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1.
Mehdi Najafi-Alamdary Alireza A. Ardalan Seyed-Rohallah Emadi 《Studia Geophysica et Geodaetica》2012,56(1):153-170
An ellipsoidal Neumann type geodetic boundary-value problem (GBVP) for the computation of disturbing potential on the surface
of the Earth based on the surface gravity disturbance as the boundary data is formulated. The solution methodology of the
GBVP can be algorithmically summarized as follows: (i) using global navigation satellite systems (GNSS) coordinates of the
gravity stations, the surface gravity disturbances are generated as the boundary data. (ii) Applying the deflection correction
to the gravity disturbances to arrive at the derivative of the surface disturbing potential along the ellipsoidal normal.
(iii) Removing the low frequencies part of the gravity field using harmonic expansion to degree and order 110. (iv) Using
the short wavelength part of the corrected gravity disturbances derived in the previous section as the boundary data within
the constructed GBVP to derive the short wavelength disturbing potential over the Earth surface. (v) The computed shortwave
length signals of disturbing potentials are converted to disturbing potential values by restoring the removed effects. 相似文献
2.
The ellipsoidal Stokes boundary-value problem is used to compute the geoidal heights. The low degree part of the geoidal heights can be represented more accurately by Global Geopotential Models (GGM). So the disturbing potential is splitted into a low-degree reference potential and a higher-degree potential. To compute the low-degree part, the global geopotential model is used, and for the high-degree part, the solution of the ellipsoidal Stokes boundary-value problem in the form of the surface integral is used. We present an effective method to remove the singularity of the high-degree of the spherical and ellipsoidal Stokes functions around the computational point. Finally, the numerical results of solving the ellipsoidal Stokes boundary-value problem and the difference between the high-degree part of the solution of the ellipsoidal Stokes boundary-value problem and that of the spherical Stokes boundary-value problem is presented. 相似文献
3.
A. Kilicoglu 《Studia Geophysica et Geodaetica》2005,49(1):1-12
Approximately nine-year data from ERS1, ERS2 and TOPEX/POSEIDON (T/P) satellite altimetry missions have been used for the recovery of gravity anomalies over the Black Sea. The Corrected Sea Surface Height product of Aviso/Altimetry has been proven to be homogeneous after a cross-over adjustment. The Least Squares Collocation method was applied in a so-called remove-restore procedure. The residual geoid heights, obtained by subtracting EGM96 geoid heights from cross-over adjusted sea surface heights, were inverted to recover residual gravity anomalies in a grid structure over the Black Sea. Finally, EGM96 free air gravity anomalies were added to the predicted residual gravity anomalies to obtain the free air gravity anomalies. In order to check the consistency with respect to an external source, these computed free air gravity anomalies were compared to ship gravity observations, and to alternative satellite altimetry derived gravity anomalies. Comparisons with the observed gravity data yielded that external consistency of the gravity anomalies computed in this study is about 3 mGal for individual ship tracks. Overall external consistency in the test area is 4.8 mGal. Comparison with other satellite altimetry derived gravity anomalies presented a good agreement. 相似文献
4.
Zdeněk Martinec 《Studia Geophysica et Geodaetica》1990,34(4):313-326
Summary A new method for computing the potential coefficients of the Earth's external gravity field is presented. The gravimetric
boundary-value problem with a free boundary is reduced to the problem with a fixed known telluroid. The main idea of the derivation
consists in a continuation of the quantities from the physical surface to the telluroid by means of Taylor's series expansion
in such a way that the terms whose magnitudes are comparable with the accuracy of today's gravity measurements are retained.
Thus not only linear, but also non-linear terms are taken into account. Explicitly, the terms up to the order of the third
power of the Earth's flattening are retained. The non-linear boundary-value problem on the telluroid is solved by an iteration
procedure with successive approximations. In each iteration step the solution of the non-linear problem is estimated by the
solutions of two linear problems utilizing the fact that the non-linear boundary condition may be split into two parts; the
linear spherical approximation of the gravity anomaly whose magnitude is significantly greater than the others and the non-linear
ellipsoidal corrections. Finally, in order to solve the problem in terms of spherical harmonics, the transform method composed
of the fast Fourier transform and Gauss Legendre quadrature is theoretically outlined. Immediate data processing of gravity
data measured on the physical Earth's surface without any continuation of gravity measurements to a reference level surface
belongs to the main advantage of the presented method. This implies that no preliminary data handling is needed and that the
error data propagation is, consequently, maximally suppressed. 相似文献
5.
6.
Hasan Yildiz 《Studia Geophysica et Geodaetica》2012,56(1):171-184
Gravity field and steady-state Ocean Circulation Explorer (GOCE) is the first satellite mission that observes gravity gradients
from the space, to be primarily used for the determination of high precision global gravity field models. However, the GOCE
gradients, having a dense data distribution, may potentially provide better predictions of the regional gravity field than
those obtained using a spherical harmonic Earth Geopotential Model (EGM). This is investigated in Auvergne test area using
Least Squares Collocation (LSC) with GOCE vertical gravity gradient anomalies (Tzz), removing the long wavelength part from EGM2008 and the short wavelength part by residual terrain modelling (RTM). The results
show that terrain effects on the vertical gravity gradient are significant at satellite altitude, reaching a level of 0.11
E?tv?s unit (E.U.) in the mountainous areas. Removing the RTM effects from GOCE Tzz leads to significant improvements on the LSC predictions of surface gravity anomalies and quasigeoid heights. Comparison
with ground truth data shows that using LSC surface free air gravity anomalies and quasi-geoid heights are recovered from
GOCE Tzz with standard deviations of 11 mGal and 18 cm, which is better than those obtained by using GOCE EGMs, demonstrating that
information beyond the maximal degree of the GOCE EGMs is present. Investigation of using covariance functions created separately
from GOCE Tzz and terrestrial free air gravity anomalies, suggests that both covariance functions give almost identical predictions. However,
using covariance function obtained from GOCE Tzz has the effect that the predicted formal average error estimates are considerably larger than the standard deviations of
predicted minus observed gravity anomalies. Therefore, GOCE Tzz should be used with caution to determine the covariance functions in areas where surface gravity anomalies are not available,
if error estimates are needed. 相似文献
7.
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
8.
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
9.
The physical meaning of the truncated geoid, which is defined by the convolution of gravity anomalies with the Stokes function on a spherical cap of specified radius, has been studied by the authors. They investigated its relation to the density distribution, generating the surface gravity, and its potential use in inversion. Some progress results for simulated studies on point mass anomalies are presented.
The behavior of the truncated geoid is controlled by the radius of the integration domain, hereinafter referred to as the truncation parameter, which is treated as a free parameter. The change of the truncated geoid in response to the change of the truncation parameter was studied in the context of the simulated mass distributions. By means of such computer simulations we have managed to demonstrate the clear sensitivity of the truncated geoid to the depths, in addition to the horizontal positions, of point mass anomalies generating the synthetic surface gravity. The objective of this paper is to illustrate, with the help of computer simulation as the method of our study, the contribution of the truncated geoid to the solution of the gravimetric inverse problem. Further work towards employing the truncated geoid in gravity exploration is being conducted. 相似文献
10.
Ali Kiliçoğlu Ahmet Direnç Hasan Yildiz Murat Bölme Bahadir Aktuğ Mehmet Simav Onur Lenk 《Studia Geophysica et Geodaetica》2011,55(4):557-578
Turkish regional geoid models have been developed by employing a reference earth gravitational model, surface gravity observations
and digital terrain models. The gravimetric geoid models provide a ready transformation from ellipsoidal heights to the orthometric
heights through the use of GPS/leveling geoid heights determined through the national geodetic networks. The recent gravimetric
models for Turkish territory were computed depending on OSU91 (TG-91) and EGM96 (TG-03) earth gravitational models. The release
of the Earth Gravitational Model 2008 (EGM08), the collection of new surface gravity observations, the advanced satellite
altimetry-derived gravity over the sea, and the availability of the high resolution digital terrain model have encouraged
us to compute a new geoid model for Turkey. We used the Remove-Restore procedure based on EGM08 and applied Residual Terrain
Model (RTM) reduction of the surface gravity data. Fast Fourier Transformation (FFT) was then used to obtain the residual
quasigeoid from the reduced gravity. We restored the individual contributions of EGM08 and RTM to the whole quasi-geoid height
(TQG-09). Since the Helmert orthometric height system is adopted in Turkey, the quasi-geoid model (TQG-09) was then converted
to the geoid model (TG-09) by making use of Bouguer gravity anomalies and digital terrain model. After all we combined a gravimetric
geoid model with GPS/leveling geoid heights in order to obtain a hybrid geoid model (THG-09) (or a transformation surface)
to be used in GPS applications. The RMS of the post-fit residuals after the combination was found to be ± 0.95 cm, which represents
the internal precision of the final combination. And finally, we tested the hybrid geoid model with GPS/leveling data, which
were not used in the combination, to assess the external accuracy. Results show that the external accuracy of the THG-09 model
is ± 8.4 cm, a precision previously not achieved in Turkey until this study. 相似文献
11.
Transformation between gravimetric and GPS/levelling-derived geoids using additional gravity information 总被引：1，自引：0，他引：1
The transformation from the gravimetric to the GPS/levelling-derived geoid using additional gravity information for the covariance function of geoid height differences has been investigated in a test area in south-western Canada. A “corrector surface” model, which accounts for datum inconsistencies, long-wavelength geoid errors, vertical network distortions and GPS errors, has been constructed using least-squares collocation. The local covariance function of geoid height differences is usually obtained from residual values between the GPS/levelling and gravimetric geoid heights after the elimination of all known systematic distortions. If additional gravity data (in the form of gravity anomalies) are available, the covariance function of geoid height differences can be determined by the following steps: (1) transforming the GPS/levelling-derived geoid heights into gravity anomalies; (2) forming differences between the computed in step 1 and given gravity anomalies; (3) determining the parameters of the local covariance function of the gravity anomaly differences; (4) constructing an analytical covariance model for the geoid height differences from the covariance function of the gravity anomaly differences using the parameters derived in step 3. The advantage of the proposed method stems from the great number of gravity data used to derive the empirical covariance function. A comparison with the least-squares adjustment shows that the standard deviation of the residuals of the predicted geoid height differences with respect to the control point values decreases by 2.4 cm. 相似文献
12.
Peter Mauersberger 《Pure and Applied Geophysics》1965,60(1):101-106
Summary The velocity potential and the shape of the free surface of a steady state gravity flow of incompressible, homogeneous groundwater inside an inhomogeneous, anisotropic aquifer are to be determined as the solution of a non-linear boundary-value problem. In this paper an equivalent variational principle has been formulated which is useful as a base of variational methods solving this boundary-value problem approximately.
Zusammenfassung Das Geschwindigkeitspotential und die Gestalt des freien Grundwasserspiegels einer stationären Strömung inkompressiblen, homogenen Grundwassers innerhalb eines anisotropen, inhomogenen Grundwasserträgers sind aus einem nichtlinearen Randwertproblem zu bestimmen. Es wird ein äquivalentes Variationsprinzip angegeben, welches als Basis für die Anwendung direkter Methoden der Variationsrechnung zur approximativen Lösung dieses Randwertproblemes dienen kann.相似文献
13.
The development of studies on estimating the accuracy of the Earth’s modern global gravity models in terms of the spherical harmonics of the geopotential in the problematic regions of the world is discussed. The comparative analysis of the results of reconstructing quasi-geoid heights and gravity anomalies from the different models is carried out for two polar regions selected within a radius of 1000 km from the North and South poles. The analysis covers nine recently developed models, including six high-resolution models and three lower order models, including the Russian GAOP2012 model. It is shown that the modern models determine the quasi-geoid heights and gravity anomalies in the polar regions with errors of 5 to 10 to a few dozen cm and from 3 to 5 to a few dozen mGal, respectively, depending on the resolution. The accuracy of the models in the Arctic is several times higher than in the Antarctic. This is associated with the peculiarities of gravity anomalies in every particular region and with the fact that the polar part of the Antarctic has been comparatively less explored by the gravity methods than the polar Arctic. 相似文献
14.
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
15.
We consider common bank filtration systems and develop an explicit analytic solution representing steady, two-dimensional, groundwater flow to a horizontal well near a river in an unconfined aquifer. For the boundary-value problem investigated, we find that a unique solution exists for all negative well discharges. For positive discharges, a maximum value exists which corresponds to the formation of a cusp on the free surface. For positive discharges less than the maximum, the solution is not unique, consisting of two alternate configurations of the free surface. One solution includes a stable free surface on a single-valued physical plane, while the alternate solution includes a looped free surface lying on two sheets of a Riemann surface. Imposing a stability condition on the free surface results in a unique solution to the problem. We use the solution to investigate the behavior of the free surface under varying well discharges to identify stable pumping rates and predict well yield. In particular, we examine the well yield and the stability of the free surface when the head in the horizontal well is maintained at the top of the well screen. This condition is shown to produce a stable free surface for a wide range of well radii; the stability is independent of the hydraulic conductivity of the aquifer, the location of the well, or the presence of a skin resistance at the well. 相似文献
16.
基于不同测量高度重力场及其梯度数据可同时对应同一场源并用于反演场源位置的分析原理,拓展不同高度场数据在欧拉反褶积法中的应用范围.首先,立足于对欧拉反褶积方法的理论研究基础,提出不同高度数据融合联合欧拉反演公式.其次,在理论模型上对多种高度数据联合反演做了测试分析计算,验证了不同高度场数据融合联合欧拉反褶积法能够改善位场解释中单一观测面数据计算带来的解的发散问题,收敛过程由此改善.最后,将本文方法应用于龙门山地区实际重力数据的解释,获得了研究区断裂分布特征. 相似文献
17.
Mariya I. Yurkina 《Studia Geophysica et Geodaetica》1996,40(1):9-13
Summary On the basis of the fundamental relations of the Molodensky's Earth's figure theory (1945), admitting the inequality of the
gravity potentials at the Major Vertical Datum W0 and on the surface of the reference level ellipsoid U0, and taken into account that potential W0 enters into equations directly, it is recomended, W0 should be adopted as a primary geodetic constant. Parameters of the best fitting ellipsoid are not needed for the solution
of geodetic problems and for the investigation of the Earth's gravity field. The reason for requiring the reference and actual
fields be close is only that the boundary-value problem can be solved in the linear approximation.
Dedicated to the Memory of M.S. Molodensky
Contribution to the I.A.G. Special Commission SC3 Fundamental Constants (SCFC). 相似文献
18.
This paper presents a survey of recent work on the gravimetric geoid. The gravity models considered are those published in the past few years by the Goddard Space Flight Center (GSFC), the Smithsonian Astrophysical Observatory (SAO) and the Ohio State University (OSU). Comparisons and analyses have been carried out through the ose of detailed gravimetric geoids which we have computed by combining the above-mentioned models with a set of 26 000, 1ox1o mean free air gravity anomalies. The accuracy of the detailed gravimetric geoid computed using the most recent Goddard Earth Model (GEM-6) in conjunction with the set 1ox1o mean free air gravity anomalies is assessed at 2 m on the continents of North America, Europe And Australia, 2 to 5 m in the North-East Pacific and North Atlantic areas and 5 to 10 m in other areas where surface gravity data are sparse. Rms differences between this detailed geoid and the detailed geoids computed using the other satellite gravity fields in conjunction with same set of surface data range from 3 to 7 m. The maximum differences in all cases occurred in the Southern Hemisphere where surface data and satellite observations are sparse. These differences exhibited wavelengths of approximately 30o to 50o in longitude. Detailed geoidal heights were also computed with models truncated to 12th degree and order as well as 8th degree and order. This truncation resulted in a reduction of the rms differences to a maximum of 5 m. Comparisons have been made with the astrogeodetic data of Rice (United States), Bomford (Europe), and Mather (Australia) and also with geoidal heights from satellite solutions for geocentric station coordinates in North America and the Caribbean. 相似文献
19.
All active midocean ridges show a uniform relationship between depth and age of the oceanic crust. Recently, it has been shown by numerical methods that convective flow in a Newtonian fluid will have a positive gravity anomaly and an upward surface deformation associated with an ascending limb. If there is thermal convection in the upper mantle, these calculations predict that there may be a correlation between free air gravity anomalies and differences from the uniform relationship between oceanic depth and age. To investigate such a correlation, we considered the crestal elevation and free air gravity anomaly over the crest of the midocean ridges. It has been suggested that the differences from the depth versus age relationship are related to spreading rate. Thus, we also considered a correlation between crestal elevation and changes in rate along the ridge axis.We found a positive correlation between free air gravity and differences in crestal depth of the midocean ridge system. We found no correlation between spreading rate and gravity and no uniform relationship which holds in all the oceans between spreading rate and observed crestal depths.The long wavelength gravity anomalies which are correlated with the differences in crestal depth cannot be supported by an 80 km thick lithosphere. Thus, they are considered evidence of flow within the aesthenosphere. Further, the correlation between gravity anomaly and differences in crestal depth has the same sign and gradient as predicted by the investigations of convection in a Newtonian fluid. 相似文献
20.
Martinec and Grafarend (1997) have shown how the construction of Green's function in the Stokes boundary-value problem with gravity data distributed on an ellipsoid of revolution is approached in the O(e
0
2
)-approximation. They have also expressed the ellipsoidal Stokes function describing the effect of ellipticity of the boundary as a finite sum of elementary functions. We present an effective method of avoiding the singularity of spherical and the ellipsoidal Stokes functions, and also an analytical expression for the ellipsoidal Stokes integral around the computational point suitable for numerical solution. We give the numerical results of solving the ellipsoidal Stokes boundary-value problem and their difference with respect to the spherical Stoke boundary-value problem. 相似文献