Recent geoid computations for the Hellenic area

New geoid computations for the Hellenic area are carried out using (a) gravity anomalies for the land area available from old and new data bases, and gravity data for the sea area derived from altimetry and a recent digitization of sea gravity maps, and (b) a 1km × 1km digital terrain model. The EGM96 geopotential model is used as the reference field. In order to assess the quality of the computed geoid heights in the continental area comparisons were carried out with GPS/leveling heights and the recently available European Gravimetric Geoid EGG97. In the sea area the geoid heights were compared with sea surface heights of the recent and more accurate TOPEX/POSEIDON (T/P) altimetry mission. At the end of this article the improvement of the data bases is discussed and some plans for further development in the methodological schedule are pointed out.     

EGY-HGM2016: an improved hybrid local geoid model for Egypt based on the combination of GOCE-based geopotential model with gravimetric and GNSS/levelling measurements

An improved hybrid gravimetric geoid model for Egypt, EGY-HGM2016, has been recently computed implementing the least-squares collocation (LSC) method through the remove-compute-restore (RCR) procedure. The computation of EGY-HGM2016 involves different datasets in terms of gravity anomalies determined from the GOCE (gravity field and steady-state ocean circulation explorer)-based global geopotential model (SPW-R4) up to d/o 200 and EGM2008 from d/o 201 to 720 combined with terrestrial gravity datasets in terms of 2140 gravity field anomalies and about 121,480 marine surface gravity anomalies. In addition, orthometric heights from 17 GPS/levelling measurements have been considered during the modelling process to improve the determination of the hybrid gravimetric geoid over the Egyptian region. The EGY-HGM2016 model estimated over Egypt provides geoid heights that are ranging from 7.677 to 21.095 m with a standard deviation (st. dev.) of about 2.534 m in the northwest of the country excluding the involvement of the orthometric heights from GPS/levelling measurements. When the later dataset is considered during the implementation of LSC process, hybrid residual height anomalies ranging from ?1.5 to +0.9 m, with a mean of 0.22 m and a st. dev. of 0.17 m, are obtained. Comparison of the predicted hybrid gravimetric geoid with the corresponding ones obtained from EGM2008, GOCE-based SPW R4 model, and GPS/levelling reveals considerable improvements of our EGY-HGM2016 model over Egypt.     

Precision assessment of the orthometric heights determination in northern part of Algeria by combining the GPS data and the local geoid model

The main purpose of this article is to discuss the use of GPS positioning together with a gravimetrically determined geoid, for deriving orthometric heights in the North of Algeria, for which a limited number of GPS stations with known orthometric heights are available, and to check, by the same opportunity, the possibility of substituting the classical spirit levelling. For this work, 247 GPS stations which are homogeneously distributed and collected from the international TYRGEONET project, as well as the local GPS/Levelling surveys, have been used. The GPS/Levelling geoidal heights are obtained by connecting the points to the levelling network while gravimetric geoidal heights were interpolated from the geoid model computed by the Geodetic Laboratory of the National Centre of Spatial Techniques from gravity data supplied by BGI. However, and in order to minimise the discordances, systematic errors and datum inconsistencies between the available height data sets, we have tested two parametric models of corrector surface: a four parameter transformation and a third polynomial model are used to find the adequate functional representation of the correction that should be applied to the gravimetric geoid. The comparisons based on these GPS campaigns prove that a good fit between the geoid model and GPS/levelling data has been reached when the third order polynomial was used as corrector surface and that the orthometric heights can be deducted from GPS observations with an accuracy acceptable for the low order levelling network densification. In addition, the adopted methodology has been also applied for the altimetric auscultation of a storage reservoir situated at 40 km from the town of Oran. The comparison between the computed orthometric heights and observed ones allowed us to affirm that the alternative of levelling by GPS is attractive for this auscultation.     

Estimation of gravity field parameters by a multiple input/output system

The recovery of gravity field parameters using various heterogeneous data is performed according to the input/output system theory (IOST) method. The combination of different data sets is carried out by the application of a multiple input — multiple output system. The theory of the algorithm is presented and some conclusions on the assumptions made for the data properties are drawn. Comparisons between a combined system and individual uncorrelated systems are made and the proper use of the data sets in each case is discussed. Finally, an application is presented, where input data, such as shipborne gravity anomalies and sea surface heights (SSHs) derived from different satellite missions, are optimally combined in order to estimate marine geoid heights and sea surface topography (SST).     

海洋卫星测高技术和海洋地形试验TOPEX卫星计划

ＴＯＰＥＸ卫星是目前精度最高的海洋测高卫星，利用ＳＬＲ技术确定的ＴＯＰＥＸ卫星轨道径向精度达到２．８ｃｍ，这使它可以有效地监测全球的海洋地形。ＴＯＰＥＸ卫星主要用于全球的海面变化和洋流研究。利用ＴＯＰＥＸ资料可以得到新的地球引力场，海洋大地水准面和海潮模型。     

Topography from land radar altimeter data: Possibilities and restrictions

Whilst satellite radar altimetry has been widely utilised over both ocean and ice surfaces for topographic mapping, applications over land have received relatively little attention. This is in part due to the complex nature of echoes returned from rapidly varying topographic land surfaces, which can cause an altimeter to generate erroneous range estimates. One approach to improving these data is to retrack using a single retracker, and construct a spatial average of heights obtained to give an estimate of mean orthometric height. This paper presents results obtained using an alternative approach: reprocessing returns at all levels of complexity through an expert system, which chooses one from a series of ten reprocessing algorithms based on an analysis of the return waveform shape. The selected algorithm then recalculates the range to surface, and hence derives an orthometric height. Utilising this approach with the geodetic mission dataset from ERS-1 has generated over 100 million height points with a near-global distribution. This paper presents selected results from this research using ERS-1 geodetic mission data together with ERS-1 and ERS-2 35 day data to demonstrate the accuracy to which orthometric heights can be determined, using global crossover analysis and comparison with ground truth. The paper illustrates applications of these data including validation and error correction of Digital Elevation Models, and discusses use and limitations of direct mapping with altimetry.     

Comparison and combination of a gravimetric quasigeoid with a levelled GPS data set by statistical analysis

For GPS levelling applications, it is convenient to express the height reference surface in a suitable geodetic reference system. This can be obtained through a set of levelled GPS points. Unfortunately, available data are sparse. A gravimetric geoid is often used to interpolate the height reference surface issued from GPS and levelling. Both surfaces do not coincide exactly with each other. At this point, one must compare two realisations of the geoid, detect outliers, retrieve (if possible) the causes of the discrepancies and finally combine the two kinds of data. The paper presents some practical solutions to these problems.     

Eastern Mediterranean gravity potential and the Hellenic subduction process

Tornographic images of the Mediterranean upper mantle P-wave velocity structure have been used to analyse the gravity potential in the vicinity of the Hellenic subduction zone. The velocity anomalies are assumed to be proportional to density variations according to Birch's law. The effect of the topography on the geoid in the region is also calculated. The results indicate that the upper mantle geoid signal probably has significant amplitudes of several metres, but it correlates poorly with the observed geoid. The geoid calculated from topography correlates well, but has an amplitude that is too large in comparison with the observed geoid. The results show that an improved understanding of the Hellenic subduction zone geoid requires refinement of the Moho topography, so that the effect of this topography can be separated from the upper mantle signature.     

Geoid model in the Western Mediterranean Sea

In this work a geoid model is presented over the Western Mediterranean area. It has been computed using marine and terrestrial gravimetric data. Differences between results including several kinds of data are also studied. Altimetric data from a year of ERS-1 mission are used to test the precision of the results, overall close to the coastal line. A first approximation to the sea surface topography in the area is made with both results: altimetric mean sea surface and gravimetric geoid.     

The use of minimum curvature surface technique in geoid computation processing of Egypt

According to the wide spread use of satellite-based positioning techniques, especially Global Navigation Satellite Systems (GNSS), a greater attention has been paid to the precise determination of geoid models. As it is known, leveling measurements require high cost and long time in observation process that make it not convenient for the practical geodetic purposes. Thus obtaining the orthometric heights by GNSS is the most conventional way of determining these heights. Verifying this goal was the main objective behind the current research. The current research introduces a numerical solution of geoid modeling by applying a surface fitting for a few sparse data points of geoid undulation using minimum curvature surface (MCS). The MCS is presented for deriving a system of linear equations from boundary integral equations. To emphasize the precise applicability of the MCS as a tool for modeling the geoid in an area using GPS/leveling data, a comparison study between EGM2008 and MCS geoid models, is performed. The obtained results showed that MCS technique is a precise tool for determining the geoid in Egypt either on regional and/or local scale with law distortion at check points.     

GPS高程拟合方法精度分析

近年来人们往往利用GPS数据来确定大地高,但大地高不同于正常高,为此,利用多项式拟合与地球重力场模型相结合的数学方法,使GPS所测大地高通过这些数学模型直接转换为具有厘米精度的正常高,将该方法得到的正常高与单独利用多项式拟合和地球重力场模型得到的结果进行了比较,其差值的标准差为±38 cm。     

Local earth gravity/potential modeling using ASCH

In Geodesy, the heights of points are normally orthometric heights measured above the geoid (an equipotential surface created by the earth masses and rotation which approximately coincides with the mean sea level) or the normal heights. It is necessary to transform the GNSS/GPS measured ellipsoidal heights (h) to classical physical heights (orthometric H/Normal H). The total gravity potential of the earth (W) is the summation of two components; gravitational potential (V) by earth masses and the centrifugal potential (Ω). The centrifugal potential is directly calculated, while the gravitational potential (V) needs to be modeled globally or locally using given measurements. The global models of the earth gravitational potential/gravity models (or so-called geoid models) are mostly given using spherical harmonics (SH). A modified approach of SH was defined to fit the use of SH for regional gravity/potential modeling called spherical cap harmonics (SCH). Due to the numerical difficulties of SCH, a simplified approach of SCH is selected to be used for a combined modeling of the earth potential using a variety of observations. This approach is called the Adjusted Spherical Cap harmonics.     

Study of geoid–quasigeoid separation obtained from terrestrial gravity data and two geopotential models

In this article, separation between the geoid and the quasigeoid was calculated using ground gravity data and the data extracted from two Global Geopotential Models (GGMs). The calculated results were compared together. To do so, the authors used the terrestrial gravity data in a vast region of Iran, comprising 8,245 stations which are kindly put in our disposal by the National Cartographic Center of Iran, as well as two GGMs, namely EGM96 and EGM2008 for comparison. The calculation of the separation for GGMs was performed by iteration method. The results showed that the geoid–quasigeoid separations obtained from the terrestrial data versus the orthometric heights are nonlinear in mountainous areas, whereas they are almost linear in flat regions due to decreasing the values of the topographic potential of the masses between the earth surface and the geoid. On the other hand, in case of GGMs, a positive correlation was observed between the separations and the orthometric heights in both mountainous and flat areas. As the difference between the separations extracted by two methods in mountainous areas—especially in the regions with ragged topography—differs strongly, it is recommended to use the dense gravity and height networks for accurate determination of the geoid–quasigeoid separation in these regions. Finally, we can conclude that the mean values of separation by two global geopotential models (EGM96 and EGM2008) are 21.87 and 21.23 cm, respectively, values which did not differ strongly, whereas this mean value obtained from ground gravity data is 16.10 cm, which differs from the GGMs’ results with approximately 5 cm.     

EGMlab, a scientific software for determining the gravity and gradient components from global geopotential models

Nowadays, Global Geopotential Models (GGMs) are used as a routine stage in the procedures to compute a gravimetric geoid. The GGMs based geoidal height also can be used for GPS/levelling and navigation purposes in developing countries which do not have accurate gravimetric geoid models. Also, the GGM based gravity anomaly including the digital elevation model can be used in evaluation and outlier detections schemes of the ground gravity anomaly data. Further, the deflection of vertical and gravity gradients components from the GGMs can be used for different geodetic and geophysical interpretation purposes. However, still a complete and user-friendly software package is not available for universities and geosciences communities. In this article, first we review the procedure for determination of the basic gravity field and gradient components from the GGMs, then general MATLAB based software is presented and applied as a sample case study for determination of gravity components based on the most recent EIGEN-GL04C GRACE model in Sweden. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

The high‐resolution gravimetric geoid of North Iberia: NIBGEO

The gravimetric geoid computed in the northern part of Iberia, is presented in this paper. This computation has been performed considering two study windows fitted to the areas with higher density of gravity data, to reduce the computation errors associated to the scarcity of gravity data, as much as possible. The bad influence of a bathymetry with poorer resolution than the topography is also reduced considering the smallest marine area possible. Moreover, the computation of this gravimetric model is based on the most recent geopotential model: EIGEN‐GL04C (obtained in 2006). The method used in the computation of the new gravimetric geoid has been the Stokes integral in convolution form. The terrain correction has been applied to the gridded gravity anomalies, to obtain the corresponding reduced anomalies. Also the indirect effect has been taken into account. Thus, a new geoid model has been calculated and it is provided as a data grid in the Geodetic Reference System of 1980, distributed for the northern part of Iberia from 40 to 44 degrees of latitude and ?10 to 4 degrees of longitude, on a 161 × 561 regular grid with a mesh size of 1.5′ × 1.5′. This new geoid and the previous geoid Iberian Gravimetric Geoid 2005, are compared with the geoid undulations measured for eight points of the European Vertical Reference Network (EUVN) on Iberia. The new geoid shows an improvement in precision and reliability, fitting the geoidal heights of these EUVN points with more accuracy than the previous geoid. Moreover, this new geoid has a smaller standard deviation (12.6 cm) than that obtained by any previous geoid developed for the Iberian area up to date. This geoid obtained for the northern part of Iberia will complement the previously obtained geoid for South Spain and the Gibraltar Strait area; both geoids jointly will give a complete picture of the geoid for Spain and the Gibraltar Strait area. This new model will be useful for orthometric height determination by GPS over this study area, because it will allow orthometric height determination in the mountains and remote areas, in which levelling has many logistic problems. This new model contributes to our knowledge of the geoid, but the surrounding areas must be better known to constrain the lithospheric and mantle models.     

The role of satellite altimetry in gravity field modelling in coastal areas

During recent years altimetry from the two geodetic missions of GEOSAT and ERS-1 has enabled the derivation of high resolution near global gravity field from altimetry [Andersen and Knudsen, 1995, 1996; Sandwell and Smith, 1997].Altimetric gravity fields are unique in the sense that they provide global uniform gravity information with very high resolution, and these global marine gravity fields are registered on a two by two minute grid corresponding to 4 by 4 kilometres at the equator.In this presentation several coastal complications in deriving the marine gravity field from satellite altimetry will be investigated using the KMS98 gravity field. Comparison with other sources of gravity field information like airborne and marine gravity observations will be carried out and two fundamentally different test areas (Azores and Skagerak) will be studied to investigated the different role of these different sources of gravity information.     

Tectonic implied results from geoid and topography signals

The topographic surface is a measure of static equilibrium from the actual density distribution within the outmost Earth's lithosphere. The natural height reference of this surface, known as geoid, reflects the mixed mass-density effects, caused by the same sources, without the contribution of topographic mass. Geoid undulation and topography are output signals, which carry in common a large part of the contribution from the causal “sources”. This contribution appears in both types of signal. Comparisons between the signals depict the geographical location and an estimation of the depth occurrence of areas with geophysical and tectonic formations depending on their correlation rate. We present results from the Greek region, known for its complex diversity in topography, tectonics and dynamics. The tests are in point and “surface” concept, from local and global signals of geoid and topography. Local geoid is represented at 91 GPS points and EGM 96 coefficients compute its global representation. The topography is point values within the area, and the ETOPO5 5′X5′ data within the geographical frame.     

Local geoid computation and evaluation

A local geoid solution for the northern part of Greece is presented based on a recent processing of newly available gravity data in the area 40.25 ≤ /o ≤ 41.00, 22.5 ≤λ ≤ 24.25. The derived gravimetric geoid heights are compared with geoid heights computed at recently measured GPS/ leveling benchmarks. A 4-parameter transformation model is applied to the differences between the two aforementioned geoid height sets, and a discussion is given on the current state of the leveling datum in the test area and the Greek territory. Regional and local transformation parameters are computed and some numerical tests are performed. A common adjustment of gravimetric geoid heights and corresponding GPS/leveling heights will be carried out in another study following an integrated procedure in order to study problems arising from the combination of different height data sets for geoid determination. Finally, some conclusions are drawn on the problems related to the optimization of a local geoid solution.     

南海卫星重力研究

用卫星雷达测高确定海面高度可以容易地转换成重力异常。南海应用密轨道的GEOSAT/GM和ERS-1卫星测高数据获得了高分辨率的重力复盖。在这个新的重力图上揭示出许多有意义的、过去未能清楚显示的构造特征,其中包括扩张脊,转换断层,岩石层弹性板厚度,大陆边缘性质,以及新的沉积盆地。     

Description and release of Australian gravity field model testing data

Gravimetric geoid and/or quasigeoid models are routinely evaluated using co-located GPS-levelling and/or astrogeodetic vertical deflections, globally and regionally. This short note describes these ground-truth data for Australia as of August 2017, which are provided as Electronic Supplementary Material. We provide ～7500 GPS-derived ellipsoidal heights, normal-orthometric heights from the 1971 adjustment of the Australian Height Datum, normal heights from a readjustment of levelling constrained to a model of the ocean's mean dynamic topography, and ～1000 historical astrogeodetic vertical deflections. Updates to these data will be posted on the Intergovernmental Committee on Surveying and Mapping GitHub repository (https://github.com/icsm-au), together with a readme.txt file describing them.