Earth’s precession–nutation motion: the error analysis of the theories IAU 2000 and IAU 2006 applying the VLBI data of the years 1984–2006

The long-term systematic errors of the analytical theories IAU 2000 and IAU 2006 of the Earth’s precession–nutational motion are studied making use of the VLBI data of 1984–2007. Several independent methods give indubitable evidence of the significant quadratic error in the IAU 2000 residuals of the precessional angle while the adopted value of the secular decrease /cy of the Earth’s ellipticity e (derived from Satellite Laser Ranging data) should manifest itself in the residuals of as the negative quadratic trend . The problem with the precession of the IAU 2006 theory adopted as a new international standard and based on the precession model P03 (Capitaine et al., Astron Astrophys 432:355–367, 2005) appears to be even more serious because the above mentioned quadratic term has already been incorporated into the P03 precession. Our analysis of the VLBI data demonstrates that the quadratic trend of the IAU 2006 residuals does amount to the expected value (30.0 ± 3) mas/cy². It means, first, that the theoretical precession rate of IAU 2006 should be augmented by the large secular correction and, second, that the available VLBI data have potentiality of estimating the rate . And indeed, processing these data by the numerical theory ERA of the Earth’s rotation (Krasinsky, Celest Mech Dyn Astron 96:169–217, 2006, Krasinsky and Vasilyev, Celest Mech Dyn Astron 96:219–237, 2006) yields the estimate /cy statistically in accordance with the satellite-based . On the other hand, applying IAU 2000/2006 models, the positive value /cy is found which is incompatible with the SLR estimate and, evidently, has no physical meaning. The large and steadily increasing error of the precession motion of the IAU 2006 theory makes the task of replacing IAU 2006 by a more accurate model be most pressing.     

An Approach of Tropospheric Correction for VLBI Phase-Referencing using GPS Data

The dominant source of error in VLBI phase-referencing is the troposphere at observing frequencies above 5 GHz. We compare the tropospheric zenith delays derived from VLBI and GPS data at VLBA stations collocated with GPS antennas. The systematic biases and standard deviations both are at the level of sub-centimeter. Based on this agreement, we suggest a new method of tropospheric correction in phase-referencing using combined VLBI and GPS data.     

利用VLBI和超导重力资料研究自由核章动周期时变特征

本文根据自由核章动在章动观测和时变重力观测中引起的与其频率相近的受迫章动项或固体潮潮波的共振特性,选取6个不同机构解算的VLBI天极偏差序列和全球超导重力仪网络提供的7个台站高精度时变重力观测资料,根据加权最小二乘方法拟合地球自由核章动参数,研究其本征周期的时间变化特征.VLBI资料获得的本征周期变化幅度在1天之内,存在十年尺度的时间变化特征,迭积多台站同时段重力资料获得的自由核章动本征周期时变特征与VLBI获得的结果相比变化幅度较大,但趋势大致符合.在此基础上,通过自由核章动的理论模型探讨了影响其本征周期的几个主要因素,结果表明FCN周期变化与电磁耦合存在相关性,核幔边界磁感应强度径向分量变化导致的电磁耦合的变化可能是造成FCN周期时变性的原因.     

Using postglacial sea level, crustal velocities and gravity-rate-of-change to constrain the influence of thermal effects on mantle lateral heterogeneities

Lateral heterogeneities in the mantle can be caused by thermal, chemical and non-isotropic pre-stress effects. Here, we investigate the possibility of using observations of the glacial isostatic adjustment (GIA) process to constrain the thermal contribution to lateral variations in mantle viscosity. In particular, global historic relative sea level, GPS in Laurentide and Fennoscandia, altimetry together with tide-gauge data in the Great Lakes area, and GRACE data in Laurentide are used. The lateral viscosity perturbations are inferred from the seismic tomography model S20A by inserting the scaling factor β to determine the contribution of thermal effects versus compositional heterogeneity and non-isotropic pre-stress effects on lateral heterogeneity in mantle viscosity. When β = 1, lateral velocity variations are caused by thermal effects alone. With β < 1, the contribution of thermal effect decreases, so that for β = 0, there is no lateral viscosity variation and the Earth is laterally homogeneous. These lateral viscosity variations are superposed on four different reference models which differ significantly in the lower mantle viscosity. The Coupled Laplace Finite Element method is used to predict the GIA response on a spherical, self-gravitating, compressible, viscoelastic Earth with self-gravitating oceans, induced by the ICE-4G deglaciation model.Results show that the effect of β on uplift rates and gravity rate-of-change is not simple and involves the trade-off between the contribution of lateral viscosity variations in the transition zone and in the lower mantle. Models with small viscosity contrast in the lower mantle cannot explain the observed uplift rates in Laurentide and Fennoscandia. However, the RF3S20 model with a reference viscosity profile simplified from Peltier's VM2 with the value of β around 0.2–0.4 is found to explain most of the global RSL data, the uplift rates in Laurentide and Fennoscandia and the BIFROST horizontal velocity data. In addition, the changes in GIA signals caused by changes in the value of β are large enough to be detected by the data, although uncertainty in other parameters in the GIA models still exists. This may encourage us to further utilize GIA observations to constrain the thermal effect on mantle lateral heterogeneity as geodetic and satellite gravity measurements are improved.     

Fast transform from geocentric to geodetic coordinates

 A new iterative procedure to transform geocentric rectangular coordinates to geodetic coordinates is derived. The procedure solves a modification of Borkowski's quartic equation by the Newton method from a set of stable starters. The new method runs a little faster than the single application of Bowring's formula, which has been known as the most efficient procedure. The new method is sufficiently precise because the resulting relative error is less than 10⁻¹⁵, and this method is stable in the sense that the iteration converges for all coordinates including the near-geocenter region where Bowring's iterative method diverges and the near-polar axis region where Borkowski's non-iterative method suffers a loss of precision. Received: 13 November 1998 / Accepted: 27 August 1999     

三维有限单元反演的数学方法

以三维节理单元为基础,讨论了利用三维双节点节理单元模型反演地形变资料的理论基础及方法的应用,推导了具体应用的有限元公式及反演的数学公式,并编制了相应的计算程序。最后,通过模型实例的实际计算,研究了方法的可行性。      

一种测定并置站垂线偏差的小网参数转换法

推导了传统全球卫星导航定位系统(GNSS)测定垂线偏差(Deflection of the Vertical, DOV)形式误差的表达式;提出一种可用以解算并置站DOV的小网参数转换法.利用乌鲁木齐南山多技术并置站控制网观测信息,开展了算法验证,并对该站内多个地点DOV开展了实测.结果表明,高精度的小网DOV仅由点位观测精度最高、覆盖面积最广的3个站点决定.个别精度较差的点会为DOV的测定值带来较大的不确定性;采用小网转换法所解算的DOV与实测值间的一致性分别为-2.3′′±4.3′′(子午分量)和0.2′′±4.6′′(卯酉分量);小网转换求取DOV的方法在精度上与经典的GNSS水准方法相当,但步骤更加简便.鉴于多技术并置站会不定期地开展本地测量,可利用该方法实现多技术并置站DOV的零成本长期监测.     

关于2000中国大地坐标系的建议

简述了建议的我国新一代大地坐标系——2000中国大地坐标系的定义和实现,给出了参考椭球的定义常数和导出常数的计算公式及其常数值,以及椭球面及其外部的正常重力公式。     

1-Gbps VLBI, The First Detection of Fringes

We report on the detection of VLBI fringes from quasars by a new VLBI system operating at 1 Gbps (1024 Mbits-per-second). Newly developed 1024 Msps (mega sample-per-second) AD samplers and 1024 Mbps recorders were used for the observations. A correlator with external buffers was used for the 1024 Mbps correlation processing of the tapes data.Our new VLBI system enabled 1024 Mbps VLBI, and this allowed the sampling of a 512 MHz bandwidth from a radio telescope receiver. This is the highest sampling speed ever used for VLBI, and the widest bandwidth used for VLBI observation. Initial sensitivity as evaluated by SNR comparison with earlier VLBI systems produced results to matched the expanded bandwidth. In our first observations, simultaneous optical fibre linked real-time VLBI observations were made to check the validity of data and precisely detemine the clock offsets among the radio telescopes.     

On post-SKA radio astronomy

It is suggested that the development of the SKA will drastically change the face of radio astronomy in the 21st Century. A FAST-style SKA would admit observations of low contrast features, and would be the best design for studying the `dark ages' of the Universe (x≫ 1) where sub-arcmin total power instruments can usefully be employed. To date there have been no proposals for post-SKA, billion square-metra instruments; we speculate that mobile communication systems can be used. In the very distant future, SKA multi-beam systems could be used to collect signals reflected by Solar system bodies such as the asteroid belt. This revised version was published online in July 2006 with corrections to the Cover Date.