范琼琪, 郑德顺, 孙风波,等.米兰科维奇旋回识别与地-月系统重建[J].河南理工大学学报（自然科学版）,2026,45(5):155-165.

FAN Q Q, ZHENG D S, SUN F B ,et al.Identification of Milankovitch cycles and reconstruction of Earth-Moon system：A case study of the middle-upper members in the Dagushi Formation on the southern margin of the North China Craton[J].Journal of Henan Polytechnic University(Natural Science) ,2026,45(5):155-165.

米兰科维奇旋回识别与地-月系统重建

范琼琪, 郑德顺, 孙风波, 李婷

河南理工大学 资源环境学院，河南 焦作 454003

摘要:目的 为识别基于旋回地层学证据的中元古代早期（~1 787 Ma）米兰科维奇旋回，并计算地-月轨道参数，包括岁差常数k、地月距离和日长，重建深时地-月系统演化历史。方法 以高分辨率X射线荧光光谱分析（X-ray fluorescence， XRF）测定得到的Fe（XRF-Fe）与Ti（XRF-Ti）元素含量数据序列作为古气候替代指标，对华北克拉通南缘济源黄背角剖面大古石组中上段进行旋回地层学分析，识别出中元古代早期主要的天文周期。由于年代地层数据和地层厚度难以准确估算沉积速率，分别采用相关系数法（ccorrelation coefficient，COCO）和年代标尺优化法（Time scale optimization method，TimeOpt）估算研究地层的平均沉积速率。此外，分别采用k+s₃和贝叶斯反演法（TimeOptMCMC）估算地-月轨道参数。结果 估算出研究段的平均沉积速率为2.36~2.53 cm/ka。频谱分析结果显示，10.150 m，2.200~2.210 m，0.427~0.436 m和0.279~0.355 m的沉积旋回分别代表轨道周期长偏心率405 ka、短偏心率86.50~87.00 ka、斜率16.48~17.28 ka和岁差13.08~14.09 ka。k+s₃法计算出岁差常数k =95.8±1.1 arcsec/a，地月距离为330 783（+937/-926） km，日长为17.86（+0.09/-0.08） h；TimeOptMCMC分析结果显示，k =92.21±1.6 arcsec/a，地-月距离为333 885（+1 426/-1 398） km，日长为18.14（+0.14/-0.12） h。在黄背角剖面大古石组记录了显著的米兰科维奇周期信号，证明中元古代早期（~1 787 Ma）沉积记录受米兰科维奇旋回控制。  结论 基于k+s₃ 和贝叶斯反演法计算的地-月系统演化参数为理解中元古代早期地-月系统演化提供了新证据。

关键词:旋回地层学;黄背角剖面;大古石组;地-月系统;华北克拉通南缘

doi:10.16186/j.cnki.1673-9787.2025100026

基金项目:国家自然科学基金资助项目（42172131， 42572141）

收稿日期:2025/10/02

修回日期:2025/12/03

出版日期:2026-07-24

Identification of Milankovitch cycles and reconstruction of Earth-Moon system：A case study of the middle-upper members in the Dagushi Formation on the southern margin of the North China Craton

Fan Qiongqi, Zheng Deshun, Sun Fengbo, Li Ting

School of Resources and Environment， Henan Polytechnic University， Jiaozuo 454003， Henan， China

Abstract: Objectives This study aimed to identify the Milankovitch cycles in the early Mesoproterozoic （~1 787 Ma） based on cyclostratigraphic evidence， and to calculate the Earth-Moon orbital parameters， including the precession constant k， Earth-Moon distance and day length，to reconstruct the evolutionary history of the deep-time Earth-Moon system.  Methods Using high-resolution Fe and Ti element concentration data from X-ray fluorescence （XRF） analysis as paleoclimate proxies， cyclostratigraphic analysis was performed on the middle-upper Dagushi Formation in the Huangbeijiao section， southern margin of the North China Craton， to identify the main astronomical cycles of the early Mesoproterozoic. Due to the lack of accurate radioisotope age constraints， the sedimentation rate could not be precisely estimated from chronostratigraphic data and formation thickness. To improve the reliability of the cyclostratigraphic interpretation， two methods—the correlation coefficient （COCO）and the time scale optimization （TimeOpt）—were employed to estimate the average sedimentation rate of the studied strata. Furthermore， Earth-Moon orbital parameters were estimated via two independent methods：k+s₃ method and Bayesian inversion （TimeOptMCMC）.  Results The average sedimentation rate for the studied strata is estimated to be 2.36~2.53 cm/ka. Spectral analysis reveals that the dominant sedimentary cycles of 10.150 m，2.200~2.210 m， 0.427~0.436 m，and 0.279~0.355 m correspond to the orbital 405 ka long eccentricity， 86.50~87.00 ka short eccentricity，16.48~17.28 ka obliquity，and 13.08~14.09 ka precession cycles， respectively. The k+s₃ approach yielded a precession constant k of 95.8±1.1 arcsec/a， an Earth-Moon distance of 330 783（+937/-926） km， and a day length of 17.86 （+0.09/-0.08）h， while the TimeOptMCMC approach yielded a precession constant k of 92.21±1.6 arcsec/a， an Earth-Moon distance of 333 885 （+1 426/-1 398） km， and a day length of 18.14（+0.14/-0.12） h.  Conclusions Significant Milankovitch cycle signals were recorded in the Dagushi Formation in the Huangbeijiao section，confirming that the sedimentary records in the early Mesoproterozoic Era（~1 787 Ma）were controlled by Milankovitch cycles. The Earth-Moon parameters derived from these two independent methods provide new evidence for understanding the evolutionary history of the Earth-Moon system during the early Mesoproterozoic.

Key words:cyclostratigraphy;Huangbeijiao section;Dagushi Formation;Earth-Moon system;southern margin of the North China Craton