Lunar gravity field determination using SELENE same-beam differential VLBI tracking data

A lunar gravity field model up to degree and order 100 in spherical harmonics, named SGM100i, has been determined from SELENE and historical tracking data, with an emphasis on using same-beam S-band differential VLBI data obtained in the SELENE mission between January 2008 and February 2009. Orbit consistency throughout the entire mission period of SELENE as determined from orbit overlaps for the two sub-satellites of SELENE involved in the VLBI tracking improved consistently from several hundreds of metres to several tens of metres by including differential VLBI data. Through orbits that are better determined, the gravity field model is also improved by including these data. Orbit determination performance for the new model shows improvements over earlier 100th degree and order models, especially for edge-on orbits over the deep far side. Lunar Prospector orbit determination shows an improvement of orbit consistency from 1-day predictions for 2-day arcs of 6 m in a total sense, with most improvement in the along and cross-track directions. Data fit for the types and satellites involved is also improved. Formal errors for the lower degrees are smaller, and the new model also shows increased correlations with topography over the far side. The estimated value for the lunar GM for this model equals 4902.80080±0.0009 km³/s² (10 sigma). The lunar degree 2 potential Love number k ₂ was also estimated, and has a value of 0.0255 ± 0.0016 (10 sigma as well).     

利用多代卫星测高数据反演海洋重力场

为了解决多代卫星测高数据之间的不协调性问题,本文基于误差验后补偿理论,提出将传统的交叉点平差整体解法简化为两步处理法,即首先使用条件平差法对交叉点观测方程进行平差计算,然后沿测高轨迹进行海面高滤波和推估。在此基础上,本文利用多代卫星测高数据联合平差获得的结果,进一步反演了中国海及其邻域地区的重力异常,并将计算结果同海面船测数据作了比对,实际算例已经证明了新方法的有效性。     

重力场模型对Swarm卫星精密定轨的影响分析

采用星载GPS观测数据与简化动力学定轨方法,在方程中引入伪随机脉冲参数,从而实现对Swarm卫星的精密定轨.详细分析了不同阶次的GOCO06s地球重力场模型对Swarm卫星简化动力学定轨精度的影响,对比了PGM2000a、EIGEN-2、EGM2008以及GECO重力场模型展开到100阶次时Swarm卫星解算的轨道精度...     

利用卫星重力数据计算地幔对流应力场

针对我国东南边缘及其邻近区域地幔对流应力场分布形态与地表构造活动特征的相关性问题,提出利用Runcorn模型及高阶卫星重力球谐系数计算欧亚板块与菲律宾板块复合接触带及其邻近区域的地幔对流应力场。结果显示,地幔对流应力矢量特征与地震应力场分布具有较好的一致性。在两大板块的接触部位均出现了显著的应力增强与汇聚趋势,同时在琉球海沟的弧后扩张带上出现的较强的地幔对流应力发散带。而在各板块相对稳定的内部区域存在微弱的地幔发散流。通过计算和分析得出,该区域下地壳小尺度的地幔对流可能是控制这一区域型构造过程的重要因素之一。     

联合多代测高数据建立中国海域重力异常模型

本文联合T/P数据、T/P新轨道数据、ERS数据、GFO数据、GeosatGM数据和ERS-1/168数据,用测高卫星记录点的位置信息直接计算沿轨大地水准面的方向导数,结合测线轨迹方向的方位角在交叉点处推求垂线偏差,然后利用逆Vening-Meinesz公式计算了中国近海(0o～41oN,105o～132oN)2′×2′格网分辨率的海域重力异常模型。将其与CLS_SHOW99重力异常模型比较,统计结果表示与该模型差异的RMS为8.15mgal,在剔除差值大于20mgal的点(剔除3.3%)以后,RMS为4.72mgal;与某海区船测重力异常比较的RMS为8.91mgal。     

Simulation of regional gravity field recovery from satellite gravity gradiometer data using collocation and FFT

When planning a satellite gravity gradiometer (SGG) mission, it is important to know the quality of the quantities to be recovered at ground level as a function of e.g. satellite altitude, data type and sampling rate, and signal variance and noise. This kind of knowledge may be provided either using the formal error estimates of wanted quantities using least-squares collocation (LSC) or by comparing simulated data at ground level with results computed by methods like LSC or Fast Fourier Transform (FFT). Results of a regional gravity field recovery in a 10^o×20^o area surrounding the Alps using LSC and FFT are reported. Data used as observations in satellite altitude (202 or161 km) and for comparison at ground level were generated using theOSU86F coefficient set, complete to degree 360. These observations are referred to points across simulated orbits. The simulated quantities were computed for a 45 days mission period and 4 s sampling. A covariance function which also included terms above degree 360 was used for prediction and error estimation. This had the effect that the formal error standard deviation for gravity anomalies were considerably larger than the standard deviations of predicted minus simulated quantities. This shows the importance of using data with frequency content above degree 360 in simulation studies. Using data at202 km altitude the standard deviation of the predicted minus simulated data was equal to8.3 mgal for gravity and0.33 m for geoid heights.     

Evaluation of the third- and fourth-generation GOCE Earth gravity field models with Australian terrestrial gravity data in spherical harmonics

In March 2013, the fourth generation of European Space Agency’s (ESA) global gravity field models, DIR4 (Bruinsma et al. in Proceedings of the ESA living planet symposium, 28 June–2 July, Bergen, ESA, Publication SP-686, 2010b) and TIM4 (Migliaccio et al. in Proceedings of the ESA living planet symposium, 28 June–2 July, Bergen, ESA, Publication SP-686, 2010), generated from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) gravity observation satellite was released. We evaluate the models using an independent ground truth data set of gravity anomalies over Australia. Combined with Gravity Recovery and Climate Experiment (GRACE) satellite gravity, a new gravity model is obtained that is used to perform comparisons with GOCE models in spherical harmonics. Over Australia, the new gravity model proves to have significantly higher accuracy in the degrees below 120 as compared to EGM2008 and seems to be at least comparable to the accuracy of this model between degree 150 and degree 260. Comparisons in terms of residual quasi-geoid heights, gravity disturbances, and radial gravity gradients evaluated on the ellipsoid and at approximate GOCE mean satellite altitude ( $h=250$  km) show both fourth generation models to improve significantly w.r.t. their predecessors. Relatively, we find a root-mean-square improvement of 39 % for the DIR4 and 23 % for TIM4 over the respective third release models at a spatial scale of 100 km (degree 200). In terms of absolute errors, TIM4 is found to perform slightly better in the bands from degree 120 up to degree 160 and DIR4 is found to perform slightly better than TIM4 from degree 170 up to degree 250. Our analyses cannot confirm the DIR4 formal error of 1 cm geoid height (0.35 mGal in terms of gravity) at degree 200. The formal errors of TIM4, with 3.2 cm geoid height (0.9 mGal in terms of gravity) at degree 200, seem to be realistic. Due to combination with GRACE and SLR data, the DIR models, at satellite altitude, clearly show lower RMS values compared to TIM models in the long wavelength part of the spectrum (below degree and order 120). Our study shows different spectral sensitivity of different functionals at ground level and at GOCE satellite altitude and establishes the link among these findings and the Meissl scheme (Rummel and van Gelderen in Manusrcipta Geodaetica 20:379–385, 1995).     

Assessment of chlorophyll variability along the Louisiana coast using multi-satellite data

Variability in surface chlorophyll (Chl) concentrations derived from the Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) were examined in conjunction with river discharge, QuikSCAT satellite-derived winds, and sea surface height (SSH) anomaly data along the Louisiana coast, USA. Surface Chl distributions exhibited rapid response to strong northerly winds following a frontal passage. A comparison of time series (1998–2010) river discharge and monthly Chl data indicated Chl variability to be well correlated to seasonal river discharge only for locations near the two river deltas, while offshore, enhancements in Chl during fall–winter was likely due to cross-shelf transport or mixing associated with strong northerly wind stress. Variance in Chl examined using wavelet analysis applied to nearly 10 years (1998–2007) of SeaWiFS data indicated patterns of significant Chl variability due to combined enhanced wind and river discharge, offshore flows associated with Ekman transport and coastal wind convergence, and the effect of Hurricane Rita in 2005. Instances of significant Chl variance were also observed to occur during years of large hypoxic zone size suggesting potential linkages to hypoxia. SSH anomaly imagery indicated the presence of warm-core eddies that were responsible for the offshore dispersal of elevated Chl observed in the monthly SeaWiFS imagery. Overall, the use of multi-satellite data better described the forcing and patterns of Chl distributions along the river-dominated Louisiana coast and shelf.     

Absolute gravity determination with JILAG-3 — improved data evaluation and instrumental technics

In addition to the on-line data evaluation during the measurements with the absolute gravity meter JILAG-3, a subsequently more intensive examination of the measured time/distance data pairs is performed. This allows an additional assessment of the gravity results, the station quality and the measurement conditions. Sinusoidal disturbances in the raw data deteriorate the determination of gravity. Incoming microseisms affect the mean result of the free-fall experiments randomly after a large number of measurements. Instrumental vibrations of the gravity meter during the measurement procedure may influence the gravity result systematically. A station comparison indicates that a 30 Hz frequency is triggered by JILAG-3 itself and influences the measurements depending on the stability of the foundation. Using a mathematical filter it is possible to separate the deteriorations from the gravity acceleration. Up to now an improvement in the absolute accuracy of gravity after filtering could not be proved, but an increase of the precision is indicated.     

Comparison of present SST gravity field models

IntroductionSince 2000 , with the launch of CHAMP satellite,several series of high-accuracy and high-resolutionstatic Earth’s gravityfield models have been createdbased on aboundent SST data. With these models ,the research in solid geophysics ,oceangraphy,andgeodesy can be promoted greatly[1].In this paper ,the SSTgravity models’accura-cyin various frequently domainis studied.First-ly,the difference among these models is compu-ted and compared,and then their accuracyis an-alyzed. Fina…     

Comparison of present SST gravity field models

Taking the main land of Europe as the region to be studied, the potential of the new satellite gravity technique: satellite-to-satellite tracking (SST) and improving the accuracy of regional gravity field model with the SST models are investigated. The drawbacks of these models are discussed. With GPM98C as the reference, the gravity anomaly residuals of several other models, the latest SST global gravity field models (EIGEN series and GGM series), were computed and compared. The results of the comparison show that in the selected region, some systematic errors with periodical properties exist in the EIGEN and GGM's S series models in the high degree and order. Some information that was not shown in the classic gravity models is detected in the low and middle degree and order of EIGEN and GGM's S series models. At last, the effective maximum degrees and orders of SST models are suggested.     

Evaluation of the first GOCE static gravity field models using terrestrial gravity,vertical deflections and EGM2008 quasigeoid heights

Recently, four global geopotential models (GGMs) were computed and released based on the first 2 months of data collected by the Gravity field and steady-state Ocean Circulation Explorer (GOCE) dedicated satellite gravity field mission. Given that GOCE is a technologically complex mission and different processing strategies were applied to real space-collected GOCE data for the first time, evaluation of the new models is an important aspect. As a first assessment strategy, we use terrestrial gravity data over Switzerland and Australia and astrogeodetic vertical deflections over Europe and Australia as ground-truth data sets for GOCE model evaluation. We apply a spectral enhancement method (SEM) to the truncated GOCE GGMs to make their spectral content more comparable with the terrestrial data. The SEM utilises the high-degree bands of EGM2008 and residual terrain model data as a data source to widely bridge the spectral gap between the satellite and terrestrial data. Analysis of root mean square (RMS) errors is carried out as a function of (i) the GOCE GGM expansion degree and (ii) the four different GOCE GGMs. The RMS curves are also compared against those from EGM2008 and GRACE-based GGMs. As a second assessment strategy, we compare global grids of GOCE GGM and EGM2008 quasigeoid heights. In connection with EGM2008 error estimates, this allows location of regions where GOCE is likely to deliver improved knowledge on the Earth’s gravity field. Our ground truth data sets, together with the EGM2008 quasigeoid comparisons, signal clear improvements in the spectral band ~160–165 to ~180–185 in terms of spherical harmonic degrees for the GOCE-based GGMs, fairly independently of the individual GOCE model used. The results from both assessments together provide strong evidence that the first 2 months of GOCE observations improve the knowledge of the Earth’s static gravity field at spatial scales between ~125 and ~110 km, particularly over parts of Asia, Africa, South America and Antarctica, in comparison with the pre-GOCE-era.     

Comprehensive evaluation of soil moisture retrieval models under different crop cover types using C-band synthetic aperture radar data

In the present study, random forest regression (RFR), support vector regression (SVR) and artificial neural network regression (ANNR) models were evaluated for the retrieval of soil moisture covered by winter wheat, barley and corn crops. SVR with radial basis function kernel was provided the highest adj. R² (0.95) value for soil moisture retrieval covered by the wheat crop at VV polarization. However, RFR provided the adj. R² (0.94) value for soil moisture retrieval covered by barley crop at VV polarization using Sentinel-1A satellite data. The adj. R² (0.94) values were found for the soil moisture covered by corn crop at VV polarization using RFR, SVR linear and radial basis function kernels. The least performance was reported using ANNR model for almost all the crops under investigation. The soil moisture retrieval outcomes were found better at VV polarization in comparison to VH polarization using three different models.     

The analytical continuation bias in geoid determination using potential coefficients and terrestrial gravity data

One important application of an Earth Gravity Model (EGM) is to determine the geoid. Since an EGM is represented by an external-type series of spherical harmonics, a biased geoid model is obtained when the EGM is applied inside the masses in continental regions. In order to convert the downward-continued height anomaly to the corresponding geoid undulation, a correction has to be applied for the analytical continuation bias of the geoid height. This technique is here called the geoid bias method. A correction for the geoid bias can also be utilised when an EGM is combined with terrestrial gravity data, using the combined approach to topographic corrections. The geoid bias can be computed either by a strict integral formula, or by means of one or more terms in a binomial expansion. The accuracy of the lowest binomial terms is studied numerically. It is concluded that the first term (of power H²) can be used with high accuracy up to degree 360 everywhere on Earth. If very high mountains are disregarded, then the use of the H² term can be extended up to maximum degrees as high as 1800. It is also shown that the geoid bias method is practically equal to the technique applied by Rapp, which utilises the quasigeoid-to-geoid separation. Another objective is to carefully consider how the combined approach to topographic corrections should be interpreted. This includes investigations of how the above-mentioned H² term should be computed, as well as how it can be improved by a correction for the residual geoid bias. It is concluded that the computation of the combined topographic effect is efficient in the case that the residual geoid bias can be neglected, since the computation of the latter is very time consuming. It is nevertheless important to be able to compute the residual bias for individual stations. For reasonable maximum degrees, this can be used to check the quality of the H² approximation in different situations.Acknowledgement The author would like to thank Prof. L.E. Sjöberg for several ideas and for reading two draft versions of the paper. His support and constructive remarks have improved its quality considerably. The valuable suggestions from three unknown reviewers are also appreciated.     

高阶地球重力场模型的评价及其优选

采用"移去-恢复"技术确定大地水准面,需要一个全球重力场模型作为参考场。本文采用基于模糊集合理论的最大隶属度原则,通过某试验区的33个GPS水准点的实测大地水准面差距与模型大地水准面差距的比较分析,从国际重力场服务提供的EGM96、EIGEN-CG01C、EIGEN-CG03C、GFZ93A、GFZ96、OSU91A、PGM2000A等七个高阶全球重力场模型中,选择OSU91A作为该地区最优的参考重力场模型。