Technical description of solution gsf2016a 2016.09.22 1. Purpose of solution: TRF/CRF and EOP series. 2. Analysis center: GSF (NASA Goddard Space Flight Center). 3. Short narrative description of solution: Solution gsf2016a estimates station position and velocity parameters in order to obtain a terrestrial reference frame (TRF) for computing an EOP time series. Source positions are also estimated. The TRF is defined in such a manner that the positions and velocities of a subset of 38 strong stations have no net translation or rotation with respect to their positions and velocities reported in the ITRF2014 [1] catalog and the resulting series of Earth orientation parameters has zero shift and drift with respect to the USNO Finals series over the range [2000.01.05 - 2016.09.07]. The CRF is defined in such a way that the positions of the 295 ICRF2 catalog [2] defining sources do not have any net rotation with respect to their coordinates reported in the ICRF2 catalog. All available dual-band X/S Mark-3/Mark-4/Mark-5/K3/K4/VLBA VLBI observations from 1979.08.03 through 2016.08.22 (except 34 VCS1, VCS2, VCS3, VCS4, VCS5, VCS6, VCS-II, and NPCS sessions) with durations of 18 hours and longer (5938 sessions, 10,807,922 group delays) were used in a single solution. The wrms postfit residual was 23.005 psec and Chi/ndg was 0.89. Parameters are split into three groups: 1) Global parameters estimated over all sessions. 2) Local parameters estimated for each 24-hour session individually. 3) Segmented parameters estimated over 20-60 minute, or 6 hr time spans. Positions and velocities of all stations were estimated as global parameters. The estimation of source positions was done in a manner similar to the generation of the ICRF2. First, all sources which did not have at least 3 good observations in at least one session were excluded from the dataset (151 sources). Three gravitational lenses, 0218+357/0218+35A/0218+35B, 1830-21A/1830-21B/1830-211, and 1422+231 were also excluded from the dataset. The positions of the 39 most unstable ICRF2 sources (the so called 'special handling' sources of ICRF2, see Appendix A) were estimated in each session individually. The positions of the remaining 1895 sources (see Appendix B) were estimated as global parameters. Two source catalogs are provided: 2016a.sou -- catalog of 1895 sources estimated as global parameters. 2016a_lso.sou -- catalog of 39 sources estimated in each session individually. Average positions are given. Mean site gradients were applied. These were computed from the GSFC Data Assimilation Office (DAO) model from met data from 1990-95. The atmospheric gradient delay is modeled as: tau = m_grad(el) * [GN*cos(az)+GE*sin(az)], where el and az are the elevation and azimuth of the observation, and the gradient mapping function is m_grad. The gradient vector has East and North components GE and GN. Refer to references [3] and [4] for more details. 3a. Differences with respect to previous (gsf2014a) solution: 513 additional databases, 2,098,511 additional observations were included. 225 additional source positions were solved for globally. Source positions are with respect to the frame defined by the 295 ICRF2 defining sources. The criteria for treating sources as global vs. local parameters was modified to match the selection criteria used for the ICRF2. 3b. Handling of earthquakes: Recent earthquakes in Chile (Feb. 27, 2010) and of the coast of Japan (March 11, 2011) have complicated the VLBI TRF. Non-linear motions have occurred at nearby stations since these earthquakes. To deal with these, we have used the post-seismic deformation models from ITRF2014 [1]. Two types of function are used in these models: exponential transient functions of the form A(1 - exp((t-t0)/Tau) and logarithmic functions of the form A log(1 + (t-t0)/Tau), where t0 is the time of the earthquake. The amplitudes A and relaxation times Tau were determined by fitting GPS data for each earthquake. Co-seismic offsets are also provided in the ITRF2014 model. There are models for the following VLBI stations: AIRA, TIGOCONC, GILCREEK, DSS15, KOGENEI, KASHIM34,KASHIM11, VERAMZSW, MISNAO10, SESHAN25, SINTOTU3, TSUKUB32, and USUDA64. In the Solve solution, we estimated episodic breaks at most of these sites even though offsets were specified in ITRF2014. The episodic breaks that were estimated are listed in section 6h. 4. Estimated parameters: a. Celestial Frame: Right Ascension, Declination (global and local). b. Terrestrial Frame: X, Y, Z, Xdot, Ydot, Zdot (global). c. Earth Orientation: X-pole, Y-pole, UT1-TAI, Xdot, Ydot, UT1dot, X-nutation, Y-nutation (local parameters). d. Zenith Troposphere: Linear spline 20-min interval; rate constraint with reciprocal weights generally 50 ps/hr; VMF1 wet partial derivative (segmented). e. Troposphere Gradient: 6-hour East and North linear splines at all stations using offset and rate constraints with reciprocal weights of 0.5 mm and 2.0 mm/day (segmented). f. Station Clocks: Quadratic (local) + linear spline with 1-hr interval (segmented); rate constraint with reciprocal weights, generally 5.0E-14. g. Baseline Clocks: As set in initial analysis usually used (local). h. Other: Global antenna axis offsets for a set of stations (Appendix C) (global). 5. Celestial Reference Frame: a. A priori source positions: /500/oper/solve_save_files/16Jun27_icrf2.src. This catalog was created from a 2016-Jun-27 astro source solution and was based on the ICRF2 catalog [2]. b. Source positions adjusted in solution: Yes. Orientation defined by a no-net-rotation tie to the ICRF2 using the 295 ICRF2 defining sources. There were 1895 global and 39 local sources. 6. Terrestrial Reference Frame: a. A priori station positions: /500/oper/solve_save_files/itrf2014_sitmod, which is from ITRF2014. b. A priori station velocities: /500/oper/solve_save_files/itrf2014_velmod, which is from ITRF2014. c. Reference epoch for site positions: 2014.01.01. d. Station positions/velocities adjusted in solution: Yes. e. Definition of origin, orientation, and their time evolution: No-net-translation and no-net-rotation of positions and velocities with respect to itrf2014_sitmod and itrf2014_velmod for 38 stations: ALGOPARK BR-VLBA DSS45 FD-VLBA FORTLEZA HARTRAO HATCREEK HAYSTACK HN-VLBA HOBART26 KASHIMA KAUAI KOKEE KP-VLBA LA-VLBA MATERA NL-VLBA NOTO NRAO20 NRAO85_3 NYALES20 ONSALA60 OV-VLBA OVRO_130 PIETOWN RICHMOND SANTIA12 SC-VLBA SESHAN25 VNDNBERG WESTFORD WETTZELL SVETLOE YEBES40M HOBART12 KATH12M YARRA12M WARK12M Values of right-hand side of net-rotation/net-translation constraints: RIGHT_PART 0.01030698 -0.02671682 -0.01689295 NO EXCEPT \ * nnt_pos RIGHT_PART 0.06006392 0.02845290 -0.01659568 NO EXCEPT \ * nnr_pos RIGHT_PART -0.00216165 0.00397288 0.00246733 NO EXCEPT \ * nnt_vel RIGHT_PART -0.00674188 -0.00172287 -0.00559031 NO EXCEPT \ * nnr_vel Units: meters for nnt_pos, meters/Earth_radius for nnr_pos, mm/yr for nnt_vel, mm/(yr*Earth_radius) for nnr_vel f. Station parameter estimation: X, Y, Z, Xdot, Ydot, Zdot - globally for all stations, some with constraints. g. Stations with constraints: A priori velocities for U, E, and N components of 38 stations listed in Appendix D were constrained to their itrf2014_velmod velocities with reciprocal weights 0.1, 3.0, and 3.0 mm/yr respectively, because these stations have very short histories of observations. Many are mobile sites occupied only once. The velocities of the 25 groups of stations listed in Appendix E were constrained to be the same. h. Stations with discontinuous positions and date of discontinuity: YAKATAGA 871201 * Earthquake SOURDOGH 871201 * Earthquake WHTHORSE 871201 * Earthquake FORTORDS 891001 * Seismic event PRESIDIO 891001 * Seismic event MOJAVE12 920627 * Earthquake DSS15 920627 * Earthquake MEDICINA 960601 * Rail reparing EFLSBERG 961001 * Rail reparing DSS65 970415 * Rail reparing MIURA 000901 * Dike intrusion, June-Aug. 2000 TATEYAMA 000901 * Dike intrusion, June-Aug. 2000 GGAO7108 030101 * Station relocation SINTOTU3 030915 * h/z MK-VLBA 061015 * Earthquake ZELENCHK 070701 * Rail repair ?????? AIRA 080614 * M7.2 Iwate Miyagi Nairiku earthquake CHICHI10 080614 * M7.2 Iwate Miyagi Nairiku earthquake KASHIM34 080614 * M7.2 Iwate Miyagi Nairiku earthquake TSUKUB32 080614 * M7.2 Iwate Miyagi Nairiku earthquake VERAMZSW 080614 * M7.2 Iwate Miyagi Nairiku earthquake TIGOCONC 100227 * Big Earthquake TSUKUB32 110311 * Big Earthquake in Japan KASHIM11 110311 * Big Earthquake in Japan KASHIM34 110311 * Big Earthquake in Japan VERAMZSW 110311 * Big Earthquake in Japan VERAISGK 110311 * Big Earthquake in Japan SINTOTU3 110311 * Big Earthquake in Japan KOGANEI 110311 * Big Earthquake in Japan USUDA64 110311 * Big Earthquake in Japan Also, the eccentricity vector for station TSUKUB32 was assigned as (0.0, 0.0, -0.0437) meters in North, East, Up in local topocentric reference frame before 1999.05.01 and (0.0, 0.0, 0.0) after 1999.05.01, according to the results of geodetic surveys [5]. Changes in the eccentricity vector were caused by repairs to the concrete foundation slab. i. Stations with nonlinear velocities: Spline functions were used to model the motion at the following stations, due to non-linear behavior for all or part of their observing histories. HRAS_085, GILCREEK, PIETOWN Gilcreek experienced non-linear behavior after a nearby earthquake. Pietown's non-linear motion is believed to be due to the effects of a varying tilt of its azimuth axis and perhaps local deformation. HRAS_085's non-linear motion was also believed to be due to some unexplained local deformation. j. Permanent tide contribution: Yes. "Yes" means that both the permanent and the periodic tides have been modeled. The model used includes tide displacements for zero frequency with Love numbers h2(freq=0) = 0.6078, l2(freq=0) = 0.0847. The Earth tide computation complies with the IERS 2010 Conventions. 7. Earth orientation: a. A priori precession/nutation model: IAU2006/2000A Precession/Nutation, IERS Conventions 2010 [6] as implementation in Calc 11. b. A priori short-period tidal variations in X, Y, UT1 due to short period tidal and nutation effects were applied. These were computed by Calc 11, as recommended in the IERS 2010 Conventions [6], chapter 5, p. 50-51. d. EOP estimation: Two tables are given: gsf2016a.eoxy: X, Y, UT1, Xdot, Ydot, UT1dot, X-nutation, Y-nutation, each session. Using a priori error of 45 mas for pole and 3 ms for UT1, 45 mas/day and 3 ms/day for pole rate and UT1 rate to allow estimation for one-baseline sessions; X-nutation and Y-nutation are relative to the IAU2000A/2006 Nutation/Precession models. The time tags of the EOP series are the middle epochs of the observing sessions. gsf2016a.eops: X, Y, UT1, Xdot, Ydot, UT1dot, Deps, Dpsi, for each session. Deps and Dpsi are relative to the IAU 1976 precession and IAU 1980 nutation models. {Internally, Calc/Solve estimated offsets to the X and Y precession/nutation quantities, relative to the IAU2000A/2006 nutation/precession models, using the IERS 2010 Conventions [6] implementation. These were converted to classical Dpsi and Deps nutation offsets relative to the IAU 2000A nutation model. These were then converted to the IAU 1976/1980 precession/nutation (Wahr) model by adding the following terms: Deps: -25.24*Cent - 6.8192 (m-arc-sec), and Dpsi: -299.65*Cent - 41.775 (m-arc-sec), where Cent is the epoch in fractional centuries since 2000.0 (Julian date 2451545.0). This conversion is not quite correct though. There are some long term drifts that are not accounted for.} High frequency variations in polar motion and UT1, as computed by Calc 11, were added to the a priori EOP during the Solve/Globl solution. The reported values of polar motion and UT1 are the sum of the adjustments and the apriori EOP without the contribution due to high frequency variations. Thus, the final series of polar motion and UT1 do not contain contributions due to high frequency variations. The networks of each individual session fall into 4 categories: 1) Very small network: baselines shorter than 150 km; 2) Small network: baselines in the range 150-1500 km; 3) Singular network: single baseline network with baseline length longer than 1500 km; 4) Global network: three or more stations with baselines longer than 1500 km. The EOPs were not estimated for very small networks. The EOPs were estimated for small networks but with strong constraints applied. The records related to these experiments were eliminated from the output EOP file. The EOP's from the remaining sessions were put into files gsf2016a.eoxy and gsf2016a.eops. The pole coordinates and UT1 from singular networks were substantially affected by weak constraints. They were removed from the output files and their values and formal uncertainties were replaced with "-0 ". The singular networks provided reasonable estimates of nutation angles. 8. A priori geophysical models: a. Troposphere: VMF1 total (dry+wet) mapping function; Saastamoinen zenith delay calculated using logged pressure and temperature; a priori mean gradients from DAO weather model. b. Solid Earth tide: IERS Conventions 2010 [6], chapter 7, steps 1 and 2, including tides of the 2-nd and 3-rd order. c. Ocean loading: 3D ocean loading displacements computed using the Hardisp model. Ocean loading coefficients computed using the TPXO7.2 model. These were obtained from the ocean loading web site at http://holt.oso.chalmers.se/loading/, which is provided by H.-G. Scherneck, Onsala Space Observatory. d. Pole tide: Mean pole coordinates used for computation of pole tide deformation were set to the IERS 2010 Conventions [6] recommended values (Chapter 7, p. 114-116). e. Ocean pole tide loading: An ocean pole tide loading correction was applied, using the model of Desai 2002 [7]. These were computed by Calc 11, and are described in the IERS Conventions (2010), chapter 7, pages 116-118. This small correction should have an ~14 month period. f. Antenna thermal deformation: Antenna heights were adjusted, based on the average daily temperatures, using the IVS antenna thermal deformation model of Nothnagel 2008 [8]. 9. Data type: Group delays only. 10. Data editing: 5 deg elevation cutoff. 11. Data weighting: Weights are defined as follows: 1/sqrt ( f**2 + a**2 ). Quantity "f" is the formal uncertainty of the ionosphere free linear combination of group delays at X- and S-band obtained by fringe fitting. The station-dependent parameter "a" was computed for each session by an iterative procedure such that the ratio of the sum of the squares of the weighted residuals to the estimate of their mathematical expectation is about 1.0. 12. Standard errors reported: All errors derived from least-squares estimation propagated from the data weights and the constraints applied to the estimated parameters. 13. Software: Calc 11, SOLVE revision date 2016.09.07. References: 1. Altamimi, Z., P. Rebischung, L. Mtivier, and X. Collilieux, "ITRF2014: A new release of the International Terrestrial Reference Frame modeling nonlinear station motions, J. Geophys. Res. Solid Earth, vol. 121, Issue #8, pp. 6109-6131, 2016. doi:10.1002/2016JB013098. 2. IERS Technical Note 35, 'The Second Realization of the International Celestial Reference Frame by Very Long Baseline Interferometry'; A.L. Fey, D. Gordon, C.S. Jacobs, editors; 2009. http://www.iers.org/IERS/EN/Publications/TechnicalNotes/tn35.html 3. MacMillan, D.S. and C. Ma, "Atmospheric gradients from very long baseline interferometry observations", Geophys. Res. Lett., 22, 1041-1044, 1995. 4. MacMillan, D.S. and C. Ma, "Atmospheric gradients and the VLBI terrestrial and celestial reference frames", Geophys. Res. Lett., 24, 453-456, 1997. 5. Takashima, K., et al., "Status and Results of GSI Domestic VLBI Network", Bulletin of the Geographical Survey Institute, Vol. 46, March 2000, p. 1-9. 6. Petit, Gerard and Luzum, Brian, 'IERS Conventions (2010), IERS Technical Note 36, 2010. 7. Desai, S.D., "Observing the pole tide with satellite altimetry," J. Geophysical Research, vol. 107 (C11), p.3186. doi:10.1029/2002JC001224. 8. Nothnagel, A., "Short Note: Conventions on Thermal Expansion Modelling of Radio Telescopes for Geodetic and Astrometric VLBI," Journal of Geodesy, DOI: 10.1007/s00190-008-0284-z, 2008. ---------------------------------------------------------------------------- Appendix A. ~~~~~~~~~~~ List of 39 special handling sources for which Right Ascensions and Declinations were estimated as local parameters: 0014+813 0235+164 0637-752 0738+313 1308+326 1448+762 2145+067 1610-771 0208-512 0438-436 0451-282 0919-260 0607-157 2243-123 NGC1052 2128-123 3C279 0106+013 2134+00 1021-006 3C273B 0528+134 2121+053 0202+149 3C454.3 1611+343 OQ208 2201+315 2234+282 OK290 4C39.25 3C345 0711+356 3C84 1739+522 1044+719 0212+735 3C309.1 3C120 Appendix B. ~~~~~~~~~~~ List of 1895 sources estimated as global parameters: 2358+189 2359-221 0000-160 0002-478 0002+200 0002+541 0003+380 0003+158 0003+340 0003-066 0005-239 0006-363 0006+061 0007-325 0007-048 IIIZW2 0007+171 0008-311 0008-421 0008-264 0009+081 0010-401 0010+405 0011-046 0013-005 0015-054 0015+145 0017+200 0017+257 0016+731 0019+058 0021+243 0022-423 0022-044 0024+224 0025+197 0026+346 0027+056 0027-426 0028-396 0032+612 0033-088 0034-220 0034+108 0035+238 0035-252 0035-024 0035+413 0037+139 0037-593 0038-326 0038-020 0038+319 0038-019 0039+230 0039+568 0040+098 0044-846 0043-392 0043-268 NGC0262 0046-315 0046+511 0047+023 0047-579 0048-097 0048-427 0046+861 0050-287 0051+291 0054+161 NGC0315 0055-059 0055-340 0055+060 0056-572 0056-001 0057-338 0058+058 0059+581 0102+511 0104-275 0103+127 0104-408 0107-610 0106+315 0108+388 0109+224 0109+351 0110-668 0110-361 0110+495 0111+021 0111+131 0112-245 0112-017 0113-283 0113-118 0114-211 0115-214 0116-219 0116+319 0118-272 0119+115 0119+041 0119-046 0119+247 0121+560 0122-514 0122-003 0124-155 0123+257 0123+731 0124-086 0125+628 0127+084 0130-171 0130-447 0131-522 0133+476 0134+311 0135-247 3C48 0136-059 0136+176 0137+012 0137+467 0138-097 0142-398 0142-278 0144+209 0144+584 0145+210 0145+420 0146+056 0147-076 0147+265 0148-177 0148+274 0149-175 0149+218 0150-144 0150-334 0151+474 0153-410 0155-549 0153+744 0158-159 0159-668 0159-117 0159-062 0202-765 0157+808 0159+723 0200+30A 0200+304 0201+113 0201+398 0201+088 0202-172 0202+319 0203-120 0203+625 0206-689 0206-625 0206-178 0206-048 0206+136 0207-078 0209+168 0210-180 0210+225 0210-075 0212-620 0211+171 0212-039 0213-026 0214-522 0213-015 0213-013 0215+015 0215-015 0216+011 0216+478 0218+095 0219+428 0220-349 UG01841 0220-023 0219+628 0221+067 0222-234 0223+113 0224-189 0226-559 0226-375 4C67.05 0227-369 0230-790 0227+403 0229+131 0229-398 0229+230 0230-288 0229+200 0232-042 0234-301 0235-618 0235+205 0234+285 0237-027 0237+040 0237-233 LSI61303 0239+175 0239+108 0241+622 0244-452 0244-470 0245-167 0246+061 0248-266 0248+430 0252-712 0250-001 0250-122 0252-549 0250+320 0253+133 0254-334 0255+288 0256+075 0256-005 0256+192 0258-184 0258+011 0259+121 0301-243 0300+470 0302-623 0302-437 0303+051 0302+625 NGC1218 0307-362 0306+102 0306+274 0306-061 0308-611 0307+380 0312-770 0309+360 0309+411 0310+410 0312+100 0315-282 0316-444 0316-164 0317+188 0318-172 0319+121 0319-133 0319+396 0322-230 0322-294 0322+222 0324-379 0324-328 0325-182 UGC02748 0325+395 0326+278 0327+467 0329-404 0329+654 0331+022 0332-403 0332-375 0332+078 0334-546 NRAO140 0334-131 HR1099 0335-364 0334+014 0335-122 0336-017 CTA26 0336+539 0338-214 0338+388 0340-140 0340+362 0341+158 0342+147 0342+538 0346-279 0345+460 0347-211 0348-120 0348-031 0350+465 0346+800 0355-669 0352+605 0354+231 0355-483 0355+055 0354+559 0356-033 NRAO150 0357-263 0358+040 0358+210 0400-319 0400+258 0402-362 0403-132 0403-179 0404-240 0405-385 0405-331 0404+065 0405-123 0405-015 0405+305 0407-658 0406-127 0406+121 0407-199 0409-280 0408+085 0409+229 0410+110 0411+054 0414-189 0415+379 0415+398 0417-302 0419-068 0418+532 0420+022 0420+210 0420-014 0420+417 0421+023 0421+145 0422-389 0422-380 0422+004 0423+051 0421+683 0423+233 0423+237 0425+048 0425+174 0426-380 0427-502 0426+273 0431-512 0430-332 0432-606 0430+289 0434-188 0433+295 0437-719 0436-129 0437-454 NRAO190 0440+345 0438+785 0442+389 0445-221 0446-265 0450-743 0446-096 0446+112 0444+634 0447-010 0454-810 0446+462 0447+227 0446+595 0449+125 0450+013 0452+068 0454-463 0454-220 0454-234 0456+060 0457+024 0458-020 0458+138 0459+060 0459+135 0459+252 0500+019 0501-067 0503-608 0502-152 0502+049 0506-612 0503+608 0454+844 0506+056 0506+101 0507+179 0508+138 0509+205 0509+152 0511-220 0510+559 0514-459 0514-161 0517-726 0516-621 0514+074 0514-156 0515-179 0515+208 0518-458 3C138 0522-611 0519+142 0521-403 0521-365 0518+600 0521-262 0524-460 0524-485 0524-237 0525-231 0525-100 0524+034 0530-727 0527-053 0527-253 0521+793 0528-250 0529+075 0531-397 0529+483 0532-378 0534-611 0531+194 0532+196 0534-340 0537-441 0537-158 0536+145 0537-286 0539-543 0539-057 0538+330 0542-735 0540-270 3C147 0540+529 0542+112 0544+273 0549-575 0547+234 0548+084 0548+378 0549+192 0552+398 0552+393 0554+242 0557-454 0556+238 0557-182 0558-396 0600+177 0600+219 0601-172 0602-424 0601+245 0602+405 0604-074 0604-004 0605-247 0602+673 0605-085 0606-223 0608-187 0604+728 0609-284 0610+171 0610+260 0611+131 0609+607 0614-349 0613+570 0615-365 0616-244 0621-787 0617+210 0620+227 0622-441 0620+389 0621+446 0615+820 0625-354 0628-671 0628-627 0627-199 0628+203 0629-418 0630-261 0629+160 0630+367 0632-235 0632-183 0633-26B 0633-26A 0634-584 0635-296 0627+814 0635-355 0634+334 0633+595 0637-337 0637-216 0639+098 0639-032 0636+680 0603+882 0639+115 0639+352 0641+126 0644-671 0641+392 3C166 0642+449 0643+548 0646-306 0645+209 0647-475 0647-410 0648-165 0648-287 0649-209 0650+371 0651+410 0652+426 0654+244 0656-062 0656+082 0657+172 0700-465 0700-197 0702+400 0704-231 0705-412 0704+384 0707+476 0709-015 0708+506 0710+439 0714+457 0713+669 0716+332 0717-198 0717-393 0716+477 0718-154 0716+714 0720-305 0721-071 0722+145 0723-189 0723-008 0718+793 0723+219 0725-381 0725+219 0726-224 0727-365 0727-115 0727+409 0728+249 0728+281 0729+259 0731+050 0733-174 0733-187 0734-044 0735+178 0736-332 0738-674 0736+017 0738+491 0742-562 0743-673 0741-444 0744-691 0741-063 0741+214 0742+263 0742+103 0743-006 0743+259 0743+277 0745-291 0745+241 0747+185 0746+483 0747+104 0748+126 0748-006 0749+540 0751+393 0750+633 0753-425 0754+100 0758-737 0755+117 0755+085 NGC2484 0800-380 0759+252 0759+183 0801+103 0802-170 0800+618 0803-047 0806-710 0759+779 0804-351 0804-153 0805+072 0805+046 0805-077 0804+499 0805+410 0806-153 0806+315 0807+103 0807+083 0809-493 0808+019 0811-179 0812+020 0812+367 0812+100 0814+425 0810+812 0813+758 0818-128 0820-578 0821+248 0821+411 0820+560 0822-152 0821+394 0822+137 0823-500 0821+621 0823+033 0823-223 0826-373 0826+180 0826+404 0827+243 0828+065 0828-222 0829+046 0829+089 0828+493 VELA-G 0832-225 0831+557 0833-450 0830+687 0833+010 0834-201 0835-339 0833+585 0834+250 0836-384 0836+290 0836+182 0838+133 0838-090 0837+448 0836+710 0842-754 0839+187 0838+456 0841-607 0843-547 0843-336 0843-371 0845-051 0847-120 0848-304 0848+089 0850+581 OJ287 0855-716 0854-108 0854+213 0855+143 0857-329 0858-313 0859-140 0859+470 0859+681 0902-309 0902-350 0903-573 0901+697 0903+500 0905+420 0906+163 0906+015 0906-048 0907+022 0908-052 0907+258 0910-414 0912-273 0912-330 0912+029 0912-204 0913-302 0912+297 0913+079 0914+029 0913+657 0915-118 0916+336 0918-534 0917-185 0918-297 0917+449 0918+140 0917+624 0920-397 0920+390 0923+171 0925-203 0925+504 0936-853 0927+469 0928+008 0928-100 0928+144 0928+280 0930+289 0932+075 0932+243 0933+503 0935+181 0936-069 0937+262 0938-133 0938+119 0939+620 0940-118 0941+522 0942+358 0943+105 0945-287 0945+408 0949+510 0949+354 0948+658 0951+175 0951+268 0952+179 SN1993J M81 0952+581 4C55.17 0955+476 0955+326 0956-409 0954+658 0958+346 0959+127 1000+125 0959+684 1003+351 1005-739 1004-500 1004+054 1004-217 1005-333 1004+141 1005+066 1009-041 1009-321 1010+495 1011+250 1012+232 1012-448 1013+127 1013+054 1013+208 1013+596 1014+615 1015-314 1015+359 1015+057 1016-311 1015+594 1016-268 1019+416 1020+400 1022-665 1022+194 1022+237 1023+131 1025+031 1026-084 1027-186 1030+415 1030+074 1030+687 1032-199 1031+567 1032+382 1034-374 1034-293 1035-268 1036-529 1038+064 1039-474 1038+52A 1038+52B 1040-414 3C245 1040+244 1039+811 1042+071 1043+066 1044+007 1045-620 1045-188 1045+019 1046-409 1046-222 1047+147 1048-526 1049-726 1048-313 1049-650 1049+215 1053+704 1054+004 1055-242 1055-301 1053+815 1055+201 1055+018 1057-797 1056+212 1058+726 1059-438 1059+282 1100+122 1101-325 1101-536 1101+077 1101+384 1104-445 1105-680 1104+728 1106+084 1106+023 1107+485 1108+527 1109-567 1111+149 1115-122 1115-306 1116-462 1116+128 1116+227 1117-248 1117-270 1117+146 1119-069 1119+183 1121+238 1121+518 1121+661 1123-356 1123+264 1124-056 1124-186 1124+571 1125+366 1125+596 1126+109 1127-443 1127-358 1127-145 1128+385 1128+517 1128-047 1129-161 1129-580 1130-741 1130+106 1130+009 1131-088 1131+730 1133-041 1133-739 1133-032 MRK180 1136-466 1137+660 1138-277 1140+668 NGC3862 1142+052 1142-225 1143+446 1143-696 1143-245 1143-287 1143+590 1143-332 1144+402 1144-379 1144+352 1145-676 1145-071 1145+268 NGC3894 1146+531 1147+245 1147-063 1147-192 1147+659 1148-001 1148-671 1149-084 1150+812 1150+497 1151+598 1151+126 1152-295 1155+169 1155+251 1156+101 1156-094 1156-663 1156-214 1156+295 1158+007 1200+068 1200+045 1200+468 1201-068 1204+399 1204-613 1204+124 1205-008 1206-238 1210+197 1210-246 1211-167 1212+087 1212+171 1213-172 1213+350 1213+097 1215+303 1215-002 1215-457 1216-010 1216+179 1216+487 NGC4261 1217+023 1217-266 1218+339 1218-341 1219+285 1219+044 1221+464 1221+809 1221+484 1222+037 1221-829 1222+216 M84 1223-188 1226-028 1226+373 1227+274 1227+255 3C274 1228-113 1228-352 1229+645 1232-338 1232+366 1234-504 1236+077 1237-101 1236-684 M104 1238-110 1239+552 1239+606 1239+376 1240+381 1241+735 1241+166 1241+176 1242+574 1243-160 1243-072 1244-255 1245+716 1245-062 1245-454 1246+489 1247-442 1247+139 1247+025 1249-673 1250+293 1251-407 1251-197 1252+119 1251-713 1254+571 1256+802 1255-316 1255-177 1256-220 1257+145 1258+145 1257-326 1300+485 1300+580 1300-105 1302-208 1302-102 1304-318 1306+360 1303-827 1307+433 1307+121 1306-395 1307+010 1308+328 1308+554 1309+355 1310-041 1312+240 1312-533 1313-333 OP326 1314-134 1315+047 1316-120 1317+520 1317+019 1318+225 1318-434 1318-263 1322+835 1319-093 1320-446 1320-338 1320-303 1323+799 1321-105 NGC5141 CEN-A 1323+321 1323+037 1323-527 1324+224 1325-133 1325+126 1326+626 1325-558 1327+504 1327+321 1326-698 1328+254 1328+522 3C286 1329-049 1329-137 1330+476 1330+022 1331+170 1332+031 1333-049 1333-082 1333-152 1333-337 1335+658 1335+023 1334-127 1335+552 1334-649 1336-237 1336-260 1337-033 1338+381 1339+129 1339-287 1342+662 1342+663 1341-171 1343+386 1343-601 1345+061 1345+125 1345+289 1346-306 1347+539 1347-163 1348+308 1348+087 1349-439 1351-018 1352-104 1352-632 1354+247 1354+195 1354-174 1354-152 1357+769 1355-416 1356+022 1400-184 1402-012 1402+044 1404-342 1406+564 1406-076 1406-267 1409+218 1412+461 1412-279 1412+087 1412-097 1412-368 1413+135 1413+349 1414+129 1415+385 1416+159 1416+067 1418+546 1417+385 1417+273 1417+172 1418-192 1420+326 1419-229 1420+044 1421+122 1417-782 1421+048 1420-725 1420-679 1423+146 1424+366 1424+240 1424-418 1427+634 1427+543 1428+422 1428+370 1429+249 NGC5675 1430-178 1424-834 1432+200 1433+304 1434+235 1435+638 1435-218 1436+373 1437+331 1437-153 1437+061 1438-151 1439+066 1441+522 1441-058 1441+252 1442+637 1442+031 OQ172 1442-245 1443-162 1444+175 1445-161 1448-648 1451+270 1451+094 1451-375 1452+301 1451-400 1454-060 1454-354 1455+247 1455+348 1456+044 1458+088 1459+480 1501+043 1501-026 1502+106 1501-343 1502+036 1504+377 1505+428 1504-166 1505-156 1505-496 1505-304 1508+572 1508-111 1508-055 1508-325 1509+022 1510-089 1508-656 1510-319 1510-421 1511-100 1511-476 1511-360 1511-558 1514+004 1514+197 1514-241 1518+162 1519+181 1520+437 1520+319 1519-294 1519-273 1525+737 1522+155 1525+613 1526+670 1526+384 1528-274 1528-684 1531-225 1532+016 1531-352 1533-653 1535+004 1537-389 1538+149 1540-077 1541+050 1545+210 1547+507 1546+027 1547-054 1548+056 1540-828 1549-242 1550-242 1551+130 1550-269 1551-416 1549-790 1555+001 1555-140 1554-643 1558+595 1557+032 1556-245 1557-053 1600+43A 1600+43B 1600+335 1600-294 1603+699 1601+160 1601+112 1600-445 1603+573 1602-115 1604+554 1604+315 1605+542 1604-333 1606+106 CTD93 1606-056 1606-398 1608+243 1613+782 1612-243 1611-710 1614+051 1613-350 1614+042 1613-586 1614-255 1614-195 1615+029 1616+063 1617+229 1619+491 1618-399 1621+078 1619-680 1621-351 1623+578 1621-067 1621-321 1622-253 1622-310 1624+416 1622-297 1627+476 1624-617 1626-172 1628+216 NGC6251 1629-458 1630-004 1633+38 1634+213 1633-409 1636+473 1637+574 1635-035 1637+166 NRAO512 1637-373 1638+118 1639+230 1639-062 1639-200 1642+690 1633-810 1639-287 1640-231 1637-771 1642-076 1647+744 1645+271 1645+174 1645+224 1645-329 1645-262 1646-506 1648+084 1647-296 1649+216 1651+391 1650-157 DA426 1653-329 1656+348 1656+477 1655+077 1656+053 1656-075 1657+265 1657-261 1659+399 1657-562 1700+320 1659-621 1705+717 1707+779 1705+456 1705+018 1705+135 1705-353 1706-174 1708+433 1708-335 1710-323 1711-208 1711-209 1714-397 1715-112 1717+178 1718-084 1718-259 1721+589 1721+343 1722+526 1718-649 1722+330 1728+774 1724-198 1726+455 1725+123 1727+502 1725+044 1730+604 NRAO530 1725-795 1732+389 1734+363 1734+508 1734+065 1733-197 1734+063 1733-565 1736+324 1738+499 1738+476 1737-081 1742+724 1739-152 1741+597 1740-190 1740-169 1741+279 1741-038 1740-517 1742-088 NGC6454 1742-078 1743+173 1745+670 1745+624 1746+470 1749+701 1750+472 1749+096 1748-253 1749-299 1750-187 1751+441 1751+288 1753+204 1755+626 1753+049 1755+578 1754+292 1753-144 1754+159 1754+155 1753-418 1759+756 1756+237 1758+388 1803+784 1800+440 1759-396 1800-045 1758-651 1801+036 1802-046 3C371 1806+456 1806-458 1812+412 1813+163 1815+531 1815-111 1818+551 1816-029 1817+387 1814-637 1817+157 1815-553 1817-254 1826+796 1820-274 1823+689 1821+107 1823+568 1822+033 1822+012 1822-173 1822-076 1826+670 1825-041 1825-214 1825-055 1824-582 1826-447 1827-272 1829-207 1832+687 1830+139 1830+285 1831-030 1830-589 1828-733 1832-113 1829-718 1831-693 1831-711 1838+575 1839+389 1839+548 3C390.3 1842+681 1843+400 1842-220 1842-289 1843-001 1846+322 1845-273 1849+670 1848+283 1851+488 1851-162 1856+736 1853+027 1853-122 1853-179 1854+061 1852-534 1855+031 1855-252 1856-252 1858-255 3C395 1901+016 1901+155 1903+097 1904+013 1905+222 1905-297 1906-217 1908+484 1907-224 1908-201 1909+161 1903-802 1910+052 1910-365 1913-272 1914-154 1916+062 1917-248 1917-386 1918-026 1919+086 1918-634 1920-211 1922+155 1921-293 1922-224 1923+210 1928+738 1925-206 1926+087 1927+256 1927+090 1925-610 1928+154 1929+476 1929+226 1929-457 1928-698 1932+106 1932+174 1932+204 1936+714 1934+226 1933-400 1934-065 1935+360 1936+046 1936+095 1934-638 1936-155 1937-101 1935-692 1936-623 1941-554 1942-313 1943+228 1945-011 1945-325 1948+505 1946-200 1947+079 1946-582 1949-052 1951+498 1951+355 1950-613 1952+138 1954+513 1954+282 1953-325 1955+343 1955+335 1954-388 CYGNUS-A 1957-135 1958-179 2000+472 2000+148 2000-330 2005+737 2007+777 2002-375 2005+642 2007+659 2005+403 2005+372 2005-044 2005-489 2007+073 OW-015 2008-159 2013+508 2014+463 2013+163 2017+743 2016-053 2018+282 2021+614 2020-122 2021+317 2022+542 2022+274 2022+171 2022+031 2023+336 2022-077 2025-538 2027-035 2029+024 2030+547 2029+121 2033+187 2030-689 2033-286 2033-219 2034+222 3C418 2036-034 2037-253 2039+037 2043+749 2043+156 2044-168 2046+429 2045-405 2047-266 CL4 2048+196 2051+745 2051+687 2051-204 2052+239 2053-044 2052-474 2054-075 2054-377 2056-369 2057+235 2059+560 2058-297 2059+034 2058-425 2100+468 2059-786 2103+213 2102-659 2105-293 2106+143 2111+801 2106-413 2107-105 2111+111 2112+283 2112-144 2113+293 2109-811 2115-305 2116-068 2118+443 2117-614 2117-642 2120+099 2121+460 2120-309 2121-199 2122-238 2123-463 2126-158 2127-096 2128+048 2136+824 2131+145 2131-021 2131-340 2135-184 2136+141 2136-251 2138-377 2139-249 2140-048 2141+175 2141-334 2142+110 2143-156 2144+568 2144+092 2142-758 2144-065 2144-362 2145+082 2146+019 2147+077 2147-186 2149+056 2149-306 2146-783 2150+173 2151-118 2152+226 2153-204 2152-699 2155+312 2155-152 2155-304 2157-255 2157+102 2157-375 2159+505 VR422201 2201+171 2201+044 2203+292 2205+743 2203-188 2204-007 2204-540 2205+166 2206+650 2205-636 2207+374 2207+356 2208+199 2208-137 2209+236 2210-257 2210+361 2211-388 2211-256 2214+350 2214+241 2215+020 2215+006 2215+150 2215-508 2216-007 2216-038 2216+178 2217+214 2220-351 2220-318 2222+600 2221-387 2223+210 2223-114 3C446 2225+247 2227-088 2226-634 2229+695 2227-399 2227-445 2229-172 CTA102 2232-488 2233-186 2233-234 2233-148 2235+731 2236+678 2236-572 2236-221 2237+121 2238-362 2239+096 2239-631 2240-064 2243+047 2244-372 2245-091 2245-128 2245-328 2246+208 2250+194 2252+618 2252-089 2253+417 2253+227 2254-367 2254+074 2254+024 2255-282 2256-084 2258+166 2259+058 2259-375 2300-307 2300-683 2301-103 2301+060 2302+232 2304+377 2305+145 2305+187 2306-312 2307+106 2309+454 2311-477 2311-373 2311-452 2312-319 2312-505 2314+038 2314-340 2314-409 2315-172 2316+238 2317-372 2318+049 2318-087 2319+317 2319+272 2319+444 2320+506 2320-035 2321-065 2321-375 2321-215 2322-411 2322+396 2324-023 2324+151 2325+093 2325-150 2326-477 2327-376 2328+107 2329-162 2329+068 2329-384 2329-415 2331-240 2333-528 2333-415 2335-181 2335-027 NGC7720 2336+598 2337-123 2337+264 2338+000 2338+191 2338-295 2340+233 2341+295 2344+09A 2344-514 2344+429 2345-167 2346-049 2346+385 2348-432 2349-014 2350-280 2351-309 2351+456 2351-154 2352+495 2353-686 2353+816 2354-021 2354-117 2355-534 2355+490 2355-106 2355-291 2356+196 2356+385 2357-318 Appendix C. ~~~~~~~~~~~ List of 94 stations with axis offsets estimated as global parameters: AIRA ALGOPARK BADARY BR-VLBA CHICHI10 CRIMEA DSS13 DSS15 DSS45 DSS65 DSS65A EFLSBERG FD-VLBA FORTLEZA GBT-VLBA GGAO7108 GIFU11 GILCREEK GOLDVENU HARTRAO HART15M HATCREEK HAYSTACK HN-VLBA HRAS_085 HOBART12 HOBART26 ISHIOKA KASHIM11 KASHIM34 KASHIMA KATH12M KAUAI KOGANEI KOKEE KP-VLBA KUNMING KWAJAL26 LA-VLBA MARCUS MARPOINT MATERA MEDICINA METSAHOV MIAMI20 MIURA MIZNAO10 MK-VLBA MOJAVE12 NL-VLBA NOTO NRAO_140 NRAO20 NRAO85_1 NRAO85_3 NYALES20 OHIGGINS ONSALA60 OV-VLBA OVRO_130 PARKES PIETOWN RAEGYEB RICHMOND SANTIA12 SC-VLBA SEJONG SESHAN25 SEST SINTOTU3 SVETLOE SYOWA TATEYAMA TIANMA65 TIDBIN64 TIGOCONC TIGOWTZL TOMAKO11 TSUKUB32 TSUKUBA UCHINOUR URUMQI VERAISGK VERAMZSW VNDNBERG WARK12M WESTFORD WETTZELL WETTZ13N YARRA12M YEBES YEBES40M YLOW7296 ZELENCHK Appendix D. ~~~~~~~~~~~ List of 38 stations with constraints on velocity: AUSTINTX AZORES BERMUDA BLOOMIND BREST CARNUSTY CARROLGA CHLBOLTN CTVASBAY CTVASTJ DAITO GRASSE HOFN HOHENFRG HOHNBERG KAINAN KANOZAN KARLBURG KIRSBERG LEONRDOK MCD_7850 METSHOVI MILESMON NOBEY_6M OCOTILLO SAGARA SEST SUWON TITIJIMA TOMAKO11 TOULOUSE USSURISK USUDA64 VERAIRIK VERAOGSW VICTORIA KUNMING UCHINOUR Appendix E. ~~~~~~~~~~~ Velocities of these 25 pairs, triplets or quadrets of stations were constrainted to be the same: DSS15 DSS13 DSS45 TIDBIN64 DSS65 DSS65A ROBLED32 FORTORDS FORT_ORD GIFU11 GIFU3 GGAO7108 GORF7102 HARTRAO HART15M HRAS_085 FTD_7900 HOBART26 HOBART12 KASHIM34 KASHIM11 KASHIMA KAUAI HALEAKAL KOGANEI KOGANEI3 METSAHOV METSHOVI MIZNAO10 MIZUSGSI VERAMZSW MOJAVE12 MOJ_7288 NRAO20 GBT-VLBA NRAO_140 NRAO85_1 NRAO85_3 ONSALA60 MV2ONSLA ONSALA85 OVRO_130 OVR_7853 RICHMOND MIAMI20 SINTOTU SINTOTU3 TSUKUB32 TSUKU3 TSUKUBA PIETOWN VLA-N8 WETTZELL WETTZ13N TIGOWTZL YEBES40M YEBES RAEGYEB YLOW7296 YELLOWKN