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1.
Geoid determination using adapted reference field, seismic Moho depths and variable density contrast 总被引：4，自引：0，他引：4
The traditional remove-restore technique for geoid computation suffers from two main drawbacks. The first is the assumption
of an isostatic hypothesis to compute the compensation masses. The second is the double consideration of the effect of the
topographic–isostatic masses within the data window through removing the reference field and the terrain reduction process.
To overcome the first disadvantage, the seismic Moho depths, representing, more or less, the actual compensating masses, have
been used with variable density anomalies computed by employing the topographic–isostatic mass balance principle. In order
to avoid the double consideration of the effect of the topographic–isostatic masses within the data window, the effect of
these masses for the used fixed data window, in terms of potential coefficients, has been subtracted from the reference field,
yielding an adapted reference field. This adapted reference field has been used for the remove–restore technique. The necessary
harmonic analysis of the topographic–isostatic potential using seismic Moho depths with variable density anomalies is given.
A wide comparison among geoids computed by the adapted reference field with both the Airy–Heiskanen isostatic model and seismic
Moho depths with variable density anomaly and a geoid computed by the traditional remove–restore technique is made. The results
show that using seismic Moho depths with variable density anomaly along with the adapted reference field gives the best relative
geoid accuracy compared to the GPS/levelling geoid.
Received: 3 October 2001 / Accepted: 20 September 2002
Correspondence to: H.A. Abd-Elmotaal 相似文献
2.
采用密度随深度呈指数变化的变密度模型来反演莫霍面深度，给出了利用指数密度模型在波数域中计算重力异常的正演公式压界面深度的反演公式。结果表明，青藏高原莫霍面呈现出边缘浅、中部深，边缘变化快、梯度大，中间变化梯度趋缓的特点。通过对常密度模型、变密度模型及地震反演得到的莫霍面的比较，证实变密度模型更适合于莫霍面结构的反演。 相似文献
3.
Geoid determination with density hypotheses from isostatic models and geological information 总被引：2，自引：3，他引：2
M. Kuhn 《Journal of Geodesy》2003,77(1-2):50-65
Geoid determination by Stokes's formula requires a complete knowledge of the topographical mass density distribution in order
to perform gravity reductions to the geoid boundary. However, deeper masses are also of interest, in order to produce a smooth
field of gravity anomalies which will improve results from interpolation procedures. Until now, in most cases a constant mass
density has been considered, which is a very rough approximation of reality. The influence on the geoid height coming from
different mass density hypotheses given by the isostatic models of Pratt/Hayford, Airy/Heiskanen and Vening Meinesz is studied.
Apart from a constant mass density value, additional density information deduced from geological maps and thick sedimentary
layers is considered. An overview of how mass density distributions act within Stokes's theory is given. The isostatic models
are considered in spherical and planar approximation, as well as with constant and lateral variable mass density of the topographical
and deeper masses. Numerical results in a test area in south-west Germany show that the differences in the geoid height due
to different density hypotheses can reach a magnitude of more than 1 decimetre, which is not negligible in a precise geoid
determination with centimetre accuracy.
Received: 7 January 2002 / Accepted: 20 September 2002
M. Kuhn now at: Western Australian Centre for Geodesy, Curtin University of Technology, GPO Box U1987, Perth, WA 6845, Australia
Acknowledgements. The author would gratefully thank Prof. Dr.-Ing. B. Heck, who was the supervisor of my PhD thesis, and the second examiner
Prof. Dr.-Ing. K.H. Ilk, as well as all other colleagues for their support of this work. Particular thanks go to the Landesvermessungsamt
Baden–Württemberg (Survey Department of Baden–Württemberg), Bureau Gravimetrique International (BGI, France) for providing
the gravity data and the Geologisches Landesamt Baden–Württemberg (Geological Department of Baden–Württemberg) for providing
data and maps of the sediment layers within the Rhine Valley. Grateful thanks goes to Prof. W.E. Featherstone and the reviewers
Prof. S.D. Pagiatakis, Dr. U. Marti as well as an unknown reviewer for their helpful comments on this paper. 相似文献
4.
Inverse Vening Meinesz formula and deflection-geoid formula: applications to the predictions of gravity and geoid over the South China Sea 总被引：12，自引：0，他引：12
C. Hwang 《Journal of Geodesy》1998,72(5):304-312
Using the spherical harmonic representations of the earth's disturbing potential and its functionals, we derive the inverse
Vening Meinesz formula, which converts deflection of the vertical to gravity anomaly using the gradient of the H function. The deflection-geoid formula is also derived that converts deflection to geoidal undulation using the gradient
of the C function. The two formulae are implemented by the 1D FFT and the 2D FFT methods. The innermost zone effect is derived. The
inverse Vening Meinesz formula is employed to compute gravity anomalies and geoidal undulations over the South China Sea using
deflections from Seasat, Geosat, ERS-1 and TOPEX//POSEIDON satellite altimetry. The 1D FFT yields the best result of 9.9-mgal
rms difference with the shipborne gravity anomalies. Using the simulated deflections from EGM96, the deflection-geoid formula
yields a 4-cm rms difference with the EGM96-generated geoid. The predicted gravity anomalies and geoidal undulations can be
used to study the tectonic structure and the ocean circulations of the South China Sea.
Received: 7 April 1997 / Accepted: 7 January 1998 相似文献
5.
F. L. Clarke 《Journal of Geodesy》1981,55(1):1-16
Comparisons of gravimetric and astrogeodetic deflections of the vertical in the Australian region indicate that the former
are affected by position dependent systematic errors, even after orientation onto the Australian Geodetic Datum. These are
probably due to errors in the predicted mean anomalies for gravimetrically unsurveyed oceanic regions to the east, south and
west of the continent. Deflection component residuals (astrogeodetic minus oriented gravimetric) at 83 control stations are
made the observables in a set of observation equations, based on the Vening Meinesz equations, from which pseudocorrections
to the mean anomalies for a set of arbitrarily selected surface elements are computed. These pseudocorrections compensate
for prediction errors in much larger unsurveyed regions. Their effects on individual deflection components are calculated
using the Vening Meinesz equations. Statistical tests indicate that pseudocorrections computed for four large offshore elements
and six smaller elements in unsurveyed areas produce corrections to the gravimetric deflections which make the ξ and η components
in seconds of arc consistent with normally distributed populations N (0.00, 0.702). 相似文献
6.
Herman van Gysen 《Journal of Geodesy》1994,68(3):173-179
Thin-plate splines — well known for their flexibility and fidelity in representing experimental data — are especially suited for the numerical evaluation of geodetic integrals in the area where these are most sensitive to the data, i.e. in the immediate vicinity of the computation point. Quadrature rules that are exact for thin-plate splines interpolating randomly spaced data are derived for the inner zone contribution (to a planar approximation) to Stokes's formula, to the formulae of Vening Meinesz and to theL
1 gradient operator in the analytical continuation solution of Molodensky's problem.The quadrature method is demonstrated by calculating the inner zone contribution to height anomalies in a mountainous area of Lesotho and carrying out a comparison with GPS-derived heights. Height anomalies are recovered with an accuracy of 6 cm. 相似文献
7.
S. Ono 《Journal of Geodesy》1985,59(3):275-288
In order to solve the problems of determining the shape of a part of the earth of national or continental extent, that is,
of rigorous constituting and computing of the astrogeodetic network, it is required to determine gravimetric deflections of
the vertical with an accuracy of, say, 0″.3. For this it is adequate to carry out additional gravity surveys in the neighborhoods
of computation points, in addition to a given uniform gravity survey (normal density gravity survey).
The study offers a method to determine the optimal distribution of gravity stations in such a gravity survey, which guarantees
a given accuracy of computed gravimetric deflections of the vertical for a given statistical condition which characterizes
the variation of the gravity field. The approach used here is based on the concept of the error of representation and the
error propagation of Vening Meinesz integrals. 相似文献
8.
9.
Hussein Abd-Elmotaal 《Journal of Geodesy》1992,66(4):325-335
Some selected test areas in the Austrian territory are presented. Free-air and Bouguer anomalies as well as isostatic anomalies (based on Vening Meinesz' isostatic model) are computed. Statistics of these anomalies are given. Also, an extensive comparison between their empirical covariance functions is made and will be discussed. The results show that the isostatic anomalies for our test areas still contain, in general, a trend part. 相似文献
10.
根据多卫星高度计海面高数据推算南中国海及菲律宾海域重力异常(英文) 总被引：1，自引：0，他引：1
t Gravity anomalies on a2.5 ×2.5 arc-minute grid in a non-tidal system were derived over the South China and Philippine Seas from multi-satellite altimetry data. North and east components of deflections of the vertical were computed from altimeter-derived sea surface heights at crossover locations, and gridded onto a 2.5 × 2.5 arc-minute resolution grid. EGM96-derived components of deflections of the vertical and gravity anomalies gridded into 2.5 × 2.5 arc-minute resolutions were then used as reference global geopotential model quantities in a remove-restore procedure to implement the Inverse Vening Meinesz formula via the 1D-FFT technique to predict the gravity anomalies over the South China and Philippine Seas from the gridded altimeter-derived components of deflections of the vertical. Statistical comparisons between the altimeter-derived and the shipboard gravity anomalies showed that there is a root-mean-square agreement of 5.7 mgals between them. 相似文献
11.
Measurements of gravity were made on boardU.S.S. Becuna (SS 319) with a Vening Meinesz pendulum apparatus and a Graf sea gravimeter at approximately the same time.
Comparison of data uncorrected for depth of submergence, E?tvos correction and second order effects of horizontal acceleration
showed that there was a change related to time of observation. These corrections were not made as they would be the same for
both sets of observations, and no provision had yet been made to take care of the horizontal accelerations for the Graf sea
gravimeter. The variation with otime could be caused by instrumental drift or scale calibration. After removal of this effect
by visually fitting the data trend with a straight line, there were three observations with large discrepancies, seventeen
with discrepancies of 3–9 mgal and thirty-nine with discrepancies of 0–3 mgal, showing close approach to a statistical distribution.
The three large discrepancies may be dismissed because of very bad depth control during the observations. The discrepancies
3–9 mgals are larger than expected and perhaps are attributable to depth control and inadequate observation time for the Graf
sea gravimeter.
It is concluded that the Graf sea gravimeter shows great promise for use on a submarine. An apparatus to take into account
the horizontal acceleration effects must be added, and suitable drift characteristic obtained. Despite its advantages of ruggedness,
ease of operation, ease of data reduction, reduced size and weight, many more comparisons of the Graf sea gravimeter with
the Vening Meinesz pendulum equipment should be made before the latter are displaced
Probably the Graf sea gravimeter will be usable on a stable platform on a surface vessel at least in calm sea states. 相似文献
12.
Global mean sea surface heights (SSHs) and gravity anomalies on a 2′×2′ grid were determined from Seasat, Geosat (Exact Repeat Mission and Geodetic Mission), ERS-1 (1.5-year mean of 35-day, and
GM), TOPEX/POSEIDON (T/P) (5.6-year mean) and ERS-2 (2-year mean) altimeter data over the region 0∘–360∘ longitude and –80∘–80∘ latitude. To reduce ocean variabilities and data noises, SSHs from non-repeat missions were filtered by Gaussian filters
of various wavelengths. A Levitus oceanic dynamic topography was subtracted from the altimeter-derived SSHs, and the resulting
heights were used to compute along-track deflection of the vertical (DOV). Geoidal heights and gravity anomalies were then
computed from DOV using the deflection-geoid and inverse Vening Meinesz formulae. The Levitus oceanic dynamic topography was
added back to the geoidal heights to obtain a preliminary sea surface grid. The difference between the T/P mean sea surface
and the preliminary sea surface was computed on a grid by a minimum curvature method and then was added to the preliminary
grid. The comparison of the NCTU01 mean sea surface height (MSSH) with the T/P and the ERS-1 MSSH result in overall root-mean-square
(RMS) differences of 5.0 and 3.1 cm in SSH, respectively, and 7.1 and 3.2 μrad in SSH gradient, respectively. The RMS differences
between the predicted and shipborne gravity anomalies range from 3.0 to 13.4 mGal in 12 areas of the world's oceans.
Received: 26 September 2001 / Accepted: 3 April 2002
Correspondence to: C. Hwang
Acknowledgements. This research is partly supported by the National Science Council of ROC, under grants NSC89-2611-M-009-003-OP2 and NSC89-2211-E-009-095.
This is a contribution to the IAG Special Study Group 3.186. The Geosat and ERS1/2 data are from NOAA and CERSAT/France, respectively.
The T/P data were provided by AVISO. The CLS and GSFC00 MSS models were kindly provided by NASA/GSFC and CLS, respectively.
Drs. Levitus, Monterey, and Boyer are thanked for providing the SST model. Dr. T. Gruber and two anonymous reviewers provided
very detailed reviews that improved the quality of this paper. 相似文献
13.
Y. Hagiwara 《Journal of Geodesy》1972,46(4):453-466
A general formula giving Molodenskii coefficientsQ
n of the truncation errors for the geoidal height is introduced in this paper. A relation betweenQ
n andq
n, Cook’s truncation function, is also obtained. Cook (1951) has treated the truncation errors for the deflection of the vertical
in the Vening Meinesz integration. Molodenskii et al. (1962) have also derived the truncation error formulas for the deflection
of the vertical. It is proved in this paper that these two formulas are equivalent. 相似文献
14.
关于地壳均衡模型的讨论 总被引：1，自引：0，他引：1
本文基于３ 个经典地壳均衡模型——普拉特模型、爱黎模型及维宁·迈尼兹模型在其表达的物理含义和方便实际应用等方面所各自具有的特点,提出改化经典模型的方法,给出一个既能反映地壳均衡的区域性补偿,又易于实现的区域性实用模型,并给出平均高的计算方法。最后还给出便于应用的两个近似模型。 相似文献
15.
全球地幔密度异常及其构造意义 总被引：4，自引：0，他引：4
利用扣除地形、莫霍面和核幔边界起伏影响的中长波大地水准面异常和全球地震层析成像资料,采用阻尼最小二乘方法反演计算了全球地幔6个不同层面上的密度异常分布。分析了全球密度异常与板块构造的关系,探讨了全球密度异常分布对板块运动的作用。全球地幔密度异常结果表明存在两个主要的密度异常中心：一个位于东经80°,北纬0°;另一个位于东经240°,北纬10°附近。 相似文献
16.
The structure of normal matrices occurring in the problem of weighted least-squares spherical harmonic analysis of measurements
scattered on a sphere with random noises is investigated. Efficient algorithms for the formation of the normal matrices are
derived using fundamental relations inherent to the products of two surface spherical harmonic functions. The whole elements
of a normal matrix complete to spherical harmonic degree L are recursively obtained from its first row or first column extended to degree 2L with only O(L
4) computational operations. Applications of the algorithms to the formation of surface normal matrices from geoid undulations
and surface gravity anomalies are discussed in connection with the high-degree geopotential modeling.
Received: 22 March 1999 / Accepted: 23 December 1999 相似文献
17.
基于均衡理论构制地球重力场模型中一个关键问题是扰动质量的确定,不同的地壳密度分布将得到不同的扰动质量。本文立足于面凝聚模型和Airy模型两种均衡补偿机制,研究了CRUST 2.0全球地壳模型在构制高分辨率地球重力场模型中的应用,推导了顾及地球物理信息的两种均衡重力场模型构建公式,分别讨论了CRUST 2.0模型和补偿深度在两种补偿机制中构建重力场模型的贡献。数值分析表明,地壳模型中Moho面深度的算术平均值22.97 km不是最佳补偿深度,而40 km相对最优,补偿深度的对模型超高阶部分影响较小;CRUST 2.0模型能够在361-1080频段内较好地改善原模型;相同补偿深度的面凝聚模型和Airy模型在不同频段的优劣性不一致。 相似文献
18.
Hussein Abd-Elmotaal 《Journal of Geodesy》1993,67(2):86-90
The representation of the topography is usually made by digital height models and digital density models. Therefore, one can produce the so-called digital Moho model (DMM) by applying a certain isostatic hypothesis. The attraction of such compensating masses is deducted. Also, some special cases are treated. The effect of neglecting the height of the computational point only on calculating the attraction of the compensating masses is studied. The results show that the height of the computational point must be taken into account on calculating the attraction of the compensating masses specially for high mountainous areas. 相似文献
19.
A new isostatic model of the lithosphere and gravity field 总被引：2，自引：0，他引：2
Based on the analysis of various factors controlling isostatic gravity anomalies and geoid undulations, it is concluded that it is essential to model the lithospheric density structure as accurately as possible. Otherwise, if computed in the classical way (i.e. based on the surface topography and the simple Airy compensation scheme), isostatic anomalies mostly reflect differences of the real lithosphere structure from the simplified compensation model, and not necessarily the deviations from isostatic equilibrium. Starting with global gravity, topography and crustal density models, isostatic gravity anomalies and geoid undulations have been determined. The initial crust and upper-mantle density structure has been corrected in a least squares adjustment using gravity. To model the long-wavelength (>2000 km) features in the gravity field, the isostatic condition (i.e. equal mass for all columns above the compensation level) is applied in the adjustment to uncover the signals from the deep-Earth interior, including dynamic deformations of the Earths surface. The isostatic gravity anomalies and geoid undulations, rather than the observed fields, then represent the signals from mantle convection and deep density inhomogeneities including remnants of subducted slabs. The long-wavelength non-isostatic (i.e. the dynamic) topography was estimated to range from –0.4 to 0.5 km. For shorter wavelengths (<2000 km), the isostatic condition is not applied in the adjustment in order to obtain the non-isostatic topography due to regional deviations from classical Airy isostasy. The maximum deviations from Airy isostasy (–1.5 to 1 km) occur at currently active plate boundaries. As another result, a new global model of the lithosphere density distribution is generated. The most pronounced negative density anomalies in the upper mantle are found near large plume provinces, such as Iceland and East Africa, and in the vicinity of the mid-ocean ridge axes. Positive density anomalies in the upper mantle under the continents are not correlated with the cold and thick lithosphere of cratons, indicating a compensation mechanism due to thermal and compositional density. 相似文献
20.
The Cartesian moments of the mass density of a gravitating body and the spherical harmonic coefficients of its gravitational
field are related in a peculiar way. In particular, the products of inertia can be expressed by the spherical harmonic coefficients
of the gravitational potential as was derived by MacCullagh for a rigid body. Here the MacCullagh formulae are extended to
a deformable body which is restricted to radial symmetry in order to apply the Love–Shida hypothesis. The mass conservation
law allows a representation of the incremental mass density by the respective excitation function. A representation of an
arbitrary Cartesian monome is always possible by sums of solid spherical harmonics multiplied by powers of the radius. Introducing
these representations into the definition of the Cartesian moments, an extension of the MacCullagh formulae is obtained. In
particular, for excitation functions with a vanishing harmonic coefficient of degree zero, the (diagonal) incremental moments
of inertia also can be represented by the excitation coefficients. Four types of excitation functions are considered, namely:
(1) tidal excitation; (2) loading potential; (3) centrifugal potential; and (4) transverse surface stress. One application
of the results could be model computation of the length-of-day variations and polar motion, which depend on the moments of
inertia.
Received: 27 July 1999 / Accepted: 24 May 2000 相似文献