An optional formula for calculating crustal thickness using Sr/Y ratio and its application to the southeastern margin of the Central Asian Orogenic Belt

Though tracking changes in crustal thickness during orogenic evolution with specific element ratios has been proven effective, available empirical formulas sometimes yield unreasonable results. In this study, we proposed a new formula for calculating the crustal thickness by the Sr/Y ratio. Global lower crust-derived magmatic rock (younger than 23 Ma) data from diverse geological settings were selected and filtered using key geochemical criteria, alternating and iteratively using K-means clustering algorithm and improved Thompson tau method to exclude outliers. Curve fitting between the filtered elemental ratios and crustal thickness showed that the formula derived from maximum Sr/Y is best fitted by quadratic fitting. The rmse value between the calculated crustal thickness using the new Sr/Y formula and the true values worldwide is 14.84, lower than those of previous formulas ranging from 19.15 to 32.77. It is shown that our new formula possibly performs better for revealing temporal variations of Paleozoic crustal thickness at the southeastern margin of the Central Asian Orogenic Belt. During the Early Paleozoic Era, the crustal thickness of the Bainaimiao arc increased, corresponding to the subduction of the Southern Bainaimiao Ocean. In the Devonian, the crust in the Bainaimiao arc and northern North China Craton both continued thinning, implying for a post-collisional setting after the amalgamation between these two blocks. Crustal thickness in northern North China experienced transition from thickening to thinning, revealing a subduction-related convergent setting in the Carboniferous and an extensional setting due to slab roll-back in the Early Permian. The crustal thickness rapidly increased in the Late Permian and decreased in the Triassic, consistent with syn-collisional and post-collisional settings, respectively, associated with final closure of the Paleo-Asian Ocean. These results demonstrated that crustal thickness evolution of an orogen can be depicted in detail by our new formula and can put more insights into the understanding the complex histories of accretionary orogenic belts.