Methodology and use of tensor invariants for satellite gravity gradiometry

Although its use is widespread in several other scientific disciplines, the theory of tensor invariants is only marginally adopted in gravity field modeling. We aim to close this gap by developing and applying the invariants approach for geopotential recovery. Gravitational tensor invariants are deduced from products of second-order derivatives of the gravitational potential. The benefit of the method presented arises from its independence of the gradiometer instrument’s orientation in space. Thus, we refrain from the classical methods for satellite gravity gradiometry analysis, i.e., in terms of individual gravity gradients, in favor of the alternative invariants approach. The invariants approach requires a tailored processing strategy. Firstly, the non-linear functionals with regard to the potential series expansion in spherical harmonics necessitates the linearization and iterative solution of the resulting least-squares problem. From the computational point of view, efficient linearization by means of perturbation theory has been adopted. It only requires the computation of reference gravity gradients. Secondly, the deduced pseudo-observations are composed of all the gravitational tensor elements, all of which require a comparable level of accuracy. Additionally, implementation of the invariants method for large data sets is a challenging task. We show the fundamentals of tensor invariants theory adapted to satellite gradiometry. With regard to the GOCE (Gravity field and steady-state Ocean Circulation Explorer) satellite gradiometry mission, we demonstrate that the iterative parameter estimation process converges within only two iterations. Additionally, for the GOCE configuration, we show the invariants approach to be insensitive to the synthesis of unobserved gravity gradients.     

A data-driven approach to local gravity field modelling using spherical radial basis functions

We propose a methodology for local gravity field modelling from gravity data using spherical radial basis functions. The methodology comprises two steps: in step 1, gravity data (gravity anomalies and/or gravity disturbances) are used to estimate the disturbing potential using least-squares techniques. The latter is represented as a linear combination of spherical radial basis functions (SRBFs). A data-adaptive strategy is used to select the optimal number, location, and depths of the SRBFs using generalized cross validation. Variance component estimation is used to determine the optimal regularization parameter and to properly weight the different data sets. In the second step, the gravimetric height anomalies are combined with observed differences between global positioning system (GPS) ellipsoidal heights and normal heights. The data combination is written as the solution of a Cauchy boundary-value problem for the Laplace equation. This allows removal of the non-uniqueness of the problem of local gravity field modelling from terrestrial gravity data. At the same time, existing systematic distortions in the gravimetric and geometric height anomalies are also absorbed into the combination. The approach is used to compute a height reference surface for the Netherlands. The solution is compared with NLGEO2004, the official Dutch height reference surface, which has been computed using the same data but a Stokes-based approach with kernel modification and a geometric six-parameter “corrector surface” to fit the gravimetric solution to the GPS-levelling points. A direct comparison of both height reference surfaces shows an RMS difference of 0.6 cm; the maximum difference is 2.1 cm. A test at independent GPS-levelling control points, confirms that our solution is in no way inferior to NLGEO2004.     

利用参考重力场模型基于能量法确定GRACE加速度计校准参数

利用多个参考重力场模型分别对GRACE一个月的实测加速度计观测数据进行检校.数值计算结果的比较分析表明了利用参考重力场模型确定加速度计校准参数是有效的.     

邹平火山岩盆地铜矿地质成因地球物理特征探讨

邹平铜矿处于齐河-广饶深大断裂带南部的邹平火山岩盆地中,形成于破火山口火山通道充填的石英正长闪长岩岩颈中央上部,包括伟晶岩型铜矿和细脉浸染状斑铜矿床两种类型。前者矿体较小,但品位高;后者品位较低,但规模中等。含矿石英正长闪长岩等密度小、磁性弱,故在火山岩系中呈现高背景重力场上的重力低和杂乱高磁场背景中的低负异常,即“重磁同低”,且高极化。重磁同低异常区和高极化率异常带,是本区寻找铜矿的有利部位。     

联合多种测高数据确定中国海及其邻域1．5′×1．5′重力异常

联合多种测高资料和Geosat/GM波形重构数据,基于EIGEN_CG01C重力场模型,采用沿轨迹加权最小二乘方法和逆Vening-Meinesz公式,确定了中国海及其邻域1.5′×1.5′重力异常。将计算结果与最新船测资料进行了比较,标准差为3.37×10-5m.s-2。     

Lake bank filtration at Nainital,India: water-quality evaluation

There are different water-supply schemes in Uttarakhand, India to tap the water from streams, rivers and lakes. At Nainital, seven tube-wells (depths 22.6–36.7 m), located at a distance of <100 m from the lake, are being used to abstract (1) lake water after passage through the soil and (2) subsurface water/groundwater flowing towards the lake. Water samples from the lake and tube-wells were analyzed in monsoon and non-monsoon periods from 1997 to 2006. Total dissolved solids, EC, alkalinity and hardness were found to be marginally greater in tube-well waters. The difference in hydrochemistry of tube-well water was mainly due to variation in flow regimes during monsoon and non-monsoon periods. Results clearly indicate that lake water as such is not potable as it contains unacceptable levels of organic matter in terms of COD (~44 mg/L), coliforms (~15.6 × 10⁴ MPN/100 mL) and nutrients. Coliform bacteria and COD have not been detected in any of the tube-well water samples over the years. Lake water, treated by sand filters did not conform to drinking water standards. These investigations have led to the closure of the treatment facility and installation of two tube-wells in addition to the existing five tube-wells.

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Résumé  Il existe divers projets d’alimentation en eau dans l’état d’Uttarakhand, Inde, afin de capter l’eau de ruisseaux, de rivières et de lacs. A Nainital, sept puits tubés (profondeur de 22.6–36.7 m), situés à une distance < à 100 m du lac, sont utilisés pour prélever (1) de l’eau du lac après transit à travers le sol et (2) de l’eau de sub-surface/eau souterraine s’écoulant vers le lac. Des échantillons d’eau du lac et des puits tubés ont été analysés en périodes de mousson et de celles sans mousson 1997 à 2006. Résidu sec, C.E., alcalinité et dureté ont été trouvés marginalement supérieurs dans l’eau des puits tubés. La différence d’hydrochimie de l’eau des puits tubés était surtout due à la variation des régimes d’écoulement pendant les périodes de mousson et de celles sans mousson. Les résultats indiquent clairement que l’eau du lac en tant que telle n’est pas potable car elle contient des teneurs inacceptables de matière organique en termes de COD (~44 mg/L), de coliformes (~15.6 × 10⁴ MPN/100 mL) et d’éléments nutritifs. Des bactéries coliformes et du COD n’ont été détectés dans aucun des échantillons d’eau de puits tubés au fil des années. L’eau du lac traitée par des filtres à sable ne se conformait pas aux normes de l’eau potable. Ces recherches ont conduit à la fermeture de l’installation de traitement et à l’implantation de deux puits tubés en plus des cinq puits existants.

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Resumen  En el estado de Uttarakhand, India, existen diferentes esquemas de abastecimiento de agua que explotan agua de arroyos, ríos y lagos. En Nainital, siete pozos (profundidades entre 22.6–36.7 m), ubicados a una distancia de <100 m del lago, se usan para extraer (1) agua del lago luego de su pasaje a través del suelo y (2) agua superficial y subterránea que fluye hacia el lago. En períodos de monzón y de no monzón de 1997 a 2006 se han analizado muestras de agua del lago y de las captaciones. Se halló que el agua de los pozos es ligeramente mayor en términos del total de sólidos disueltos, la conductividad eléctrica, la alcalinidad y la dureza. La diferencia en la hidroquímica del agua de las perforaciones se debe principalmente a la variación de los regímenes de flujo durante los períodos de monzón y de no monzón. Los resultados claramente indican que el agua del lago no es potable por su contenido inaceptable de materia orgánica medida como demanda de carbono orgánico/oxígeno –DCO- (~44 mg/L), coliformes (~15.6 × 10⁴ NMP/100 mL) y nutrientes. En el período, no se han detectado bacterias coliformes ni DCO en las muestras de agua de las captaciones. El agua del lago, tratada con filtros de arena, no conformó los estándares de agua para bebida. Estas investigaciones han demostrado la necesidad de clausurar las instalaciones de tratamiento y la adición de dos captaciones a las cinco ya existentes.

     

The Glueckstadt Graben of the North-German Basin: new insights into the structure from 3D and 2D gravity analyses

The structure of the Glueckstadt Graben has been investigated by use of 3D gravity backstripping technique and by 2D gravity and magnetic modelling. Subtracting the gravity effects of the Meso-Cenozoic sediments together with Permian salt reveals a positive residual anomaly within the Glueckstadt Graben. This anomaly includes two local maxima over the Westholstein and Eastholstein Troughs. The 2D gravity models point to the presence of a high-density body within the lower crust of the Glueckstadt Graben. In addition, the results of 2D magnetic modelling indicate that the central part of the high-density body is overlain by an area with high susceptibility. Most probable, the formation of this high-density body is a result of complex poly-phase tectonic history of the study area. Finally, the results of gravity modelling indicate that Permian salt is not homogeneous. 3D gravity analysis and, especially, 2D gravity modelling have distinguished the differences in degree of salt saturation in salt-rich bodies, and elucidate the proportion of Rotliegend salt.     

基于ICCP算法的重力辅助惯性导航

迭代最近等值线算法(ICCP)是一种重要的匹配导航算法,文中首先介绍ICCP算法的基本原理,随后在0.2′×0.2′重力异常数据库的基础上,利用ICCP算法进行仿真计算得到最佳匹配位置。最后为了验证匹配位置是否可用于修正惯导误差,提出将匹配位置误差作为观测量,用卡尔曼滤波对惯导系统误差进行最优估计。由最后的仿真结果可以看出,ICCP算法可有效抑制惯导纬度误差的增长,且最大纬度误差不超过2,′以匹配位置误差作为观测量可以用来估计惯导方位误差角。     

关于海平面上升及其环境效应

沿海地区地质环境复杂。由于国民经济的迅速发展,人类活动日益增多,对地质环境进一步造成严重的不利影响。特别是“温室效应”引发的海平面上升,使各种地质灾害更加激化。文章详细探讨了海平面上升的影响因素,理论海平面与相对海平面升降幅度的评估,以及海平面上升所造成的地质环境效应与相应的防治对策,特别强调控制沿海城市地面沉降,以减轻海平面相对上升造成的危害,具有特殊而重要的意义。     

Tectonic relation between northeastern China and the Korean peninsula revealed by interpretation of GRACE satellite gravity data

The major continental blocks in northeastern Asia are the North China block and the South China block, which have collided starting from the Korean peninsula. Geologic and geophysical interpretations reveal a well defined suture zone in northeastern China from Qinling through Dabie to Jiaodong. The discovery of high-pressure metamorphic rocks in the Hongseong area of the Korean peninsula, prominent evidence for the collision zone, indicates extension of the collision zone in northeastern China into the Korean peninsula. Interpretation of the GRACE satellite gravity dataset shows two prominent structural boundaries in the Yellow Sea. One extends from the Jiaodong Belt in eastern China to the Imjingang Belt in the Korean peninsula. The other extends from near Nanjing, eastern China, to Hongseong. Tectonic movement in or near the suture zone may be responsible for seismic activity in the western Korean peninsula and the development of the Yellow Sea sedimentary basin.