7个月周期极移的非线性动力机制

从滞弹性阻尼形变摄动造成CW频率调制假设出发，对CW的共振激发模型加上参数的时变调制，变成了参数共振模型。经正演计算发现，参数共振模型完全符合CW的实际，表明滞弹性阻尼形变摄动造成频率的3％调制，进一步使得CW振幅调制可达70％以上。这一参数共振模型是一个非线性动力系统，在非线性情况下，运动将发生分岔，即多解。     

用极移数据直接测算钱德勒摆动Q值

运用已经发展起来的共振激发和参数共振模型,在频率调制的基础上,对IERS极移数据测算出钱德勒摆动的Q值,得到平均值为63,并以每百年0.8的速率在增大。这一结果与Q的滞弹性PREM模型理论值69十分接近,表明共振激发模型和参数共振模型完全与钱德勒摆动滞弹理论相容。     

三轴弹性地球自转的动力学方程

整体地球自转动力学理论一般假设地球是旋转对称的,但实际上地球是一个非对称的旋转椭球体。因此,三轴地球自转的研究是符合现实的。本文在弹性地球自转Liouville方程的基础上,在推导过程中所有量保留到极移平方和椭率乘积量级而忽略其更小量级的情况下,给出了适用于地球自转研究的三轴弹性地球自转的动力学方程。同时也列出了求解三轴弹性地球自转自由摆动的两种方法,即椭圆积分方法和椭圆函数方法。最后指出,如果在推导过程中保留更小量级,则弹性地球模型的自转动力学方程无解析解;旋转对称地球自转的线性解是三轴地球模型在极移量级下的一种特例,且三轴弹性地球模型不可能出现第二自由摆动。     

On long-period polar motion

 Five separate polar motion series are examined in order to understand what portion of their variations at periods exceeding several years represents true polar motion. The data since the development of space-geodetic techniques (by themselves insufficient for study of long-period motion), and a variety of historical astrometric data sets, allow the following tentative conclusions: retrograde long-period polar motion below about −0.2 cpy (cycles per year) in pre-space-geodetic data (pre-1976) is dominantly noise. For 1976–1992, there is poor agreement between space-geodetic and astrometric series over the range −0.2 to +0.2 cpy, demonstrating that classical astrometry lacked the precision to monitor polar motion in this frequency range. It is concluded that all the pre-1976 astrometric polar motion data are likely to be dominated by noise at periods exceeding about 10 years. The exception to this is possibly a linear trend found in some astrometric and space geodetic series. At frequencies above prograde +0.2 cpy (periods shorter than about 5 years), historical astrometric data may be of sufficient quality for comparisons with geophysical excitation time series. Even in the era of space geodesy, significant differences are found in long-period variations in published polar motion time series. Received: 27 March 2001 / Accepted: 15 October 2001     

液核地球极移和章动理论模型的改进

以经典的液核弹性地球自转动力学理论为基础,通过引入章动坐标系相对惯性空间的运动,建立液核地球极移和章动的联合动力学方程。由此定义液核地球的CIP轴,并对其进行解算。研究表明新方法克服了传统方法不能解决的一些问题(例如CEP和CIP的定义),简化了传统方法求解的复杂性。值得注意的是新方法可同时求解极移和章动,特别是在Smith M.L.(1977)理论中出现的倾斜模(TOM),在此只是作为一个特解而存在。     

对钱德勒参数进行时变修正的CLS+AR模型在极移预测中的应用

根据LS模型参数中钱德勒项的时变性质,提出了基于钱德勒参数时变修正的CLS模型,并用CLS+AR对极移进行预测。实验结果表明,CLS+AR模型在极移预测精度上较LS+AR模型有较大改善。     

Comparison of polar motion with oceanic and atmospheric angular momentum time series for 2-day to Chandler periods

During a 4-year period starting in July 1996 and using intervals ranging from 3 days to 4 years, four precise polar motion (PM) series have been compared to excitation by atmospheric angular momentum (AAM) augmented with oceanic angular momentum (OAM) data. The first three series (C03, C04 and Bulletin A) are multi-technique combinations generated by the International Earth Rotation and Reference Systems Service (IERS) and the fourth combined series (IGS00P02) is produced by the International GPS Service (IGS) using only GPS data. The IGS PM compared the best with the combined excitations of atmosphere and oceans (AAM+OAM) at all intervals, showing high overall correlation of 0.8–0.9. Even for the interval of only three days, the IGS PM gave a significant correlation of about 0.6. Moreover, during the interval of February 1999 – July 2000, which should be representative of the current precision of the IGS PM, a significant correlation (>0.4) extended to periods as short as 2.2 days and 2.5 days for the x_p and y_p PM components, respectively. When using the IERS Bulletin B (C04) PM and an interval of almost 6 years, starting in November 1994, the combined OAM+AAM accounted for practically all the annual, semi-annual and Chandler wobble (CW) PM signals. When only AAM was used, either the US National Centers for Environment Prediction reanalysis data, which were used throughout this study, or the Japanese Meteorological Agency data, two large and well-resolved amplitude peaks of about 0.1 mas/day, remained at the retrograde annual and CW periods.     

Nonlinear analysis of the three-dimensional datum transformation [conformal group ℂ7(3)]

 The weighted Procrustes algorithm is presented as a very effective tool for solving the three-dimensional datum transformation problem. In particular, the weighted Procrustes algorithm does not require any initial datum parameters for linearization or any iteration procedure. As a closed-form algorithm it only requires the values of Cartesian coordinates in both systems of reference. Where there is some prior information about the variance–covariance matrix of the two sets of Cartesian coordinates, also called pseudo-observations, the weighted Procrustes algorithm is able to incorporate such a quality property of the input data by means of a proper choice of weight matrix. Such a choice is based on a properly designed criterion matrix which is discussed in detail. Thanks to the weighted Procrustes algorithm, the problem of incorporating the stochasticity measures of both systems of coordinates involved in the seven parameter datum transformation problem [conformal group ℂ₇(3)] which is free of linearization and any iterative procedure can be considered to be solved. Illustrative examples are given. Received: 7 January 2002 / Accepted: 9 September 2002 Correspondence to: E. W. Grafarend     

A bound for the Euclidean norm of the difference between the best linear unbiased estimator and a linear unbiased estimator

 A bound is established for the Euclidean norm of the difference between the best linear unbiased estimator and any linear unbiased estimator in the general linear model. The bound involves the spectral norm of the difference between the dispersion matrices of the two estimators, and the residual sum of squares, all evaluated at the assumed model, but is independent of the provenance of the observation vector at hand. The bound, a straightforward consequence of first principles in Gauss–Markov theory, generalizes previous results on the difference between the best linear unbiased estimator and the ordinary least-squares estimator. In a numerical example from repeated precise levelling, the bound is used to analyse the sensitivity of estimates of vertical motion to the choice of estimator. Received: 9 September 1999 / Accepted: 15 March 2002     

Present-day crustal deformation in China relative to ITRF97 kinematic plate model

 A global plate motion model is established based on the ITRF97 velocity fields and geological model NUVEL1. Sub-plate models are estimated by using the velocity fields derived from 45 global positioning system (GPS) sites under the ITRF97 reference frame in China. Comparisons between space geodesy and geological models are given. It is found that the Euler vector of the AFRC–EURA pair has an obvious discrepancy between space geodetic and geological models. The motion patterns of tectonic blocks in China predicted by GPS are consistent with those of geological data on the whole. Received: 9 November 2000 / Accepted: 17 September 2001     

Robust estimator for correlated observations based on bifactor equivalent weights

 A new robust parameter estimator for the adjustment of correlated observations is developed based on a `bifactor reduction' model of weight elements. A shrinking factor for weight elements is proposed. The new equivalent weight matrix composed by the bifactor weight elements preserves the symmetry and keeps the original correlation coefficients unchanged. The new parameter estimator with its error influence function is derived. The robustness and efficiency of the new robust estimator is demonstrated with a simulated example and some conclusions are drawn. Received: 5 March 2001 / Accepted: 17 January 2002     

How to handle topography in practical geoid determination: three examples

 Three different methods of handling topography in geoid determination were investigated. The first two methods employ the residual terrain model (RTM) remove–restore technique, yielding the quasigeoid, whereas the third method uses the classical Helmert condensation method, yielding the geoid. All three methods were used with the geopotential model Earth Gravity Model (1996) (EGM96) as a reference, and the results were compared to precise global positioning system (GPS) levelling networks in Scandinavia. An investigation of the Helmert method, focusing on the different types of indirect effects and their effects on the geoid, was also carried out. The three different methods used produce almost identical results at the 5-cm level, when compared to the GPS levelling networks. However, small systematic differences existed. Received: 18 March 1999 / Accepted: 21 March 2000     

Atmospheric and oceanic forcing of the rapid polar motion

The rapid polar motion for periods below 20 days is revisited in light of the most recent and accurate geodetic and geophysical data. Although its amplitude is smaller than 2 mas, it is excited mostly by powerful atmospheric processes, as large as the seasonal ones. The residual amplitude, representing about 20% of the total excitation, stems from the oceans. Rapid polar motion has an irregular nature that is well explained by the combined influence of the atmosphere and the oceans. An overall spectrum reveals cycles principally at 20, 13.6 (fortnightly tidal period) and 10 days (corresponding to the normal atmospheric mode Y₃¹{\Psi_3^1}), but this is only an averaged feature hiding its strong variability over seasonal time scales. This explains why it is so delicate to determine an empirical model of the tidal effect on polar motion. The variability in both amplitude and phase of the 13.6-day term is probably caused by a lunar barometric effect, modulated by some sub-seasonal thermal processes. The irregularities of the prominent cycles of the short-term polar motion are well explained by the atmospheric and oceanic excitations. The oceanic variability reinforces the atmospheric one, as they were triggered by the same agent, maybe seasonal and inter-annual thermal variations.     

Molodensky potential telluroid based on a minimum-distance map. Case study: the quasi-geoid of East Germany in the World Geodetic Datum 2000

 A potential-type Molodensky telluroid based upon a minimum-distance mapping is derived. With respect to a reference potential of Somigliana–Pizzetti type which relates to the World Geodetic Datum 2000, it is shown that a point-wise minimum-distance mapping of the topographical surface of the Earth onto the telluroid surface, constrained to the gauge W(P)=u(p), leads to a system of four nonlinear normal equations. These normal equations are solved by a fast Newton–Raphson iteration. Received: 7 February 2000 / Accepted: 23 October 2001     

利用LS_AR模型对极移参数的中长期预报

为了满足深空探测器自主导航定位对极移参数中长期预报的需求,阐述了基于LS_AR模型的极移参数中长期预报和精度评定的原理,提出了4种改进方案对LS_AR模型的构建进行优化,并利用IERS提供的1990～1996年的极移参数的时间序列检验4种优化方案,得到了最优的预报模型,在400 d跨度上,其预报结果的平均绝对误差比未优化的模型小3 mas左右。     

Evidence and cause of climate cycles in polar motion

 The long-term variation of polar motion contains a number of periods similar to climate cycles. Two possible causes for these long-term variations are mass redistributions produced by variations of atmospheric and oceanic circulation, and mass exchanges between the cryosphere and hydrosphere. Inner-core wobble, which can be inferred from the observed motion of the geomagnetic pole, is another phenomenon with periods similar to climate cycles. Only observations relating to mass redistributions caused by atmosphere dynamics and inner-core wobble are available for sufficiently long periods of time to investigate their influence on climate cycles in polar motion. Both processes contribute to climate cycles in polar motion, but they cannot completely explain these cycles. Possible sources of climate cycles are discussed. Received: 20 December 1999 / Accepted: 28 August 2000     

GPS network monitors the Western Alps' deformation over a five-year period: 1993–1998

  The Western Alps are among the best studied collisional belts with both detailed structural mapping and also crustal geophysical investigations such as the ECORS and EGT seismic profile. By contrast, the present-day kinematics of the belt is still largely unknown due to small relative motions and the insufficient accuracy of the triangulation data. As a consequence, several tectonic problems still remain to be solved, such as the amount of N–S convergence in the Occidental Alps, the repartition of the deformation between the Alpine tectonic units, and the relation between deformation and rotation across the Alpine arc. In order to address these problems, the GPS ALPES group, made up of French, Swiss and Italian research organizations, has achieved the first large-scale GPS surveys of the Western Alps. More than 60 sites were surveyed in 1993 and 1998 with a minimum observation of 3 days at each site. GPS data processing has been done by three independent teams using different software. The different solutions have horizontal repeatabilities (N–E) of 4–7 mm in 1993 and 2–3 mm in 1998 and compare at the 3–5-mm level in position and 2-mm/yr level in velocity. A comparison of 1993 and 1998 coordinates shows that residual velocities of the GPS marks are generally smaller than 2 mm/yr, precluding a detailed tectonic interpretation of the differential motions. However, these data seem to suggest that the N–S compression of the Western Alps is quite mild (less than 2 mm/yr) compared to the global convergence between the African and Eurasian plate (6 mm/yr). This implies that the shortening must be accomodated elsewhere by the deformation of the Maghrebids and/or by rotations of Mediterranean microplates. Also, E–W velocity components analysis supports the idea that E–W extension exists, as already suggested by recent structural and seismotectonic data interpretation. Received: 27 November 2000 / Accepted: 17 September 2001     

The parameter distributions of the integer GPS model

 A parameter estimation theory is incomplete if no rigorous measures are available for describing the uncertainty of the parameter estimators. Since the classical theory of linear estimation does not apply to the integer GPS model, rigorous probabilistic statements cannot be made with reference to the classical results. The fact that integer parameters are involved in the estimation process forces a reappraisal of the propagation of uncertainty. It is with this purpose in mind that the joint and marginal distributional properties of both the integer and non-integer parameters of the GPS model are determined. These joint distributions can also be used to determine the distribution of functions of the parameters. As an important example, the distribution of the vector of ambiguity residuals is determined. Received: 30 January 2001 / Accepted: 31 July 2001     

Precise estimation of residual tropospheric delays using a regional GPS network for real-time kinematic applications

 A new method called Trop_NetAdjust is described to predict in real time the residual tropospheric delays on the GPS carrier phase observables using the redundant measurements from a network of GPS reference stations. This method can not only enhance the effectiveness and reliability of real-time kinematic users within the network, but also provide a valid approach to tropospheric parameter variation forecasting. Trop_NetAdjust is theoretically based upon LS prediction criteria and enables the prediction of residual tropospheric delays remaining after a standard model has been applied to the raw GPS measurements. Two cases are analyzed, namely a first case when the delay is required for an existing satellite at a new point within the network and a second case when the delay is required for a new satellite. Field tests were conducted using data collected in a network of 11 reference stations covering a 400×600 km region in southern Norway. The results were analyzed in the measurement domain (ionospheric-free double-difference residuals) and showed improvements of 20 to 65% RMS errors using Trop_NetAdjust. The estimates of the Trop_NetAdjust prediction accuracy were also obtained using the covariance analysis method. The agreement was consistently better than 30% when compared with data from a real network. Received: 28 February 2000 / Accepted: 9 January 2001     

On fine orbit selection for particular geodetic and oceanographic missions involving passage through resonances

 The identification of mean semi-major axes (suitably defined) for satellite orbits to satisfy a variety of requirements for geodesy, geophysics and oceanography, in terms of repeat orbits (with orbital resonances), is investigated. Various options for the definition of semi-major axis, from the viewpoint of satellite dynamics, are described. Simple simulations of the expected resonant changes in inclination are presented, and tools for the analysis of orbit resonances to extract certain lumped harmonic coefficients of the geopotential (e.g. from the very precise CHAMP orbit) are resurrected. Finally, a preliminary example of the 46th-order resonance analysis possible for CHAMP, based on the mean orbital elements produced by GFZ (GeoForschungs Zentrum) for ephemeris prediction, is presented. Received: 10 July 2001 / Accepted: 17 July 2002 Correspondence to: J. Klokočník at Ondřejov Observatory Acknowledgements. We thank Prof. Dr. Ch. Reigber, Dr. P. Schwintzer, Dr. T. Gruber and Dr. R. K?nig from GFZ Potsdam for various consultations and discussions, and for the CHAMP two-line mean elements. This investigation was performed under the aegis of CEDR (Center for Earth's Dynamics Research, Prague-Ondřejov); it has been supported by project LN00A005 (provided by the Ministry of Education of the Czech Republic) and by grant A 3004 of the Grant Agency of the Academy of Sciences of the Czech Republic.