The impact of radio source structure on European geodetic VLBI measurements

European geodetic very long baseline interferometry (VLBI) sessions (also known as EUROPE sessions) have been carried out on a regular basis for the past 15 years to study relative crustal motions within Europe. These sessions are based on observations of extragalactic radio sources, which serve as distant fiducial marks to establish an accurate and stable celestial reference frame for long-term geodetic measurements. The radio sources, however, are not always point-like on milliarcsecond scales, as VLBI imaging has revealed. In this work, we quantify the magnitude of the expected effect of intrinsic source structure on geodetic bandwidth synthesis delay VLBI measurements for a subset of 14 sources regularly observed during the EUROPE sessions. These sources have been imaged at both X-band (8.4 GHz) and S-band (2.3 GHz) based on dedicated observations acquired with the European VLBI Network (EVN) in November 1996. The results of this calculation indicate that the reference source 0457+024 causes significant structural effects in measurements obtained on European VLBI baselines (about 10 picoseconds on average), whereas most of the other sources produce effects that are only occasionally larger than a few picoseconds. Applying the derived source structure models to the data of the EUROPE5-96 session carried out at the same epoch as the EVN experiment shows no noticeable changes in the estimated VLBI station locations.     

Geodetic VLBI with an artificial radio source on the Moon: a simulation study

We perform extensive simulations in order to assess the accuracy with which the position of a radio transmitter on the surface of the Moon can be determined by geodetic VLBI. We study how the quality and quantity of geodetic VLBI observations influence these position estimates and investigate how observations of such near-field objects affect classical geodetic parameters like VLBI station coordinates and Earth rotation parameters. Our studies are based on today’s global geodetic VLBI schedules as well as on those designed for the next-generation geodetic VLBI system. We use Monte Carlo simulations including realistic stochastic models of troposphere, station clocks, and observational noise. Our results indicate that it is possible to position a radio transmitter on the Moon using today’s geodetic VLBI with a two-dimensional horizontal accuracy of better than one meter. Moreover, we show that the next-generation geodetic VLBI has the potential to improve the two-dimensional accuracy to better than 5 cm. Thus, our results lay the base for novel observing concepts to improve both lunar research and geodetic VLBI.     

Radio source instability in VLBI analysis

The source position time-series for many of the frequently observed radio sources in the NASA geodetic very long baseline interferometry (VLBI) program show systematic linear and non-linear variations of as much as 0.5 mas (milli-arc-seconds) to 1.0 mas, due mainly to source structure changes. In standard terrestrial reference frame (TRF) geodetic solutions, it is a common practice to only estimate a global source position for each source over the entire history of VLBI observing sessions. If apparent source position variations are not modeled, they produce corresponding systematic variations in estimated Earth orientation parameters (EOPs) at the level of 0.02–0.04 mas in nutation and 0.01–0.02 mas in polar motion. We examine the stability of position time-series of the 107 radio sources in the current NASA geodetic source catalog since these sources have relatively dense observing histories from which it is possible to detect systematic variations. We consider different strategies for handling source instabilities where we (1) estimate the positions of unstable sources for each session they are observed, or (2) estimate spline parameters or rate parameters for sources chosen to fit the specific variation seen in the position-time series. We found that some strategies improve VLBI EOP accuracy by reducing the biases and weighted root mean square differences between measurements from independent VLBI networks operating simultaneously. We discuss the problem of identifying frequently observed unstable sources and how to identify new sources to replace these unstable sources in the NASA VLBI geodetic source catalog.     

VLBI observations of GNSS-satellites: from scheduling to analysis

The possibility of observing satellites with the very long baseline interferometry (VLBI) technique has been discussed for several years in the geodetic community, with observations of either existing satellites of the global navigation satellite systems or of satellites dedicated to realise a space tie. Such observations were carried out using the Australian telescopes in Hobart and Ceduna which, for the first time, integrated all the necessary steps: planning the observations (automated scheduling), correlation of the data and the generation of a series of time delay observables suitable for a subsequent geodetic analysis. We report on the development of new and the adaptation of existing routines for observing and data processing, focusing on technology development. The aim was to use methods that are routinely used in geodetic VLBI. A series of test experiments of up to six hours duration was performed, allowing to improve the observations from session to session and revealing new problems still to be solved. The newly developed procedures and programs now enable more observations. Further development assumed, this bears the prospect of being directly applied to the observation of dedicated space-tie satellites.     

New VLBI2010 scheduling strategies and implications on the terrestrial reference frames

In connection with the work for the next generation VLBI2010 Global Observing System (VGOS) of the International VLBI Service for Geodesy and Astrometry, a new scheduling package (Vie_Sched) has been developed at the Vienna University of Technology as a part of the Vienna VLBI Software. In addition to the classical station-based approach it is equipped with a new scheduling strategy based on the radio sources to be observed. We introduce different configurations of source-based scheduling options and investigate the implications on present and future VLBI2010 geodetic schedules. By comparison to existing VLBI schedules of the continuous campaign CONT11, we find that the source-based approach with two sources has a performance similar to the station-based approach in terms of number of observations, sky coverage, and geodetic parameters. For an artificial 16 station VLBI2010 network, the source-based approach with four sources provides an improved distribution of source observations on the celestial sphere. Monte Carlo simulations yield slightly better repeatabilities of station coordinates with the source-based approach with two sources or four sources than the classical strategy. The new VLBI scheduling software with its alternative scheduling strategy offers a promising option with respect to applications of the VGOS.     

组合VLBI和SLR数据估计的全球板块运动参数

本文组合应用ＶＬＢＩ和ＳＬＲ数据导出了一个完全基于空间技术实测数据的现时板块运动模型，称为ＳＧＰＭＭ１。ＳＧＰＭＭ１与地学板块运动模型ＮＵＶＥＬ－１的比较指出：空间大地测量数据估计的板块运动总体上与地学估计值一致。经过地磁极倒转时间尺度修正，并考虑到冰斯后地壳回弹的影响，空间大地测量数据估计的北美，欧亚和澳大利亚板块之间的相对运动速率与地学估计值有极好的一致，但太平洋板块相对于北美、欧亚和澳大利亚     

组合GPS和VLBI数据建立板块运动模型

利用GPS和VLBI的组合数据,解算了北美、欧亚、太平洋等12板块之间的相对运动欧拉矢量,得到了实测的板块运动模型GVM1。与地学模型(NUVEL1A)的比较指出,GVM1大体上与地学模型一致;EURANOAM的极位置与NUVEL1A的相应极比较接近,旋转速率略微偏大;澳大利亚板块在最近几年内是稳定的;太平洋板块与其他板块对的极位置与地学模型较为接近,这表明多种技术的组合数据提高了板块运动模型建立的精确性和可靠性。     

Advanced relativistic VLBI model for geodesy

Our present relativistic part of the geodetic VLBI model for Earthbound antennas is a consensus model which is considered as a standard for processing high-precision VLBI observations. It was created as a compromise between a variety of relativistic VLBI models proposed by different authors as documented in the IERS Conventions 2010. The accuracy of the consensus model is in the picosecond range for the group delay but this is not sufficient for current geodetic purposes. This paper provides a fully documented derivation of a new relativistic model having an accuracy substantially higher than one picosecond and based upon a well accepted formalism of relativistic celestial mechanics, astrometry and geodesy. Our new model fully confirms the consensus model at the picosecond level and in several respects goes to a great extent beyond it. More specifically, terms related to the acceleration of the geocenter are considered and kept in the model, the gravitational time-delay due to a massive body (planet, Sun, etc.) with arbitrary mass and spin-multipole moments is derived taking into account the motion of the body, and a new formalism for the time-delay problem of radio sources located at finite distance from VLBI stations is presented. Thus, the paper presents a substantially elaborated theoretical justification of the consensus model and its significant extension that allows researchers to make concrete estimates of the magnitude of residual terms of this model for any conceivable configuration of the source of light, massive bodies, and VLBI stations. The largest terms in the relativistic time delay which can affect the current VLBI observations are from the quadrupole and the angular momentum of the gravitating bodies that are known from the literature. These terms should be included in the new geodetic VLBI model for improving its consistency.     

Ionospheric calibration of single frequency VLBI and GPS observations using dual GPS data

Summary The ionospheric effect is one of the main sources of error in Very Long Baseline Interferometry (VLBI) and Global Positioning System (GPS) high precision geodesy. Although the use of two frequencies allows the estimation of this effect, in some cases dual observations are not possible due to the available equipment or the type of observation. This paper presents the ionospheric calibration of single frequency VLBI and GPS observations based on the ionospheric electron content estimated from dual frequency GPS data. The ionospheric delays obtained with this procedure and the VLBI baseline length results have been compared with those obtained with dual frequency data. For the European geodetic VLBI baselines, both solutions agree at the 3–5 parts in 10^–9 level. The noise introduced by the GPS-based calibration is in the order of 3 cm for the VLBI observables and of 10 cm for the GPS observables.     

Effect of the selection of reference radio sources on geodetic estimates from VLBI observations

This paper evaluates the effect of the accuracy of reference radio sources on the daily estimates of station positions, nutation angle offsets, and the estimated site coordinates determined by very long baseline interferometry (VLBI), which are used for the realization of the international terrestrial reference frame (ITRF). Five global VLBI solutions, based on VLBI data collected between 1979 and 2006, are compared. The reference solution comprises all observed radio sources, which are treated as global parameters. Four other solutions, comprising different sub-sets of radio sources, were computed. The daily station positions for all VLBI sites and the corrections to the nutation offset angles were estimated for these five solutions. The solution statistics are mainly affected by the positional instabilities of reference radio sources, whereas the instabilities of geodetic and astrometric time-series are caused by an insufficient number of observed reference radio sources. A mean offset of the three positional components (Up, North, East) between any two solutions was calculated for each VLBI site. From a comparison of the geodetic results, no significant discrepancies between the respective geodetic solutions for all VLBI sites in the Northern Hemisphere were found. In contrast, the Southern Hemisphere sites were more sensitive to the selected set of reference radio sources. The largest estimated mean offset of the vertical component between two solutions for the Australian VLBI site at Hobart was 4 mm. In the worst case (if a weak VLBI network observed a limited number of reference radio sources) the daily offsets of the estimated height component at Hobart exceeded 100 mm. The exclusion of the extended radio sources from the list of reference sources improved the solution statistics and made the geodetic and astrometric time-series more consistent. The problem with the large Hobart height component offset is magnified by a comparatively small number of observations due to the low slewing rate of the VLBI dish (1°/ s). Unless a minimum of 200 scans are performed per 24-h VLBI experiment, the daily vertical positions at Hobart do not achieve 10 mm accuracy. Improving the slew rate at Hobart and/or having an increased number of new sites in the Southern Hemisphere is essential for further improvement of geodetic VLBI results for Southern Hemisphere sites.     

Influence of subdaily polar motion model on nutation offsets estimated by very long baseline interferometry

This paper studies the connection between the subdaily model for polar motion used in the processing of very long baseline interferometry (VLBI) observations and the estimated nutation offsets. By convention accepted by the International Earth Rotation Service, the subdaily model for polar motion recommended for routine processing of geodetic observations does not contain any daily retrograde terms due to their one-to-one correlation with the nutation. Nevertheless, for a 24-h VLBI solution a part of the signal contained in the polar motion given by the used subdaily model is numerically mistaken for a retrograde daily sidereal signal. This fictitious retrograde daily signal contributes to the estimated nutation, leading to systematic differences between the nutation offsets from VLBI solutions computed with different subdaily polar motion models. We demonstrate this effect using solutions for all suitable 24-h VLBI sessions over a time span of 11 years (2000–2011). By changing the amplitudes of one tidal term in the underlying subdaily model for polar motion and comparing the estimated parameters to the solutions computed with the unchanged subdaily model, the paper shows and explains theoretically the effects produced by the individual subdaily terms on the VLBI nutation estimates.     

Geodetic VLBI correlation in software

Correlation algorithms for geodetic very long baseline interferometry (VLBI) can now be effectively implemented on parallel computers of modest size. We have undertaken a detailed comparison of the output from a trusted geodetic correlator, one that has supported global geodetic VLBI observations for many years, with the output of a software correlator implemented on a small parallel computing cluster. We show that the correlator outputs agree closely, within expected error bounds, after accounting for the differences in the adopted geometric delay models, and therefore that use of the software correlator is feasible for geodetic VLBI processing, as a first step toward routine geodetic data processing. Recent developments in software correlation for geodesy are discussed, including the possibility of real-time processing options.     

Refined discrete and empirical horizontal gradients in VLBI analysis

Missing or incorrect consideration of azimuthal asymmetry of troposphere delays is a considerable error source in space geodetic techniques such as Global Navigation Satellite Systems (GNSS) or Very Long Baseline Interferometry (VLBI). So-called horizontal troposphere gradients are generally utilized for modeling such azimuthal variations and are particularly required for observations at low elevation angles. Apart from estimating the gradients within the data analysis, which has become common practice in space geodetic techniques, there is also the possibility to determine the gradients beforehand from different data sources than the actual observations. Using ray-tracing through Numerical Weather Models (NWMs), we determined discrete gradient values referred to as GRAD for VLBI observations, based on the standard gradient model by Chen and Herring (J Geophys Res 102(B9):20489–20502, 1997.  https://doi.org/10.1029/97JB01739) and also for new, higher-order gradient models. These gradients are produced on the same data basis as the Vienna Mapping Functions 3 (VMF3) (Landskron and Böhm in J Geod, 2017.  https://doi.org/10.1007/s00190-017-1066-2), so they can also be regarded as the VMF3 gradients as they are fully consistent with each other. From VLBI analyses of the Vienna VLBI and Satellite Software (VieVS), it becomes evident that baseline length repeatabilities (BLRs) are improved on average by 5% when using a priori gradients GRAD instead of estimating the gradients. The reason for this improvement is that the gradient estimation yields poor results for VLBI sessions with a small number of observations, while the GRAD a priori gradients are unaffected from this. We also developed a new empirical gradient model applicable for any time and location on Earth, which is included in the Global Pressure and Temperature 3 (GPT3) model. Although being able to describe only the systematic component of azimuthal asymmetry and no short-term variations at all, even these empirical a priori gradients slightly reduce (improve) the BLRs with respect to the estimation of gradients. In general, this paper addresses that a priori horizontal gradients are actually more important for VLBI analysis than previously assumed, as particularly the discrete model GRAD as well as the empirical model GPT3 are indeed able to refine and improve the results.     

A Global Terrestrial Reference Frame from simulated VLBI and SLR data in view of GGOS

In this study, we assess the impact of two combination strategies, namely local ties (LT) and global ties (GT), on the datum realization of Global Terrestrial Reference Frames in view of the Global Geodetic Observing System requiring 1 mm-accuracy. Simulated Very Long Baseline Interferometry (VLBI) and Satellite Laser Ranging (SLR) data over a 7 year time span was used. The LT results show that the geodetic datum can be best transferred if the precision of the LT is at least 1 mm. Investigating different numbers of LT, the lack of co-located sites on the southern hemisphere is evidenced by differences of 9 mm in translation and rotation compared to the solution using all available LT. For the GT, the combination applying all Earth rotation parameters (ERP), such as pole coordinates and UT1-UTC, indicates that the rotation around the Z axis cannot be adequately transferred from VLBI to SLR within the combination. Applying exclusively the pole coordinates as GT, we show that the datum can be transferred with mm-accuracy within the combination. Furthermore, adding artificial stations in Tahiti and Nigeria to the current VLBI network results in an improvement in station positions by 13 and 12%, respectively, and in ERP by 17 and 11%, respectively. Extending to every day VLBI observations leads to 65% better ERP estimates compared to usual twice-weekly VLBI observations.     

卫星VLBI测轨资料处理中的电离层延迟改正

结合我国探月项目卫星VLBI测轨资料分析中的实际需求讨论了两个问题：一是在S、X波段时延测量精度均为1ns情况下，电离层延迟改正所能够达到的精度；二是在飞行器VLBI测轨过程中，不能确保S、X波段双频观测情况下获取电离层时延改正的可能途径，包括借助于相关电离层模型、利用常规VLB1历史观测资料积累、借助于局域GPS观测网和IGS网单站GPS测量以及借助于专门设计的单站GPS测量等。最后对电离层VLB1和GPS技术实测结果进行了比较和问题分析。     

Results of the VLBI experiments conducted with Syowa Station, Antarctica

The first successful geodetic Very Long Baseline Interferometry (VLBI) observations to Antarctica were made on baselines from Syowa Station (Antarctica) to Tidbinbilla (Australia) and to Kashima (Japan) in January 1990. Regular geodetic experiments started in 1998 with the installation of a permanent VLBI terminal at Syowa Station. These observations are conducted at the standard geodetic VLBI frequencies of 2.3 and 8.4 GHz, S- and X-Bands. In the first year, the 11-m multipurpose antenna at Syowa Station observed together with the 26-m radio telescope of the University of Tasmania in Australia and the 26-m radio telescope of the Hartebeesthoek Radio Astronomy Observatory in South Africa. From 1999, the experiments were expanded to also include the O’Higgins Station in Antarctica, Fortaleza in Brazil and Kokee on Hawaii. From 1999 until the end of 2003, 25 observing sessions have been reduced and analyzed using the CALC/SOLVE geodetic VLBI data reduction package. The results show that the horizontal baseline of Syowa-Hobart is increasing at the rate of 57.0±1.9 mm/year. The baseline Syowa-Hartebeesthoek is also increasing, but at the lower rate of 9.8±1.9 mm/year. The VLBI result of 2.0±3.1 mm/year and the GPS result of −1.9±0.7 mm/year for the Syowa-O’Higgins horizontal baseline support the hypothesis of one rigid Antarctic plate without intra-plate deformation, which is consistent with the NNR-NUVEL-1A global plate motion model. The location of the Euler pole of the Antarctic plate by VLBI is estimated as 59.7°S and 62.6°E with a rotation rate of 0.190 deg/Myr, while that by GPS in our study is estimated as 60.6°S and 42.2°E with a rotation rate of 0.221 deg/Myr. These pole positions are slightly different to that implied by the NNR-NUVEL-1A model of 63.0°S and 64.2°E with a rotation rate of 0.238 deg/Myr. VLBI observations over a longer time span may resolve small discrepancy of current plate motion from the NNR-NUVEL-1A model. The consistency of the VLBI coordinates with the GPS coordinates at Syowa Station, after correction for the local tie vector components between the two reference markers, is also discussed.     

Height bias and scale effect induced by antenna gravitational deformations in geodetic VLBI data analysis

The impact of signal path variations (SPVs) caused by antenna gravitational deformations on geodetic very long baseline interferometry (VLBI) results is evaluated for the first time. Elevation-dependent models of SPV for Medicina and Noto (Italy) telescopes were derived from a combination of terrestrial surveying methods to account for gravitational deformations. After applying these models in geodetic VLBI data analysis, estimates of the antenna reference point positions are shifted upward by 8.9 and 6.7 mm, respectively. The impact on other parameters is negligible. To simulate the impact of antenna gravitational deformations on the entire VLBI network, lacking measurements for other telescopes, we rescaled the SPV models of Medicina and Noto for other antennas according to their size. The effects of the simulations are changes in VLBI heights in the range [−3, 73] mm and a net scale increase of 0.3–0.8 ppb. The height bias is larger than random errors of VLBI position estimates, implying the possibility of significant scale distortions related to antenna gravitational deformations. This demonstrates the need to precisely measure gravitational deformations of other VLBI telescopes, to derive their precise SPV models and to apply them in routine geodetic data analysis.     

Ka波段天测与测地VLBI观测的利弊分析

分析了天测与测地甚长基线干涉测量（very long baseline interferometry,VLBI）观测频率设置的必要性,重点分析了Ka波段观测的利弊。相比于X波段,Ka波段观测的优点包括河外源更致密、核移效应更小,更有利于提高射电天球参考架的实现精度以及与天体物理学全球天体测量干涉仪（global astrometric interferometer for astrophysics,Gaia）计划准惯性光学参考架的连接精度。在深空探测方面的优点表现为遥测数据率高,VLBI跟踪测量精度高,更有利于减小大气电离层和太阳等离子体对测量时延的不利影响。缺点包括河外源相对较弱,天线反射面精度和指向精度要求较高,大气吸收和辐射效应的影响更大等,但是这些因素所造成的系统灵敏度的降低有望通过高数据率采样而得到补偿。结合我国VLBI技术现状提出了发展建议。     

空间VLBI观测量估计大地测量参数的模拟计算

介绍了研究空间VLBI在大地测量等领域应用的意义，探讨了空间VLBI的观测量类型、观测模型及其涉及的大地测量所关心的参数；并采用1980～2004年的VLBI观测数据进行了计算，对大地测量所关心的几种参数的计算结果进行了分析。     

The effects of frequency-dependent quasar variability on the celestial reference frame

We examine the relationship between source position stability and astrophysical properties of radio-loud quasars making up the International Celestial Reference Frame (ICRF2). Understanding this relationship is important for improving quasar selection and analysis strategies, and therefore reference frame stability. We construct flux density time series, known as light curves, for 95 of the most frequently observed ICRF2 quasars at both the 2.3 and 8.4 GHz geodetic very long baseline interferometry (VLBI) observing bands. Because the appearance of new quasar components corresponds to an increase in quasar flux density, these light curves alert us about potential changes in source structure before they appear in VLBI images. We test how source position stability depends on three astrophysical parameters: (1) flux density variability at X band; (2) time lag between flares in S and X bands; (3) spectral index root-mean-square (rms), defined as the variability in the ratio between S and X band flux densities. We find that the time lag between S and X band light curves provides a good indicator of position stability: sources with time lags $<$ 0.06 years are significantly more stable ( $>$ 20 % improvement in weighted rms) than sources with larger time lags. A similar improvement is obtained by observing sources with low $(<$ 0.12) spectral index variability. On the other hand, there is no strong dependence of source position stability on flux density variability in a single frequency band. These findings can be understood by interpreting the time lag between S and X band light curves as a measure of the size of the source structure. Monitoring of source flux density at multiple frequencies therefore appears to provide a useful probe of quasar structure on scales important to geodesy. The observed astrometric position of the brightest quasar component (the core) is known to depend on observing frequency. We show how multi-frequency flux density monitoring may allow the dependence on frequency of the relative core positions along the jet to be elucidated. Knowledge of the position–frequency relation has important implications for current and future geodetic VLBI programs, as well as the alignment between the radio and optical celestial reference frames.