Completion of the nationwide GPS-gravimetric geoid solution for Hungary

The establishment of the Hungarian National GPS Network (OGPSH) had been completed in 1997. It is exclusively settled on the traditional horizontal network sites, no leveling benchmarks were included. The OGPSH network consists more than 1100 GPS points, but less than 30% of the sites have trustful leveled heights. Our task was to supply the remaining points with cm-accuracy heights above the geoid in a uniform system. For this purpose a technique had been developed using the GPS data and the geoid information available. A specialized geoid solution, covering the whole country was computed and used for supporting the GPS-heighting procedure.The OGG98B GPS-gravimetric geoid solution made the GPS-heighting very simple and efficient. The accuracy of the technique was extensively tested and proved to be accurate not worse than ±3 cm. Higher residuals were found only at some points, where the height information was questionable. The improved technique is planned to be used in the 3rd order leveling network in Hungary.This paper shortly summarizes the computational procedure of the GPS-gravimetric geoid and presents some results on the GPS-heighting had been performed in the OGPSH network.     

A new high-resolution gravimetric geoid for South Spain and the Gibraltar Strait area: SOSGIS

A new gravimetric geoid is computed for South Spain and the Gibraltar Strait area. This geoid is located just in the junction between two tectonic plates (Euro-Asiatic and African plates) and in the junction of two gravimetric geoids: IGG2005 (the Iberian Gravimetric Geoid obtained in 2005) and MORGEO (the MORoccan GEOid). IGG2005 is the Iberian geoid and MORGEO is the Moroccan geoid, both geoids have been previously obtained. The new geoid is the gravimetric geoid solution that connects the two above-mentioned geoids, getting a more accurate and reliable picture of this area than the other previous geoids. The method used is the Stokes integral in convolution form, which shows to be an efficient method to reach the proposed objective. The terrain correction and the indirect effect have been taken into account. The new geoid is obtained as a regular grid (with a mesh size of 1.5′ × 1.5′) in the GRS80 reference system, covering the study area from 34° to 40° of latitude and from −8° to 0° of longitude. This gravimetric geoid and the previous geoids: IGG2005 and MORGEO; are compared to the geoid undulations derived at the validation points located on the study area (four GPS/levelling points measured on Morocco and five points of the European vertical reference network (EUVN) measured on Iberia). As it is expected, the new geoid is a more precise and reliable model, fitting the geoidal heights of these validation points with more accuracy than the other previous geoids. This new model will be useful for orthometric height determination by GPS in the mountains and remote areas, where levelling has many logistic problems. Also, it can be interesting for other geophysical purposes different to the height measurements, because it can provide a constraint for the density distribution, the thermal state of Lithosphere and the viscosity in the mantle. Such details can be inferred from a geoid model and the seismic velocity structure.     

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.     

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.     

Geoid modelling based on EGM08 and recent Earth gravity models of GOCE

In this paper an estimator for geoid is presented and applied for geoid computation which considers the topographic and atmospheric effects on the geoid. The total atmospheric effect is mathematically developed in terms of spherical harmonics to degree and order 2,160 based on a recent static atmospheric density model. Also the contribution of its higher degrees is formulated. Another idea of this paper is to combine one of the recent Earth gravity models (EGMs) of the Gravity field and steady-state Ocean Circulation Explorer (GOCE) mission with EGM08 and the terrestrial gravimetric data of Fennoscandia in an optimum way. To do so, the GOCE EGMs are compared with the Global Positioning System (GPS)/levelling data over the area for finding the most suited one. This comparison is done in two different ways: with and without considering the errors of the EGMs. Comparison of the computed geoids with the GPS/levelling data shows that a) considering the total atmospheric effect will improve the geoid by about 5 mm, b) GOCO03S is the most suited GOCE EGM for Fennoscandia, c) the errors of some of the GOCE EGMs are optimistic and far from reality. Combination of GOCO03S from degree 120 to 210 and EGM08 for the rest of degrees shows its good quality in these frequencies.     

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.     

Factors affecting FFT gravimetric geoid determination precision

The Fast Fourier Transformation (FFT) has become a routine mathematical tool for the refinement of the Earth's gravity field, such as the computation of precise gravimetric geoid and terrain corrections, particularly over a large area. This paper presents ideas and methodologies to evaluate the accuracy of geoid undulation computations using FFT. A global geopotential model is used as a ‘ground truth’ gravity field model to assess the geoid determination precision by using FFT technique. It is demonstrated that special considerations must be given for a high precision FFT gravimetric geoid determination. A maximum of a few decimetres error could be introduced by the FFT algorithm if the gravity anomalies are not long wavelength filtered and/or no zero padding is applied.     

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.     

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.     

Plate kinematics and the gravity field

Both the system of plate motions and the global gravity field or the geoid are now so precisely known that it seems worthwhile to look for quantitative relationships. Some aspects, such as the general occurrence of positive gravity and geoid anomalies in regions of plate convergence, have long been known. Our aim is to describe the gravitational field in terms of plate-kinematic parameters and we present a preliminary step in this direction: for four plates (Pacific, Nazca, Indian, American) we have computed the correlation of the Gem 8 geoid heights (with reference to an ellipsoid of 1/298.255 ellipticity) with distance from the poles of motion and distance from the axes in an “absolute” frame. The geoid tends first to drop from the ridge axes to at least 10° distance and then to rise toward the convergence zones. This trend is strongest for the Indian plate in collision with Eurasia, is smaller, but very clear for the oceanic Pacific and Nazca plates, and is not developed for the American plate which does not subduct. We did not find a consistent relationship for the geoid with distance from the pivots. A possible interpretation of the results is the return flow of the large-scale mantle circulation.     

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.     

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.     

Investigation of the Co-seismic Gravity Field Variations Caused by the 2004 Sumatra-Andaman Earthquake Using Monthly GRACE Data

Gravity Recovery and Climate Experiment(GRACE) observations have been used to de-tect the co-seismic and post-seismic gravity field variations due to the Mw=9.3 Sumatra-Andaman earthquake that occurred on December 26,2004.This article focuses on investigating some gravita-tional effects caused by this huge earthquake.We computed the geoid height changes,the equivalent water height(EWH) changes,and the gravity changes using the GRACE Level-2 monthly spherical harmonic(SH) solutions released by University of ...     

Geodetic reference systems for crustal motion studies

The behaviour of geodetic reference systems as a function of time cannot be ignored in determinations of position for secular geodynamic modelling. While non-specialist users are likely to appreciate the uncertainty surrounding the concept of a “fixed” point in regional surveys for crustal motion, its extension to global surveys based on techniques in dynamic geodesy is not widely understood. Such solutions are related to the natural coordinate system defined by the instantaneous geocentre (earth's centre of mass) and the instantaneous rotation axis whose location in earth space cannot be expected to be time invariant.The effect of such movements of the natural system of reference on the coordinates of points at the earth's surface is computed for a plausible model of the former. The resulting changes in solutions for three-dimensional position from dynamic considerations are discussed. It is shown that for the model adopted, the earth-space variations of the natural reference system with time produce coordinate changes with magnitudes not dissimilar to those resulting from reasonable variations in the earth's figure, though with different wavelengths, when computed from three-dimensional considerations alone.The resulting displacements, along with an accepted model for plate motions, are used to study changes in the shape of the level surfaces of the earth's gravity field with time. It is shown that plausible models for the deformation of the earth's figure produce significant changes in the geopotential and the shape of the geoid. However, the transfer of mass implied in extreme models of plate motion produce no significant changes in the datum level surface for crustal motion studies over periods as long as 10² yr.     

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.     

Utilisation of Fast Fourier Transform and Least-squares Modification of Stokes formula to compile a gravimetric geoid model over Khartoum State: Sudan

We use Fast Fourier Transform (FFT) and least-squares modification (LSM) of Stokes formula to compute the geoid over Khartoum State in Sudan. The two methods (FFT and LSM) have been utilised to test their efficiency with respect to EGM08 and the local GPS-levelling data. The FFT method has many advantages, it is fast and it reduces the computational complexity. The modification of Stokes formula is widely used in geoid modelling; however, its implementation based on point-wise summation requires a considerable amount of time. In FFT, we combine the terrestrial gravity data and the global geopotential model (GGM) by means of a remove-compute-restore procedure and we successfully apply the modification of the Stokes formula in the least-squares sense. FFT and LSM geoid solutions are evaluated against EGM2008 and the GPS-levelling data. The analysis of the undulation differences shows that the LSM solution is more compatible with EGM08 and GPS-levelling data. The discrepancies of the differences are removed using a 4-parameter model, the standard deviation (STD) of the undulation differences of LSM decreased from 0.41 to 0.37 m and from 0.48 to 0.39 m for FFT solution. There is no significant impact to the LSM geoid when adding the additive corrections, while the FFT geoid solution is slightly improved when terrain correction is applied.     

基坑支护可拆型锚杆技术研究及应用

为了避免给周围后续工程造成施工障碍和引起法律上的纠纷,基坑支护中的临时锚杆在失去作用后应将其拆除。通过对锚杆荷载传递特性的分析和在现场原型试验研究的基础上,提出了一种仅拆除拉杆材料的可拆型锚杆技术。该技术通过在拉杆材料和注浆体之间设置隔离措施来拆卸锚杆,并通过带传力杆的承载体将锚拉力分散传递于注浆体中。工程实例表明该技术方法简单可行,且由于受力合理,可拆型锚杆的技术性能也较普通锚杆明显有所提高。     

电化学导流法提高原油采收率试验研究

电化学导流提高原油采收率技术,在油田各个开发阶段都可达到增油降水的效果.目前多数主力油层内部剩余油分布零散,注水效果差,新增储量的油层大多数是渗透率低、物性差的薄油层.现场试验证明,应用电动法这一新技术,已初步实现了增加原油渗流速度、提高油水流动的相对渗透率和解除油层堵塞等的效果,工艺上是可行的.且用导线传输直流电场与其它传输方式相比,对井口及地面通电设备的安全性也较好.     

Different ways to handle topography in practical geoid determination

In this paper two different methods of how to handle topography in geoid determination is investigated. First method employs the Residual Terrain Model (RTM) remove-restore technique and yields the quasigeoid, whereas the second method is the classical Helmert condensation method, yielding the geoid. Both methods were used with the Earth Gravity Model (1996) (EGM96) geopotential model as reference, and results are compared to precise Global Positioning System (GPS) levelling networks in Scandinavia, especially an accurate GPS data set from the very rugged Sognefjord region, where the topography was represented by either a detailed (100 m) or a coarse (1000 m) digital terrain model. The inclusion of bathymetry in the terrain model was also investigated.Even if two different methods were used, they produced almost identical results at the 5 cm level in the mountains, but small systematic differences exist. Results show the importance of comparing the right types of geoid (classical geoid or quasigeoid), since differences in residuals are significant.     

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.