Direct BEM for high-resolution global gravity field modelling

The paper presents a high-resolution global gravity field modelling by the boundary element method (BEM). A direct BEM formulation for the Laplace equation is applied to get a numerical solution of the linearized fixed gravimetric boundary-value problem. The numerical scheme uses the collocation method with linear basis functions. It involves a discretization of the complicated Earth’s surface, which is considered as a fixed boundary. Here 3D positions of collocation points are simulated from the DNSC08 mean sea surface at oceans and from the SRTM30PLUS_V5.0 global topography model added to EGM96 on lands. High-performance computations together with an elimination of the far zones’ interactions allow a very refined integration over the all Earth’s surface with a resolution up to 0.1 deg. Inaccuracy of the approximate coarse solutions used for the elimination of the far zones’ interactions leads to a long-wavelength error surface included in the obtained numerical solution. This paper introduces an iterative procedure how to reduce such long-wavelength error surface. Surface gravity disturbances as oblique derivative boundary conditions are generated from the EGM2008 geopotential model. Numerical experiments demonstrate how the iterative procedure tends to the final numerical solutions that are converging to EGM2008. Finally the input surface gravity disturbances at oceans are replaced by real data obtained from the DNSC08 altimetryderived gravity data. The ITG-GRACE03S satellite geopotential model up to degree 180 is used to eliminate far zones’ interactions. The final high-resolution global gravity field model with the resolution 0.1 deg is compared with EGM2008.     

Derivation of the CHAMP-only global gravity field model TUG-CHAMP04 applying the energy integral approach

A global gravity field model TUG-CHAMP04, derived from CHAMP (CHAllenging Minisatellite Payload) satellite-to-satellite GPS tracking observations in the high-low mode (SST-hl) in combination with CHAMP accelerometry, is presented and described in detail in this paper. For this purpose the energy integral approach was applied to precise kinematic orbits and accelerometer data. The advantage of these kinds of orbits is that they are derived from purely geometrical information, hence no external gravity field information is used for the determination of the positions. The disadvantage of precise kinematic orbit information is, that no velocities are delivered and hence a procedure has to be elaborated to deduce the velocities from kinematic positions. This work is done in preparation for ESA’s GOCE (Gravity field and steady state Ocean Circulation Explorer) satellite mission (scheduled launch November 2006), aiming at a high precision and high-resolution gravity field model on a global scale. This paper concentrates on the CHAMP data processing, where, in contrast to the usual standard method (processing in the Earth fixed frame), an approach in the inertial frame is chosen. Focus is taken on the data preprocessing of both accelerometer and orbit data, emphasising on the correct treatment of data-gaps and outlier detection. Furthermore an arc-wise weighting strategy is introduced and the advantages/disadvantages of this approach are discussed. Finally, the TUG-CHAMP04 model, calculated from one year of CHAMP data is compared with the official CHAMP gravity field model EIGEN-3p and terrestrial data (GPS levelling data).     

Grim4-C1, -C2p: combination solutions of the global earth gravity field

On the basis of the GRIM4-S1 satellite-only Earth gravity model, being accomplished in a common effort by DGFI and GRGS, a combination solution, called GRIM4-C1, has been derivcd using 1° × 1° mean gravity anomalies and 1° × 1° Seasat altimeter derived mean geoid undulations. In the meantime improvements could be achieved by incorporating more tracking data (GEOSAT, SPOT2-DORIS) into the solution, resulting in the two new parallel versions, the satellite-only gravity model GRIM4-S2 and the combined solution GRIM4-C2p (preliminary). All GRIM4 Earth gravity models cover the spectral gravitational constituents complete up to degree and order 50.In this report the emphasis is on the discussion of the combined gravity models: combination and estimation techniques, capabilities for application in precise satellite orbit computation and accuracies in long wavelength geoid representation. It is shown that with the new generation of global gravity models general purpose satellite-only models are no longer inferior to combination solutions if applied to satellite orbit restitution.     

小行星引力场综述

近年来小行星探测已成为各航天大国的热点,小行星引力场对研究其内部结构、组成成分、早期演化和探测器轨道设计、着陆等方面有着极其重要的作用.随着小行星探测数据的不断更新、探测任务的增多和观测技术改进,针对小行星引力场的研究也在不断增多并产生新的进展.目前获取小行星引力场的方法主要为利用探测器飞掠过程中得到的轨道跟踪数据反演...     

重力辅助惯性导航中的重力场多尺度特性研究

重力辅助惯性导航是真正的无源导航,它已成为21世纪无源导航定位技术的主要研究方向之一.本文在进行了一般性的尺度概念及多尺度系统理论概述之后,结合重力场的固有特性,分别从重力场的模型尺度特性、空间尺度特性以及时间尺度特性详细介绍了地球重力场固有的多尺度特性.另外,根据重力辅助惯性导航系统中重力场数据的作用,从利用重力场实...     

One technique for refining the global Earth gravity models

The results of the theoretical and experimental research on the technique for refining the global Earth geopotential models such as EGM2008 in the continental regions are presented. The discussed technique is based on the high-resolution satellite data for the Earth’s surface topography which enables the allowance for the fine structure of the Earth’s gravitational field without the additional gravimetry data. The experimental studies are conducted by the example of the new GGMplus global gravity model of the Earth with a resolution about 0.5 km, which is obtained by expanding the EGM2008 model to degree 2190 with the corrections for the topograohy calculated from the SRTM data. The GGMplus and EGM2008 models are compared with the regional geoid models in 21 regions of North America, Australia, Africa, and Europe. The obtained estimates largely support the possibility of refining the global geopotential models such as EGM2008 by the procedure implemented in GGMplus, particularly in the regions with relatively high elevation difference.     

Highly-reduced dynamic orbits and their use for global gravity field recovery: A simulation study for GOCE

The so-called highly reduced-dynamic (HRD) orbit determination strategy and its use for the determination of the Earth’s gravitational field are analyzed. We discuss the functional model for the generation of HRD orbits, which are a compromise of the two extreme cases of dynamic and purely geometrically determined kinematic orbits. For gravity field recovery the energy integral approach is applied, which is based on the law of energy conservation in a closed system. The potential of HRD orbits for gravity field determination is studied in the frame of a simulated test environment based on a realistic GOCE orbit configuration. The results are analyzed, assessed, and compared with the respective reference solutions based on a kinematic orbit scenario. The main advantage of HRD orbits is the fact that they contain orbit velocity information, thus avoiding numerical differentiation on the orbit positions. The error characteristics are usually much smoother, and the computation of gravity field solutions is more efficient, because less densely sampled orbit information is sufficient. On the other hand, the main drawback of HRD orbits is that they contain external gravity field information, and thus yield the danger to obtain gravity field results which are biased towards this prior information.     

On the parameters of the normal earth's gravity field

Summary The parameters of the normal Earth's gravity field, determined from contemporary satellite data are discussed and compared with the parameters of the normal Helmert system (1901 to 1909).Dedicated to Academician Alois Zátopek on His 65th Birthday     

Satellite gravity gradiometry: Secular gravity field change over polar regions

The ESA Gravity and steady state Ocean and Circulation Explorer, GOCE, mission will utilise the principle of satellite gravity gradiometry to measure the long to medium wavelengths in the static gravity field. Previous studies have demonstrated the low sensitivity of GOCE to ocean tides and to temporal gravity field variations at the seasonal scale. In this study we investigate the sensitivity of satellite gradiometry missions such as GOCE to secular signals due to ice-mass change observed in Greenland and Antarctica. We show that unaccounted ice-mass change signal is likely to increase GOCE-related noise but that the expected present-day polar ice-mass change is below the GOCE sensitivity for an 18-month mission. Furthermore, 2–3 orders of magnitude improvement in the gradiometry in future gradiometer missions is necessary to detect ice-mass change with sufficient accuracy at the spatial resolution of interest.     

Accuracy of the earth's gravity field models

Accuracy tests on the most recent GEM (Goddard Earth Model) gravity models for the representation of the Earth's gravity field, using specially devised statistical techniques of comparative evaluation, show that there is steady improvement in these models with time. On this comparative basis, the accuracy of determination for the spherical harmonic coefficients of the Earth's gravity field is ～ 100% for n = 2–6, 90–99% for n = 7–10, 55–80% for n = 11–14 and ? 50% for n ? 15, deteriorating rapidly with increasing n. The higher degree coefficients corresponding to n ≥ 15 do not seem to be determined accurately enough to be useful from a geophysical standpoint, though their cumulative contribution is undoubtedly useful for specific orbital computations. The estimated errors are 0.3 mGal for n = 2–6, 1.5 mgal for the frequency range n = 2–10, 3 mGal for n = 2–14 and 5–6 mGal for n = 2–22. These error estimates, especially the ones for the higher frequency range, may have been affected by possible errors in the comparison standards used for this evaluation. Consequently, some of the higher degree coefficients of recent GEM models may be more accurate than predicted by these tests.Due to the inherent deficiency of the comparison standards, the errors given in this paper should be treated as error estimates. The steady and progressive improvement, shown by the various GEM gravity models when tested against comparison standards 10E and WGS 72, i.e. the more recent a gravity model, the better it tests against the comparison standards in contrast to its predecessors, is remarkable, as the comparison standards themselves are several years older than the gravity models tested here. This clearly validates our choice of comparison standards, as well as the premises and predictions of our evaluation techniques. It also demonstrates the power and potential of these techniques, which only seem to be limited by the level of accuracy of the available standard of comparison.     

Parameters of the normal gravity field deduced from satellite observations

Summary The parameters of the normal gravity field were deduced from the harmonic coefficients[3, 4] upto n=6 and compared with the parameters used hitherto. The symbols used are the same as in papers[5, 6, 8] with which this paper connects up.     

The product spectra of gravity and barometric pressure in Europe

A total of 111 000 hourly values of gravity and barometric pressure from stations in Europe is analysed. The data consist of two sets of records from Brussels, an early set of 36 000 h length and a more recent set of 21 000 h length, a set of records from Bad Homburg of 24 000 h length, and a set of records from Strasbourg of 30 000 h length. All of the gravity measurements were made with similar superconducting instruments and the pressure data were recorded simultaneously at each superconducting gravimeter site. The four sets of records have different time bases, and to bring out common features and suppress individual station systematic errors, the product spectrum is introduced. Spectral density estimates are first computed for a common spectral window for each record, and the product spectrum is formed by multiplying individual spectral estimates across records. The cumulative distribution function is found for the product spectrum and confidence intervals are calculated from it by iteration. The product spectrum in gravity reveals a triplet of resonances in the subtidal band which are shown by an automated computer search to be uniquely associated with the translational modes of the solid inner core. The product spectrum in barometric pressure clearly reveals the first 10 solar heating tides in the atmosphere, but otherwise does not show common features with the gravity product spectrum. In particular, the triplet of resonances in the subtidal band of the gravity product spectrum do not show up in the product spectrum of barometric pressure, climinating the atmosphere as their source.     

Comparison of different gravity field implied density models of the topography

Density within the Earth crust varies between 1.0 and 3.0 g/cm³. The Bouguer gravity field measured in south Iran is analyzed using four different regional-residual separation techniques to obtain a residual map of the gravity field suitable for density modeling of topography. A density model of topography with radial and lateral distribution of density is required for an accurate determination of the geoid, e.g., in the Stokes-Helmert approach. The apparent density mapping technique is used to convert the four residual Bouguer anomaly fields into the corresponding four gravity im-plied subsurface density (GRADEN) models. Although all four density models showed good correlation with the geological density (GEODEN) model of the region, the GRADEN models obtained by high-pass filter-ing and GGM high-pass filtering show better numerical correlation with GEODEN model than the other models.     

Spatial and temporal variation of gravity field in the capital region

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Regional gravity field modeling using free-positioned point masses

A two-step free-positioned point mass method is used for regional gravity field modeling together with the remove-compute-restore (RCR) technique. The Quasi-Newton algorithm (L-BFGS-B) is implemented to solve the nonlinear problem with bound constraints in the first step, while in the second step the magnitudes of the point masses are re-adjusted with known positions in the least-squares sense. In order to reach a good representation of the gravity field, a number of parameter sets have to be defined carefully before the computations. The effects of four important parameter sets (depth limits, number of point masses, original/reduced basis functions and optimization directions) are investigated for regional gravity field modeling based on two numerical test cases with synthetic and real data. The results show that the selection of the initial depth and depth limits is of most importance. The number of point masses for obtaining a good fit is affected by the data distribution, while a dependency on the data variability (signal variation) is negligible. Long-wavelength errors in the predicted height anomalies can be reduced significantly by using reduced basis functions, and the radial-direction optimization proves to be stable and reliable for regular and irregular data scenarios. If the parameter sets are defined properly, the solutions are similar to the ones computed by least-squares collocation (LSC), but require fewer unknowns than LSC.     

文安5．1级地震前的重力场变化

绘制了重力测值的时序变化曲线和空间等值线,从动态的角度分析了2006年7月文安5．1级地震前的流动重力异常的演化及特征。结果显示,地震的孕育过程与重力场变化有关,震中位于重力变化高梯度区的“0”等值线附近。     

利用小波变换研究民乐M6.1地震前区域重力场变化特征

对民乐M 6.1地震前4年河西地区重力场变化进行小波分解,结果表明:重力异常变化一阶小波分体呈现随机性与局部性,反映浅层和局部质量变化引起重力变化;二阶小波分解与地质结构一致,反映断层活动引起的重力变化;三阶小波分解结果表明,在民乐M 6.1地震前,重力显著改变,显示深部物质状态发生变化是引起此次地震发生的重要因素;四阶小波分解反映深部物质状态引起重力变化,对此次民乐M 6.1地震反应不明显。地震发生后,震区构造活动减弱,各阶小波分解对地震反应不明显。     

An analysis on short—wave components of the global stress field

Introduction The intraplate stresses are affected by two types of forces: one is called the first-order stresses (Zoback, 1992) or the long-wave components of stresses, which are closely related to the driving mechanism of the plate motions such as ridge push, continental collision resistance, slab pull (suc-tion) and mantle drag force (Richardson, 1992; WEI, 2000). This type of stress field is character-ized by a uniform feature in very large horizontal scale with 50 times or more of the th…