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.

尽管利用特征元素比值追踪造山演化过程中的地壳厚度变化已被证实有效，但现有经验公式有时会得出不合理的结果。本研究提出了一种基于Sr/Y比值(Sr/Y ratio)计算地壳厚度的新公式。我们选取了来自不同地质背景、年龄小于23百万年(23 Ma)的全球下地壳成因岩浆岩数据，并通过关键地球化学判别标准，交替迭代使用K均值聚类算法(K-means clustering algorithm)与改进的Thompson tau检验法(improved Thompson tau method)对数据进行筛选以剔除异常值。对筛选后的元素比值与地壳厚度进行曲线拟合后发现，基于最大Sr/Y比值推导得到的公式以二次拟合效果最优。利用新的Sr/Y比值公式计算得到的地壳厚度与全球真实地壳厚度之间的均方根误差(Root Mean Square Error, RMSE)为14.84，低于此前各类经验公式的均方根误差（19.15至32.77）。研究表明，该新公式在揭示中亚造山带(Central Asian Orogenic Belt)东南缘古生代地壳厚度的时空变化方面表现更优。早古生代时期，白乃庙弧(Bainaimiao arc)的地壳厚度逐渐增加，这与南白乃庙洋(Southern Bainaimiao Ocean)的俯冲作用相对应。泥盆纪时期，白乃庙弧与华北克拉通(North China Craton)北缘的地壳均持续减薄，指示两地块拼合后进入碰撞后构造环境。华北克拉通北缘的地壳厚度经历了从增厚到减薄的转变：石炭纪时期处于与俯冲作用相关的汇聚构造环境，早二叠世时期则因板片回撤形成伸展构造环境。晚二叠世时期地壳厚度快速增加，三叠世时期则发生减薄，这分别对应古亚洲洋(Paleo-Asian Ocean)最终闭合过程中的同碰撞与碰撞后构造环境。上述结果表明，本研究提出的新公式可详细刻画造山带的地壳厚度演化过程，为深入理解增生造山带(accretionary orogenic belts)的复杂演化历史提供新的认识。