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.     

Efficient GOCE satellite gravity field recovery based on least-squares using QR decomposition

We develop and apply an efficient strategy for Earth gravity field recovery from satellite gravity gradiometry data. Our approach is based upon the Paige-Saunders iterative least-squares method using QR decomposition (LSQR). We modify the original algorithm for space-geodetic applications: firstly, we investigate how convergence can be accelerated by means of both subspace and block-diagonal preconditioning. The efficiency of the latter dominates if the design matrix exhibits block-dominant structure. Secondly, we address Tikhonov-Phillips regularization in general. Thirdly, we demonstrate an effective implementation of the algorithm in a high-performance computing environment. In this context, an important issue is to avoid the twofold computation of the design matrix in each iteration. The computational platform is a 64-processor shared-memory supercomputer. The runtime results prove the successful parallelization of the LSQR solver. The numerical examples are chosen in view of the forthcoming satellite mission GOCE (Gravity field and steady-state Ocean Circulation Explorer). The closed-loop scenario covers 1 month of simulated data with 5 s sampling. We focus exclusively on the analysis of radial components of satellite accelerations and gravity gradients. Our extensions to the basic algorithm enable the method to be competitive with well-established inversion strategies in satellite geodesy, such as conjugate gradient methods or the brute-force approach. In its current development stage, the LSQR method appears ready to deal with real-data applications.     

中国西部现今地壳形变与地震活动特征

以1999-2004年间中国西部地区近650个GPS站点的观测资料为基础,采用二维“高张力样条”函数内插算法获得了连续地壳形变场。结果表明,相对于稳定欧亚参考框架,中国西部现今地壳运动西强东弱,北向运动从西向东逐渐减弱,东向运动逐渐增强,青藏高原东缘及附近地区是东向运动的消减区带;主应变从西向东由压缩应变转变为拉伸应变;最大剪应变主要位于喜马拉雅地块及其东部地区;中国西部地区地震活动在空间分布上似乎集中发生在印度板块北东向挤压欧亚板块的两条共扼带内,与地壳形变场有一定对应关系,地壳形变的高应变率区为中强地震多发地带。     

Study on Recovering the Earth＇s Potential Field Based on GOCE Gradiometry

Given the second radial derivative Vrr（P） ｜δs of the Earth＇s gravitational potential V（P） on the surface δS corresponding to the satellite altitude, by using the fictitious compress recovery method, a fictitious regular harmonic field rrVrr（P）^＊ and a fictitious second radial gradient field V：（P） in the domain outside an inner sphere Ki can be determined, which coincides with the real field V（P） in the domain outside the Earth. Vrr^＊（P）could be further expressed as a uniformly convergent expansion series in the domain outside the inner sphere, because rrV（P）^＊ could be expressed as a uniformly convergent spherical harmonic expansion series due to its regularity and harmony in that domain. In another aspect, the fictitious field V^＊（P） defined in the domain outside the inner sphere, which coincides with the real field V（P） in the domain outside the Earth, could be also expressed as a spherical harmonic expansion series. Then, the harmonic coefficients contained in the series expressing V^＊（P） can be determined, and consequently the real field V（P） is recovered. Preliminary simulation calculations show that the second radial gradient field Vrr（P） could be recovered based only on the second radial derivative V（P）｜δs given on the satellite boundary. Concerning the final recovery of the potential field V（P） based only on the boundary value Vrr （P）｜δs, the simulation tests are still in process.     

兰州—白银多目标地球化学调查野外工作方法浅析

多目标区域地球化学调查从调查区表层、深层采样土壤元素分布特征入手建立土壤元素地球化学分配机制,以景观、地貌及地质特征为基础,选择合理的采样位置,正确的采样方法、采样层位,应用掌上机（Pocket PC）及数字填图系统（Rgmap）采集野外样品,本文以兰州—白银黄土覆盖区景观区为例,对表层、深层采样方法和技术要求进行探讨,对全省开展多目标地球化学调查,特别是野外工作方法提供借鉴。     

河西走廊疏勒河流域地质灾害危险性现状评估方法的应用——以甘肃省河西走廊(疏勒河)农业灌溉暨移民安置综合开发建设项目8个移民社区及配套工程建设为例

依据“建设用地地质灾害危险性评估技术要求”、利用野外踏勘及相关资料,对“甘肃省河西走廊（疏勒河）农业灌溉暨移民安置综合开发建设项目8个移民社区及配套工程”进行地质灾害危险性现状评估。结果认为：评估区发育和分布的地质灾害类型有土壤盐渍化、风蚀沙埋和洪水冲蚀。现状评估结果：土壤盐渍化和洪水冲蚀危险性均小;风蚀沙埋有1处危险性中等,其它危险性小。     

天然气溶解过程中组分分馏模型及其应用

天然气不同组分在水中溶解度的差异,导致溶解相与残留游离相天然气组分组成不同,即发生组分的溶解分馏效应。溶解分馏效应在天然气水溶运移、溶解散失等过程中均有发生。揭示天然气组分的溶解分馏规律、建立定量分馏模型,有助于天然气气源对比和成藏过程示踪。以Henry定律为依据,对不同组分溶解特征分析,提出了溶解度分数的概念,并建立了溶解分馏模型。根据该模型和各组分的溶解度分数和天然气溶解量,可计算各组分的溶解分馏量,恢复天然气初始组成特征。计算表明,威远震旦系气藏初期的天然气组成为:CH4为72.70%,C2H6为0.09%,CO2为22.41%,N2为4.07%,干燥系数(C1/C1-5)为99.876%。溶解作用使天然气中CO2含量显著降低,烃类气体含量增加,而天然气干燥系数降低。结果有助于天然气成因判识和气源对比等。     

New perspectives on Mars’ crustal magnetic field

The planet Mars lacks, today, a planetary, dynamic magnetic field, but strong, intense, localized magnetic fields of lithospheric origin, one to two orders of magnitude larger than the terrestrial lithospheric field, are present. This lithospheric magnetic field is the result of magnetization processes in the presence of a magnetic dynamo and of demagnetization processes after the dynamo shutdown, such as impact or volcanoes. This crude scenario can be more accurately specified by interpreting global and local models of the current magnetic field of Mars. Some specific areas are studied, including the intensely magnetized Terra Sirenum, as well as the magnetic anomaly associated with Apollinaris Patera. Magnetic minerals could be of primary and/or secondary origin; this latter would imply an early hydration of a basaltic crust. A scenario, in which Mars experienced a major polar wander due to the Tharsis bulge, prior to the cessation of its dynamo, is proposed and discussed.     

西藏札达盆地控盆断裂有限元数值模拟

札达盆地是喜马拉雅构造带中的一个山间断陷盆地,其演化过程与盆地两侧的控盆构造密切相关。对控盆断裂的构造应力场进行模拟计算,将有助于进一步深化对本区构造控盆的认识。因此,在对盆地构造地质进行详细调查的基础上,结合本区的深部地质与地球物理资料,对札达盆地控盆断裂的构造应力场进行了模拟。计算结果表明,札达盆地的演化明显受盆地两侧边界断裂的控制,札达盆地是在整体南北向挤压应力的作用下,不同块体差异隆升作用的结果。其南侧的控盆断裂为北倾的正断层,北侧的控盆断裂为南倾的逆断层,二者共同形成了南降北升的翘板式断陷盆地运动过程,是喜马拉雅地块在陆内汇聚挤压构造环境中构造应力场调整的一种方式。