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1.
In this paper, the definition of latitudinal density and density flattening of the level ellipsoid is given, and integral
formulas of latitudinal density for pole gravity and equator gravity are derived. According to the pole gravity condition
and equator gravity condition for the level ellipsoid, latitudinal density distribution function of the level ellipsoid is
obtained. It is proved mathematically that latitudinal density of the earth’s equator is larger than that of the pole, the
earth’s density flattening calculated preliminarily is 1/322, and hypothesis of the earth’s latitudinal normal density is
further proposed, so that theoretical preparation for studying the forming cause of the earth gravity in problems such as
continent drift, mantle convection, and submarine extension is made well. 相似文献
2.
Mehdi Eshagh 《Acta Geophysica》2011,59(1):29-54
Solution of the gradiometric boundary value problems leads to three integral formulas. If we are satisfied with obtaining
a smooth solution for the Earth’s gravity field, we can use the formulas in regional gravity field modelling. In such a case,
satellite gradiometric data are integrated on a sphere at satellite level and continued downward to the disturbing potential
(geoid) at sea level simultaneously. This paper investigates the gravity field modelling from a full tensor of gravity at
satellite level. It studies the truncation bias of the integrals as well as the filtering of noise of data. Numerical studies
show that by integrating T
zz
with 1 mE noise and in a cap size of 7°, the geoid can be recovered with an error of 12 cm after the filtering process. Similarly,
the errors of the recovered geoids from T
xz,yz
and T
xx-yy, 2xy
are 13 and 21 cm, respectively. 相似文献
3.
A new gravimetric, satellite altimetry, astronomical ellipsoidal boundary value problem for geoid computations has been developed and successfully tested. This boundary value problem has been constructed for gravity observables of the type (i) gravity potential, (ii) gravity intensity (i.e. modulus of gravity acceleration), (iii) astronomical longitude, (iv) astronomical latitude and (v) satellite altimetry observations. The ellipsoidal coordinates of the observation points have been considered as known quantities in the set-up of the problem in the light of availability of GPS coordinates. The developed boundary value problem is ellipsoidal by nature and as such takes advantage of high precision GPS observations in the set-up. The algorithmic steps of the solution of the boundary value problem are as follows:
- - Application of the ellipsoidal harmonic expansion complete up to degree and order 360 and of the ellipsoidal centrifugal field for the removal of the effect of global gravity and the isostasy field from the gravity intensity and the astronomical observations at the surface of the Earth.
- - Application of the ellipsoidal Newton integral on the multi-cylindrical equal-area map projection surface for the removal from the gravity intensity and the astronomical observations at the surface of the Earth the effect of the residual masses at the radius of up to 55 km from the computational point.
- - Application of the ellipsoidal harmonic expansion complete up to degree and order 360 and ellipsoidal centrifugal field for the removal from the geoidal undulations derived from satellite altimetry the effect of the global gravity and isostasy on the geoidal undulations.
- - Application of the ellipsoidal Newton integral on the multi-cylindrical equal-area map projection surface for the removal from the geoidal undulations derived from satellite altimetry the effect of the water masses outside the reference ellipsoid within a radius of 55 km around the computational point.
- - Least squares solution of the observation equations of the incremental quantities derived from aforementioned steps in order to obtain the incremental gravity potential at the surface of the reference ellipsoid.
- - The removed effects at the application points are restored on the surface of reference ellipsoid.
- - Application of the ellipsoidal Bruns’ formula for converting the potential values on the surface of the reference ellipsoid into the geoidal heights with respect to the reference ellipsoid.
- - Computation of the geoid of Iran has successfully tested this new methodology.
Keywords: Geoid computations; Ellipsoidal approximation; Ellipsoidal boundary value problem; Ellipsoidal Bruns’ formula; Satellite altimetry; Astronomical observations 相似文献
4.
P. Novák 《Studia Geophysica et Geodaetica》2007,51(3):351-367
Satellite missions CHAMP and GRACE dedicated to global mapping of the Earth’s gravity field yield accurate satellite-to-satellite
tracking (SST) data used for recovery of global geopotential models usually in a form of a finite set of Stokes’s coefficients.
The US-German Gravity Recovery And Climate Experiment (GRACE) yields SST data in both the high-low and low-low mode. Observed
satellite positions and changes in the intersatellite range can be inverted through the Newtonian equation of motion into
values of the unknown geopotential. The geopotential is usually approximated in observation equations by a truncated harmonic
series with unknown coefficients. An alternative approach based on integral inversion of the SST data of type GRACE into discrete
values of the geopotential at a geocentric sphere is discussed in this article. In this approach, observation equations have
a form of Green’s surface integrals with scalar-valued integral kernels. Despite their higher complexity, the kernel functions
exhibit features typical for other integral kernels used in geodesy for inversion of gravity field data. The two approaches
are discussed and compared based on their relative advantages and intended applications. The combination of heterogeneous
gravity data through integral equations is also outlined in the article.
panovak@kma.zcu.cz 相似文献
5.
М. И. юркиив 《Studia Geophysica et Geodaetica》1965,9(2):101-108
Summary Following Molodensky's suggestions anomalies of the vertical gradient of gravity were used to achieve a greater accuracy in
the determination of the figure of the Earth by gravimetrical methods. The existing methods of computing this quantity do
not take into account inclinations of the physical surface of the Earth. Using the Laplace equation, the second derivative
∂2
T/∂v
2 (1) of the disturbing potentialT is expressed by the second derivatives ofT along the tangentsτ
1 andτ
2 to the physical surface of the Earth in mutually perpendicular planes and by the derivatives of gravity anomalies (2). The
derivatives ∂2
T/∂τ
1
2
and ∂2
T/∂τ
2
2
have been determined using the Molodensky method [4] of solving his integral equation for the single layer density. In the
zero approximation, the Noumerov formula [2] was obtained; however, the results obtained using this formula should be referred
to the physical surface of the Earth, not to the Listing geoid. The correction of the first approximation is given by formula
(16). The second vertical derivative of gravity anomalies can be determined using the expression (20).
相似文献
6.
The sea surface cannot be used as reference for Major Vertical Datum definition because its deviations from the ideal equipotential surface are very large compared to rms in the observed quantities. The quasigeoid is not quite suitable as the surface representing the most accurate Earth's model without some additional conditions, because it depends on the reference field. The normal Earth's model represented by the rotational level ellipsoid can be defined by the geocentric gravitational constant, the difference in the principal Earth's inertia moments, by the angular velocity of the Earth's rotation and by the semimajor axis or by the potential (U
0
) on the surface of the level ellipsoid. After determining the geopotential at the gauge stations defining Vertical Datums, gravity anomalies and heights should be transformed into the unique vertical system (Major Vertical Datum). This makes it possible to apply Brovar's (1995) idea of determining the reference ellipsoid by minimizing the integral, introduced by Riemann as the Dirichlet principle, to reach a minimum rms anomalous gravity field. Since the semimajor axis depends on tidal effects, potential U
0
should be adopted as the fourth primary fundamental geodetic constant. The equipotential surface, the actual geopotential of which is equal to U
0
, can be adopted as reference for realizing the Major Vertical Datum. 相似文献
7.
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
8.
On the basis of the reality of recent tectonic movement and discarding such a viewpoint that the isostatic adjust-ment only results from excessive or insufficient compensation,we have discussed the tectonic stress causing ine-auality and regarded the isostatic anomaly as a load on the earth‘s interior,thus the earth‘s inner stress can be cal-culated.The research results show that in the East China Sea and its eastern marginal seas the change of the verti-cal stress derived from the isostatic gravity anomaly is more marked than that of the horizontal stress.Along the Ryukyu trench there is an enhancement of vertical stress by 5MPa,which evidently reflects the effect of plate subduction.On contrary,along the island are to the northwest of the trench the vertical stress weakens by about5MPa.The horizontal stresses in eastern and western parts are obviously different,the east westward stress on the oceanic crust σx is negative(while the pressure is positive)but on the continental crust in positive.These facts indicate the effect of compression between plates. 相似文献
9.
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
10.
The relation between the gravity variation features and Ms=8.1 earthquake in Qinghai-Xizang monitoring area is analyzed preliminarily,by using spatial dynamic variation results of regional gravity field from absolute gravity and relative gravity observation in 1998 and 2000.The results show that:1)Ms\8.1 earthquake in Kulun mountain pass westem occurred in the gravity variation high gradient near gravity‘s high negative variation;2)The Main tectonic deformation and emnergy accumulation before MS=8.1 earthquake are distributed at south side of the epicenter;3)The range of gravity‘s high negative variation at east of the MS=8.1 earthquake epicenter relatively coincides with that rupture region according to field geology investigation;4)Gravity variation distribution in high negative value region is just consistent with the second shear strain‘s high value region of strain field obtained from GPS observation. 相似文献
11.
The undulation of the geoid, the gravity anomaly and the deflection of the vertical are the three basic observations describing the shape and the gravity field of the earth. The Stokes’ formula that computes the undulation of the geoid using the gravity anomaly on the geoid under spherical approximate conditions was first put forward by Stokes[1]. According to Stokes’ theory, The Vening-Meinesz formula that computes the meridian and the prime vertical components of the deflection of the ve… 相似文献
12.
Summary Using the geocentric constant GM=398 601.3 × 10
9
m
3s
–2
, the known value of the angular velocity of the Earth's rotation , Stokes' constants J
n
(k)
and S
n
(k)
upto n=21 (zonal), n=16 (tesseral and sectorial) [2], the geocentric co-ordinates and heights above sea-level of SAO satellite stations [2], the following will be derived: the potential on the geoid Wo, the scale factor for lengths Ro=GM/Wo, the radius-vector of the surface W=Wo, the parameters of the best-fitting Earth tri-axial ellipsoid, and the components of the deflections of the vertical with respect to the geocentric rotational IAG ellipsoid (Lucerne 1967), as well as to the best-fitting geocentric tri-axial ellipsoid. Some of the differences in the structure of the gravity field over the Northern and Southern Hemispheres will be given, and the mean values of gravity over the equatorial zone, determined from the dynamics of satellite orbits, on the one hand, and from terrestrial gravity data, on the other, will be compared.Presented at the Fifteenth IUGG General Assembly, Moscow, July 30 — August 14, 1971. 相似文献
13.
ZHANG Renhua WANG Jinfeng ZHU Caiying SUN Xiaomin & ZHU Zhilin .Institute of Geographical Sciences Natural Resources Chinese Academy of Sciences Beijing China .Institute of Surveying Mapping Information Engineering University of the Chinese People''''s Liberation Army Zhengzhou China 《中国科学D辑(英文版)》2004,47(12):1134-1146
The research for the land surface fluxes has madea quiet great progress for its breakthroughs in the fieldof regional or global interactions between land surfaceand atmosphere. However, many remote sensing mod-els for estimating the land surface fluxes need the pa-rameters of surface momentum, heat, resistance ofwater vapor at a referenced height, which are the func-tion of aerodynamic surface roughness zad. It hasbeen validated that the retrieval of the land surfacefluxes is very sensitive to… 相似文献
14.
Summary The integral mean values of gravity on the surface W=W
0
, obtained from satellite observations with the use of harmonic coefficients[3, 7] and from terrestrial gravity measurements[12], are compared. The squares and products of the harmonic coefficients were neglected, with the exception of [J
2
(0)
]
2
, which was taken into account. The Potsdam correction and the geocentric constant are being discussed. The paper ties up with[13–15] and the symbols used are the same. The given problem was treated, e.g., in[2, 4, 6, 8–10]; in the present paper the values of gravity are compared directly. 相似文献
15.
A new method of reconstruction of the temperature profile in the lunar mantle from the velocities of seismic P- and S-waves for different models of chemical composition is developed. The procedure of the solution of an inverse problem is realized
with the help of the minimization of the Gibbs free energy and the equations of state of a mantle substance, taking into account
phase transformations, anharmonicity, and the effects of inelasticity. The geophysical and geochemical constraints on composition
and temperature distribution in Moon’s mantle are established. The upper mantle can be composed of olivine pyroxenite, depleted
by low-volatile oxides (∼2 wt % of CaO and Al2O3). On the contrary, the lower mantle must be enriched by low-volatile oxides (∼4–6 wt % of CaO and Al2O3). Its composition can be represented by a mineral association of the olivine + clinopyroxene + garnet or olivine + orthopyroxene
+ clinopyroxene + garnet type, which is close in composition to pyrolite. The temperature distribution at depths 50–1000 km
are approximated by the equation: T(°C) = 351 + 1718[1–exp (−0.00082H)]. The constraints inferred make it possible to conclude that the published values of the velocities of P- and S-waves for the lunar mantle, obtained by processing the data of seismic experiments of the Apollo lunar mission are inconsistent
with each other at depths below 300 km. Otherwise, the variations in the velocities of P- and S-waves disturb the symmetry between the petrological model (composition), the temperature profile, and the seismic profile. 相似文献
16.
Explicit formula for the geoid-quasigeoid separation 总被引：1，自引：0，他引：1
The explicit formula for the geoid-to-quasigeoid correction is derived in this paper. On comparing the geoidal height and
height anomaly, this correction is found to be a function of the mean value of gravity disturbance along the plumbline within
the topography. To evaluate the mean gravity disturbance, the gravity field of the Earth is decomposed into components generated
by masses within the geoid, topography and atmosphere. Newton’s integration is then used for the computation of topography-and
atmosphere-generated components of the mean gravity, while the combined solution for the downward continuation of gravity
anomalies and Stokes’ boundary-value problem is utilized in computing the component of mean gravity disturbance generated
by mass irregularities within the geoid. On application of this explicit formulism a theoretical accuracy of a few millimetres
can be achieved in evaluation of the geoid-to-quasigeoid correction. However, the real accuracy could be lower due to deficiencies
within the numerical methods and to errors within the input data (digital terrain and density models and gravity observations). 相似文献
17.
Michele Caputo 《Pure and Applied Geophysics》1964,57(1):66-82
Summary Adopting thePizzetti-Somigliana method and using elliptic integrals we have obtained closed formulas for the space gravity field in which one of the equipotential surfaces is a triaxial ellipsoid. The same formulas are also obtained in first approximation of the equatorial flattening avoiding the use of the elliptic integrals. Using data from satellites and Earth gravity data the gravitational and geometric bulge of the Earth's equator are computed. On the basis of these results and on the basis of recent gravity data taken around the equator between the longitudes 50° to 100° E, 155° to 180° E, and 145° to 180° W, we question the advantage of using a triaxial gravity formula and a triaxial ellipsoid in geodesy. Closed formulas for the space field in which a biaxial ellipsoid is an equipotential surface are also derived in polar coordinates and its parameters are specialized to give the international gravity formula values on the international ellipsoid. The possibility to compute the Earth's dimensions from the present Earth gravity data is the discussed and the value ofMG=(3.98603×1020 cm3 sec–2) (M mass of the Earth,G gravitational constant) is computed. The agreement of this value with others computed from the mean distance Earth-Moon is discussed. The Legendre polinomials series expansion of the gravitational potential is also added. In this series the coefficients of the polinomials are closed formulas in terms of the flattening andMG.Publication Number 327, and Istituto di Geodesia e Geofisica of Università di Trieste. 相似文献
18.
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
19.
Roland Klees 《Surveys in Geophysics》1993,14(4-5):419-432
The Boundary Element Method (BEM), a numerical technique for solving boundary integral equations, is introduced to determine the earth's gravity field. After a short survey on its main principles, we apply this method to the fixed gravimetric boundary value problem (BVP), i.e. the determination of the earth's gravitational potential from measurements of the intensity of the gravity field in points on the earth's surface. We show how to linearize this nonlinear BVP using an implicit function theorem and how to transform the linearized BVP into a boundary integral equation using the single layer representation. A Galerkin method is used to transform the boundary integral equation using the single layer representation. A Galerkin method is used to transform the boundary integral equation into a linear system of equations. We discuss the major problems of this approach for setting up and solving the linear system. The BVP is numerically solved for a bounded part of the earth's surface using a high resolution reference gravity model, measured gravity values of high density, and a 50 50 m2 digital terrain model to describe the earth's surface. We obtain a gravity field resolution of 1 1 km2 with an accuracy of the order 10–3 to 10–4 in about 1 CPU-hour on a Siemens/Fujitsu SIMD vector pipeline machine using highly sophisticated numerical integration techniques and fast equation solvers. We conclude that BEM is a powerful numerical tool for solving boundary value problems and may be an alternative to classical geodetic techniques. 相似文献
20.
Studies of the rocks′ electrical properties under high temperature and pressure have found favors in the geophysicist′s eyes, because those studies are becoming to be the important methods to understand the earth′s interior materials, their migration and evolution. This article introduces the development and significant of those studies from the measurements, instruments and affections, etc. 相似文献