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1.
Jitka Hájková 《Studia Geophysica et Geodaetica》2011,55(3):515-528
A mathematical model used for determination of a local geoid model by combining airborne gravity disturbances and the Earth
Gravitational Model 2008 (EGM08) is shortly reviewed. The precision of the estimated local geoid model of Taiwan is tested
by its comparison with the “real” geoid at Global Satellite Navigation Systems (GNSS)/levelling points. The same comparison
at GNSS/levelling points is done for the geoid evaluated only by using EGM08. Conclusions concerning a rate of improvement
of the “global” geoid from EGM08 using the “local” geoid from airborne gravity data are presented. 相似文献
2.
The EGM08 geopotential model complete to degree and order 2159 was used in a remove-compute-restore (RCR) method for the geoid
computation in the State of Rio de Janeiro, Brazil. Terrain and indirect effect corrections were computed using a 6-arcsec
resolution DTE, derived from the TOPODATA Project (Shuttle Radar Topography Mission data) raised by the National Institute
for Space Research. INPE, Brazil. We applied Voronoi/Delaunay discretisations for discrete Stokes integration. In these schemes,
target area is partitioned into polygons/triangles, respectively, and the computation is carried out by point-wise numerical
integration and no gridding is mandatory. For both procedures, the cells were produced using either observed gravity data
combined with gridded Bouguer derived information. Particularly in Delaunay scheme, as the gravity anomalies are interpolated
into the triangular cells, and geoid undulations are computed for their vertices, Stokes function singularity was gone. Externally
estimated errors resulting from a comparison with GPS/leveling data were presented for both the schemes and classical ones,
as well as for the EGM08 undulations. They yielded RMS differences equal to 0.105 m, 0.110 m, 0.110 m, 0.115 m and 0.228 m,
respectively, for Voronoi, Delaunay, Voronoi/Delaunay with gridded-data alone and EGM08, computed between 32 GPS/leveling
points. 相似文献
3.
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
4.
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
5.
6.
The variable elevation of the groundwater table in the St. Louis area was estimated using multiple linear regression (MLR), ordinary kriging, and cokriging as part of a regional program seeking to assess liquefaction potential. Surface water features were used to determine the minimum water table for MLR and supplement the principal variables for ordinary kriging and cokriging. By evaluating the known depth to the water and the minimum water table elevation, the MLR analysis approximates the groundwater elevation for a contiguous hydrologic system. Ordinary kriging and cokriging estimate values in unsampled areas by calculating the spatial relationships between the unsampled and sampled locations. In this study, ordinary kriging did not incorporate topographic variations as an independent variable, while cokriging included topography as a supporting covariable. Cross validation suggests that cokriging provides a more reliable estimate at known data points with less uncertainty than the other methods. Profiles extending through the dissected uplands terrain suggest that: (1) the groundwater table generated by MLR mimics the ground surface and elicits a exaggerated interpolation of groundwater elevation; (2) the groundwater table estimated by ordinary kriging tends to ignore local topography and exhibits oversmoothing of the actual undulations in the water table; and (3) cokriging appears to give the realistic water surface, which rises and falls in proportion to the overlying topography. The authors concluded that cokriging provided the most realistic estimate of the groundwater surface, which is the key variable in assessing soil liquefaction potential in unconsolidated sediments. 相似文献
7.
A method for splitting sea surface height measurements from satellite altimetry into geoid undulations and sea surface topography is presented. The method is based on a combination of the information from altimeter data and a dynamic sea surface height model. The model consists of geoid undulations and a quasi-geostrophic model for expressing the sea surface topography. The goal is the estimation of those values of the parameters of the sea surface height model that provide a least-squares fit of the model to the data. The solution is accomplished by the adjoint method which makes use of the adjoint model for computing the gradient of the cost function of the least-squares adjustment and an optimization algorithm for obtaining improved parameters. The estimation is applied to the North Atlantic. ERS-1 altimeter data of the year 1993 are used. The resulting geoid agrees well with the geoid of the EGM96 gravity model. 相似文献
8.
以湖南地区为例,利用超高阶地球重力位模型EGM2008计算了研究区的重力大地水准面,并采用棱柱体公式和球体公式相结合的方法分别进行了完全地形改正和Airy-Heiskanen局部均衡改正,得到布格大地水准面和均衡大地水准面.对三种大地水准面进行不同波长分量的分离处理,得到包含不同深度异常信息的剩余大地水准面,并结合其他地球物理资料对研究区进行了详细的地球物理解释.结果表明,剩余重力大地水准面可以有效地反映出研究区内的深部构造特征,如深大断裂带分布、构造块体位置、上地幔密度横向分布等,但对地壳内异常结构反映不明显;研究区岩石圈密度变化相对平缓,厚度由东向西增加;根据剩余均衡大地水准面及研究区Airy局部均衡莫霍面,可以大致推测出研究区的莫霍面起伏形态以及均衡状态,可作为一种有用的参考信息. 相似文献
9.
National height reference systems have conventionally been linked to the local mean sea level, observed at individual tide gauges. Due to variations in the sea surface topography, the reference levels of these systems are inconsistent, causing height datum offsets of up to ±1–2 m. For the unification of height systems, a satellite-based method is presented that utilizes global geopotential models (GGMs) derived from ESA’s satellite mission Gravity field and steady-state Ocean Circulation Explorer (GOCE). In this context, height datum offsets are estimated within a least squares adjustment by comparing the GGM information with measured GNSS/leveling data. While the GNSS/leveling data comprises the full spectral information, GOCE GGMs are restricted to long wavelengths according to the maximum degree of their spherical harmonic representation. To provide accurate height datum offsets, it is indispensable to account for the remaining signal above this maximum degree, known as the omission error of the GGM. Therefore, a combination of the GOCE information with the high-resolution Earth Gravitational Model 2008 (EGM2008) is performed. The main contribution of this paper is to analyze the benefit, when high-frequency topography-implied gravity signals are additionally used to reduce the remaining omission error of EGM2008. In terms of a spectral extension, a new method is proposed that does not rely on an assumed spectral consistency of topographic heights and implied gravity as is the case for the residual terrain modeling (RTM) technique. In the first step of this new approach, gravity forward modeling based on tesseroid mass bodies is performed according to the Rock–Water–Ice (RWI) approach. In a second step, the resulting full spectral RWI-based topographic potential values are reduced by the effect of the topographic gravity field model RWI_TOPO_2015, thus, removing the long to medium wavelengths. By using the latest GOCE GGMs, the impact of topography-implied gravity signals on the estimation of height datum offsets is analyzed in detail for representative GNSS/leveling data sets in Germany, Austria, and Brazil. Besides considerable changes in the estimated offset of up to 3 cm, the conducted analyses show that significant improvements of 30–40% can be achieved in terms of a reduced standard deviation and range of the least squares adjusted residuals. 相似文献
10.
Modelling the fine-structure of the geoid: Methods,data requirements and some results 总被引：2，自引：0，他引：2
Rene Forsberg 《Surveys in Geophysics》1993,14(4-5):403-418
The requirements for precise geoid models on local and regional scales have increased in recent years, primarily due to the ongoing developments in height determination by GPS on land, but also due to oceanographic requirements in using satellite altimetry for recovering dynamic sea-surface topography. Suitable methods for geoid computations from gravity data include Stokes integration, FFT methods, and least-squares collocation. Especially the FFT methods are efficient in handling large amounts of gravity data, and new variants of the methods taking earth curvature rigorously into account provide attractive methods for obtaining continental-scale, high-resolution geoid models. The accuracy of such models may be from 2–5 cm locally, to 50–100 cm on regional scales, depending on gravity data coverage, long wave-length gravity field errors, and datum problems. When approaching the cm-level geoid basic geoid definition questions (geoid or quasigeoid?) become very significant, especially in rugged areas. In the paper the geoid modelling methods and problems are reviewed, and some investigations on local data requirements for cm-level geoid prediction are presented. Some actual results are presented from Scandinavia, where a recent regional high-resolution geoid model yields apparent accuracies of 2–10 cm over GPS baselines of 50 to 2000 km. 相似文献
11.
So far the recent Earth's gravity model, EGM08, has been successfully applied for different geophysical and geodetic purposes. In this paper, we show that the computation of geoid and gravity anomaly on the reference ellipsoid is of essential importance but error propagation of EGM08 on this surface is not successful due to downward continuation of the errors. Also we illustrate that some artefacts appear in the computed geoid and gravity anomaly to lower degree and order than 2190. This means that the role of higher degree harmonics than 2160 is to remove these artefacts from the results. Consequently, EGM08 must be always used to degree and order 2190 to avoid the numerical problems. 相似文献
12.
Angel Martin Ana Belén Anquela Jorge Padín José Luís Berné 《Studia Geophysica et Geodaetica》2010,54(3):347-366
A new generation of global geopotential models (GGM) is being developed. These solutions offer a file with fully-normalized
spherical harmonic coefficients of the Earth’s gravitational potential up to a degree greater than 2000 with very low commission
errors. This paper analyses the recent Earth Gravitational Model EGM2008, developed up to degree and order 2159 with additional
coefficients to degree 2190 and order 2159, which means recovering the gravitational field up to approximately 20 km wavelengths.
223 GPS/levelling points of the new Spanish High Precision Levelling Network in the Valencia region (Eastern Spain) are used
as external tool for evaluation in that particular region. The same evaluation has been performed to other different global
(EGM96 and EIGENCG03C), continental (EGG97), regional (IGG2005 and IBERGEO2006) and local (GCV07) geoid models for comparison
purposes only. These comparisons show that EGM2008 is the geoid model that best fits to the GPS/levelling data in that region. 相似文献
13.
传统动力学法的观测方程以6个初始轨道参数和先验力模型为初值进行线性化,其线性化误差随积分弧长拉长而增大.本文直接以重力卫星的几何观测轨道为初值进行线性化,其线性化误差与轨道弧长无关,且不需要初始重力场模型和初始轨道参数.导出了基于卫星轨道观测值反演重力场模型的相关公式,利用JPL公布的RL02版本2008年全年的GRACE双星轨道数据和加速度计数据解算了90阶次的地球重力场模型TJGRACE01S,并以EGM2008模型为基准与其他模型进行了比较分析,结果表明:TJGRACE01S模型直到90阶次的大地水准面累积误差为17.6 cm,优于同阶次的EIGEN-CHAMP03S和EIGEN-CHAMP05S模型,前27阶位系数整体精度优于EIGEN-GRACE01S,前15阶位系数整体精度与EIGEN-GRACE02S模型精度大致相当.利用美国8221个GPS水准点数据的分析结果也表明,本文模型也优于同阶次的EIGEN-CHAMP03S和EIGEN-CHAMP05S模型. 相似文献
14.
This work presents a validation study of global geopotential models (GGM) in the region of Fagnano Lake, located in the southern Andes. This is an excellent area for this type of validation because it is surrounded by the Andes Mountains, and there is no terrestrial gravity or GNSS/levelling data. However, there are mean lake level (MLL) observations, and its surface is assumed to be almost equipotential. Furthermore, in this article, we propose improved geoid solutions through the Residual Terrain Modelling (RTM) approach. Using a global geopotential model, the results achieved allow us to conclude that it is possible to use this technique to extend an existing geoid model to those regions that lack any information (neither gravimetric nor GNSS/levelling observations). As GGMs have evolved, our results have improved progressively. While the validation of EGM2008 with MLL data shows a standard deviation of 35 cm, GOCO05C shows a deviation of 13 cm, similar to the results obtained on land. 相似文献
15.
From the late 1990s, many studies on local geoid construction have been made in South Korea. However, the precision of the previous geoid has remained about 15 cm due to distribution and quality problems of gravity and GPS/levelling data. Since 2007, new land gravity data and GPS/levelling data have been obtained through many projects such as the Korean Land Spatilaization, Unified Control Point and Gravity survey on the Benchmark. The newly obtained data are regularly distributed to a certain degree and show much better improvement in their quality. In addition, an airborne gravity survey was conducted in 2008 to cover the Korean peninsula (South Korea only). Therefore, it is expected that the precision of the geoid could be improved. In this study, the new South Korean gravimetric geoid and hybrid geoid are presented based on land, airborne, ship‐borne, altimeter gravity data, geopotential model and topographic data. As for the methodology, the general remove‐restore approach was applied with the best chosen parameters in order to produce a precise local geoid. The global geopotential model EGM08 was used to remove the low‐frequency components using degree and order up to 360 and the short wavelength part of the gravity signal was dealt with by using the Shuttle Radar Topography Mission data. The parameters determined empirically in this study include for Stokes’ integral 0.5° and for Wong‐Gore kernel 110–120°, respectively and 10 km for both the Bjerhammar sphere depth and attenuation factor. The final gravimetric geoid in South Korea ranges from 20–31 m with a precision of 5.45 cm overall compared to 1096 GPS/levelling data. In addition, the South Korean hybrid geoid produces 3.46 cm and 3.92 cm for degrees of fitness and precision, respectively and a better statistic of 2.37 cm for plain and urban areas was achieved. The gravimetric and hybrid geoids are expected to improve further when the refined land gravity data are included in the near future. 相似文献
16.
Integrating the deflections of the vertical along the flight line can yield geoid profiles which are valuable in the study of geodesy and geophysics, fortunately, the deflections can be measured directly by vector gravimetry. Airborne vector gravimetry using a Strapdown Inertial Navigation System and the Global Navigation Satellite System (SINS/GNSS) has shown promising results in previous studies. However, the quality of the SINS and GNSS is a major limitation; in particular, the attitude errors induced by the gyros will result in large measurement errors to the horizontal components of the gravity disturbance, and these measurement errors represent the behavior of low-frequency trend. An airborne vector gravimetry method used to remove the bias and low-frequency trends in the gravity disturbance estimated for each survey line has been developed. This method uses the horizontal components of the gravity disturbance computed from EGM2008 (Earth Gravitational Model 2008) as a reference. Firstly, the horizontal measurement results obtained from the gravimeter are divided into high- and low-frequency components according to the resolution of the EGM2008, and then, the bias and low-frequency trends of the low-frequency components are corrected using a linear fit to the EGM2008 reference data. Finally, the ultimate results can be acquired after combining the high-frequency components and the corrected low-frequency components. The data used was obtained from the SGA-WZ, which is the first strapdown airborne gravimeter developed in China. The results of this method are promising. The internal accuracy of the gravity disturbance's horizontal components for repeated survey lines exceeds 3.5 mGal, and the corresponding resolution is approximately 4.8 km based on 160-s data smoothing and an airplane averaging speed of approximately 216 km/h. After applying the WCF (Wavenumber Correlation Filter), the internal accuracy of the horizontal components exceeds 2 mGal. This can satisfy the requirement of the application in geodesy and solid earth geophysics. 相似文献
17.
An alternative “direct method” to “mean dynamic topography” (MDT) computations using satellite altimetry-derived “mean sea
surface” (MSS) and “global geopotential model” (GGM), without direct application of the geoid, is devised. The developed approach,
which is based on derivation of an equipotential surface of the gravity field of the Earth that fits to global MSS in least
squares sense, is formulated via a constrained optimization problem. The validity of our method is numerically tested by computing
a global MDT model based on DNSC08 MSS model and EGM2008 GGM as input data. 相似文献
18.
V. N. Koneshov V. B. Nepoklonov O. V. Polovnev 《Izvestiya Physics of the Solid Earth》2017,53(1):108-115
The results of the theoretical and experimental research on the technique for refining the global Earth geopotential models such as EGM2008 in the continental regions are presented. The discussed technique is based on the high-resolution satellite data for the Earth’s surface topography which enables the allowance for the fine structure of the Earth’s gravitational field without the additional gravimetry data. The experimental studies are conducted by the example of the new GGMplus global gravity model of the Earth with a resolution about 0.5 km, which is obtained by expanding the EGM2008 model to degree 2190 with the corrections for the topograohy calculated from the SRTM data. The GGMplus and EGM2008 models are compared with the regional geoid models in 21 regions of North America, Australia, Africa, and Europe. The obtained estimates largely support the possibility of refining the global geopotential models such as EGM2008 by the procedure implemented in GGMplus, particularly in the regions with relatively high elevation difference. 相似文献
19.
JIANG Tao LI JianCheng DANG YaMin ZHANG ChuanYin WANG ZhengTao KE BaoGui 《中国科学:地球科学(英文版)》2014,57(7):1637-1644
Regional gravity field modeling with high-precision and high-resolution is one of the most important scientific objectives in geodesy,and can provide fundamental information for geophysics,geodynamics,seismology,and mineral exploration.Rectangular harmonic analysis(RHA)is proposed for regional gravity field modeling in this paper.By solving the Laplace’s equation of gravitational potential in local Cartesian coordinate system,the rectangular harmonic expansions of disturbing potential,gravity anomaly,gravity disturbance,geoid undulation and deflection of the vertical are derived,and so are the formula for signal degree variance and error degree variance of the rectangular harmonic coefficients(RHC).We also present the mathematical model and detailed algorithm for the solution of RHC using RHA from gravity observations.In order to reduce the edge effects caused by periodic continuation in RHA,we propose the strategy of extending the size of computation domain.The RHA-based modeling method is validated by conducting numerical experiments based on simulated ground and airborne gravity data that are generated from geopotential model EGM2008 and contaminated by Gauss white noise with standard deviation of 2 mGal.The accuracy of the 2.5′×2.5′geoid undulations computed from ground and airborne gravity data is 1 and 1.4cm,respectively.The standard error of the gravity disturbances that downward continued from the flight height of 4 km to the geoid is only 3.1 mGal.Numerical results confirm that RHA is able to provide a reliable and accurate regional gravity field model,which may be a new option for the representation of the fine structure of regional gravity field. 相似文献
20.
Four new gravity field models from GOCE, two of them combined with GRACE, are compared here with EGM2008. The objectives are to look into the differences in consecutive ranges of the spherical harmonic expansion globally as well as in selected geographical regions and in the regions of the various data sources used for EGM2008. In general, GOCE is able to contribute to improved global gravity models in the spherical harmonic range between 120 and 200 (and above). The agreement between EGM2008 and the GOCE models is very good in well-surveyed regions such as North America, Europe and Australia, with geoid RMS-differences on the order of 4–6 cm. In other regions, where the surface gravity data available for the development of EGM2008 were poor, such as South America, Africa, South-East Asia or China the RMS-differences are on a level of 30 cm. Here GOCE leads to a significant improvement. These findings are confirmed by the analysis of the areas of the various EGM2008 data sources. In the regions of the so-called “fill-in” data of EGM2008 RMS-geoid height differences are high. In Antarctica GOCE also gives important improvements in terms of spatial resolution and accuracy. In general, the agreement between EGM2008 and the GOCE-models up to degree and order (d/o) 200 is good, with a global (excluding the polar gaps of GOCE orbits, throughout) geoid difference RMS of 11 cm, in the ocean areas 8 cm and 20 cm in the continental areas. GOCE models are better suited for ocean circulation studies because no prior ocean information enters into the data reduction process, as it is the case when deducing gravity anomalies from an altimetric mean sea surface. On the other hand, the good consistency between GOCE-models and EGM2008 in ocean areas very likely indicates that the influence of ocean circulation information on EGM2008 is rather small. The four tested GOCE models behave similarly except at the highest latitudes where GOCE lacks data due to its orbit inclination of 96.5° and some form of regularization which has to be applied. 相似文献