共查询到20条相似文献，搜索用时 31 毫秒
1.
Robert Tenzer Pavel Novák Ilya Prutkin Artu Ellmann Peter Vajda 《Studia Geophysica et Geodaetica》2009,53(2):157-167
To reduce the numerical complexity of inverse solutions to large systems of discretised integral equations in gravimetric
geoid/quasigeoid modelling, the surface domain of Green’s integrals is subdivided into the near-zone and far-zone integration
sub-domains. The inversion is performed for the near zone using regional detailed gravity data. The farzone contributions
to the gravity field quantities are estimated from an available global geopotential model using techniques for a spherical
harmonic analysis of the gravity field. For computing the far-zone contributions by means of Green’s integrals, truncation
coefficients are applied. Different forms of truncation coefficients have been derived depending on a type of integrals in
solving various geodetic boundary-value problems. In this study, we utilise Molodensky’s truncation coefficients to Green’s
integrals for computing the far-zone contributions to the disturbing potential, the gravity disturbance, and the gravity anomaly.
We also demonstrate that Molodensky’s truncation coefficients can be uniformly applied to all types of Green’s integrals used
in solving the boundaryvalue problems. The numerical example of the far-zone contributions to the gravity field quantities
is given over the area of study which comprises the Canadian Rocky Mountains. The coefficients of a global geopotential model
and a detailed digital terrain model are used as input data. 相似文献
2.
Two integral transformations between the stress function, differentiation of which gives the meridian and prime vertical components of the sub-crustal stress due to mantle convection, and the satellite-to-satellite tracking (SST) data are presented in this article. In the first one, the SST data are the disturbing potential differences between twin-satellites and in the second one the line-of-sight (LOS) gravity disturbances. It is shown that the corresponding integral kernels are well-behaving and therefore suitable for inversion and recovery of the stress function from the SST data. Recovery of the stress function and the stress components is also tested in numerical experiments using simulated SST data. Numerical studies over the Himalayas show that inverting the disturbing potential differences leads to a smoother stress function than from inverting LOS gravity disturbances. Application of the presented integral formulae allows for recovery of the stress from the satellite mission GRACE and its planned successor. 相似文献
3.
Far-zone gravity field contributions corrected for the effect of topography by means of molodensky’s truncation coefficients 总被引：1，自引：0，他引：1
Robert Tenzer Pavel Novák Peter Vajda Artu Ellmann Ahmed Abdalla 《Studia Geophysica et Geodaetica》2011,55(1):55-71
A spectral representation of the topographic corrections to gravity field quantities is formulated in terms of spherical height
functions. When computing the far-zone contributions to the topographic corrections, various types of the truncation coefficients
are applied to a spectral representation of Newton’s integral. In this study we utilise Molodensky’s truncation coefficients
in deriving the expressions for the far-zone contributions to topographic corrections. The expressions for computing the far-zone
gravity field contributions corrected for the effect of topography are then obtained by combining the expressions for the
far-zone contributions to the gravity field quantities and to the respective topographic corrections, both expressed in terms
of Molodensky’s truncation coefficients. The numerical examples of the far-zone contributions to the topographic corrections
and to the topography-corrected gravity field quantities are given over the study area situated in the Canadian Rocky Mountains
with adjacent planes. Coefficients of the global elevation and geopotential models are used as the input data. 相似文献
4.
In this paper, we attempt to use satellite gravity data and a new inversion method to study the lateral density anomaly distribution
in the mantle.
First, density difference Δρ(τ,θ,φ) is expanded in terms of a three—dimensional orthogonal function system, the coefficients of the expansion are to be determined.
Then, a set of observation equations is established from the relationship between density anomaly and disturbing geopotential.
In the equations the unknown vector contains the coefficients of density anomaly expansion, the observational vector is obtained
by computing geopotential perturbations using the potential coefficients of GEM10B, and a filtering process is done for the
observational values by properly selecting the harmonic degrees of geopotentical. Finally, the lateral density variations
in the lower mantle (670 km toCM boundary) are investigated. In this case, the degrees of disturbing geopotential are selected as 2–11, the truncated degrees
of density anomaly expansion are taken asL=6 andK=4, and the damping least squares method is used to solve the observation equations.
The resulting model shows the high level of density perturbations at 670 km discontinuity and core — mantle boundary, a high
— density zone circumscribing the Pacific and a lower—density region under the center of Pacific. These features are in agreement
with the three—dimensional seismic velocity variation features by Dziewonski (1984). In the Antarctic region and some parts
of Atlantic and Indian Ocean, however, the resulting density anomalies are negatively correlated with the seismic velocity
anomalies, the cause resulting in these phenomena is preliminarily analysed in this paper.
The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 53–65, 1991.
The principle and method represented in this paper can also be suitable to study the lateral density anomaly distribution
in the earth’s crust and the upper mantle. 相似文献
5.
从两个方面模拟研究了低低卫-卫跟踪观测技术恢复地球重力场的空间分辨率. 利用重力位系数作为扰动量，积分30天的轨道，研究重力位系数变化引起低低卫-卫跟踪星间距离和速率变化，结果表明，对于地球重力场模型EGM96的前120阶，998%和97%的位系数扰动引起星间距离和速率变化的均方差大于1×１０-５m和１×１０-７m/s，并且星间距离观测值对地球重力场的反应更为敏感. 不考虑非保守力误差的影响，用随机误差为１×１０－５m和１×１０－６m/s的星间距离和速率变化作模拟观测量，恢复了78阶地球重力场位系数，结果表明，采用随机误差为１×１０－５m的星间距离恢复地球重力场的精度明显高于１×１０－６m/s的星间速率结果，但是如果考虑非保守力误差影响，则星间测速的优越性大大增强. 相似文献
6.
Satellite gradiometry is an observation technique providing data that allow for evaluation of Stokes’ (geopotential) coefficients.
This technique is capable of determining higher degrees/orders of the geopotential coefficients than can be achieved by traditional
dynamic satellite geodesy. The satellite gradiometry data include topographic and atmospheric effects. By removing those effects,
the satellite data becomes smoother and harmonic outside sea level and therefore more suitable for downward continuation to
the Earth’s surface. For example, in this way one may determine a set of spherical harmonics of the gravity field that is
harmonic in the exterior to sea level.
This article deals with the above effects on the satellite gravity gradients in the local north-oriented frame. The conventional
expressions of the gradients in this frame have a rather complicated form, depending on the first-and second-order derivatives
of the associated Legendre functions, which contain singular factors when approaching the poles. On the contrary, we express
the harmonic series of atmospheric and topographic effects as non-singular expressions. The theory is applied to the regions
of Fennoscandia and Iran, where maps of such effects and their statistics are presented and discussed. 相似文献
7.
8.
本文试图采用卫星重力资料和一种新的反演方法来研究地幔的横向密度异常分布.先将密度异常△（r,,（?））在一个三维正交函数系下进行展开,其展开系数待定.然后,根据密度异常与重力扰动位之间的关系建立观测方程组,其中未知向量由密度异常展开系数组成,重力扰动观测向量由 GEM10B 重力模型中的位系数计算而得,并通过适当选取重力位系数的阶数,对观测向量进行滤波.最后,就下地幔（670km——CM 界面）作了实际计算.计算中,重力扰动位阶数取为2——11阶,密度异常展开式的截断阶数取为 K=4和 L=6,求解观测方程组时采用阻尼最小二乘法.结果表明:密度扰动值在670km 不连续面及核幔界面处达到极大值,且在环太平洋地区存在一高密度带,太平洋中部对应于一低密度区,这些特征与 Dziewonski 得到的下地幔三维波速异常分布特征相一致.但是,在南极地区、大西洋及印度洋部分地区,所得的密度异常分布与三维波速异常分布呈负相关,文章就其原因作了初步分析. 相似文献
9.
The continuous efforts on establishment and modernization of the geodetic control in Turkey include a number of regional geoid
models that have been determined since 1976. The recently released gravimetric Geoid of Turkey, TG03, is used in geodetic
applications where GPS-heights need to be converted to the local vertical datum. To reach a regional geoid model with improved
accuracy, the selection of the appropriate global geopotential model is of primary importance. This study assesses the performance
of a number of recent satellite-only and combined global geopotential models (GGMs) derived from CHAMP and GRACE missions’
data in comparison to the older EGM96 model, which is the underlying reference model for TG03. In this respect, gravity anomalies
and geoid heights from the global geopotential models were compared with terrestrial gravity data and low-pass filtered GPS/levelling
data, respectively. Also, five new gravimetric geoid models, computed by the Fast Fourier Transform technique using terrestrial
gravity data and the geopotential models, were validated at the GPS/levelling benchmarks. The findings were also compared
with the validation results of the TG03 model.
The tests showed that as it was expected any of the high-degree combined models (EIGEN-CG03C, EIGEN-GL04C, EGM96) can be employed
for determining the gravity anomalies over Turkey. In the west of Turkey, EGM96 and EIGEN-CHAMP03S fit the GPS/levelling surface
better. However, all the tested GGMs revealed equal performance when they were employed in gravimetric geoid modelling after
de-trending the gravimetric geoid model with corrector surface fitting. The new geoid models have improved accuracy (after
fit) compared to TG03. 相似文献
10.
The paper presents a high-resolution global gravity field modelling by the boundary element method (BEM). A direct BEM formulation
for the Laplace equation is applied to get a numerical solution of the linearized fixed gravimetric boundary-value problem.
The numerical scheme uses the collocation method with linear basis functions. It involves a discretization of the complicated
Earth’s surface, which is considered as a fixed boundary. Here 3D positions of collocation points are simulated from the DNSC08
mean sea surface at oceans and from the SRTM30PLUS_V5.0 global topography model added to EGM96 on lands. High-performance
computations together with an elimination of the far zones’ interactions allow a very refined integration over the all Earth’s
surface with a resolution up to 0.1 deg. Inaccuracy of the approximate coarse solutions used for the elimination of the far
zones’ interactions leads to a long-wavelength error surface included in the obtained numerical solution. This paper introduces
an iterative procedure how to reduce such long-wavelength error surface. Surface gravity disturbances as oblique derivative
boundary conditions are generated from the EGM2008 geopotential model. Numerical experiments demonstrate how the iterative
procedure tends to the final numerical solutions that are converging to EGM2008. Finally the input surface gravity disturbances
at oceans are replaced by real data obtained from the DNSC08 altimetryderived gravity data. The ITG-GRACE03S satellite geopotential
model up to degree 180 is used to eliminate far zones’ interactions. The final high-resolution global gravity field model
with the resolution 0.1 deg is compared with EGM2008. 相似文献
11.
Xiwen Wang 《地震学报(英文版)》1992,5(1):133-143
In this paper, the application of Backus—Gilbert’s inversion method to the potential field anomalies for evaluating gravity
and magnetic inversion solutions is discussed. Errors in data and singularity of kernels in the equations result in difficulties
in solving equations. The application of regularization method similar to spectral expansion method makes calculation fast
and easily. To make solution stable, constraints are used, which make the spread of solutions become narrow, standard deviation
become small and iterative computations of inversion become fast. Finally, the author analyses specifically two profiles of
Yunchen basin and calculated the Moho interface and the Curie isotherm of these two profiles.
The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 212–221, 1991. 相似文献
12.
GRACE重力卫星任务即将结束,后续GRACE Follow-On卫星计划于2017年发射,在此期间,迫切需要一个新的卫星计划继续对全球时变重力场进行连续监测,以保证时变重力场信息时间序列的连贯性.SWARM计划包括三颗轨道高为300~500 km的近极轨卫星星座,类似于三颗CHAMP卫星,具有接替时变重力场探测的潜力.本文首先分析SWARM(模拟)、CHAMP、GRACE反演至60阶时变重力场球谐系数的误差特性及不同高斯平滑半径对高频误差的抑制效果,然后分别利用SWARM、CHAMP、GRACE的时变重力场模型恢复全球质量变化,结果表明,SWARM模拟观测数据的高频误差低于CHAMP观测数据,探测时变重力场的整体精度优于CHAMP,略低于GRACE探测精度;其次,对比2003年1月—2009年12月期间CHAMP(hl-SST)和GRACE(ll-SST)时变重力场模型反演格陵兰岛冰盖质量变化趋势,结果显示,CHAMP数据得到格陵兰岛冰盖质量变化趋势为-50.2±2.0 Gt/a,GRACE所得结果为-41.2±1.6 Gt/a,两者相差21.8%;最后,对比2000年1月—2004年12月间SWARM模拟数据和"真实"模型数据反演的格陵兰岛冰盖质量变化趋势,结果表明,两者相差19.2%.本文研究表明,利用SWARM hl-SST数据探测时变重力场可以达到20%相对精度水平,有潜力用于填补GRACE和GRACE Follow-On期间探测地球时变重力场的空白. 相似文献
13.
The satellite missions CHAllenging Minisatellite Payload (CHAMP) and Gravity Recovery And Climate Experiment (GRACE) provide
accurate data that are routinely inverted into spherical harmonic coefficients of the geopotential forming a global geopotential
model (GGM). Mean square errors of these coefficients, in some cases even entire covariance matrices, are included in the
GGM. Due to estimation procedures with a large redundancy and insufficiently propagated observation errors, they often do
not represent the actual accuracy of the harmonic coefficients, thus also gravity field parameters synthesized from the respective
GGM. Since in most cases standard methods validating the GGMs reached their limits, new procedures and independent data are
being currently sought. This article discusses an alternative validation procedure based on comparison of the GGMs with independent
data represented by a set of GPS/leveling stations. Due to a different spectral content of the height anomalies synthesized
from the GGMs and of those derived by combination of GPS-based ellipsoidal and leveled normal heights, the GGM-based low frequency
height anomaly is enhanced for a high frequency component computed from local ground gravity and elevation data. The methodology
is applied on a set of selected points of the European Vertical Reference Network and Czech trigonometric stations. In accordance
with similar tests based on entirely independent data of cross-over altimetry, obtained results seem to indicate low-frequency
deficiencies in the current GGMs, namely in those estimated from data of single-satellite missions. 相似文献
14.
Pavel Novák 《Surveys in Geophysics》2010,31(1):1-21
During the General Assembly of the European Geosciences Union in April 2008, the new Earth Gravitational Model 2008 (EGM08)
was released with fully-normalized coefficients in the spherical harmonic expansion of the Earth’s gravitational potential
complete to degree and order 2159 (for selected degrees up to 2190). EGM08 was derived through combination of a satellite-based
geopotential model and 5 arcmin mean ground gravity data. Spherical harmonic coefficients of the global height function, that
describes the surface of the solid Earth with the same angular resolution as EGM08, became available at the same time. This
global topographical model can be used for estimation of selected constituents of EGM08, namely the gravitational potentials
of the Earth’s atmosphere, ocean water (fluid masses below the geoid) and topographical masses (solid masses above the geoid),
which can be evaluated numerically through spherical harmonic expansions. The spectral properties of the respective potential
coefficients are studied in terms of power spectra and their relation to the EGM08 potential coefficients is analyzed by using
correlation coefficients. The power spectra of the topographical and sea water potentials exceed the power of the EGM08 potential
over substantial parts of the considered spectrum indicating large effects of global isostasy. The correlation analysis reveals
significant correlations of all three potentials with the EGM08 potential. The potential constituents (namely their functionals
such as directional derivatives) can be used for a step known in geodesy and geophysics as the gravity field reduction or
stripping. Removing from EGM08 known constituents will help to analyze the internal structure of the Earth (geophysics) as
well as to derive the Earth’s gravitational field harmonic outside the geoid (geodesy). 相似文献
15.
基于卫星轨道运动的能量积分方程,可导出利用卫星跟踪卫星数据求解地球重力场的实用公式.本文在Jekeli给出的公式基础上导出了基于能量守恒方程利用两颗低-低卫星跟踪的扰动位差求解重力位系数的严密关系式.基于两颗GRACE卫星的观测数据,采用本文导出的严密能量积分方法求解得到120阶的GRACE地球重力场模型,命名为WHU-GM-05;将WHU-GM-05模型与国际上同类重力场模型EIGEN-GRACE系列和GGM02S分别在阶方差和大地水准面高等方面作了比较,并与美国和中国的部分地区GPS水准观测值进行了精度分析.结果表明基于本文推导的严密双星能量守恒方程得到的WHU-GM-05重力场模型精度与国际上同类重力场模型的精度相当. 相似文献
16.
本文利用GRACE(Gravity Recovery And Climate Experiment)level 1b数据和径向基函数RBF(radial basis function)方法解算了全球时变地球重力场.RBF基函数相比传统球谐(spherical harmonic)基函数,其高度的空域局部特性使得正则化过程易于添加先验协方差信息,从而可能揭示更加准确的重力场信号.本文研究表明,RBF基函数算法在精化现有的GRACE全球时变重力场模型,如提升部分区域信号幅度等方面具有一定优势.本文通过将RBF的尺度因子作为待解参数,基于GRACE卫星的Level 1b数据和变分方程法,成功获取了2009-2010年90阶无约束全球时变重力场RBF模型Hust-IGG03,以及正则化全球时变重力场RBF模型Hust-IGG04.通过与GRACE官方数据处理中心GFZ发布的最新90阶球谐基时变模型RL05a进行对比,结果表明:(1)无约束RBF模型Hust-IGG03和GFZ RL05a在空域和频域表现基本一致;(2)正则化RBF模型Hust-IGG04无需进行后处理滤波已经显示较高信噪比,噪音水平接近于球谐基模型GFZ RL05a经400 km高斯滤波后的效果;(3)HustIGG04相比400 km高斯滤波GFZ RL05a在周年振幅图和趋势图上显示出更多的细节信息,并且呈现出更强的信号幅度,如在格陵兰冰川融化趋势估计上Hust-IGG04比GFZ RL05a提高了24.2%.以上结果均显示RBF方法有助于进一步挖掘GRACE观测值所包含的时变重力场信息. 相似文献
17.
1 Introduction Large-scale mass redistribution, or temporal varia- tion of mass within the Earth system, the driving force of interactions between solid Earth and geophysical fluids envelope (i.e., atmosphere, ocean, and hydro- sphere), is an important geophysical process critical to human life. Most of the interactions between solid Earth and the atmosphere/oceans happen at seasonal and inter-annual time scales. One important contribu- tor of mass redistribution at seasonal and inter-annual … 相似文献
18.
Roland Pail Thomas Fecher Michael Murböck Moritz Rexer Monika Stetter Thomas Gruber Claudia Stummer 《Studia Geophysica et Geodaetica》2013,57(2):155-173
The reprocessing of Gravity field and steady-state Ocean Circulation Explorer (GOCE) Level 1b gradiometer and star tracker data applying upgraded processing methods leads to improved gravity gradient and attitude products. The impact of these enhanced products on GOCE-only and combined GOCE+GRACE (Gravity Recovery and Climate Experiment) gravity field models is analyzed in detail, based on a two-months data period of Nov. and Dec. 2009, and applying a rigorous gravity field solution of full normal equations. Gravity field models that are based only on GOCE gradiometer data benefit most, especially in the low to medium degree range of the harmonic spectrum, but also for specific groups of harmonic coefficients around order 16 and its integer multiples, related to the satellite’s revolution frequency. However, due to the fact that also (near-)sectorial coefficients are significantly improved up to high degrees (which is caused mainly by an enhanced second derivative in Y direction of the gravitational potential — VYY), also combined gravity field models, including either GOCE orbit information or GRACE data, show improvements of more than 10% compared to the use of original gravity gradient data. Finally, the resulting gradiometry-only, GOCE-only and GOCE+GRACE global gravity field models have been externally validated by independent GPS/levelling observations in selected regions. In conclusion, it can be expected that several applications will benefit from the better quality of data and resulting GOCE and combined gravity field models. 相似文献
19.
高精度高程基准重力位的确定往往依赖于高精度全球重力场模型,其对全球和区域高程基准的高精度统一非常关键,GRACE、GOCE卫星重力计划极大地提高了全球重力场模型中长波的精度.本文首先对GRACE/GOCE卫星重力场模型的内符合和外符合精度进行讨论分析,结果说明卫星重力模型的截断误差影响可达到分米级水平,在确定高程基准重力位时该影响不可忽略.利用EGM2008模型扩展GRACE/GOCE卫星重力场模型至2190阶,可有效减弱卫星重力模型的截断误差影响,但不同模型扩展时的最优拼接阶次不同,其中DIR-1、DIR-5模型对应的最优拼接阶次分别为180阶和220阶,以GPS水准数据检验,扩展模型在中国区域的精度均优于18cm.最后,基于最优拼接阶次获得的扩展重力场模型对我国1985高程基准重力位进行了估计,DIR-5和TIM-5模型对应数值分别为62636853.47m~2·s~(-2)和62636853.49m~2·s~(-2),精度均为1.51m~2·s~(-2);发现在中国区域模型大地水准面与GPS/水准数据的差值存在微弱的系统性倾斜,东西向倾斜约为9cm,南北向倾斜约为1.4cm,考虑倾斜改正后基于DIR-5和TIM-5模型估计我国1985高程基准重力位的精度提高了0.16m~2·s~(-2). 相似文献
20.
One of the main problems on the numerical solution of integral equations is the resolution of input data. Among the integral equations used in geodesy we have the “onestep inversion” based on the first derivative of the Poisson integral, which transforms gravity values on the Earth’s surface to the gravity potential on the reference ellipsoid. In this study, it is shown that the required spatial resolution of the input gravity data on the Earth’s surface for correct one-step inversion depends on the height of the computational region, the fact that if overlooked can cause totally wrong results. Consequently the following two major questions are posed: (i) How could one know whether the spatial resolution of the input gravity data for correct one-step inversion is sufficient? (ii) What should be done if the spatial resolution is not sufficient? By studying the behaviour of the integral kernel, an algorithm is presented which enables an appropriate answer to the former question. In order to address the latter question, a method is proposed to modify the integral kernel which overcomes the adverse effect of insufficient spatial resolution of the input gravity data. Our answers, which possess the novelty of the study, are numerically verified by means of real and simulated gravity data. The numerical results approve the efficiency of the proposed method in solving the problem of insufficient spatial resolution of the input gravity data for correct one-step inversion. 相似文献