy metals was influenced by both natural and anthropogenic factors, and the multi-scale characteristics of heavy metals played a key role in analyzing their influencing factors. Taking arsenic (As) of an oil refining site in Shandong as an example, the As was firstly decomposed into intrinsic mode functions (IMFs) at different scales and a residual using two-dimensional empirical mode decomposition (EMD). Secondly, the spatial variation scales of As, the IMFs, and the residual were quantified by their semi-variograms, respectively. Finally, local spatial correlation analysis and random forest model were employed to analyze the multi-scale features of As, the IMFs, the residual, and environmental variables. The results indicated that the As was decomposed into IMF1, IMF2, IMF3, and a residual using the two-dimensional EMD method, and the corresponding spatial ranges were 72.60 m, 159.30 m, 448.00 m, and 592.36 m, respectively. IMF3 had the highest percentage of variance with a value of 57.56%, indicating that the spatial variation of As was mainly concentrated on a large scale. There were correlations between As and aspect and land use type. However, after the scale decomposition of two-dimensional EMD, there were significant correlations between oil residue thickness and IMF1, land use type and IMF3, land use type, and aspect and residual, respectively. The IMFs and residual had a significant scale–location dependence on environment variables, and the impact of anthropogenic factors on As was mainly reflected at the small and medium scales, while the influence of natural factors was mainly reflected at the large scale. The developed method can provide a methodological framework for the spatial analysis and pollution control of soil heavy metals.