Two deterministic and three stochastic modifications of Stokes’s formula: a case study for the Baltic countries     

A. Ellmann 《Journal of Geodesy》2005,79(1-3):11-23

In regional gravimetric geoid determination, it is customary to use the modified Stokes formula that combines local terrestrial data with a global geopotential model. This study compares two deterministic and three stochastic modification methods for computing a regional geoid over the Baltic countries. The final selection of the best modification method is made by means of two accuracy estimates: the expected global mean square error of the geoid estimator, and the statistics of the post-fit residuals between the computed geoid models and precise GPS-levelling data. Numerical results show that the modification methods tested do not provide substantially different results, although the stochastic approaches appear formally better in the selected study area. The 2.8–5.3 cm (RMS) post-fit residuals to the GPS-levelling points indicate the suitability of the new geoid model for many practical applications. Moreover, the numerical comparisons reveal a one-dimensional offset between the regional vertical datum and the geoid models based upon the new GRACE-only geopotential model GGM01s. This gives an impression of a greater reliability of the new model compared to the earlier, EGM96-based and somewhat tilted regional geoid models for the same study area.  相似文献   

The ellipsoidal correction to the Stokes kernel for precise geoid determination     

M. Najafi-Alamdari  S. R. Emadi  K. Moghtased-Azar 《Journal of Geodesy》2006,80(12):675-689

Solving the geodetic boundary-value problem (GBVP) for the precise determination of the geoid requires proper use of the fundamental equation of physical geodesy as the boundary condition given on the geoid. The Stokes formula and kernel are the result of spherical approximation of this fundamental equation, which is a violation of the proper relation between the observed quantity (gravity anomaly) and the sought function (geoid). The violation is interpreted here as the improper formulation of the boundary condition, which implies the spherical Stokes kernel to be in error compared with the proper kernel of integral transformation. To remedy this error, two correction kernels to the Stokes kernel were derived: the first in both closed and spectral forms and the second only in spectral form. Contributions from the first correction kernel to the geoid across the globe were [−0.867 m, +1.002 m] in the low-frequency domain implied by the GRIM4-S4 purely satellite-derived geopotential model. It is a few centimeters, on average, in the high-frequency domain with some exceptions of a few meters in places of high topographical relief and sizable geological features in accordance with the EGM96 combined geopotential model. The contributions from the second correction kernel to the geoid are [−0.259 m, +0.217 m] and [−0.024 m, +0.023 m] in the low- and high-frequency domains, respectively.  相似文献   

西藏与南亚地区大地水准面的场源及其动力效应初探          下载免费PDF全文

张赤军  方剑 《地球物理学报》1996,39(Z1):114-120

根据西藏与南亚地区重力大地水准面的分布，对其相应的场源作了分析．其中除分别来自地球表层的地质构造和深部的核幔起伏外，剩下的主要部分可能是由密度较小的地幔热柱所形成，地幔热柱中心位置处于东经８２°和纬度０°附近，这和该处的热流密度异常位置十分吻合．所反演的热柱有关参数：上顶深１００ｋｍ，下底深２８５０ｋｍ，半径１００ｋｍ，与周围地幔的密度差为３０ｋｇ／ｍ^３；另外，还讨论了在对流状态下该地幔热柱引起的动力效应，计算出对流速度和剪切力分别为４．８－４８ｃｍ／ａ和１１－１１０ＭＰａ，该力对我国岩石层应力场的构成和青藏高原的隆起有重要影响．  相似文献   

Updating and computing the geoid using two dimensional fast Hartley transform and fast T transform     

M. E. Ayhan 《Journal of Geodesy》1997,71(6):362-369

In the analyses of 2D real arrays, fast Hartley (FHT), fast T (FTT) and real-valued fast Fourier transforms are generally preferred in lieu of a complex fast Fourier transform due to the advantages of the former with respect to disk storage and computation time. Although the FHT and the FTT in one dimension are identical, they are different in two or more dimensions. Therefore, first, definitions and some properties of both transforms and the related 2D FHT and FTT algorithms are stated. After reviewing the 2D FHT and FTT solutions of Stokes' formula in planar approximation, 2D FHT and FTT methods are developed for geoid updating to incorporate additional gravity anomalies. The methods are applied for a test area which includes a 64×64 grid of 3^′×3^′ point gravity anomalies and geoid heights calculated from point masses. The geoids computed by 2D FHT and FTT are found to be identical. However, the RMS value of the differences between the computed and test geoid is ±15 mm. The numerical simulations indicate that the new methods of geoid updating are practical and accurate with considerable savings on storage requirements. Received: 15 February 1996; Accepted: 22 January 1997  相似文献   

Refinement of the geopotential scale factorR 0 on     

David Nesvorný  Zdislav Šíma 《Earth, Moon, and Planets》1994,65(1):79-88

Altimetric measurements of the GEOSAT satellite were used for the determination of geopotential scale factorR ₀. The geopotential valueW ₀ on the geoid surface was then computed (W ₀ =GM/R ₀).The GEOSAT Geophysical Data Records (GDR's) covering an initial period of the Exact Repeat Mission (ERM) were filtered and processed. The necessary corrections were made in order to allow a precise detection of the sea surface. Gravitational geopotential, rotation and permanent tides were taken into account and the equipotential surface which is the best approximation of the sea surface was found.The determination of the potential valueW ₀ on the mean geoid surface in this way is very promising. An associated value withW ₀ - the geopotential scale factorR ₀ - seems to be a very good Earth dimension defining quantity. Moreover, there are many possible applications ofW ₀ (R ₀) in modern geophysics.The incorporation of one of these parameters - we now recommendR ₀ - into the set of the Primary Geodetic Parameters (PGP) is discussed and suggested.  相似文献   

National height datum,the Gauss–Listing geoid level value w0 and its time variation 0 (Baltic Sea Level Project: epochs 1990.8, 1993.8, 1997.4)     

A. Ardalan  E. Grafarend  J. Kakkuri 《Journal of Geodesy》2002,76(1):1-28

 A methodology for precise determination of the fundamental geodetic parameter w ₀, the potential value of the Gauss–Listing geoid, as well as its time derivative ₀, is presented. The method is based on: (1) ellipsoidal harmonic expansion of the external gravitational field of the Earth to degree/order 360/360 (130 321 coefficients; http://www.uni-stuttgard.de/gi/research/ index.html projects) with respect to the International Reference Ellipsoid WGD2000, at the GPS positioned stations; and (2) ellipsoidal free-air gravity reduction of degree/order 360/360, based on orthometric heights of the GPS-positioned stations. The method has been numerically tested for the data of three GPS campaigns of the Baltic Sea Level project (epochs 1990.8,1993.4 and 1997.4). New w ₀ and ₀ values (w ₀=62 636 855.75 ± 0.21 m²/s², ₀=−0.0099±0.00079 m²/s² per year, w ₀/&γmacr;=6 379 781.502 m,₀/&γmacr;=1.0 mm/year, and &γmacr;= −9.81802523 m²/s²) for the test region (Baltic Sea) were obtained. As by-products of the main study, the following were also determined: (1) the high-resolution sea surface topography map for the Baltic Sea; (2) the most accurate regional geoid amongst four different regional Gauss–Listing geoids currently proposed for the Baltic Sea; and (3) the difference between the national height datums of countries around the Baltic Sea. Received: 14 August 2000 / Accepted: 19 June 2001  相似文献   

中国及邻区大地水准面异常的场源深度探讨   总被引：7，自引：0，他引：7       下载免费PDF全文

方剑  许厚泽 《地球物理学报》2002,45(1):42-48

利用中国及邻区地形、地震层析成像、沉积层底面、Moho面及岩石层底面资料,正演计算出中国及邻区岩石圈大地水准面异常;再从全阶大地水准面异常中扣除正演模拟得到的岩石圈大地水准面异常与不同阶次波段的大地水准面进行比较,寻求表示中国及邻区地幔物质不均匀的大地水准面异常的最佳阶次为2-60阶. 结果表明,对应于岩石圈的大地水准面异常的重力位球谐函数阶数为61-20阶;下地幔重力位球谐函数阶数为2-6阶;而-60阶重力位球谐函数则表示中国及邻近区域上地幔大地水准面异常.  相似文献   

二次曲面拟合法在区域似大地水准面精化中的应用   总被引：1，自引：0，他引：1  

雷伟伟  郑红晓 《测绘与空间地理信息》2008,31(6)

以某市为例,介绍了二次曲面拟合法在区域似大地水准面精化中的应用,拟合得到厘米级的似大地水准面模型,并给出有益结论.  相似文献   

GPS RTK与区域大地水准面精化技术代替数字测图中的控制测量的应用探讨     

姜建慧 《现代测绘》2008,31(2):19-21

通过GPS RTK与区域大地水准面精化技术和导线测量技术在大比例尺地形测量控制中得到的成果的对比试验,表明GPS RTK技术在精化大地水准面基础上可以代替数字测图中的控制测量,并提出注意的问题。  相似文献   

A rapid method to map the crustal and lithospheric thickness using elevation, geoid anomaly and thermal analysis. Application to the Gibraltar Arc System, Atlas Mountains and adjacent zones   总被引：1，自引：0，他引：1  

J. Fullea  M. Fernndez  H. Zeyen  J. Vergs 《Tectonophysics》2007,430(1-4):97-117

We present a method based on the combination of elevation and geoid anomaly data together with thermal field to map crustal and lithospheric thickness. The main assumptions are local isostasy and a four-layered model composed of crust, lithospheric mantle, sea water and the asthenosphere. We consider a linear density gradient for the crust and a temperature dependent density for the lithospheric mantle. We perform sensitivity tests to evaluate the effect of the variation of the model parameters and the influence of RMS error of elevation and geoid anomaly databases. The application of this method to the Gibraltar Arc System, Atlas Mountains and adjacent zones reveals the presence of a lithospheric thinning zone, SW–NE oriented. This zone affects the High and Middle Atlas and extends from the Canary Islands to the eastern Alboran Basin and is probably linked with a similarly trending zone of thick lithosphere constituting the western Betics, eastern Rif, Rharb Basin, and Gulf of Cadiz. A number of different, even mutually opposite, geodynamic models have been proposed to explain the origin and evolution of the study area. Our results suggest that a plausible slab-retreating model should incorporate tear and asymmetric roll-back of the subducting slab to fit the present-day observed lithosphere geometry. In this context, the lithospheric thinning would be caused by lateral asthenospheric flow. An alternative mechanism responsible for lithospheric thinning is the presence of a hot magmatic reservoir derived from a deep ancient plume centred in the Canary Island, and extending as far as Central Europe.  相似文献