低低跟踪模式地球重力场反演与星座设计

   地球重力场恢复及气候探测卫星 (Gravity Recovery And Climate Experi-ment, GRACE) 和GRACE后续任务 (GRACE Follow-On, GRACE-FO) 具备高时空分辨率监测地球表层质量迁移的能力，为大地测量学、水文学、冰川学和地震学等地球科学注入新的活力。然而，如何从海量的重力卫星观测数据中提取出高时空分辨率的地表质量迁移信号，一直是卫星重力学的关注热点和研究难点。

   本文以低低卫星跟踪卫星测量模式的GRACE重力卫星数据反演地表质量迁移模型为主线框架，研究内容分为时变重力场球谐系数模型解算、时变重力场Mascon模型解算以及下一代重力卫星任务相关的星座设计与性能评估。

研究成果和创新点主要包含以下四方面：

1.     完善并改进了“基于低轨卫星数据解算地球重力场系统 — 球谐系数方案” (The ANalyst of Gravity Estimation with Low-orbit Satellites - Spherical Harmonic solution recovery, ANGELS-SH) 时变重力场解算系统：提高背景力模型的计算精度，使其媲美国外主流机构对背景力模型的解算精度；聚焦于短弧长法解算时变重力场球谐系数模型过程中若干关键参数进行了深入的分析与讨论。研究结果表明：本文解算的GCL-SH2022模型精度与国际官方解算机构发布的RL06版本球谐系数模型精度相当。

2.     建立了卫星观测量与Mascon参数的显式偏导数，基于短弧长法实现了从Level-1B数据反演Mascon时变重力场函数模型的构建与解算系统ANGELS-M的研发，填补了国内外短弧长法解算Mascon模型的研究空缺。此外，研究了时变重力场Mascon模型解算过程中若干关键问题：在常规背景力模型的基础上，镶嵌了额外两种背景力模型用以考虑冰川均衡所引发的动力学信号和由地球弹性形变所触发的时变重力信号；依据海陆及流域边界构建了更加符合物理规律的Mascon网格，并根据重力卫星的空间分辨率对网格尺度做出最优化选择。研究结果表明：本文解算的GCL-Mascon2023模型具备时变信号捕获的能力，其精度与国际官方解算机构发布的RL06版本Mascon模型精度相当。

3.     构建了兼顾空域和时域双重优化的目标函数，并引入差分进化算法对GRACE-FO和中国未来重力卫星任务组建的双极轨重力卫星星座进行优化设计，将解算时变重力场的时间分辨率提升了一倍。首次分析了双极轨重力卫星星座时间分辨率的提升对地球科学的潜在价值，研究结果表明：半月解能够提升亚湿润气候类型流域水文信号约36%精度；半月解能够在格陵兰冰盖质量平衡计算中减少约25%误差；半月解可以捕获之前被月解忽略地震同震位移的高频质量迁移信号，其精度约提高33%。

4.     针对（近）极轨型重力卫星编队/星座解算的时变重力场受到较为严重相关噪声的干扰，在双极轨重力卫星星座基础上探索如何设计第三组重力卫星编队才能将三重力卫星组合星座的性能最大化。采用球形位错理论模拟计算了不同震级的地震同震信号，着重对三重力卫星组合星座进行了地震敏感性分析。研究结果表明：GRACE-FO随着地震震级的减小而逐渐达到其探测上限，三重力卫星组合星座的地震探测优势逐渐凸显，其在捕获Mw7.7左右地震的同震重力信号时具有60%左右的精度提升。

The Gravity Recovery And Climate Experiment (GRACE), and its successor mission, GRACE-Follow on (GRACE-FO), possess the unique ability to monitor the mass migration of the Earth's surface with high temporal and spatial resolution. It injects new vitality into various fields, including geodesy, hydrology, glaciology, and seismology. However, the challenge of accurately solving the mass transport model with high temporal and spatial resolution from the massive observation data of gravity satellites remains the research hotspot and difficulty in satellite gravimetry.

The dissertation takes the inversion of surface mass variations from the gravity satellite in low-low tracking mode (i.e., GRACE) as the main framework. It is mainly divided into recovering the temporal gravity field represented in terms of spherical harmonic coefficients and Mascon models, as well as constellation design and performance evaluation related to the next generation gravity mission.

The main work and contributions of this dissertation cover mainly:

1. The self-developed ANalyst of Gravity Estimation with Low-orbit Satellites - Spherical Harmonic solution recovery software (ANGELS-SH) was further enhanced by improving the computational accuracy of the background force models. Additionally, this dissertation has addressed several key issues that arise during the spherical harmonic solutions recovery using the short-arc approach. The research results indicate that the GCL-SH2022 models solved in this dissertation are comparable in accuracy to the RL06 version of the spherical harmonic coefficient solutions released by international official institutions.
2. In order to recover the Mascon solutions from level-1B data, this dissertation used explicit partial derivatives with analytical expression for mass concentration to relate the inter-satellite rangerate measurements to the individual mascons. This algorithm has addressed the research gap in the short-arc approach for recovering Mascon models both domestically and internationally. To that end, it comprehensively analyzes the key parameters required for implementing Mascon inversion using the short-arc approach. The dissertation addressed several critical issues in the Mascon solution recovery. In addition to the conventional background force model, two additional ones were incorporated to account for dynamic signals induced by glacial isostatic adjustment and temporal signals triggered by Earth's elastic deformation. Mascon grids, in greater conformity with physical laws, were developed by delineating the boundaries of seas, lands, and river basins, with an optimized selection of scales for land and ocean grids according to GRACE spatial resolution. The comprehensive analyses demonstrate that GCL-Mascon2023, recovered by this dissertation, achieves accuracy comparable to the Mascon models released by international official institutions in the RL06 version.
3. The dissertation formulated an objective function that considers both spatial and temporal aspects and utilized the Differential Evolution algorithm to optimize the Dual GRACE-like Polar satellite Constellation, which combines GRACE-FO and the Chinese Future Gravity Mission. The optimized constellation doubled the temporal resolution of the estimated temporal gravity field. The potential value of improving temporal resolution through the Dual GRACE-like Polar satellite Constellation was analyzed in Earth sciences. The research results indicate that semi-monthly solutions can enhance the accuracy of hydrological signals in sub-humid climate regions by approximately 36%. Furthermore, semi-monthly solutions can improve the accuracy of glacier ablation signals by about 25% better than the monthly solutions. For postseismic gravitational deformation caused by instantaneous earthquakes, the semi-monthly solutions can capture mass transport signals previously ignored by the monthly solutions, which leads to accuracy being improved by about 33%.
4. Due to the considerable impact of correlation noise on the gravity field determined by the polar-orbiting gravity satellite formation, there is a need to investigate the optimal design for the Third Inclined-pair satellite Formation based on the Dual GRACE-like Polar satellite Constellation. This exploration aims to enhance the overall performance of the Triple Gravity Satellite Constellation. This dissertation employed the spherical dislocation theory to model and compute earthquake coseismic signals of various magnitudes, concentrating on the seismic sensitivity analysis from the Triple Gravity Satellite Constellation. The research results indicate that GRACE-FO gradually reaches its detection limit as the magnitude of seismic events decreases. In contrast, the seismic detection advantage of the Triple Gravity Satellite Constellation becomes increasingly evident. It exhibits an accuracy improvement of approximately 60% in capturing co-seismic gravity signals for earthquakes around Mw7.7.

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