Analysis of the first year of Earth rotation parameters with a sub-daily resolution gained at the CODE processing center of the IGS

 The solutions of the CODE Analysis Center submitted to the IGS, the International Global Position System (GPS) Service for Geodynamics, are based on three days of observation of about 80–100 stations of the IGS network. The Earth rotation parameters (ERPs) are assumed to vary linearly over the three days with respect to an a priori model. Continuity at the day boundaries as well as the continuity of the first derivatives are enforced by constraints. Since early April 1995 CODE has calculated a new ERP series with an increased time resolution of 2 hours. Again continuity is enforced at the 2-hours-interval boundaries. The analysis method is described, particularly how to deal with retrograde diurnal terms in the ERP series which may not be estimated with satellite geodetic methods. The results obtained from the first year of data covered by the time series (time interval from 4 April 1995 to 30 June 1996) are also discussed. The series is relatively homogeneous in the sense of the used orbit model and the a priori model for the ERPs. The largest source of excitation at daily and sub-daily periods is likely to be the effect of the ocean tides. There is good agreement between the present results and Topex/Poseidon ocean tide models, as well as with models based on Very Long Baseline Interferometry (VLBI) and Satellite Laser Ranging (SLR) data. Non-oceanic periodic variations are also observed in the series. Their origin is most probably a consequence of the GPS solution strategy; other possible sources are the atmospheric tides. Received: 13 July 1999 / Accepted: 21 March 2000     

Comparison of length of day with oceanic and atmospheric angular momentum series

This is a companion paper to earlier comparisons and study of operational polar motion series, published recently in the same journal. In this contribution, four operational, publicly available, length-of-day (LOD) time series have been compared to the atmospheric angular momentum (AAM) augmented with recent oceanic angular momentum (OAM) data during September 1997–July 2000, using several intervals ranging from 3 days to almost 3 years. Additionally, the LOD of the International GNSS Service (IGS) historical series and a new LOD combination (CMB) were also analyzed. All the six LOD series showed an overall correlation exceeding 0.99 for the complete interval of almost 3 years. Even for the shortest interval of only 3 days, the correlation was still higher than 0.60. The combined AAM + OAM series with inverted barometer corrections always gave the best correlation. The Rapid Service LOD of the International Earth Rotation and Reference Systems Service (IERS) compared the best at all intervals but the shortest one, where the CMB LOD was the best with a correlation of 0.73, followed by both IGS series with a correlation of about 0.71. Prior to all the correlation analyses, in addition to the removal of all the known (conventional) LOD tidal variations with periods ranging from 5.6 days to 18.6 years and lunar fortnightly and monthly oceanic tides, small corrections of lunar fortnightly and monthly tides, semi-annual, annual periodical signals, drift and scale had to be estimated with respect to the combined AAM + OAM series.     

Polar motion of the triaxial nonrigid Earth and atmospheric excitation

The present study aims to extend the traditional rotation theory of the rotational-symmetric Earth to the triaxial Earth.We re-formulate the Liouville equations and their general solutions for the triaxial nonrigid Earth and find that the traditional theory intro-duces some theoretical errors in modeling the excitation functions.Furthermore,we apply that theory to the atmospheric excitation and find that theoretical errors should not be neglected given the present measurement accuracy.Thus we conclude that the traditional the-ory of the rotation of the rotational-symmetric Earth should be revised and upgraded to include the effects of the Earth’s triaxiality.     

Combinations of Earth-orientation measurements: SPACE97, COMB97, and POLE97

Independent Earth-orientation measurements taken by the space-geodetic techniques of lunar and satellite laser ranging, very-long-baseline interferometry, and the global positioning system have been combined using a Kalman filter. The resulting combined Earth-orientation series, SPACE97, consists of values and uncertainties for universal time, polar motion, and their rates spanning the period 28 September 1976 to 3 January 1998 at daily intervals. The space-geodetic measurements used to generate SPACE97 have then been combined with optical astrometric measurements to form two additional combined Earth-orientation series: (1) COMB97, consisting of values and uncertainties for universal time, polar motion, and their rates spanning the period 20 January 1962 to 1 January 1998 at 5-day intervals, and (2) POLE97, consisting of values and uncertainties for polar motion and its rate spanning the period 20 January 1900 to 21 December 1997 at monthly intervals. Received: 10 August 1998 / Accepted: 31 May 1999     

Combination procedure for length-of-day time series according to the noise frequency behavior

 Length-of-day (LOD) estimates from seven Global Positioning System (GPS) and three satellite laser ranging (SLR) analysis centers were combined into an even-spaced time series for a 27-month period (1996–1998). This time series was compared to the multi-technique Earth-orientation-parameter (EOP) combined solution (C04) derived at the Central Bureau of the International Earth Rotation Service (IERS/CB). Due to inhomogeneities in the different series derived from the various techniques (time, length, quality, and spatial resolution), the concept of a combined solution is justified. The noise behavior in LOD for different techniques varies with frequency; the data series were divided into frequency windows after removing both biases and trends. Different weight factors were assigned in each window, discriminating by technique, and produced one-technique combined solutions. Finally, these one-technique combined solutions were combined to obtain the final multi-technique solution. The LOD combined time series obtained by the present method based on the frequency windows combined series (FWCS) is very close to the IERS C04 solution. It could be useful to generate a new LOD reference time series to be used in the study of high-frequency variations of Earth rotation. Received: 28 March 2000 / Accepted: 15 February 2001     

A note on Earth's rotation angular velocity in the general-relativity framework

 The value of the Earth's rotational angular velocity determined from observations is given in the GCRS (geocentric celestial reference system) defined by Resolution B1 of the 2000 IAU General Assembly. The same quantity derived from dynamical theories of the Earth's rotation, such as SMART97, is referred to the␣DGRSC (dynamically non-rotating ecliptical reference system). The relativistic theory of reference systems (RSs) enables unambiguous general-relativity relations between these quantities to be derived. Received: 9 November 2000 / Accepted: 9 July 2001     

Wavelet analysis of interannual LOD, AAM, and ENSO: 1997–98 El Niño and 1998–99 La Niña signals

 On the basis of the data series of the length of day (LOD), the atmospheric angular momentum (AAM) and the Southern Oscillation Index (SOI) for January 1970–June 1999, the relationship among Interannual LOD, AAM, and the EL Ni?o/Southern Oscillation (ENSO) is analyzed by the wavelet transform method. The results suggest that they have similar time-varying spectral structures. The signals of 1997–98 El Ni?o and 1998–99 La Ni?a events can be detected from the LOD or AAM data. Received: 25 January 2000 / Accepted: 9 January 2001     

The temporal variation of the spherical and Cartesian multipoles of the gravity field: the generalized MacCullagh representation

 The Cartesian moments of the mass density of a gravitating body and the spherical harmonic coefficients of its gravitational field are related in a peculiar way. In particular, the products of inertia can be expressed by the spherical harmonic coefficients of the gravitational potential as was derived by MacCullagh for a rigid body. Here the MacCullagh formulae are extended to a deformable body which is restricted to radial symmetry in order to apply the Love–Shida hypothesis. The mass conservation law allows a representation of the incremental mass density by the respective excitation function. A representation of an arbitrary Cartesian monome is always possible by sums of solid spherical harmonics multiplied by powers of the radius. Introducing these representations into the definition of the Cartesian moments, an extension of the MacCullagh formulae is obtained. In particular, for excitation functions with a vanishing harmonic coefficient of degree zero, the (diagonal) incremental moments of inertia also can be represented by the excitation coefficients. Four types of excitation functions are considered, namely: (1) tidal excitation; (2) loading potential; (3) centrifugal potential; and (4) transverse surface stress. One application of the results could be model computation of the length-of-day variations and polar motion, which depend on the moments of inertia. Received: 27 July 1999 / Accepted: 24 May 2000     

Atmospheric, oceanic and hydrological contributions to seasonal variations in length of day

 The annual and semiannual residuals derived in the axial angular momentum budget of the solid Earth–atmosphere system reflect significant signals. They must be caused by further excitation sources. Since, in particular, the contribution for the wind term from the atmospheric layer between the 10 and 0.3 hPa levels to the seasonal variations in length of day (LOD) is still missing, it is necessary to extend the top level into the upper stratosphere up to 0.3 hPa. Under the conservation of the total angular momentum of the entire Earth, variations in the oceanic angular momentum (OAM) and the hydrological angular momentum (HAM) are further significant excitation sources at seasonal time scales. Focusing on other contributions to the Earth's axial angular momentum budget, the following data are used in this study: axial atmospheric angular momentum (AAM) data derived for the 10–0.3 hPa layer from 1991 to 1997 for computing the missing wind effects; axial OAM functions as generated by oceanic general circulation models (GCMs), namely for the ECHAM3 and the MICOM models, available from 1975 to 1994 and from 1992 to 1994, respectively, for computing the oceanic contributions to LOD changes, and, concerning the HAM variations, the seasonal estimates of the hydrological contribution as derived by Chao and O'Connor [(1988) Geophys J 94: 263–270]. Using vector representation, it is shown that the vectors achieve a close balance in the global axial angular momentum budget within the estimated uncertainties of the momentum quantities on seasonal time scales. Received: 6 April 2000 / Accepted: 13 December 2000     

数字地球与3维地理信息系统研究

美国副总统戈尔关于“数字地球”的演讲引起许多国家政界、学术界的关注。基于“数字地球”的概念,在全球信息数字化过程中,３维地理信息系统起着重要作用。由于空间对象和３维ＧＩＳ的复杂性,在处理各种空间现象时,如地质现象的表示和矿山应用,宜根据实际应用的需要,采用不同的数据结构和可视化方式,包括２维、２．５维、３维的以及它们的结合,以取得良好效果和效益。     

Rotation of the Earth as a Triaxial Rigid Body

The Earth is taken as a triaxial rigid body, which rotates freely in the Euclidian space. The starting equations are the Euler dynamic equations, with A smaller than B and B smaller than C. The Euler equations are solved, and the numerical results are provided. In the calculations, the following parameters are used: (C-B)/A=0.003 273 53; (B-A)/C=0.000 021 96; (C-A)/B=0.003 295 49, and the mean angular velocity of the Earth's rotation, ω =0.000 072 921 15 rad/s. Calculations show that, besides the self-rotation of the Earth and the free Euler procession of its rotation, there exists the free nutation: the nutation angle, or the angle between the Earth's momentary rotation axis and the mean axis that periodically change with time. The free nutation is investigated.     

Google Earth支持下校园真实感三维建模方法及应用

以Google Earth为平台,结合SketchUp的建筑物真实感三维建模功能,以西南交通大学校园为例建立校园真实感三维模型,并对其应用进行分析。该方法实现地形数据与建筑物三维模型的精确叠加,解决建模过程中的数据获取和融合问题,为虚拟环境的构建提供具有参考价值的解决方案。     

Seasonal length-of-day changes and atmospheric angular momentum oscillations in their temporal variability

Recently, effective atmospheric-angular-momentum (AAM) functions as calculated from National Centers for Environmental Prediction (NCEP) (formerly National Meteorological Center, NMC) and National Center for Atmospheric Research (NCAR) Reanalyses have become available for the years 1958 to 1998. Concerning the wind terms, the top level in the atmosphere used here is 10 hPa. Compared with earlier NMC model versions, which incorporate wind fields up to 100 hPa since 1976 and up to 50 hPa since 1981, the reanalyses have produced improved data series over a longer period than before. The axial AAM component χ₃ is associated with changes in length of day (LOD). Motivated by better quality and continuity of the series AAM (NCEP) Reanalysis, the problem of the seasonal imbalances in the solid Earth–atmosphere axial angular momentum budget is re-examined. To assess better the estimates of the annual and semiannual oscillations in LOD and AAM and of the residual oscillations derived as difference series between LOD and AAM, the series of LOD data from three analysis centers [International Earth Rotation Service (IERS), GeoForschungZentrum Potsdam (GFZ) and Jet Propulsion Laboratory Pasadena (JPL)] and of AAM data in terms of χ₃(W), χ₃(P) and χ₃(P+IB) from four meteorological centers [NCEP, Japan Meteorological Agency (JMA), European Centre for Medium-Range Weather Forecasts (ECMWF) and the UK Meteorological Office (UKMO)] are used in this study. The main analysis steps were removing gaps, filtering out the seasonal oscillations, calculating optimal estimates of the parameters of the oscillations and calculating the difference series between the LOD and AAM systems as well as the residuals in the axial angular momentum budget in the LOD–AAM systems. The results derived as difference series between the different LOD, AAM and LOD–AAM systems show to what extent the variations reflect systematic differences and significant signals, respectively, which is important for future activities in this field. Received: 2 February 1999 / Accepted: 30 November 1999     

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     

A unified approach to the Clenshaw summation and the recursive computation of very high degree and order normalised associated Legendre functions

 Spherical harmonic expansions form partial sums of fully normalised associated Legendre functions (ALFs). However, when evaluated increasingly close to the poles, the ultra-high degree and order (e.g. 2700) ALFs range over thousands of orders of magnitude. This causes existing recursion techniques for computing values of individual ALFs and their derivatives to fail. A common solution in geodesy is to evaluate these expansions using Clenshaw's method, which does not compute individual ALFs or their derivatives. Straightforward numerical principles govern the stability of this technique. Elementary algebra is employed to illustrate how these principles are implemented in Clenshaw's method. It is also demonstrated how existing recursion algorithms for computing ALFs and their first derivatives are easily modified to incorporate these same numerical principles. These modified recursions yield scaled ALFs and first derivatives, which can then be combined using Horner's scheme to compute partial sums, complete to degree and order 2700, for all latitudes (except at the poles for first derivatives). This exceeds any previously published result. Numerical tests suggest that this new approach is at least as precise and efficient as Clenshaw's method. However, the principal strength of the new techniques lies in their simplicity of formulation and implementation, since this quality should simplify the task of extending the approach to other uses, such as spherical harmonic analysis. Received: 30 June 2000 / Accepted: 12 June 2001     

3维城市模型建模方法分类与建模流程探讨

3维城市模型建模方法有很多种,每种方法在数据量、建模效率、逼真度、数据管理、适用范围、拓扑复杂度、几何复杂度、纹理复杂度等诸多方面都存在差异,如何选择一种适合实际情况的3维城市模型建模方法,规范建模流程,是一个值得讨论的问题。     

The theory and application of the structure light engineering surveying based on a laser theodolite with three freedoms of rotation

The concepts of “confining structure” and structure light are illuminated in this paper. A laser theodolite with three freedoms of rotation, which is aimed at “confining structure”, is developed. Various scanning modes and their mathematical models based on laser theodolite with three freedoms of rotation are discussed. According to the features of a huge object the structure light engineering surveying based on laser theodolite with three freedoms of rotation is determined as the main method in an actual application. The observation of four sound concrete posts and forced centering plates. Subsequently, it is transformed into the huge object coordinate system. The scanning mode with plumb plane is selected as the main mode in the whole work. And other assistant methods, such as close range photogrammetry and the method of using reflection sheet, are applied to the work of “scanning dead angle”. At last, a surveying accuracy estimation of this method is done and a surveying accuracy test is finished. It can be concluded that the structure light engineering surveying based on laser theodolite with three freedoms of rotation is considered to be an effective and applied method, and has many superiority to some other surveying methods in the work of surveying “confining structure”.     

THE THEORY AND APPLICATION OF THE STRUCTURE LIGHT ENGINEERING SURVEYING BASED ON A LASER THEODOLITE WITH THREE FREEDOMS OF ROTATION

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On comparison of the Earth orientation parameters obtained from different VLBI networks and observing programs

In this paper, a new geometry index of very long baseline interferometry (VLBI) observing networks, the volume of network V, is examined as an indicator of the errors in the Earth orientation parameters (EOP) obtained from VLBI observations. It has been shown that both EOP precision and accuracy can be well described by the power law σ = aV ^c in a wide range of the network size from domestic to global VLBI networks. In other words, as the network volume grows, the EOP errors become smaller following a power law. This should be taken into account for a proper comparison of EOP estimates obtained from different VLBI networks. Thus, performing correct EOP comparison allows us to investigate accurately finer factors affecting the EOP errors. In particular, it was found that the dependence of the EOP precision and accuracy on the recording data rate can also be described by a power law. One important conclusion is that the EOP accuracy depends primarily on the network geometry and to lesser extent on other factors, such as recording mode and data rate and scheduling parameters, whereas these factors have a stronger impact on the EOP precision.     

基于数据手套和跟踪器的虚拟手臂建模

文中利用数据手套和跟踪器获取手臂各关节运动数据,根据关节运动限制对所获取数据进行处理,建立了符合人体运动规律的虚拟手臂数学模型,实现了虚拟环境中与试验者的手臂同步运动、效果逼真的虚拟手臂模型.