Multiple fractal characterization for elemental soil contamination across Yushu City, Qinghai Province, China

Establishing soil element background values and risk thresholds is crucial for pollution control in fragile ecosystems. However, defining local standards for elements lacking national guidelines remains challenging. This study focuses on Yushu City, Qinghai Province, which has a complex geological background and minimal anthropogenic disturbance. We analyzed the spatial heterogeneity of 17 soil elements (As, Ba, Cd, Co, Cr, Cu, I, La, Pb, Rb, Sb, Sn, Th, Tl, U, V, and W) using multifractal theory. For elements without national standards, such as La, Rb, and Th, we calculated risk screening values. Through multifractal analysis of the 17 soil elements, we established local background values (mg/kg) for key elements: As (17.78), Cd (0.20), Cr (66.07), La (33.88), and Rb (104.71). The fractal dimension values for Cd (D2 = 3.95), As (D2 = 4.63), Cr (D2 = 4.66), and other elements were low, indicating spatially heterogeneous distributions and a critical pollution diffusion trend. Furthermore, the study shows that multifractal theory can accurately identify the superposition characteristics of natural background and anthropogenic pollution in complex geological environments. It can also effectively differentiate geological high values from polluted inputs, providing a scientific basis for soil risk classification and control in alpine, ecologically fragile areas.