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.     

地面重力数据结合GPS/水准数据精化兴城物探实验区大地水准面

区域大地水准面的确定是GPS测量常需解决的问题。目前确定大地水准面的方法主要包括重力法、GPS水准几何法及组合法,其中组合法因其精度和可靠性都较高,常用于计算高精度区域大地水准面。高精度的大地水准面模型是组合法确定区域大地水准面的关键。在我国,EGM2008全球重力场模型精度和分辨率均高于此前的所有模型,研究基于该模型的组合法大地水准面精化具有重要的实践意义。笔者以吉林大学兴城教学实习基地物探实验区为例,基于实测重力数据、EGM2008重力场模型和GPS水准数据,采用组合法精化了区域大地水准面,比较了组合法大地水准面模型和无重力实测数据的几何法大地水准面模型的精度差异,分析了该方法在物探测量中的适用性。结果表明,实验区组合法大地水准面模型精度最高达到1.2 cm,并且误差分布区间较小,总体上精度和可靠性高于对比的几何方法,并且组合法和几何法获取的两种大地水准面模型均能满足大比例尺物探测量要求。EGM2008模型精度较高,故平坦地区使用组合法时,高密度的实测重力数据可能带来高频扰动,有可能降低EGM2008重力场模型本身的精度,所以重力数据采集过程中要顾及重力点的密度和空间分布。本文方法更适用于地形复杂的地区。     

EGM2008重力场模型在兴城物探测量中的应用

以吉林大学兴城物探教学实习测网为例,基于EGM2008重力场模型,采用二次曲面、移动曲线、最小二乘配置、三次样条和反距离加权改正插值法,计算了不同GPS水准点密度情况下的水准面模型,并利用二等水准测量方法验证了计算精度,分析了该模型的适定性。结果表明,三次样条插值法的精度和稳定性最高,其次是移动曲线法和最小二乘配置法;二次曲面拟合的精度最低,反距离加权改正法稳定性最差。所有算法都表明,在研究区,当GPS水准点间隔20 km时,基于EGM2008模型确定的大地水准面精度在0.1 m以内;而采用单独GPS水准点的区域大地水准面模型能达到14cm,完全满足各种比例尺情况下的石油物探测量要求。     

Towards a cm-geoid for Hungary: Recent efforts and results

Some steps were taken recently for Hungary aiming at the determination of geoid heights with a cm-accuracy. The present HGTUB98 gravimetric solution was based on terrestrial gravity data, height data and the EGM96 geopotential model, and was computed with the 1D Spherical FFT method. The gravity data were used in the area 45.5 ° ≤ϑ ≤ 49 °, 16 ° ≤ λ ≤ 23 °, the resolution of the grid was 30″ × 50″. The DTM used had a resolution of 1 km × 1 km.Our solution was evaluated using GPS/levelling data at 340 and 308 points respectively and at 138 vertical deflection points. We have compared our solution to the European EGG97 geoid solution, the gravimetric solution HGR97B developed by A. Kenyeres and the litospheric geoid solution by G. Papp. We have correlated our recent HGTUB98 solution to the Moho model of Central Europe. The comparison with GPS/levelling yielded respectively an accuracy of ±8.7 cm and ±4.4 cm (in terms of standard deviation) when a linear trend was removed. The comparison of the 1D planar FFT solution for the deflections of the vertical with 138 astrogeodetic deflections yielded an accuracy (in terms of standard deviation) of ±0.62″ and ±0.52″ for ξ and η, respectively.     

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.     

The gravitational field and the Geoid of Australia

A map of the geoid in Australia and surrounding oceanic areas has been produced on a scale of 1:5M. There are two variants, both of which employ Bouguer anomalies for the land areas. For the ocean areas in the first variant, anomalies have been obtained as the difference between the observed and theoretical values of gravity at sea level. In the second variant, a correction has been introduced to reduce the density of the water layer to the average density of the Earth's crust. The height of the geoid in Australia is calculated in the same way. The effect of distant zones has been allowed for in accordance with the data of Kozai (1967) and Köhnlein (1967), and a high precision for the geoid height for Australia has been obtained. Discrepancies between the new data and the observations of Mather (1969) amount to + 2 m for the regions investigated and ± 4 m for the entire continent. Coordinates have also been obtained for the centre of the Australian ellipsoid relative to the centre of the Earth's mass.     

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.     

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。     

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.     

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.     

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.     

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.     

Deep Geodynamics of the Himalaya Orogeny

DEEP GEODYNAMICS OF THE HIMALAYA OROGENYRFBR( grant 990 56 56 38)     

Multiresolution tectonic features over the Earth inferred from a wavelet transformed geoid

Geoid signals give information about the underlying density structure and can be used to locate the source depth of the mass anomalies. Wavelet analysis allows a multiresolution analysis of the signal and permits one to zoom into a specific area bounded by a particular length scale. The ability of wavelets to resolve the geoid signal into individual wavelength components without losing the spatial information makes this method superior to the more common spherical harmonic method. The wavelet analysis allows one to zoom into a specific area and look at the regional geology. We have used a wavelet transform of the geoid to study the regional geology of Japan and the Philippine Plate, South America, Europe, North America, East Africa and the Middle East, India and the Himalayas, China and Southeast Asia, and Australia. By filtering the Earth’s geoid anomalies with 2-D Gaussian wavelets at various horizontal length scales, one can detect the subduction zones along South America, the Aleutians, and the western Pacific; the Himalayas; the Zagros Mountains; the Mid-Atlantic ridge; and the island chains of the mid-Pacific. We have processed geoid data with a horizontal resolution down to approximately 200 km. Using an adjustable wavelet, one can detect structures that can only be picked up visually with much higher resolution spherical harmonic gravity data. We have also looked at the wavelength at which the maximum signal occurs over a range of scales. This method, known as E-max and k-max, is especially effective for detecting plate tectonic boundaries and ancient suture zones along with areas of strong non-isostatic gravitational potential due to high differential stress. These areas are likely to be at high risk of earthquakes. These methods will be especially useful to future studies of the geoid potentials of other planets, such as Mars and Venus, since they will allow careful studies of the regional geology variations with geoid data of the resolution available from satellites.     

A new global topographic-isostatic model

This is a preliminary report of our on-going research on a global topographic-isostatic model. The model comes from a completely new idea — the geoid undulation is the responses of an elastic earth to the topographic mass load. Assuming the topography as a condensed surface mass load, we derive expressions for calculating the vertical displacement, potential and equipotential surface changes, based on the load theory proposed in Sun and Sjöberg (1996). The modeled geoid is composed of three parts: loading potential, surface displacement and mass redistribution. The mass redistribution of the earth compensates to some extent the topography. We mainly calculate and discuss the vertical displacements and equipotential surface changes for three depths: the earth's surface, d = 36 km and the core-mantle boundary. Numerical results show that the displacements at depth 36 km and the earth's surface have the same distribution pattern and magnitude, while the vertical movement of the core-mantle boundary appears much smoother and smaller. The modeled geoid undulations vary between −352 and +555 m. The comparison between the modeled and observed geoid undulations shows that there are strong positive correlations between them, but a compensation only by elastic deformations is not sufficient to explain the observed undulations because of the big difference in magnitude between the two geoids. More geodynamic effects should be considered to better explain the long-wavelength geoid features.     

Effects of mantle upwelling in a compressional setting: the Atlas Mountains of Morocco

We discuss the implications of a lithospheric model of the Moroccan Atlas Mountains based on topography, heat flow, gravity and geoid anomalies, taking into account the regional geology. The NW African cratonic lithosphere, some 160–180 km thick, thins to c. 80 km beneath the Atlas fold-thrust belts, in contrast with the shortening regime prevailing there since the early Cenozoic. This fact explains several geological and geophysical features as high topography with modest tectonic shortening, the occurrence of alkaline magmatism contemporaneous to compression, the absence of large crustal roots to support elevation, the scarce development of foreland basins, and a marked geoid high. The modelled lithosphere thinning is related to a thermal upwelling constrained between the Iberia–Africa convergent plate boundary and the Saharan craton.     

基于D—InSAR的九寨沟地震同震形变场反演分析

利用覆盖九寨沟地区的RadarSat—2数据与Sentinel—1A数据,采用精轨数据进行定轨,消除轨道误差,并结合合成孔径差分(D-InSAR)方法中的双轨差分技术,获取2017年8月8日Mw7. 0级地震的同震形变场。结果表明,视线方向(LOS)最大沉降量约为20 cm,隆起量达9 cm。基于弹性半空间形变模型反演该地震的断层滑动分布,得出该地震断层滑动以左旋走滑为主,走向为330°,倾角为32°,滑动角为-170°,同震滑动分布主要集中在4～12 km深度处,最大滑动量位于9 km处,约为6. 14 m,平均滑动量为0. 57 m。反演获得的地震标量矩为4. 06E+18N·m,震级Mw约为6. 4,深度为19. 5 km。     

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.     

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.     

江苏省土壤元素地球化学基准值

土壤元素地球化学基准是指自然环境中土壤元素正常含量,属于土壤固有的化学组成与结构特征。江苏省现有国土面积约102 600 km2,至2007年已经完成全省1∶250 000多目标区域地球化学调查。按照4 km2采集1个样品、采样深度150～200 cm,16 km2分析测试1个组合样,共获得全省6 127个代表自然环境土壤之样品的52个元素与TOC含量的数据,剔除异常含量数据后,以平均含量代表全省土壤元素地球化学基准值、"基准值±1.5或2倍标准离差"表示元素基准值变化范围,获得了江苏省土壤52个元素及TOC的地球化学基准值,为土壤环境评价等提供了基础资料。结果表明:(1)全省土壤大多数元素含量数据不服从正态分布,但剔除异常数据后对平均含量影响不明显;(2)人为活动因素导致江苏土壤的Cd、Hg、Se、N等元素在地表20 cm以上深度发生显著富集,给建立土壤元素地球化学基准值增添了新的难度;(3)成土母质、土壤成因类型与地貌等差异是影响江苏土壤元素含量分布的基本要素。