Alternative mission architectures for a gravity recovery satellite mission

Since its launch in 2002, the Gravity Recovery and Climate Experiment (GRACE) mission has been providing measurements of the time-varying Earth gravity field. The GRACE mission architecture includes two satellites in near-circular, near-polar orbits separated in the along-track direction by approximately 220 km (e.g. collinear). A microwave ranging instrument measures changes in the distance between the spacecraft, while accelerometers on each spacecraft are used to measure changes in distance due to non-gravitational forces. The fact that the satellites are in near-polar orbits coupled with the fact that the inter-satellite range measurements are directed in the along-track direction, contributes to longitudinal striping in the estimated gravity fields. This paper examines four candidate mission architectures for a future gravity recovery satellite mission to assess their potential in measuring the gravity field more accurately than GRACE. All satellites were assumed to have an improved measurement system, with an inter-satellite laser ranging instrument and a drag-free system for removal of non-gravitational accelerations. Four formations were studied: a two-satellite collinear pair similar to GRACE; a four-satellite architecture with two collinear pairs; a two-satellite cartwheel formation; and a four-satellite cartwheel formation. A cartwheel formation consists of satellites performing in-plane, relative elliptical motion about their geometric center, so that inter-satellite measurements are, at times, directed radially (e.g. parallel to the direction towards the center of the Earth) rather than along-track. Radial measurements, unlike along-track measurements, have equal sensitivity to mass distribution in all directions along the Earth’s surface and can lead to higher spatial resolution in the derived gravity field. The ability of each architecture to recover the gravity field was evaluated using numerical simulations performed with JPL’s GIPSY-OASIS software package. Thirty days of data were used to estimate gravity fields complete to degree and order 60. Evaluations were done for 250 and 400 km nominal orbit altitudes. The sensitivity of the recovered gravity field to under-sampled effects was assessed using simulated errors in atmospheric/ocean dealiasing (AOD) models. Results showed the gravity field errors associated with the four-satellite cartwheel formation were approximately one order of magnitude lower than the collinear satellite pair when only measurement system errors were included. When short-period AOD model errors were introduced, the gravity field errors for each formation were approximately the same. The cartwheel formations eliminated most of the longitudinal striping seen in the gravity field errors. A covariance analysis showed the error spectrum of the cartwheel formations to be lower and more isotropic than that of the collinear formations.     

Comparing seven candidate mission configurations for temporal gravity field retrieval through full-scale numerical simulation

The goal of this contribution is to focus on improving the quality of gravity field models in the form of spherical harmonic representation via alternative configuration scenarios applied in future gravimetric satellite missions. We performed full-scale simulations of various mission scenarios within the frame work of the German joint research project “Concepts for future gravity field satellite missions” as part of the Geotechnologies Program, funded by the German Federal Ministry of Education and Research and the German Research Foundation. In contrast to most previous simulation studies including our own previous work, we extended the simulated time span from one to three consecutive months to improve the robustness of the assessed performance. New is that we performed simulations for seven dedicated satellite configurations in addition to the GRACE scenario, serving as a reference baseline. These scenarios include a “GRACE Follow-on” mission (with some modifications to the currently implemented GRACE-FO mission), and an in-line “Bender” mission, in addition to five mission scenarios that include additional cross-track and radial information. Our results clearly confirm the benefit of radial and cross-track measurement information compared to the GRACE along-track observable: the gravity fields recovered from the related alternative mission scenarios are superior in terms of error level and error isotropy. In fact, one of our main findings is that although the noise levels achievable with the particular configurations do vary between the simulated months, their order of performance remains the same. Our findings show also that the advanced pendulums provide the best performance of the investigated single formations, however an accuracy reduced by about 2–4 times in the important long-wavelength part of the spectrum (for spherical harmonic degrees ${<}50$ ), compared to the Bender mission, can be observed. Concerning state-of-the-art mission constraints, in particular the severe restriction of heterodyne lasers on maximum range-rates, only the moderate Pendulum and the Bender-mission are beneficial options, of course in addition to GRACE and GRACE-FO. Furthermore, a Bender-type constellation would result in the most accurate gravity field solution by a factor of about 12 at long wavelengths (up to degree/order 40) and by a factor of about 200 at short wavelengths (up to degree/order 120) compared to the present GRACE solution. Finally, we suggest the Pendulum and the Bender missions as candidate mission configurations depending on the available budget and technological progress.     

地球重力场模型正演计算软件系统的设计

本文介绍了自主开发的地球重力场模型正演（计算高程异常、重力异常、垂线偏差等）计算软件—EGMCAL,给出了该软件的整体设计框架和功能。利用GFZ（德国地学中心）研制的相关软件验证了该软件的正确性,并利用EGMCAL对我国东部某大桥高程控制网数据进行了处理,得出三种精度最高的模型在此区域的计算结果。     

月球重力场模型研究进展和我国将来月球卫星重力梯度计划实施

本文介绍了基于国际探月观测数据建立的月球重力场模型:8×4、15×8、13×13、5×5、7×7、16×16-1/2/3、Lun60d、GLGM-1/2、LP75D/G、LP100K/J、LP165P、LP150Q和SGM90d;通过对比SST-HL/LL-Doppler-VLBI和SST-HL/SGG-Doppler-VLBI跟踪观测模式的优缺点,建议我国将来首期月球卫星重力测量计划采用SST-HL/SGG-Doppler-VLBI较优;其次,通过对比静电悬浮、超导和量子卫星重力梯度仪的优缺点,建议我国将来首期月球卫星重力梯度计划采用静电悬浮重力梯度仪;并建议我国将来首颗月球重力梯度卫星的轨道高度(50～100 km)选择在已有月球探测卫星的测量盲区,轨道倾角(90°±3°)设计为有利于月球卫星观测数据全球覆盖的近极轨模式。     

智慧地球时代测绘地理信息学的新使命

本文首先指出智慧地球是数字地球、物联网和云计算等有机的融合,随后分析了智慧地球的主要特性,并重点阐述了智慧地球时代测绘地理信息学的新使命。作者认为我们已经从绘制地形图为主的小测绘发展成为当今以地理空间信息服务为主的大测绘,现在必须抓住机遇,不失时机地拓展智慧地球时代测绘地理信息学的新使命,将传统测绘提升为能够实时、智能地采集和处理海量空间数据、提供空间信息和知识服务的智慧测绘新阶段。     

Design considerations for a dedicated gravity recovery satellite mission consisting of two pairs of satellites

Future satellite missions dedicated to measuring time-variable gravity will need to address the concern of temporal aliasing errors; i.e., errors due to high-frequency mass variations. These errors have been shown to be a limiting error source for future missions with improved sensors. One method of reducing them is to fly multiple satellite pairs, thus increasing the sampling frequency of the mission. While one could imagine a system architecture consisting of dozens of satellite pairs, this paper explores the more economically feasible option of optimizing the orbits of two pairs of satellites. While the search space for this problem is infinite by nature, steps have been made to reduce it via proper assumptions regarding some parameters and a large number of numerical simulations exploring appropriate ranges for other parameters. A search space originally consisting of 15 variables is reduced to two variables with the utmost impact on mission performance: the repeat period of both pairs of satellites (shown to be near-optimal when they are equal to each other), as well as the inclination of one of the satellite pairs (the other pair is assumed to be in a polar orbit). To arrive at this conclusion, we assume circular orbits, repeat groundtracks for both pairs of satellites, a 100-km inter-satellite separation distance, and a minimum allowable operational satellite altitude of 290 km based on a projected 10-year mission lifetime. Given the scientific objectives of determining time-variable hydrology, ice mass variations, and ocean bottom pressure signals with higher spatial resolution, we find that an optimal architecture consists of a polar pair of satellites coupled with a pair inclined at 72°, both in 13-day repeating orbits. This architecture provides a 67% reduction in error over one pair of satellites, in addition to reducing the longitudinal striping to such a level that minimal post-processing is required, permitting a substantial increase in the spatial resolution of the gravity field products. It should be emphasized that given different sets of scientific objectives for the mission, or a different minimum allowable satellite altitude, different architectures might be selected.     

内核地球模型的形变场和地球参考系

讨论了内核地球模型的形变场（ 位移、速度） 和地球参考系的确立, 为内核地球动力学的研究提供了依据。     

建设国家对地观测体系,构筑"数字地球"

论述了“数字地球”的特征与重要意义,指出对地观测是“数字地球”的核心内容之一。建议中国不失时机地组织建设国家对地观测体系。该体系可在信息获取、处理与应用３个层面上构建,并提出近期中国对地观测应优先发展的领域,以持续地为“数字地球”发展作贡献     

数字地面模型LOD算法的实现

利用点的三角形化构建一个3维地面模型,设计了一个基于三角形折叠的LOD算法,该算法不需任何计算即可达到快速实现模型的渐进式还原,大大提高了3维显示速度,最后调用OpenGL函数有效地显示3维地形模型。     

数字地面模型LOD算法的实现

利用点的三角形化构建一个3维地面模型，设计了一个基于三角形折叠的LOD算法，该算法不需任何计算即可达到快速实现模型的渐进式还原，大大提高了3维显示速度，最后调用OpenGL函数有效地显示3维地形模型。     

A stream-based Parasitic Model for implementing Mobile Digital Earth

A Parasitic Model is proposed in this study for Digital Earth running on mobile phones through a mobile network. Because of mobile phones' limited capabilities in high-performance computing, rendering, storing, and networking (CRSN), these functions are accomplished by a superior host computer in this model. Rendered virtual scenes are compressed in a time-series as a data stream and are sent to the mobile phone through a mobile network, thus allowing Digital Earth to be operated on a mobile phone. This study examines a prototype and shows that a Mobile Digital Earth based on a Parasitic Model can achieve functionality beyond the mobile phone's actual hardware capabilities and can reduce network traffic. These results demonstrate quasi-real-time interactions, but with bandwidth increases in next-generation mobile networks such as 4G and 5G, there is potential for real-time interactions in the near future.     

弹性椭球地球模型的海潮效应

本文推证了比较完整的弹性椭球地球模型的海潮负荷理论和计算公式,它对弹性球型地球模型海潮效应计算的发展起了一定的作用。     

Direct gravity formula for the Geodetic Reference System 1967

A Direct Gravity Formula, polynomial in latitude, has been obtained from the series expansion of the closed gravity formula of Somigliana by a telescoping procedure. The use of the 7 coefficient formula gives a result as accurate as the closed expression. With 6 coefficients it gives an order of magnitude better accuracy than that of the widely used Chebyshev approximation and with 5 coefficients a result that is accurate to better than that of the conventional form of computing theoretical gravity. The derived approximation is not only simpler than other forms, but also at least 11 and 17 times faster on the CDC CYBER 74 computer than the Chebyshev approximation and the closed gravity formula respectively. Contribution from the Earth Physics Branch N^o 720.     

GRACE模式确定重力场的关键技术探讨

美德合作的GRACE计划可以利用卫星跟踪卫星技术 (SST)获取有关地球重力场、大气和海洋等方面有史以来最为全面的信息。它们为广泛开展相关领域的科学研究提供了前所未有的丰富资料。其中 ,GRACE提供的稳态的和时变的地球重力场数据可以反映地球内部构造、地表水体运动等地球物理信息 ,是GRACE目标的最重要的方面。本文深入探讨了GRACE卫星有效载荷对于研究地球重力场的贡献 ,并给出相应结论。     

Forward simulation of gravity for crustal structure of Xiachayu-Gonghe profile in eastern Tibetan plateau

The crustal structure of Xiachayu-Gonghe geophysical profile in eastern Tibetan plateau is simulated with Bouguer anomaly corrected for sediments and lithosphere.The forward simulation shows that the thickness of upper crust in eastern Tibetan plateau is about 20 km,and the density is 2.78 3 3 × 10 kg/m.The bottom interface of middle crust changes from 30 km to 40 km,the density of middle crust is 2.89 3 3 × 10 kg/m.The materials with low density of 2.78 3 3 × 10 kg/mexist in middle crust,and those with hig...     

Forward simulation of gravity for crustal structure of Xiachayu-Gonghe profile in eastern Tibetan plateau

The crustal structure of Xiachayu-Gonghe geophysical profile in eastern Tibetan plateau is simulated with Bouguer anomaly corrected for sediments and lithosphere. The forward simulation shows that the thickness of upper crust in eastern Tibetan plateau is about 20 km, and the density is 2.78×103kg/m3. The bottom interface of middle crust changes from 30 km to 40 km, the density of middle crust is 2.89×103kg/m3. The materials with low density of 2.78 ×103kg/m3 exist in middle crust, and those with high density of 3.33 ×103kg/m3 exist at the bottom of middle crust between Wenquan and Tanggemu. The density is 3.10 ×103kg/m3 in lower crust. The shallowest depth of Moho interface is about 56 km, and the deepest one is about 74 km, the undulation of interface is large, the deep Moho is located in Xiachayu, Chayu, Nujiang, and Wenquan. The crustal density of eastern Tibetan plateau is larger than that of central section; the low velocity layers are located in middle crust and bottom in eastern Tibetan plateau and at the bottom of the upper crust in the central plateau.     

卫星跟踪卫星测量主要技术指标仿真分析软件的设计与实现

针对如何确定卫星跟踪卫星(SST)系统的技术指标问题,本文以解析法恢复地球重力场的理论为基础,基于Visual C++6.0开发平台研制了SST系统主要技术指标仿真分析软件。重点讨论了该软件的设计思想、设计目标、软件结构与功能,以及在软件实现时的一些关键技术及对策。模拟实验结果表明,该软件可应用于SST系统主要技术指标的初步设计。     

面向城市规划的空间数据库动态更新模型研究

本文针对长期困扰城市空间数据库建设的"更新冲突"和"更新速度慢"问题进行了深入分析,在研究、借鉴前人的时空数据更新方法的基础上,根据城市规划空间数据实际生产特点,将时间维引入城市空间数据库,按照事件驱动思想,提出了基于对象特征的数据动态更新模型和动态更新机制,解决数据管理与数据生产之间数据并发性更新需要,并能实现数据库不同历史时期版本输出问题。按照此数据动态更新模型,作者在内外业系统上进行开发实现,并通过生产实验验证,分析应用效果。