Observable quality assessment of broadband very long baseline interferometry system
Ming H. Xu, James M. Anderson, Robert Heinkelmann, Susanne Lunz, Harald Schuh, Guang L. Wang
NNoname manuscript No. (will be inserted by the editor)
Observable quality assessment of broadband very longbaseline interferometry system
Ming H. Xu · James M. Anderson · Robert Heinkelmann · Susanne Lunz · Harald Schuh · Guangli Wang
Received: 29 Nov. 2019 / Accepted: Feb. 2021
Abstract
The next-generation, broadband geodetic very long baseline interferom-etry system, named VGOS, is developing its global network, and VGOS networkswith a small size of 3–7 stations have already made broadband observations from2017 to 2019. We made quality assessments for two kinds of observables in the21 VGOS sessions currently available: group delay and differential total electroncontent ( δ TEC). Our study reveals that the random measurement noise of VGOSgroup delays is at the level of less than 2 ps (1 ps = 10 − s), while the contributionsfrom systematic error sources, mainly source structure related, are at the level of20 ps. Due to the significant improvement in measurement noise, source structureeffects with relatively small magnitudes that are not overwhelming in the S/XVLBI system, for instance 10 ps, are clearly visible in VGOS observations. Anothercritical error source in VGOS observations is discrete delay jumps, for instance, Ming H. XuAalto University Mets¨ahovi Radio Observatory, Mets¨ahovintie 114, 02540 Kylm¨al¨a, Finland;Aalto University Department of Electronics and Nanoengineering, PL15500, FI-00076 Aalto,Finland; Technische Universit¨at Berlin, Institut f¨ur Geod¨asie und Geoinformationstechnik,Fakult¨at VI, Sekr. KAI 2-2, Kaiserin-Augusta-Allee 104-106, D-10553 Berlin, Germany;Shanghai Astronomical Observatory, Chinese Academy of Sciences, 200030 Shanghai, ChinaE-mail: minghui.xu@aalto.fiJames M. AndersonTechnische Universit¨at Berlin, Institut f¨ur Geod¨asie und Geoinformationstechnik, Fakult¨at VI,Sekr. KAI 2-2, Kaiserin-Augusta-Allee 104-106, D-10553 Berlin, Germany; Helmholtz CentrePotsdam, GFZ German Research Centre for Geosciences, Telegrafenberg, 14473 Potsdam,GermanyRobert Heinkelmann, Susanne LunzHelmholtz Centre Potsdam, GFZ German Research Centre for Geosciences, Telegrafenberg,14473 Potsdam, GermanyHarald SchuhHelmholtz Centre Potsdam, GFZ German Research Centre for Geosciences, Telegrafenberg,14473 Potsdam, Germany; Technische Universit¨at Berlin, Institut f¨ur Geod¨asie undGeoinformationstechnik, Fakult¨at VI, Sekr. KAI 2-2, Kaiserin-Augusta-Allee 104-106, D-10553Berlin, GermanyGuangli WangShanghai Astronomical Observatory, Chinese Academy of Sciences, 200030 Shanghai, China a r X i v : . [ a s t r o - ph . I M ] F e b Ming H. Xu et al. a systematic offset of about 310 ps or integer multiples of that. The predominantcausative factor is found to be related to source structure. The measurement noiselevel of δ TEC observables is about 0.07 TECU, but the systematic effects arefive times larger than that. A strong correlation between group delay and δ TECobservables is discovered with a trend of 40 ps/TECU for observations with largestructure effects; there is a second trend in the range 60 ps/TECU to 70 ps/TECUwhen the measurement noise is dominant.
Keywords
VGOS observations · Ionosphere effects · VLBI · IVS · Space geodesy · Radio astronomy
Geodetic very long baseline interferometry (VLBI) is a space-geodetic techniquethat has regularly made global astrometric/geodetic observations since 1979, whichare the basis for creating the International Celestial Reference Frame (ICRF2; Feyet al., 2015) and obtaining a full set of Earth Orientation Parameters. Togetherwith the other three space geodetic techniques, VLBI plays an important role inestablishing the International Terrestrial Reference Frame (ITRF2014; Altamimiet al., 2016). At the beginning of this century, the International VLBI Servicefor Geodesy and Astrometry (IVS ; Schuh and Behrend, 2012; Nothnagel et al.,2017) proposed to develop the next-generation geodetic VLBI system, initiallycalled VLBI2010 (Niell et al., 2006) but subsequently renamed the VLBI GlobalObserving System (VGOS). This new VLBI system relies mainly on the advantagesof small ( ∼
12 meters in diameter) and fast-slewing antennas, ultra-wide observingfrequency receivers (from 2 GHz to 14 GHz), and the expectation of continuousoperation, 24 hours a day and seven days a week (Petrachenko et al., 2009). In orderto achieve its goal of 1 mm position accuracy and 0.1 mm/yr velocity stability onglobal scales, the first strategy proposed by the VGOS working group was to reducethe random noise component of the group delays (Niell et al., 2007). Building aglobal VGOS network with a sufficient number of stations is in progress, and asmall VGOS network has started to make broadband observations. The technicalimplementation of the VGOS system can be found in Niell et al. (2018), and thedata correlation and processing of VGOS observations from a single baseline canbe referred to in Kondo and Takefuji (2016) and Niell et al. (2018). Analyzingthese actual VGOS observations allows us to investigate the measurement noiselevel and the systematic behaviors of the VGOS observations.In this paper we investigate the contribution of random measurement noiseand systematic error sources in VGOS delay and differential total electron content( δ TEC) observables . The relationship between these two types of observablesis also studied. We use a different method of assessing the error level of theVGOS system than that in Elosegui et al. (2018) and Niell et al. (2018), whodemonstrated the post-fit residuals from geodetic VLBI solutions. Furthermore, https://ivscc.gsfc.nasa.gov/index.html An observable refers to a specific kind of quantity, such as amplitude, phase, delay orrate, that has been measured by maximizing the correlation between the recorded signals of adistant radio source at the two stations of a baseline; in addition, δ TEC estimate is includedas another kind of observable in VGOS.bservable quality assessment of VGOS 3 instead of studying observations of one short baseline, we present the results ofVGOS observations from a global network. In section 2 we present the VGOSobservations currently available and introduce the method of data analysis thatwe used. A quality assessment of group delay observables is given in section 3. Insection 4 we demonstrate the measurement noise level and systematic errors in δ TEC observables, estimated simultaneously in VGOS observations. The strongcorrelation between VGOS group delay and δ TEC observables is studied insection 5. In section 6 we summarize and discuss the results.
The IVS conducted a continuous observing campaign with three VLBI networks(two legacy S/X networks and one VGOS broadband network) in 2017, calledCONT17 (Behrend et al., 2020). The VGOS broadband network in CONT17 hada smaller number of stations than the two legacy networks, and it observed onlyfor one third of the whole CONT17 period. However, it provides the first publicdata set of the VGOS broadband system, which was originally proposed about20 years ago. As of 15th Nov. 2019, 16 other VGOS sessions carried out in 2019were released , as listed in Table 1. On average, 24-hour VGOS sessions obtainabout 2.2 times as many as scans than the legacy 24-hour VLBI sessions. Thesebroadband observations were made simultaneously at four 512-MHz-wide bandscentered at 3.2, 5.5, 6.6 and 10.4 GHz. (The detailed technical description of theobserving frequency setup is available in Niell et al. (2018).) The median and meanof the formal errors for group delay and δ TEC observables in each session are alsoshown in the table. The median formal errors of group delay observables for these21 sessions are in the range of 1.2 ps (1 ps = 10 − s) to 3.0 ps, and those for δ TECobservables are in the range of 0.029 TECU (1 TECU = 10 electrons per squaremeter) to 0.060 TECU.We processed the 21 VGOS sessions to determine error contributions in groupdelay observables, including measurement noise and source structure effects, bydoing closure analysis (Xu et al., 2016, 2017; Anderson and Xu, 2018). We adoptedthe same procedure of closure analysis for the VGOS sessions as was developedfor the CONT14 sessions described in Anderson and Xu (2018). (The technicaldescription of our closure analysis can be found in the supplemental informationto Anderson and Xu (2018).) In short, the method of closure analysis statisticallydetermines the baseline equivalent delay error of each individual observation from all the available closure delays involving that observation, called closure-based error estimate; the weighted root-mean-square (WRMS) delay error of agroup of data can then be derived by combining the closure-based error estimatesof the delay observables in the group. The method has two major advantages: Data are available through the NASA CDDIS server:https://cddis.nasa.gov/archive/vlbi/ivsdata/vgosdb/ A scan consists of simultaneous observations of a radio source by two or more stations overan interval on the order of 5 seconds to 2 minutes. In the remainder of this paper, “observation” is used with the restricted meaning of a pairof two stations — a baseline — observing a radio source over a short duration, typically onthe order of 5 seconds to 2 minutes. Ming H. Xu et al. (1) the station-based errors are canceled out exactly in closure delays; and (2)complementary to the post-fit residuals from geodetic solutions, it provides anindependent way of assessing the observable quality. Except for baseline clocks,which in some cases are included in the parameterization as a constant offsetin delays for a specific baseline and can thus only reduce a constant offset inclosure delays, no geodetic parameters in a routine VLBI solution can absorbnonzero closure delays. They therefore contribute entirely to the residuals of theVLBI solution and can bias the estimates of geodetic parameters. In the recentresearch of Bolotin et al. (2019), structure model parameters were included in theVLBI solution of the CONT17 VGOS sessions to reduce the large residual delaysof the sources 0552+398 and 2229+695, which can thus reduce the magnitudesof the delay misclosures. However, the method has not been demonstrated tobe applicable to general cases of radio sources with structure at different scalesor insufficient numbers of observations. In the paper, closure delays, measuringintrinsic structure of sources as closure phases and closure amplitudes, are treatedas errors in VGOS broadband delays only because the effects of source structurebias the geodetic parameters.Closure analysis was also applied to the estimated ionosphere-like phasedispersion parameter, called δ TEC, from these VGOS sessions. δ TEC is thedifference of the total electron content (TEC) along the line of sight from a sourceto each station of a baseline during a scan. Closure δ TEC over a triangle of threeantennas therefore gives insight into the errors in δ TEC measurements.The conditions for the exclusion of an observation, called flagging, aresummarized here: (1) observations with signal-to-noise ratio (SNR) less than 7;(2) station
RAEGYEB from the second day to the last day of CONT17 VGOSobservations, that is the sessions B17338, B17339, B17340 and B17341; and (3) allthe observations on the baseline
ONSA13NE – ONSA13SW .For completeness, we briefly recall the basic equations of the closure analysisand describe the terminology used. Closure delay is the sum of delay observablesover a closed triangle of three stations. For a triangle of three stations, a , b , and c , closure delay is defined by τ clr ≡ τ ab + τ bc + τ ca , (1)where, for instance, τ ab is the delay observable from station a to station b . Thereference-time convention in geodetic VLBI defines that the timestamp of thedelay observable as the time of arrival of the wavefront at the first antenna of abaseline. For instance, delay τ ab ( t ) refers to the delay for a wavefront that arrivesat station a at epoch of t . Therefore, the geodetic delay observables for multiplebaselines in a scan, although they have the same timestamp, do not necessarilyrefer to the same wavefront. When these delay observables are used to deriveclosure delays, a correction is needed to make the geometry of a triangle completelyclose; detailed discussions and dedicated equations can be found in Section 2 of Xuet al. (2016) and in Section 4.1 of Anderson and Xu (2018). An alternative way of forming closure delays is to use the delay observables with geocentric timestamps We refer to effects such as atmosphere, ionosphere, clock, and geometry as station-based—when there is a change at one epoch for a station for any of these effects the correspondingchanges with the same magnitude will happen to all the observations on the baselines of thatstation within the scan of that epoch—and the errors in modeling these effects as station-basederrors.bservable quality assessment of VGOS 5
Table 1
Observing sessions of the VGOS broadband networkDate Session Number Number of Number Station list Delay formal err. δ TEC formal err.(yyyy/mm/dd) name of scans observations of sources Median Mean Median Mean(1) (2) (3) (4) (5) (6) [ps] [TECU]2017/12/03 B17337 1180 5999 67 GsIsK2YjWfWs 1.71 2.12 0.039 0.0462017/12/04 B17338 1170 5037 66 GsIsK2YjWfWs 3.01 5.00 0.060 0.0982017/12/05 B17339 1180 5833 65 GsIsK2YjWfWs 2.86 4.86 0.057 0.0952017/12/06 B17340 1130 5166 66 GsIsK2YjWfWs 2.41 4.50 0.051 0.0892017/12/07 B17341 1246 6043 66 GsIsK2YjWfWs 2.43 4.47 0.050 0.0882019/01/07 VT9007 1132 8310 64 GsK2OeOwYjWfWs 1.70 2.37 0.039 0.0492019/01/22 VT9022 1024 6070 64 K2OeOwYjWfWs 1.45 2.00 0.035 0.0432019/02/04 VT9035 1043 4622 64 GsK2OeYjWfWs 1.39 1.72 0.036 0.0422019/02/19 VT9050 1115 7668 62 GsK2OeYjWfWs 1.37 1.79 0.035 0.0422019/03/04 VT9063 1129 7645 63 GsK2OeYjWfWs 1.34 1.76 0.033 0.0412019/03/18 VT9077 1080 5586 61 GsK2OeYjWfWs 1.29 1.77 0.032 0.0412019/04/01 VT9091 1121 7651 62 GsK2OeYjWfWs 1.43 1.83 0.034 0.0422019/04/15 VT9105 1105 5102 61 GsK2OeWfWs 1.44 1.85 0.035 0.0432019/04/29 VT9119 1126 5142 63 GsK2OeWfWs 1.72 2.19 0.040 0.0482019/05/13 VT9133 1123 4120 63 GsK2OeWfWs 1.71 2.25 0.038 0.0482019/05/28 VT9148 676 1444 60 GsOeWs 1.21 1.67 0.031 0.0392019/06/11 VT9162 1125 4891 64 GsK2OeWfWs 1.43 1.84 0.034 0.0412019/06/24 VT9175 1110 5097 66 GsK2OeWfWs 1.71 2.20 0.039 0.0472019/07/08 VT9189 776 1860 60 GsOeWs 1.17 1.64 0.029 0.0372019/07/22 VT9203 1093 6235 67 GsK2OeOwWfWs 1.94 2.44 0.042 0.0502019/08/05 VT9217 1174 11541 74 GsK2OeOwYjWfWs 1.63 2.29 0.039 0.050
Note 1
Two-letter station codes in column 6 have the following meanings: Gs=
GGAO12M ,Is=
ISHIOKA , K2=
KOKEE12M , Yj=
REAGYEB , Wf=
WESTFORD , Ws=
WETTZ13S , Oe=
ONSA12NE , andOw=
ONSA12SW . Refer to ftp://cddis.gsfc.nasa.gov/pub/vlbi/ivscontrol/ns-codes.txt for moreinformation about these stations. The values in the last four columns are the median andmean of the formal errors for group delay and for the δ TEC observables for observations withSNR > (the astronomical convention), rather than the delay observables used in geodeticsolutions; the former need no correction.The uncertainty of a closure delay is calculated from the formal errors of thethree observables forming it by assuming that they are independent.For the delay observable τ ab at a single epoch, its closure-based error estimate, ∆τ ab , is statistically determined from all the closure delays that are formed by τ ab together with the other un-flagged observations in the scan at that epoch, writtenas ∆τ ab = (cid:80) Ni =1 | τ i clr − ab |√ N , (2)where N is the number of such closure delays and τ i clr − ab is the i -th one. The number √ τ ab was repeated for all observations one by one to derive their closure-based errorestimates, ∆τ , whenever possible. Ming H. Xu et al.
The WRMS delay error (not uncertainty), δτ , is obtained by combining theclosure-based error estimates as follows: δτ = (cid:118)(cid:117)(cid:117)(cid:116) (cid:80) lj =1 w j ( ∆τ j ) (cid:80) lj =1 w j , (3)where l is the number of un-flagged observations with closure-based error estimatesavailable in a data group of interest (e.g., all observations of a particular source orsome selected sources or all observations in one session), ∆τ j is the closure-basederror estimate of the j -th observation, and w j is its weight. The weighting is doneby setting an equal weight for all the delay observables, named uniform weighting,or by using the reciprocal of the square of the uncertainty (formal error) of eachindividual delay, named natural weighting. (The uniform and natural weightingschemes used here have different meanings to those used in the astrophysicalimaging studies.) The same procedure of this closure analysis was applied to study δ TEC measurements; closure δ TEC, closure-based error estimate of δ TEC andWRMS δ TEC error are likewise defined.Note that the closure analysis derives the baseline equivalent error for eachobservation from closure quantities. It is obvious that the closure-based errorestimate of an observation is affected (can be enlarged or reduced) by sourcestructure effects and measurement noise in the observations of the other baselinesin the scan. It is not appropriate to use closure-based error estimate to quantify theerrors at the level of a single observation; however, the aim of closure analysis is touse closure-based error estimates only to determine the overall variance of sourcestructure effects and measurement noise for a given group of data, as defined byequation 3. In this case, it will work without introducing significant biases whenthe random measurement noise, independent between different observations, isthe dominant error source. On the other hand, if the systematic error sourcesdominate, the mean of the absolute values of all the closures formed with a commonobservation maximizes the possibility of determining these systematic errors inthat observation; it was then scaled by a factor of √ closure-based error estimates and the corresponding WRMS errors.In closure analysis, we also directly compare the closure delays for a givensource between various triangles and for a specific triangle between differentsources, which can yield insight into the properties of individual sources, baselines,and stations. bservable quality assessment of VGOS 7 Table 2
WRMS delay errors determined by closure analysis (in units of picoseconds)Session/Group N obs N CloErr
Uniform Weighting Natural Weighting(1) (2) (3) (4) (5)B17337 5999 5620 22.5 17.9B17338 5037 3279 26.8 19.1B17339 5833 3556 20.6 17.2B17340 5166 3042 24.4 20.3B17341 6043 3742 24.1 21.1VT9007 8310 7508 36.1 33.8VT9022 6070 5222 23.3 18.9VT9035 4622 4283 18.5 14.1VT9050 7668 7511 18.8 17.0VT9063 7645 7503 20.9 19.3VT9077 5586 5294 20.7 17.4VT9091 7651 7325 21.0 21.1VT9105 5102 4835 19.2 18.6VT9119 5142 4856 21.0 25.4VT9133 4120 3786 21.7 17.7VT9148 1444 1146 22.9 25.4VT9162 4891 4583 21.5 19.2VT9175 5097 4830 21.3 16.9VT9189 1860 1611 23.6 28.5VT9203 6235 5827 20.9 26.0VT9217 11541 11348 22.7 20.6
ALL 121062 106707 22.9 21.0ALL-19 106682 93977 21.5 20.0CARMS-0.25 20998 17702 6.2 2.4
Note 2 N obs is the number of observations in each session or subgroup of data, and N CloErr is the number of observations that were not flagged out and formed at least one closure delaywith un-flagged observations allowing the derivation of closure-based error estimates.
Apart from session VT9007, the WRMS delay errors for the other 20 sessionsare in the range of 18.5 ps to 26.8 ps based on the uniform weighting and in therange of 14.1 ps to 28.5 ps based on the natural weighting. The WRMS delay errors for the 21 sessions combined, labelled as “ALL” in the table, are about 23 psand 21 ps based on the two weighting schemes. This is a significant improvementcompared to the corresponding values of 35.3 ps (uniform) and 25.2 ps (natural) forthe CONT14 sessions(Anderson and Xu, 2018), which represent the best observingcampaign of the legacy S/X VLBI system.
Ming H. Xu et al.
For session VT9007 the WRMS delay errors are remarkably high — 36 psand 34 ps from the two weighting schemes. This is due to an exceptionally largenumber of misclosures of about 310 ps or −
310 ps in the closure delays, as shownin Fig. 1. The vast majority of these misclosures involve station
ONSA13SW , dueto its phasecal problem at the 6.6-GHz frequency band (Brian Corey, personalcommunication, September 7, 2020). After 390 closure delays of station
ONSA13SW with absolute values of about 310 ps were flagged, the WRMS delay error for sessionVT9007 was redetermined to be 23.0 ps (uniform) and 18.9 ps (natural). TheWRMS delay errors for the “ALL” group were recalculated from the 19 sessionsexcluding VT9007 and VT9022—the latter session undergoes the same issue butwith offsets of around 1100 ps and − ONSA13SW , butnot as many. The WRMS delay errors for the 19 sessions are 21.5 ps (uniform) and20.0 ps (natural), labelled as “ALL-19” group in Table 2. In summary, we arguethat the magnitude of the random measurement noise and the systematic errorsin the VGOS observations is in the range of 20.0 ps to 22.9 ps.Except for sessions like VT9148 and VT9189 with an observing network ofthree stations, the natural weighting scheme generally gives significantly smallervalues of the WRMS delay error than the uniform weighting scheme. This is tobe expected when the non-Gaussian delay values due to source structure areadded to the closure delays with an otherwise noise-like distribution. On theother hand, because source structure effects not only cause structure delays indelay observables but also reduce observed amplitudes and thus the observations’SNR, natural weighting will underestimate the magnitude of their actual impacts.Thus, while the natural weighting statistics are appropriate for evaluating theproperties of the delay/ δ TEC observables, the uniform weighting statistics can beuseful for identifying sources with systematic errors, such as those due to sourcestructure. Furthermore, the SNRs of VGOS observations are typically very high,for instance, the median SNR for the CONT17 VGOS observations is ∼
90; uniformweighting should be used to investigate the systematic error levels, especially ifthese systematic errors are significantly larger than the random measurement noiseand are correlated with the SNRs, for example, source structure effects.In order to further investigate the random measurement noise level in VGOSsessions, we adopted the closure amplitude RMS (CARMS) values based on thebasic weighting scheme from Table 2 in Xu et al. (2019) to identify the sourceswith minimum structure in these VGOS sessions. For the definition of CARMS,please consult equations (2)–(4) and (6)–(8) in Xu et al. (2019). The CARMSvalue of each individual source was calculated using all the available closureamplitudes for X-band only from historical VLBI observations from 1980 to Aug.2018 (no VGOS broadband observations are included). Apart from thermal noise,observations of an ideal point source will always give log closure amplitudes equal to zero, while those of radio sources with extended structure will have logclosure amplitudes deviating from zero, leading to larger CARMS values. Hence, ingeneral, a smaller CARMS value of a source indicates that it causes less structureeffects. Our recent study has demonstrated the correlation between the magnitudes of the radio-to-optical source position differences and CARMS values (Xu et al., It assumes that the noise floor in log closure amplitudes is 0.1 and thus adds 0.1 to theirformal errors in the quadrature sense for weighting. Note that the natural logarithm was adopted in the definition of closure amplitude tocalculate CARMS values, as shown in the equation (3) in Xu et al. (2019).bservable quality assessment of VGOS 9 −400−2000200400 C l o s u r e D e l a y [ p s ] GMST [Hour] −400−2000200400 C l o s u r e D e l a y [ p s ] GMST [Hour] −400−2000200400 C l o s u r e D e l a y [ p s ] GMST [Hour] −400−2000200400 C l o s u r e D e l a y [ p s ] GMST [Hour]
ALL 19JAN07VG Nclr=7085 Nsess=1
Fig. 1
All closure delays of session VT9007 excluding triangles with baseline
ONSA13NE – ONSA13SW . Closure delay uncertainties are shown as black bars. There are 7085 closure delaysin total. A large number of closure delays with an absolute offset of about 310 ps is visible. Allthe closure delays exceeding the limits of the Y axis are shown on the top or bottom of the plotas open circles. This convention applies to all of the closure plots in the paper; plots with noopen-circle points on the bottom and top have no excessively large closure delays. Two solidhorizontal lines with an absolute value of 150 ps are provided as guides. − CARMS-0.25 sources, such as 0716+714 and 0133+476.As discussed at the end of section 2, the median value was also used to deriveclosure-based error estimates and then to calculate the corresponding WRMS delayerrors. The differences in WRMS delay error values between the two techniquesare very small for both weighting schemes, no more than 0.5 ps in most cases.
Table 3
Source group with CARMS less than 0.25, CARMS-0.25 for shortIVS CARMS N obs ICRF3Design. category(1) (2) (3) (4)0048 −
097 0.11 95 D0054+161 0.10 56 D0133+476 0.23 2906 D0237 −
027 0.15 193 D0446+112 0.24 589 O0529+483 0.21 3120 D0536+145 0.17 13 D0627 −
199 0.15 92 D0656+082 0.24 36 O0716+714 0.20 4865 D0723+219 0.18 13 O0727 −
115 0.24 727 D0804+499 0.20 211 D1040+244 0.17 815 D1124 −
186 0.21 312 D1243 −
160 0.13 288 D1300+580 0.18 1386 D1417+385 0.17 53 O1519 −
273 0.18 119 D1636+473 0.24 141 D1749+096 0.22 1163 D1908 −
201 0.20 222 D2059+034 0.24 33 D2141+175 0.21 730 O2215+150 0.22 1656 D2227 −
088 0.24 692 D2255 −
282 0.18 89 O2309+454 0.21 383 O
Note 3 N obs in column 3 is the totalnumber of VGOS observations in these 21 sessions for each source. + Closure delay plots for source 0059+581 are shown in Fig. 4 for twotriangles,
GGAO12M – ISHIOKA – WETTZ13S and
KOKEE12M – WESTFORD – WETTZ13S . Thefirst triangle was observed only in CONT17 and has 119 closure delays in total.
The pattern of two peaks with opposite signs separated by a 12-hour GMST periodis a normal behavior of source structure effects. The second triangle, which wasobserved in 18 VGOS sessions, produced 329 closure delays. Through it, the source-structure time evolution is well demonstrated: the peak in the closure delay patternchanged from −
30 ps in Dec. 2017 to around 0 ps in early 2019, increased to +60 ps bservable quality assessment of VGOS 11 −200−1000100200 C l o s u r e D e l a y [ p s ] GMST [Hour] −200−1000100200 C l o s u r e D e l a y [ p s ] GMST [Hour] −200−1000100200 C l o s u r e D e l a y [ p s ] GMST [Hour] −200−1000100200 C l o s u r e D e l a y [ p s ] GMST [Hour]
ALL VGOS 0529+483 Nclr=4053 Nsess=21
Fig. 2
All closure delays of source 0529+483 in the 21 VGOS sessions with black bars givingthe 1- σ measurement uncertainties based on the formal errors of delay observables. There arefour closure delays of about 310 ps from one scan of session VT9007 showing as one opencircle on the top right of the figure and five closure delays of about 1100 ps or − −20−1001020 C l o s u r e D e l a y [ p s ] GMST [hour] −20−1001020 C l o s u r e D e l a y [ p s ] GMST [hour] −20−1001020 C l o s u r e D e l a y [ p s ] GMST [hour] −20−1001020 C l o s u r e D e l a y [ p s ] GMST [hour]
KOKEE12M WESTFORD WETTZ13S VGOS 0529+483 Nclr=231 Nsess=19
Fig. 3
Zoom-in plot of closure delays of source 0529+483 for triangle
KOKEE12M – WESTFORD – WETTZ13S . They are not randomly distributed around zero, suggesting that there are systematiceffects with a magnitude of a few picoseconds for this source. Three solid horizontal lines areprovided to guide the reader. in March and decreased back to +30 ps in the middle of 2019. Source 0059+581 isa very typical geodetic source and has been the most frequently observed sourceboth by the legacy VLBI system and the VGOS system so far. For the triangle
GGAO12M – ISHIOKA – WETTZ13S , it is seen that the structure effects have a magnitudeof as large as 20 ps but the WRMS closure delay is only 6.9 ps. Source structure effects are more easily visible in VGOS observations than in the legacy VLBIobservations because the measurement noise in VGOS is well below 3 ps. This isone reason why source structure effects are so critical for VGOS. −100−50050100 C l o s u r e D e l a y [ p s ] C l o s u r e D e l a y [ p s ] C l o s u r e D e l a y [ p s ] C l o s u r e D e l a y [ p s ] GGAO12M ISHIOKA WETTZ13S VGOS 0059+581 Nclr=119 Nsess=5 −100−50050100 C l o s u r e D e l a y [ p s ] GMST [Hour] −100−50050100 C l o s u r e D e l a y [ p s ] GMST [Hour] −100−50050100 C l o s u r e D e l a y [ p s ] GMST [Hour] −100−50050100 C l o s u r e D e l a y [ p s ] GMST [Hour]
KOKEE12M WESTFORD WETTZ13S VGOS 0059+581 Nclr=329 Nsess=18
Fig. 4
Closure delays for source 0059+581 as a function of GMST for two triangles,
GGAO12M – ISHIOKA – WETTZ13S (top) and
KOKEE12M – WESTFORD – WETTZ13S (bottom). The colorcoding indicates the observation date, and the corresponding legend is shown on the bottom-right corner of the bottom plot. The top plot shows a normal pattern of source structureeffects, while the bottom one clearly shows the source-structure time evolution from CONT17in Dec. 2017 to 2019 and even within 2019. Two solid horizontal lines with an absolute valueof 30 ps are provided as guides. + Source 0016+731 is another of the important geodetic sources. Theclosure delays for source 0016+731 are shown in Fig. 5 for triangle
KOKEE12M – WESTFORD – WETTZ13S , which is the same triangle shown in Fig. 3 for source0529+483 and in the bottom plot of Fig. 4 for source 0059+581. It has 460 closuredelays in 19 VGOS sessions. The source structure changed significantly from 2017to 2019. The magnitudes of structure effects are as large as 100 ps in 2019. bservable quality assessment of VGOS 13 −200−1000100200 C l o s u r e D e l a y [ p s ] GMST [Hour] −200−1000100200 C l o s u r e D e l a y [ p s ] GMST [Hour] −200−1000100200 C l o s u r e D e l a y [ p s ] GMST [Hour] −200−1000100200 C l o s u r e D e l a y [ p s ] GMST [Hour]
KOKEE12M WESTFORD WETTZ13S VGOS 0016+731 Nclr=460 Nsess=19
Fig. 5
Plot of closure delays for source 0016+731 as a function of GMST for triangle
KOKEE12M – WESTFORD – WETTZ13S , which was shown also for source 0529+483 in Fig. 3 and for source0059+581 in the bottom of Fig. 4. Source 0016+731 is another one of the important geodeticsources. However, its structure effects have significantly larger amplitudes than those of source0059+581. Two solid horizontal lines with an absolute value of 60 ps are provided as guides.
Source 3C418 is a representative of the extremely extended sources ingeodetic VLBI and has been observed frequently in the VGOS sessions. Closuredelays for triangle
ISHIOKA – KOKEE12M – WETTZ13S are shown in the bottom plot ofFig. 6. With replaceable S/X and broadband receivers at the
ISHIOKA station andco-located S/X VLBI stations at the sites of both
KOKEE12M and
WETTZ13S , it ispossible to have a similar triangle of stations observing in the S/X mode. Closuredelays at X-band from the IVS S/X observations in 2018 and 2019 for triangle ISHIOKA – KOKEE – WETTZELL were calculated and are shown in the top of the figure.Since the source structure effects in VGOS delays are due to the structure at thefour frequency bands in the range over 3.0 GHz to 10.7 GHz in a complex mannerand those in the X-band observations are due to structure at the frequenciesaround 8.4 GHz, the variation patterns in these two plots do not necessarily matchwith each other. However, the scatters of the closure delays along the variablecurves, indicating the random measurement noise level, are far smaller for VGOSobservations than for the S/X observations. And even for an extended sourcelike 3C418, those scatters for VGOS observations are at the level of just a fewpicoseconds. In the bottom plot, the closure delays with absolute magnitudes largerthan 150 ps are very likely due to the jumps instead of source structure effects in thedelay observables. The delay jump issue is discussed further in the next subsection.3.3 Delay jumps
In the S/X VLBI mode, multi-band group delay observables have ambiguities,typically with spacings of 50 ns (1 ns = 10 − s) at X-band and 100 ns at S-band,while the VGOS broadband delays have an ambiguity spacing of 31.25 ns; they can https://cddis.nasa.gov/archive/vlbi/ivsdata/vgosdb/4 Ming H. Xu et al. −400−2000200400 C l o s u r e D e l a y [ p s ] GMST [Hour] −400−2000200400 C l o s u r e D e l a y [ p s ] GMST [Hour] −400−2000200400 C l o s u r e D e l a y [ p s ] GMST [Hour] −400−2000200400 C l o s u r e D e l a y [ p s ] GMST [Hour]
ISHIOKA KOKEE WETTZELL IVS (X) 3C418 Nclr=299 Nsess=40 −400−2000200400 C l o s u r e D e l a y [ p s ] GMST [Hour] −400−2000200400 C l o s u r e D e l a y [ p s ] GMST [Hour] −400−2000200400 C l o s u r e D e l a y [ p s ] GMST [Hour] −400−2000200400 C l o s u r e D e l a y [ p s ] GMST [Hour] −400−2000200400 C l o s u r e D e l a y [ p s ] GMST [Hour] −400−2000200400 C l o s u r e D e l a y [ p s ] GMST [Hour] −400−2000200400 C l o s u r e D e l a y [ p s ] GMST [Hour]
ISHIOKA KOKEE12M WETTZ13S VGOS 3C418 Nclr=65 Nsess=5
Fig. 6
Plots of closure delays for source 3C418 as a function of GMST for two triangles,
ISHIOKA – KOKEE – WETTZELL (top, legacy X-band) and
ISHIOKA – KOKEE12M – WETTZ13S (bottom,VGOS). With replaceable S/X and broadband receivers at station
ISHIOKA , the first triangleobserved in the S/X mode while the second one observed in the broadband mode. These twotriangles with a similar geometry allow the direct comparison of structure effects between thelegacy VLBI system and the VGOS system. The VGOS triangle observed only in CONT17 andthe S/X triangle observed in 40 sessions in 2018 and 2019. The closure delays with absolutemagnitudes larger than 150 ps in the VGOS plot are very likely due to delay jumps insteadof source structure effects directly, which is discussed in subsection 3.3. Two solid horizontallines with an absolute value of 150 ps are provided as guides. usually be resolved based on a priori information prior to performing a geodeticVLBI solution. In the broadband VGOS observations reported here, jumps ingroup delays have been found to be at least two orders of magnitude smaller thanthe ambiguity spacing of S/X observations, but only 2–3 times the ambiguity spacing of phase delay at X-band. These delay jumps exist in all of the VGOSsessions.Closure delays for 3C418 are shown in Fig. 7 for two triangles,
GGAO12M – ONSA13NE – WESTFORD and
KOKEE12M – WESTFORD – WETTZ13S . For the first triangle,offsets with a magnitude of ∼
310 ps occurred during the time period of GMST bservable quality assessment of VGOS 15
KOKEE12M – WESTFORD – WETTZ13S , but no such jumps show up in the twobottom plots of Figs. 4 and 5 for 0059+581 and 0016+731, which cover the sametriangle. These delay jumps are more easily identified in a plot of closure delaysversus closure TEC as shown in Figs. 9 and 10. They also happen frequentlyfor other extended sources such as 0119+115 (CARMS=0.39) and 0229+131(CARMS=0.61). As demonstrated in Figure 3 of Cappallo (2016), which showsthe two-dimensional fringe amplitudes as a function of δ TEC and group delay,one would expect big jumps in δ TEC and in group delay if the wrong peak ismistakenly picked up. Since these jumps tend to happen in the case of extendedsources and only a few tens of closure delays and closure δ TEC for the CARMS-0.25 sources have jumps, it is likely that the causative factor is source structure.Nevertheless, other reasons are possible as well, for instance, the phasecal problemas found in session VT9007. The sizes of the jumps identified in closure delaysseem to be rather stable; however, further studies are necessary to verify if theyhave a fixed spacing or at what level they can change.
The investigation of δ TEC observables in VGOS is interesting because (1) unlikethe S/X VLBI system, the design of the VGOS system requires that the dispersionconstant in the phase be determined simultaneously with the group delay, and (2)there is a strong correlation, larger than 0.9, between δ TEC and group delayestimates based on the current frequency settings, as shown in the variance-covariance analysis of Cappallo (2014, 2016). Observations on the single baseline
ISHIOKA – KASHIM34 in Kondo and Takefuji (2016) showed that the standarddeviation of the differences between VGOS δ TEC observables and the global TECmodel was 0.25 TECU. Even though the baseline length of
KASHIM34 – ISHIOKA (about 50 km) is too short to make a solid conclusion, the differences are farbeyond the formal errors of VGOS δ TEC observables. The observations of thesingle baseline
GGAO12M – WESTFORD in Niell et al. (2018) showed a consistencybetween the VGOS δ TEC observables and differenced GNSS TEC estimates atco-located sites at the level of 1 TECU. A bias of GPS relative to VLBI of − ± δ TECused for comparison; consequently, it is not clear if these differences come fromthe VGOS δ TEC estimates or not. The accuracy of, and the potential biases in,VGOS δ TEC estimates need to be better understood.The WRMS δ TEC errors are seen in Table 4 to be in the range 0.24 TECU to0.49 TECU for the 20 sessions excluding VT9007, for which the WRMS error valueis 0.73 TECU. Excluding sessions VT9007 and VT9022, the WRMS δ TEC errors,labelled as “ALL-19”, are 0.31 TECU to 0.34 TECU for the two weighting schemes.
They are about one order of magnitude larger than the uncertainties of the δ TECobservables, which implies that there are additional error sources in the δ TECobservables. The closure analysis of observations of individual sources showed thatthose additional errors in δ TEC are source-dependent. The WRMS δ TEC error ofthe observations for the sources with minimum structure (the CARMS-0.25 group) −400−2000200400 C l o s u r e D e l a y [ p s ] GMST [Hour] −400−2000200400 C l o s u r e D e l a y [ p s ] GMST [Hour] −400−2000200400 C l o s u r e D e l a y [ p s ] GMST [Hour] −400−2000200400 C l o s u r e D e l a y [ p s ] GMST [Hour]
GGAO12M ONSA13NE WESTFORD VGOS 3C418 Nclr=447 Nsess=13 −400−2000200400 C l o s u r e D e l a y [ p s ] GMST [Hour] −400−2000200400 C l o s u r e D e l a y [ p s ] GMST [Hour] −400−2000200400 C l o s u r e D e l a y [ p s ] GMST [Hour] −400−2000200400 C l o s u r e D e l a y [ p s ] GMST [Hour]
KOKEE12M WESTFORD WETTZ13S VGOS 3C418 Nclr=326 Nsess=18
Fig. 7
Closure delays for source 3C418 as a function of GMST for two triangles,
GGAO12M – ONSA13NE – WESTFORD (top) and
KOKEE12M – WESTFORD – WETTZ13S (bottom). For comparison,closure delays of the second triangle can be seen for sources 0528+483, 0059+581 and 0016+731in Figs. 3, 4 and 5, respectively. is only 0.07 TECU based on the natural weighting scheme. Source structure musttherefore play a crucial role in the δ TEC measurements. δ TEC and group delay observables from VGOS
A covariance analysis using the VGOS frequency setup predicts a strong correlationbetween the group delay and δ TEC estimates (see Cappallo, 2015). It can bemore straightforward to understand that correlation and its influence on VGOS observations by analyzing the actual data. Figures 8 and 9 demonstrate thecorrelation by showing closure delays and closure TECs for the sources 0016+731and 3C418 using two plots each. The trends, obtained from least-square fitting(LSQ), are 68.3 ± ± bservable quality assessment of VGOS 17 Table 4
WRMS δ TEC errors determined by closure analysis (in units of TECU)Session/Group Uniform Weighting Natural Weighting(1) (2) (3)B17337 0.34 0.32B17338 0.45 0.34B17339 0.32 0.30B17340 0.37 0.37B17341 0.35 0.34VT9007 0.56 0.73VT9022 0.33 0.29VT9035 0.28 0.24VT9050 0.28 0.26VT9063 0.32 0.30VT9077 0.33 0.28VT9091 0.33 0.32VT9105 0.32 0.30VT9119 0.32 0.38VT9133 0.33 0.27VT9148 0.33 0.37VT9162 0.36 0.28VT9175 0.34 0.24VT9189 0.39 0.49VT9203 0.34 0.37VT9217 0.40 0.32ALL 0.36 0.35
ALL-19 0.34 0.31CARMS-0.25 0.15 0.07
In the bottom plot of Fig. 9, the points deviating significantly from the redline form basically four straight lines that are parallel to the red line with offsetsof 133 ps in delay or 3.3 TECU in δ TEC from each other. It confirms the jumps ineither or both the group delay and δ TEC observables.Figure 10 shows the closure delays as a function of the closure TEC for allsources and all triangles in the 21 sessions. The closure quantities in the upper plotare from un-flagged observations, whereas those in the bottom plot have at leastone of the three observations in a triangle flagged due to the three cases listed insection 2. Two main linear trends between closure delay and δ TEC were identified.In the upper plot the data points grouped in the lines parallel to the red line wereused jointly to determine the slope with a result of 40.5 ± the WRMS residual. These two linear trends seem to have different origins: (1)the trend in the range 59.9 ps/TECU to 68.9 ps/TECU agrees with the value of ∼
62 ps/TECU from Cappallo (2016) and is due to the random measurement noisein the channel phases across the four bands; (2) the trend of ∼
40 ps/TECU resultsfrom the systematic variations in the channel phases due to source structure. −200−1000100200 C l o s u r e D e l a y [ p s ] GMST [Hour] −200−1000100200 C l o s u r e D e l a y [ p s ] GMST [Hour] −2−1012 C l o s u r e T E C [ T E CU ] −2−1012 C l o s u r e T E C [ T E CU ] GGAO12M ISHIOKA KOKEE12M VGOS 0016+731 Nclr=152 Nsess=5 −200−1000100200 C l o s u r e D e l a y [ p s ] −2 −1 0 1 2 Closure
TEC [TECU] −200−1000100200 C l o s u r e D e l a y [ p s ] −2 −1 0 1 2 Closure
TEC [TECU] −200−1000100200 C l o s u r e D e l a y [ p s ] −2 −1 0 1 2 Closure
TEC [TECU]
GGAO12M ISHIOKA KOKEE12M VGOS 0016+731 Linear trend : 68.3 ± Fig. 8
Demonstration of the strong correlation between δ TEC and group delay observablesfrom VGOS. Closure delays (blue dots) and closure TEC (red dots) for source 0016+731 fortriangle
GGAO12M – ISHIOKA – KOKEE12M as a function of GMST are shown in the top plot, whereasthese closure delays versus closure TEC are in the bottom plot. The changing pattern in closureTEC is the same as that of closure delays. There is a strong correlation between them, andthe linear trend is 68.3 ± Figure 11 is an equivalent plot for CARMS-0.25 sources. Other than the smallisolated groups of closures in the upper right and lower left, which are associated primarily with only two of the 28 sources in this category, there are no jumpscomparable to those seen in Fig. 10. Were the points for the CARMS-0.25 sourcesremoved, the jumps would still be prevalent. Since the closures shown in Fig. 10 arefor all sources, removing the points for the CARMS-0.25 sources would leave theclosures for the sources with CARMS greater than 0.25; these are the sources with bservable quality assessment of VGOS 19 nominally the more extended source structure. Therefore, our findings indicatethat the predominant causative factor of the jumps in delay and δ TEC is sourcestructure, which can cause large frequency-dependent phase variations across thefour bands. This has been demonstrated by our recent imaging results based onclosure phases and closure amplitudes (figures 11 and 12 in Xu et al., 2020). −400−2000200400 C l o s u r e D e l a y [ p s ] GMST [Hour] −400−2000200400 C l o s u r e D e l a y [ p s ] GMST [Hour] −4−2024 C l o s u r e T E C [ T E CU ] −4−2024 C l o s u r e T E C [ T E CU ] KOKEE12M WESTFORD WETTZ13S VGOS 3C418 Nclr=326 Nsess=18 −400−2000200400 C l o s u r e D e l a y [ p s ] −4 −2 0 2 4 Closure
TEC [TECU] −400−2000200400 C l o s u r e D e l a y [ p s ] −4 −2 0 2 4 Closure
TEC [TECU] −400−2000200400 C l o s u r e D e l a y [ p s ] −4 −2 0 2 4 Closure
TEC [TECU]
KOKEE12M WESTFORD WETTZ13S VGOS 3C418 Linear trend : 39.9 ± Fig. 9
Demonstration of the strong correlation between δ TEC and group delay observablesfrom VGOS and the jumps in them. Closure delays (blue dots) and closure TEC (red dots)for source 3C418 for triangle
GGAO12M – KOKEE12M – WETTZ13S as a function of GMST are shownin the top plot, whereas these closure delays versus closure TEC are in the bottom plot. Thelinear trend between them is 39.9 ± We processed the 21 VGOS sessions that have been publicly released and madequality assessments for two kinds of VGOS observables, group delay and δ TEC,that are determined simultaneously in the process of broadband bandwidthsynthesis. The measurement noise level and the contributions of systematic errorsources in these two types of observables were determined by running closureanalysis for the whole data set and for the selected sources with minimum structurebased on our previous work. By performing closure analysis, two importantfeatures in group delay and δ TEC observables have been revealed, which are thestrong correlation between them and the jumps in both observables.The random measurement noise level of VGOS group delays was found tobe below 2 ps based on the observations from all the VGOS radio sources thathave CARMS values smaller than 0.25. The estimated random measurement noiselevel agrees well with the delay formal errors, as listed in Table 1. However, thecontributions from other systematic error sources, mainly source structure related,are at the level of 20 ps, as indicated by the WRMS delay errors for observationsof all sources. Due to the significant reduction in measurement noise over the S/Xsystems, source structure effects with magnitudes of 10 ps are clearly visible. Ingeneral, source structure evolves at time scales of a few weeks, which causes theclosure delays to change at magnitudes of a few tens of picoseconds. It thus willbe a big challenge to correct source structure effects in VGOS in order to fulfillits goals. Evidence for another critical error source in the VGOS system is thepresence of discrete jumps in the closure delays and closure TECs, for instancewith a delay offset of about 310 ps or integer multiples of that. The likely causeis found to be source-structure-induced phase changes across the four bands (Xuet al., 2020).Closure delays on individual triangles were shown for four sources, 0529+483(CARMS=0.21), 0059+581 (CARMS=0.27), 0016+731 (CARMS=0.31), and 3C418(CARMS=0.61) in figures 3, 4, 5, and 7 to demonstrate the source structureeffects in VGOS delay observables. By showing the closure delays from the sametriangle
KOKEE12M – WESTFORD – WETTZ13S in these four figures, the differences in themagnitudes of these effects can be compared among radio sources with structure atvarious scales as indicated by their CARMS values. The magnitudes of structureeffects on the triangle were less than 10 ps for source 0529+483, about 50 ps forsource 0059+581, and about 100 ps for source 0016+731; they were larger andmore complicated for source 3C418. Delay jumps occurred for the observations ofonly 3C418 among these four sources.The random measurement noise level of δ TEC observables was determinedto be below about 0.07 TECU, which is comparable to the formal errors. Thesystematic effects are five times larger than that. A strong correlation betweengroup delay and δ TEC observables is clearly demonstrated, with two main lineartrends. For observations with large structure effects, there is a dominant slopeof ∼
40 ps/TECU. The slope of the second trend is in the range 60 ps/TECU to
70 ps/TECU. Due to this strong correlation and the simultaneous determination ofthem, group delay and δ TEC observables need to be studied together and further.The δ TEC estimates from other sources, such as GPS or global TEC models with asufficient accuracy, might improve the determination of the source structure effectsin δ TEC observables; based on the stable linear coefficients between delay and bservable quality assessment of VGOS 21
Fig. 10
Closure delays versus closure TEC with un-flagged observations (top) and with atleast one of the three observations in a triangle flagged out due to the three cases listed insection 2 (bottom). All sources and all triangles available in the 21 sessions are included.There are two main linear trends between them. The slope of the trend indicated by the redline was determined to be 40.5 ± RAEGYEB in the last four sessions in CONT17; while the closuresof the observations flagged due to the other two reasons are nearly all beyond the limits of theplotting axes. The observations of station
RAEGYEB have a median SNR of 17-23 in these foursessions, while the rest observations in CONT17 have a median SNR of 92–115. On average,the closures in the bottom plot are from observations with SNRs smaller by a factor of fivethan those in the upper plot. Another difference in the observations between the two plots isthe significant decrease in the channel visibility amplitudes of station
RAEGYEB with increasingfrequency due to the antenna pointing issue since the second day during the CONT17.2 Ming H. Xu et al.
Fig. 11
Equivalent plot to Fig. 10 for the closure quantities of the CARMS-0.25 observationsonly. Of 20,337 pairs of closure quantities in the plot, there are 17 and 47 pairs in the upper-right and the bottom-left corners, respectively. Most of them involve the observations of sources0133+476 and 0716+714. The median value of the absolute closure delays in the plot is 2.38 ps,and that of the absolute closure TEC is 0.059 TECU. δ TEC, the source structure effects in group delay observables might be determinedwithout requiring any model of source structure itself. For example, external δ TECestimates can be used to detect the systematic effects in VGOS δ TEC estimates,which may be able to predict those effects in delay observables by the linear trends,as discussed in this work.Delay jumps in the VGOS system need to be understood further. Closuredelays have been demonstrated to be useful, and the correlation between groupdelay and δ TEC observables can also be of great help for the delay jump detection.However, the delay spacing of these jumps will have to be studied in detail. Theexact origins of the two dominant linear trends between broadband delays and δ TEC, the causes of such jumps, and the method to fix them are our near-futurework.
Acknowledgements
We would like to thank Sergei Bolotin, Arthur Niell, and Brian Coreyfor their efforts to review the manuscript and for their helpful comments of high qualitywhich improved its comprehensibility. The results reported in this paper were producedusing the data owned by the International VLBI Service (IVS) and its international self-funded member organizations. We are grateful to the IVS VGOS stations at GGAO (MITHaystack Observatory and NASA GSFC, USA), Ishioka (Geospatial Information Authorityof Japan), Kokee Park (U.S. Naval Observatory and NASA GSFC, USA), Onsala (OnsalaSpace Observatory, Chalmers University of Technology, Sweden), Westford (MIT HaystackObservatory), Wettzell (Bundesamt f¨ur Kartographie und Geod¨asie and Technische Universit¨atbservable quality assessment of VGOS 23M¨unchen, Germany), and Yebes (Instituto Geogr´afico Nacional, Spain), to the staff at theMPIfR/BKG correlator center, the VLBA correlator at Socorro, and the MIT HaystackObservatory correlator for performing the correlations and the fringe fitting of the data, andto the IVS Data Centers at BKG (Leipzig, Germany), Observatoire de Paris (France), andNASA CDDIS (Greenbelt, MD, USA) for the central data holds.This research has made use of the Generic Mapping Tools package , the pgplot library , andthe SAO/NASA Astrophysics Data System .MHX was supported by the Academy of Finland project No. 315721 and by the NationalNatural Science Foundation of China (No. 11973023 and 11873077). JMA, RH, SL, and HSwere supported by the German Research Foundation grants HE5937/2-2 and SCHU1103/7-2. Author contributions
MHX and JMA designed the research; MHX performed the research, analyzedthe data, and wrote the paper; JMA, RH, SL, HS, and GW contributed to theinterpretation of the results and provided suggestions in writing and revising thepaper.
Data Availability
All the VGOS data in the vgosDB data format are available at the CDDIS server:https://cddis.nasa.gov/archive/vlbi/ivsdata/vgosdb/. The closure delays, closureTECs, closure phases and amplitudes from these VGOS sessions are available uponthe request to the corresponding author.
References
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