卫星重力梯度测量在海洋科学中的应用分析

简述了卫星重力梯度测量技术的基本原理和GOCE数据特点;基于三个不同的重力场模型,采用不同阶次,联合卫星测高平均海面高模型分别推算出全球海面地形,并对结果作了比较分析;探讨了卫星重力梯度测量技术在海洋科学各相关领域的具体应用前景,指出卫星重力梯度测量技术的发展将为海洋科学发展带来巨大的变化。     

卫星重力测量系统的发展和测量模式

从地球重力场测量要素出发,按照局部重力场模型、区域重力场模型、全球重力场模型求解的发展思路,分析了对地球重力场测量技术手段的要求。根据高-低卫星跟踪卫星的距离和距离变率开展定轨研究的概念,梳理了卫星跟踪卫星重力测量系统的发展。针对卫星跟踪卫星重力测量技术的内涵,分析了高-低卫星跟踪卫星测量模式（SST-hl）和高-低低卫星跟踪卫星测量模式（SST—hll）的地球重力场测量本质。     

利用高精度地球重力场模型计算扰动重力垂直梯度

探讨了利用地球重力场模型计算扰动重力垂直梯度的理论方法,介绍了高精度地球重力场模型和最新的EGM2008模型,并利用EGM2008模型的360阶和720阶完全规格化地球位系数,分别计算了西太平洋区域和全球范围的扰动重力垂直梯度。从绘制的计算结果分布图可以看出,扰动重力垂直梯度能够清晰反映并显示地球地质构造的变化特征与陆地边界轮廓。统计分析表明,随着位系数截断阶次从360阶增至720阶,计算结果的变化较为明显,均值接近于零,其数值分布近似服从正态分布。     

利用卫星测高、GRACE和GOCE资料估计全球海洋表面地转流

重力恢复和气候试验GRACE(gravity recovery and climate experiment)卫星极大地提高了地球重力场的精度和分辨率,特别是中长波分量,联合卫星测高数据可获得全球海洋表面大尺度洋流循环。另外,新一代地球重力和海洋环流探测卫星GOCE(gravity field and steady-state ocean circulation explorer)于2009年3月成功发射,采用卫星重力梯度测量原理,对重力场的高频部分非常敏感,使其高分辨率监测全球海洋循环成为可能。本文利用1~7年GRACE观测数据确定的重力场模型和18个月GOCE观测数据确定的地球重力场模型GO_CONS_GCF_2_TIM_R3,联合卫星测高确定的平均海面高模型MSS_CNES_CLS_11,分别估计全球海洋表面地转流,并且与实测浮标数据结果进行比较。分析表明GOCE重力卫星确定的重力场模型具有更高的空间分辨率,能够确定高精度和高空间分辨率的全球海洋地转流,如墨西哥湾暖流的细节和特征,并且与实测浮标结果基本一致。而基于1~4年GRACE观测资料的模型不能很好估计全球地转流特征,基于7年GRACE观测资料的重力场模型ITG-Grace2010s确定的全球地转流的精度仍低于18个月GOCE观测数据确定的地球重力场模型GO_CONS_GCF_2_TIM_R3的结果,估计的全球地转流仍含有较大的噪声,不能很好地反应中小尺度地转流细节特征。并计算ITG_Grace2010s和GOCE_TIM3的稳态海面地形和全球平均地转流的内符合精度,结果显示,在全球范围内,GOCE_TIM3的稳态海面地形和全球平均地转流的精度都比ITG_Grace2010s结果的精度有着很大的改善,其中ITG_Grace2010s的稳态海面地形的精度为21.6cm,而GOCE_TIM3的结果则为7.45cm,ITG_Grace2010s的全球平均地转流的精度为40.7cm/s,而GOCE_TIM3的结果则为19.6cm/s。     

利用EGM2008模型快速构建扰动重力梯度基准图

重力梯度张量是重力位二阶导,相比重力异常能够更好反映局部区域的细节特征。因此重力梯度导航理论上能为惯性导航提供更好的辅助。重力梯度导航的关键技术之一是背景基准图的构建,推导了扰动重力梯度张量与扰动位在局部指北坐标系中的关系式,并基于EGM2008地球重力场模型构建了一块范围的海域扰动重力梯度张量基准图。为了快速构建基准图,选取了合适的勒让德函数,并将每一个梯度张量的计算式改变求和顺序来提高同一纬度圈上的计算点的计算速度。最后利用梯度张量对角线上三元素满足拉普拉斯约束条件的原理验证了所得基准图的正确性。     

基于Grace月重力场模型的稳态地球重力场模型分析

基于106个月的Grace（gravity recovery and climate experiment）月重力场模型（120阶次）,消除了月重力场的月、季度及年度变化,得到了稳态的地球重力场模型（Grace_sta）。在2～120阶次之间,Grace_sta与已有高阶重力场EGM2008及EGM96三个模型的阶方差是一致的。在2～100阶次之间,Grace_sta模型误差阶方差要小于EGM2008与EGM96误差阶方差。在全球范围内,Grace_sta重力场的大地水准面与EGM2008相应阶次的大地水准面标准差约为3cm,与EGM96模型大地水准面差异则高达52cm。结果表明,Grace_sta足可以取代EGM2008重力场模型2～100阶次的低阶部分,新得到的稳态重力场模型可为海面地形分析提供了可靠的参考场。     

利用卫星测高资料确定全球海洋重力场

详细描述了卫星测高数据的平滑处理、高斯低通滤波、交叉点剩余垂线偏差计算、网格化方法以及根据逆的威宁·曼尼兹公式利用 1DFFT技术反演海域重力异常的解算过程 ,介绍一种确定正常轨道地面轨迹交叉点位置的简便方法 ,导出了海面地形对垂线偏差影响的改正公式以及剩余网格垂线偏差模型值的计算公式。所确定的全球 82°S～ 82°N ,0°～ 36 0°海域 30′× 30′网格平均重力异常与船测平均重力异常比较表明 ,精度达到± 4 .1～± 4 .7毫伽。     

利用DEM数据计算地形质量重力梯度的新方法

重力梯度由低频、中频和高频信息构成,其高频信息主要受地形质量的影响,为了更好地利用地形数据获取重力梯度高频信息,提出一种全新的方法——高斯-勒让德积分法,根据模型算例和实测DEM数据验证了该方法的有效性。结果表明,高斯-勒让德积分法作为一种全新的解算方法,与传统的棱柱法和直接积分法相比,在一定的精度条件下解算效率更高,在重力梯度测量相对落后和重力资料欠缺的情况下,利用该方法由DEM数据来解算重力梯度的高频部分是可行的,相较于传统解算方法而言,其具有一定的优势。     

GRACE重力卫星运行管理的参考借鉴

低低跟踪重力卫星在全球重力获取、反演应用等方面有着重要的战略作用,我国已布局相关卫星的研制建设。为确保未来我国自主低低跟踪重力卫星系统的高效稳定运行,重点对GRACE及其后续星组GRACE-FO卫星的组织模式和管理机制进行了系统梳理与总结分析。基于我国重力卫星技术发展研究现状,对未来卫星运行管理模式进行了探讨分析,给出了实用的工程运行管理建议,可为后续卫星运行管理提供参考借鉴。     

卫星高度计海上定标场及定标方法研究进展

介绍了卫星高度计定标中海面高度和后向散射系数的定标方法。在后向散射系数的定标中介绍了利用有源定标器和微波辐射计定标两种方法。结合卫星高度计的特点,提出了海上定标场选取所需注意的问题,并介绍了目前比较成功的几个定标场及其定标结果,旨在为我国今后发射的卫星高度计绝对定标和定标场的选取提供依据。     

重力梯度张量计算重力场元

根据体谐函数一阶、二阶水平导数（广义球函数）也是球面正交函数系的性质,详细推导了水平重力梯度边值问题的级数解.根据扰动位与重力场元的微分关系,导出了由水平重力梯度计算重力异常、垂线偏差的公式.完善了全张量重力梯度的有关应用.     

Comparison of Satellite-Only Gravity Field Models Constructed with All and Parts of the GOCE Gravity Gradient Dataset

The impact of GOCE Satellite Gravity Gradiometer data on gravity field models was tested. All models were constructed with the same Laser Geodynamics Satellite (LAGEOS) and Gravity Recovery and Climate Experiment (GRACE) data, which were combined with one or two of the diagonal gravity gradient components for the entire GOCE mission (November 2009 to October 2013). The Stokes coefficients were estimated by solving large normal equation (NE) systems (i.e., the direct numerical approach). The models were evaluated through comparisons with the European Space Agency's (ESA) gravity field model DIR-R5, by GPS/Leveling, GOCE orbit determination, and geostrophic current evaluations. Among the single gradient models, only the model constructed with the vertical ZZ gradients gave good results that were in agreement with the formal errors. The model based only on XX gradients is the least accurate. The orbit results for all models are very close and confirm this finding. All models constructed with two diagonal gradient components are more accurate than the ZZ-only model due to doubling the amount of data and having two complementary observation directions. This translates also to a slower increase of model errors with spatial resolution. The different evaluation methods cannot unambiguously identify the most accurate two-component model. They do not always agree, emphasizing the importance of evaluating models using many different methods. The XZ gravity gradient gives a small positive contribution to model accuracy.     

利用卫星测高垂线偏差计算其他重力场元的特性分析

利用卫星测高技术确定海洋重力场,垂线偏差数据作为导出观测量在实际工作中被普遍采用。利用物理大地测量边值问题的定义以及扰动位在球面边界条件下的解,给出了由垂线偏差计算大地水准面高、重力异常和扰动重力的公式。分析了不同积分计算公式在重力场阶谱表达形式下对垂线偏差误差的抑制作用,也分析了不同积分核函数的变化特性,得出基本结论:在利用卫星测高数据求解海洋重力场时,当以格网化海面垂线偏差数据计算重力场参数时,求解的大地水准面高的有效性和稳定性优于重力异常和扰动重力。     

惯性技术视角下动态重力测量技术评述(四):无陀螺惯性导航与重力梯度测量的融合

加速度差分式重力梯度仪与无陀螺惯性导航系统都采用一组在三维空间中布置的加速度计,二者在硬件配置和工作原理层面都具有紧密联系。从比力测量的空间差分公式出发,详细推导了重力梯度测量和无陀螺惯性导航系统共同的工作原理,指出当前对后者的研究中存在的忽略重力梯度的问题,并论述了二者的融合应用。     

Program News Bright Prospects for a Significant Improvement of the Earth's Gravity Field Knowledge

Concern over the impact of change in sea level is of topical interest internationally, but for the small island states of the Caribbean, a significant increase would prove to be catastrophic. The potential problem is being addressed as part of the much larger issue of climate change, and just this year a regional Climate Change Centre was established in Belize. Means of adapting to accommodate change will be considered under the Mainstream Adaptation to Climate Change (MACC) project, but initially the threat needs to be quantified. While meteorological offices have been accumulating weather data in some parts of the region for many years, sea level data is more scarce. This work puts least squares methods to test by applying them to spectral analysis of intermittent data sets acquired over periods of 6 and 9 years at two locations in Trinidad. The resulting sea level models that include 13 periodic components, datum bias, trend and atmospheric pressure are validated using fundamental historical information and observations that form the subject of discussion among local professional surveyors. Results show that while sea level at a location in North Trinidad is rising at the rate of about 1 mm a year, the change at a Southern site is about four times this amount. Horizontal movement has been measured across a tectonic fault that parts the island, and it is now apparent that there may be some vertical motion on this or some other fault lines in the region.     

Comparison of Satellite Altimetric Gravity and Global Geopotential Models with Shipborne Gravity in the Red Sea

The determination of high-resolution geoid for marine regions requires the integration of gravity data provided by different sources, e.g. global geopotential models, satellite altimetry, and shipborne gravimetric observations. Shipborne gravity data, acquired over a long time, comprises the short-wavelengths gravitation signal. This paper aims to produce a consistent gravity field over the Red Sea region to be used for geoid modelling. Both, the leave-one-out cross-validation and Kriging prediction techniques were chosen to ensure that the observed shipborne gravity data are consistent as well as free of gross-errors. A confidence level equivalent to 95.4% was decided to filter the observed shipborne data, while the cross-validation algorithm was repeatedly applied until the standard deviation of the residuals between the observed and estimated values are less than 1.5 mGal, which led to the elimination of about 17.7% of the shipborne gravity dataset. A comparison between the shipborne gravity data with DTU13 and SSv23.1 satellite altimetry-derived gravity models is done and reported. The corresponding results revealed that altimetry models almost have identical data content when compared one another, where the DTU13 gave better results with a mean and standard deviation of ?2.40 and 8.71 mGal, respectively. A statistical comparison has been made between different global geopotential models (GGMs) and shipborne gravity data. The Spectral Enhancement Method was applied to overcome the existing spectral gap between the GGMs and shipborne gravity data. EGM2008 manifested the best results with differences characterised with a mean of 1.35 mGal and a standard deviation of 11.11 mGal. Finally, the least-squares collocation (LSC) was implemented to combine the shipborne gravity data with DTU13 in order to create a unique and consistent gravity field over the Red Sea with no data voids. The combined data were independently tested using a total number of 95 randomly chosen shipborne gravity stations. The comparison between the extracted shipborne gravity data and DTU13 altimetry anomalies before and after applying the LSC revealed that a significant improvement is procurable from the combined dataset, in which the mean and standard deviation of the differences dropped from ?3.60 and 9.31 mGal to ?0.39 and 2.04 mGal, respectively.     

输入—输出系统理论在重力场扰动场元推估中的应用分析

研究了输入—输出系统理论用于扰动场元推估的一般形式,以重力异常推估大地水准面为例,推导了双输入—单输出系统用于重力场推估的具体形式。通过实际算例表明：输入—输出系统在推估效果上等效于最小二乘配置,利用局部重力异常推估大地水准面的精度在0.4m左右。     

From Discrete Gravity Survey Data to a High-resolution Gravity Field Representation in the Nordic-Baltic Region

The deduction of a regularly spaced gravity anomaly grid from scattered survey data is studied, addressing mainly two aspects: reduction of gravity to anomalies and subsequent interpolation by various methods. The problem is illustrated in a heterogeneous study area and contrasting test areas including mountains, low terrains, and a marine area. Provided with realistic error estimates, Least Squares Collocation interpolation of Residual Terrain Model anomalies yields the highest quality gravity grid. In most cases, the Bouguer reduction and other interpolation methods tested are equally viable. However, spline-based interpolation should be avoided in marine areas with trackwise survey data.