Comparison of undulation difference accuracies using gravity anomalies and gravity disturbances

Errors are considered in the outer zone contribution to oceanic undulation differences as obtained from a set of potential coefficients complete to degree 180. It is assumed that the gravity data of the inner zone (a spherical cap), consisting of either gravity anomalies or gravity disturbances, has negligible error. This implies that error estimates of the total undulation difference are analyzed. If the potential coefficients are derived from a global field of 1°×1° mean anomalies accurate to ε_Δg=10 mgal, then for a cap radius of 10°, the undulation difference error (for separations between 100 km and 2000 km) ranges from 13 cm to 55 cm in the gravity anomaly case and from 6 cm to 36 cm in the gravity disturbance case. If ε_Δg is reduced to 1 mgal, these errors in both cases are less than 10 cm. In the absence of a spherical cap, both cases yield identical error estimates: about 68 cm if ε_Δg=1 mgal (for most separations) and ranging from 93 cm to 160 cm if ε_Δg=10 mgal. Introducing a perfect 30-degree reference field, the latter errors are reduced to about 110 cm for most separations.     

国际重力卫星研究进展和我国将来卫星重力测量计划

本文首先分别介绍了国际已经成功发射的专用地球重力测量卫星CHAMP、GRACE以及即将发射的GOCE、GRACE Follow-On和专用月球重力探测卫星GRAIL的研制机构、轨道参数、关键载荷、跟踪模式、测量原理、科学目标和技术特征;其次,阐述了当前相关学科对地球重力场测量精度的需求;最后,建议我国在将来实施的卫星重力测量计划中首选卫星跟踪卫星高低\低低模式,尽快开展轨道参数优化选取的定量系统研究论证和重力卫星系统的误差分析,依据匹配精度指标先期开展重力卫星各关键载荷的研制以及尽早启动卫星重力测量系统的虚拟仿真研究。     

重力归算及其对大地水准面及外部重力场的影响

本文论述并探讨了各种不同的重力归算方法对大地水准面以及地球外部重力场的影响,讨论了与确定cm级大地水准面相关的一些问题,特别阐述了高程误差对大地水准面的影响。     

Storage and retrieval of gravity data

At the Earth Physics Branch in Ottawa, storage and retrieval of gravity data has progressed from the pencil and paper system used until the late 1950’s to the current file-oriented gravity library operated on a large, high speed computer. The main impetus for the development of this computer library has been the requirements of the petroleum and mineral exploration industry, but military requirements and those of physical geodesy, geology and geophysics have had a large influence on the system at some or all stages of its development. The current system is user-oriented and tends to be complex internally to preserve a simple and convenient interface to the user. The results of approximately150,000 gravity measurements are contained on the main output file: the principal factors file. These observations are mainly those of the Earth Physics Branch, but a small percentage have been provided by commerical geophysical companies, other government agencies and universities. Current plans call for more emphasis on extending the system to serve as a national library for gravity and related data. Data reduction within the system is a partitionened process which employs a static model as a basis for the computation. Only a relatively minor change is required to develop a dynamic model for data reduction by eliminating the partitioned fashion in which field data are reduced. The capability of recognizing and computing accurately the magnitude of changes in the value of gravity and their geographic distribution will be a tremendous asset to studies of the dynamics of the earth.     

On the combination of gravity anomalies and gravity disturbances for geoid determination in Western Australia

The geoid gradient over the Darling Fault in Western Australia is extremely high, rising by as much as 38 cm over only 2 km. This poses problems for gravimetric-only geoid models of the area, whose frequency content is limited by the spatial distribution of the gravity data. The gravimetric-only version of AUSGeoid98, for instance, is only able to resolve 46% of the gradient across the fault. Hence, the ability of GPS surveys to obtain accurate orthometric heights is reduced. It is described how further gravity data were collected over the Darling Fault, augmenting the existing gravity observations at key locations so as to obtain a more representative geoid gradient. As many of the gravity observations were collected at stations with a well-known GRS80 ellipsoidal height, the opportunity arose to compute a geoid model via both the Stokes and the Hotine approaches. A scheme was devised to convert free-air anomaly data to gravity disturbances using existing geoid models, followed by a Hotine integration to geoid heights. Interestingly, these results depended very weakly upon the choice of input geoid model. The extra gravity data did indeed improve the fit of the computed geoid to local GPS/Australian Height Datum (AHD) observations by 58% over the gravimetric-only AUSGeoid98. While the conventional Stokesian approach to geoid determination proved to be slightly better than the Hotine method, the latter still improved upon the gravimetric-only AUSGeoid98 solution, supporting the viability of conducting gravity surveys with GPS control for the purposes of geoid determination. AcknowledgementsThe author would like to thank Will Featherstone, Ron Gower, Ron Hackney, Linda Morgan, Geoscience Australia, Scripps Oceanographic Institute and the three anonymous reviewers of this paper. This research was funded by the Australian Research Council.     

Simulation of regional gravity field recovery from satellite gravity gradiometer data using collocation and FFT

When planning a satellite gravity gradiometer (SGG) mission, it is important to know the quality of the quantities to be recovered at ground level as a function of e.g. satellite altitude, data type and sampling rate, and signal variance and noise. This kind of knowledge may be provided either using the formal error estimates of wanted quantities using least-squares collocation (LSC) or by comparing simulated data at ground level with results computed by methods like LSC or Fast Fourier Transform (FFT). Results of a regional gravity field recovery in a 10^o×20^o area surrounding the Alps using LSC and FFT are reported. Data used as observations in satellite altitude (202 or161 km) and for comparison at ground level were generated using theOSU86F coefficient set, complete to degree 360. These observations are referred to points across simulated orbits. The simulated quantities were computed for a 45 days mission period and 4 s sampling. A covariance function which also included terms above degree 360 was used for prediction and error estimation. This had the effect that the formal error standard deviation for gravity anomalies were considerably larger than the standard deviations of predicted minus simulated quantities. This shows the importance of using data with frequency content above degree 360 in simulation studies. Using data at202 km altitude the standard deviation of the predicted minus simulated data was equal to8.3 mgal for gravity and0.33 m for geoid heights.     

Response of GPS occultation signals to atmospheric gravity waves and retrieval of gravity wave parameters

We show that the amplitude of the Global Positioning System (GPS) signals in the radio occultation (RO) experiments is an indicator of the activity of the gravity waves (GW) in the atmosphere. The amplitude of the GPS RO signals is more sensitive to the atmospheric wave structures than is the phase. Early investigations used only the phase of the GPS occultation signals for statistical investigation of the GW activity in the height interval 10–40 km on a global scale. In this study, we use the polarization equations and Hilbert transform to find the 1-D GW radio image in the atmosphere by analyzing the amplitude of the RO signal. The radio image, also called the GW portrait, consists of the phase and amplitude of the GW as functions of height. We demonstrate the potential of this method using the amplitude data from GPS/Meteorology (GPS/MET) and satellite mission Challenge Mini-satellite Payload (CHAMP) RO events. The GW activity is nonuniformly distributed with the main contribution associated with the tropopause and the secondary maximums related to the GW breaking regions. Using our method we find the vertical profiles of the horizontal wind perturbations and its vertical gradient associated with the GW influence. The estimated values of the horizontal wind perturbations are in fairly good agreement with radiosonde data. The horizontal wind perturbations v(h) are ±1 to ±5 m s with vertical gradients dv/dh ±0.5 to ±15 m s km at height 10–40 km. The height dependence of the GW vertical wavelength was inferred through the differentiation of the GW phase. Analysis of this dependence using the dispersion relationship for the GW gives the estimation of the projection of the horizontal background wind velocity on the direction of the GW propagation. For the event considered, the magnitude of this projection changes between 1.5 and 10 m s at heights of 10–40 km. We conclude that the amplitude of the GPS occultation signals contain important information about the wave processes in the atmosphere on a global scale.     

海底控制网测量和解算中的几个关键问题

剖析了影响海底控制网定位精度的几个问题,认为海洋声速短时变化大且规律性不强,构建声速场模型是削弱声速代表性误差的有效途径。声速对测距定位影响还与波束入射角和深度相关,影响显著,不容忽视;在声速稳定水域,利用入射角近似相同的观测距离差分定位可取得较高的精度,否则精度难以保证。引入压力传感器提供的深度或深度差,利于改善控制网垂直解精度,但需顾及两点间潮高差。     

Gravity gradient modeling using gravity and DEM

A model of the gravity gradient tensor at aircraft altitude is developed from the combination of ground gravity anomaly data and a digital elevation model. The gravity data are processed according to various operational solutions to the boundary-value problem (numerical integration of Stokes’ integral, radial-basis splines, and least-squares collocation). The terrain elevation data are used to reduce free-air anomalies to the geoid and to compute a corresponding indirect effect on the gradients at altitude. We compare the various modeled gradients to airborne gradiometric data and find differences of the order of 10–20 E (SD) for all gradient tensor elements. Our analysis of these differences leads to a conclusion that their source may be primarily measurement error in these particular gradient data. We have thus demonstrated the procedures and the utility of combining ground gravity and elevation data to validate airborne gradiometer systems.     

月球形状及其重力场EI北大核心CSCD

本文首先从测绘科学与技术在月球探测中的应用角度,对月球形状及重力场的研究进展、获取方法及代表性成果进行了综述;进而针对现有的月球DEM及重力场模型中存在的主要问题进行分析,并提出了解决方案;最后结合各国的探月计划和我国正在实施的“嫦娥”四期工程,对月球形状和重力场研究面临的机遇和挑战进行了展望。     

Improvement of inertial surveys through post-mission network adjustment and self-calibration

Present day inertial surveys are limited to single traverse runs in which the number of unknown system parameters to be determined are few, depending on the number of control points available along the traverse. Further, conventional inertial surveys are generally restricted to the determination of coordinates with no possibility for a rigorous post-mission adjustment of the observations. The consequence is the continued presence of systematic trends in the residuals, even after the use of error models such as those proposed by Ball, Gregerson or Kouba. Future work aiming at higher accuracies obviously requires more comprehensive models and rigorous adjustment procedures. These can be accomplished by the development of such error models and by the use of “area surveys”, instead of the single traverses, together with rigorous adjustment procedures suitable for the network of criss-crossing lines inertially surveyed. In such a network the cross-over points serve as constraints for the geodetic parameters (latitude, longitude, height, gravity anomaly, deflection components) and allow the addition of hardware and software related error parameters. Thus an opportunity is provided to effectively self-calibrate the system—a concept successfully used, for example, in photogrammetry or in satellite tracking. The number and the strength of such parameters depend on the number of control and cross-over points. The adjustment, of course, also provides the necessary statistical information on the adjusted parameters, such as their precision and the correlation between them. The presentation will describe current work at OSU in this area. Presented at the Second International Symposium on Inertial Technology for Surveying and Geodesy, Banff, Canada, June 1–5, 1981.     

卫星重力与卫星测高的研究进展

该文介绍了GRACE和GOCE重力卫星在地球重力场模型以及局部变化等方面的研究成果,介绍了卫星测高的检核与校验、全球和局部海平面变化监测、内陆湖和水库水位变化监测等方面的研究进展,对综合利用卫星重力、卫星测高以及合成孔径雷达差分干涉测量(DInSAR)等技术方法监测冰川和冰盖变化的成果进行了介绍,重点介绍了南极冰盖变化监测的研究成果。对综合卫星重力、卫星测高、DInSAR、GNSS/水准、GNSS等多种技术在冰川冰盖、局部形变监测等方面的应用进行了展望。     

航空重力测量技术及应用研究

精细化的重力场信息我国现代国家测绘基准体系中不可或缺的基础性数据,航空重力测量是提升国家高程基准水平的主要手段和必由之路,航空重力测量理论方法得到国内外学者广泛而深入的研究.     

海底管道检测数据平面偏差与管道状态分析研究

当前海底管道研究内容主要集中在检测方法、管道三维模拟和系统建设方面,对检测数据分析与方法讨论较少.本文介绍了海底管道检测数据来源及其内容,讨论了海底管道节点平面偏差分析原理,对不同测次管道平面偏差比较的采样点选取展开研究,并分析了海底管道状态成果数据编制与历次管道状态比较内容,对管道状态区间跨度计算存在的情况进行详细讨论,同时给出相应的解决方法.本研究成果已应用于杭州湾海底管道检测数据分析,为其他海底管道检测数据分析提供借鉴与参考.     

Evaluation of the third- and fourth-generation GOCE Earth gravity field models with Australian terrestrial gravity data in spherical harmonics

In March 2013, the fourth generation of European Space Agency’s (ESA) global gravity field models, DIR4 (Bruinsma et al. in Proceedings of the ESA living planet symposium, 28 June–2 July, Bergen, ESA, Publication SP-686, 2010b) and TIM4 (Migliaccio et al. in Proceedings of the ESA living planet symposium, 28 June–2 July, Bergen, ESA, Publication SP-686, 2010), generated from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) gravity observation satellite was released. We evaluate the models using an independent ground truth data set of gravity anomalies over Australia. Combined with Gravity Recovery and Climate Experiment (GRACE) satellite gravity, a new gravity model is obtained that is used to perform comparisons with GOCE models in spherical harmonics. Over Australia, the new gravity model proves to have significantly higher accuracy in the degrees below 120 as compared to EGM2008 and seems to be at least comparable to the accuracy of this model between degree 150 and degree 260. Comparisons in terms of residual quasi-geoid heights, gravity disturbances, and radial gravity gradients evaluated on the ellipsoid and at approximate GOCE mean satellite altitude ( $h=250$  km) show both fourth generation models to improve significantly w.r.t. their predecessors. Relatively, we find a root-mean-square improvement of 39 % for the DIR4 and 23 % for TIM4 over the respective third release models at a spatial scale of 100 km (degree 200). In terms of absolute errors, TIM4 is found to perform slightly better in the bands from degree 120 up to degree 160 and DIR4 is found to perform slightly better than TIM4 from degree 170 up to degree 250. Our analyses cannot confirm the DIR4 formal error of 1 cm geoid height (0.35 mGal in terms of gravity) at degree 200. The formal errors of TIM4, with 3.2 cm geoid height (0.9 mGal in terms of gravity) at degree 200, seem to be realistic. Due to combination with GRACE and SLR data, the DIR models, at satellite altitude, clearly show lower RMS values compared to TIM models in the long wavelength part of the spectrum (below degree and order 120). Our study shows different spectral sensitivity of different functionals at ground level and at GOCE satellite altitude and establishes the link among these findings and the Meissl scheme (Rummel and van Gelderen in Manusrcipta Geodaetica 20:379–385, 1995).     

Local relationships between the disturbing density, the disturbing potential and the disturbing gravity of the Earth's gravity field

A function having some properties of a wavelet and being harmonic around a given point in R ³ is defined, and three models showing the local relationships between the disturbing density, the disturbing potential and the disturbing gravity are established by using the function as the kernel function of the integrals in the models. The local relationship has two meanings. One is that we can evaluate with a high accuracy the integrals in the models by using mainly high-accuracy and high-resolution data in a local area. The other is that we can obtain a stable solution with high resolution when we invert the integrals in the models because of the rapid decrease of the kernel function of the integrals. As a result, with these models we evaluate one quantity with high resolution, in a band limited by the maximum degree of a set of geopotential coefficients or by the resolution (spacing) of the local data, from another quantity (or quantities) in a local area, and the resulting solution is stable. Received: 6 April 1998 / Accepted: 16 June 1999