Technical description of solution gsf2011a 2011.04.26 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 gsf2011a 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 36 strong stations have no net translation or rotation with respect to their positions and velocities reported in the ITRF2008 [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 [1997.01.01, 2011.04.07]. 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 the coordinates reported in the ICRF2 catalog. All available dual-band Mark-3/Mark-4/Mark-5/K3/K4/VLBA VLBI observations from 1979.08.03 through 2011.04.07 (except 26 VCS1, VCS2, VCS3, VCS4, VCS5, VCS6, NPCS sessions, 3 gravity sessions and 12 VLBA K-band and 4 VLBA Q-band sessions) with durations of 18 hours and longer (4943 sessions, 7228628 group delays) were used in a single solution. The wrms postfit residual was 22.154 psec and Chi/ndg was 0.896. 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 had no good observations, only 1 or 2 good observation in 1 session, and all sources which did not have at least 3 good observations in at least one session were excluded from the dataset. 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 sources (the so called 'special handling' sources of ICRF2, see Appendix A) were estimated in each session individually. The positions of the remaining 1327 sources (see Appendix B) were estimated as global parameters. Two source catalogs are provided: 2011a.sou -- catalog of 1340 sources estimated as global parameters. 2011a_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 (gsf2010a) solution: 131 additional databases, and 3415292 additional observations were included. 83 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. ZELENCHK was included in the list of stations with episodic motion. Rail repairs were made there in mid-2007. They do not report any offset due to these repairs. However the solutions support a small displacement of ~1 cm in the Up direction. The episodic adjustment at ZELENCHK gives a significantly lower vertical velocity, which is more in line with the GPS velocity for ZELENCHK. TICOCONC was affected by a large nearby earthquake in Chile on Feb. 27, 2010, and experienced an episodic offset of more than 3 meters, mostly in the westward direction. The motion there since the earthquake has been clearly non-linear, and a single episodic break cannot model the motion properly. Therefore a new user partial program was created to estimate offsets at TIGOCONC for each session after the earthquake. Both TIGOCONC and ZELENCHK were removed from the list of stations used for a no-net-rotation, no-net-translation constraint. An new version of Solve was used which directly estimates the X and Y nutation/precession components. The IAU2006 precession model was also applied. These are also converted into the classical nutation offsets, Dpsi and Deps with respect to the IAU200A/2006 precession/nutation models, and then into the older IAU1980/1976 (Wahr) classical nutation offsets. 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; VMF wet partial derivative (segmented). e. Troposphere Gradient: 6-hour East and North linear splines at all stations, except a set of 98 stations (Appendix C); offset and rate constraints with reciprocal weights 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 D) (global). 5. Celestial Reference Frame: a. A priori source positions: /500/oper/solve_save_files/icrf2.src. This catalog was created from the ICRF2 catalog [2]. Additional source positions are either from new observations since ICRF2 (several RDV's), or from apriori positions. b. Source positions adjusted in solution: Yes. Orientation defined by a no-net-rotation tie to the ICRF2 using the 295 ICRF2 defining sources. 1340 global and 39 local sources. 6. Terrestrial Reference Frame: a. A priori station positions: /500/oper/solve_save_files/itrf2008.sit, from ITRF2008 [1]. b. A priori station velocities: /500/oper/solve_save_files/itrf2008.vel, from ITRF2008 [1]. c. Reference epoch for site positions: 2008.0. 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 position with respect to ITRF2008A for 36 stations: ALGOPARK BR-VLBA DSS45 FD-VLBA FORTLEZA HARTRAO HATCREEK HAYSTACK HN-VLBA HOBART26 KASHIM34 KASHIMA KAUAI KOKEE KP-VLBA LA-VLBA MATERA MK-VLBA NL-VLBA NOTO NRAO20 NRAO85_3 NYALES20 ONSALA60 OV-VLBA OVRO_130 PIETOWN RICHMOND SANTIA12 SC-VLBA SESHAN25 TSUKUB32 VNDNBERG WESTFORD WETTZELL SVETLOE No-net-translation and no-net-rotation of velocity with respect to ITRF2008 for the same 36 stations. Values of right-hand side of net-rotation/net-translation constraints: RIGHT_PART 0.06386704 0.02201004 0.02305177 NO EXCEPT \ * nnt_pos RIGHT_PART -0.04901472 0.05586586 0.09614829 NO EXCEPT \ * nnr_pos RIGHT_PART 0.00075550 0.00462229 0.00309244 NO EXCEPT \ * nnt_vel RIGHT_PART -0.00657139 0.00364146 -0.00523887 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 (except the newest station WARK12M), some with constraints. g. Stations with constraints: A priori velocities for U, E, and N components of 38 stations listed in Appendix E were constrained to their ITRF2008 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 F 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 ! Earthquake PRESIDIO 891001 ! Earthquake MOJAVE12 920627 ! Earthquake DSS15 920627 ! Earthquake MEDICINA 960601 ! Rail repair EFLSBERG 961001 ! Rail repair DSS65 970415 ! Rail repair MIURA 000701 ! Seismic event TATEYAMA 000701 ! Seismic event GGAO7108 030101 ! Station relocation SINTOTU3 030915 ! h/z ZELENCHK 070701 ! Rail repair Also, the eccentricity vector for station TSUKUB32 was assigned as (-0.0437, 0.0, 0.0) meters in Up, East, North 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. Relativity scale: The terrestrial reference frame is defined using the following metric tensor: G_oo = -(1 - (2W/c^2 + W^2/c^4) + 2L_g ) G_oa = -4W^a/c^3 G_ab = \delta_ab (1 + 2W/c^2 - 2L_g) ) Specifically, the old formula 29 in IERS Conventions 1992, page 127-136 was used, although it is known to have a deficiency. THIS METRIC TENSOR DOES NOT CONFORM TO IAU 2000 RESOLUTIONS! k. 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 2003 Conventions. 7. Earth orientation: a. A priori precession/nutation model: IAU2000A Precession-Nutation, IERS 2003 [6] implementation, modified using the IAU2006 precession model. 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 10.0, as recommended in the IERS 2003 Conventions [6], chapter 5, p. 5. d. EOP estimation: Two tables are given: gsf2011.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 IAU2000A/2006 Nutation/Precession models. Time tag of the EOP series is the middle epoch of the observing session. gsf2011.eops: X, Y, UT1, Xdot, Ydot, UT1dot, Deps, Dpsi, 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 2003 Conventions [6] implementation and the difference due to the IAU2006 Precession model. 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. See reference [7].} High frequency variations in polar motion and UT1, as computed by Calc 10, 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 contribution due to the 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 gsf2011a.eoxy and gsf2011a.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: VMF 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 2003 [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 by SPOTL software. The model of displacements caused by ocean loading contains 28 constituents. The following ocean tide models were used: Harmonic Phase rad Frequency rad/sec Model Comment k2-a 1.324501D+00 1.458530140651D-04 GOT00 admittance k2 3.506941D+00 1.458423171028D-04 GOT00 s2 6.283185D+00 1.454441043329D-04 GOT00 s2-a 4.312500D-02 1.452450074576D-04 GOT00 admittance m2 2.169437D+00 1.405189027044D-04 GOT00 m2-a 1.210284D+00 1.405082057420D-04 GOT00 admittance n2 6.097067D+00 1.378796996516D-04 GOT00 k1-a 1.141827D+00 7.293185551375D-05 GOT00 admittance k1 3.324267D+00 7.292115855138D-05 GOT00 k1-b 2.365113D+00 7.291046158901D-05 GOT00 admittance p1 2.958919D+00 7.252294578148D-05 GOT00 p1-a 3.002044D+00 7.232384890619D-05 GOT00 admittance o1 5.128356D+00 6.759774415297D-05 GOT00 o1-a 1.027610D+00 6.758704719061D-05 GOT00 admittance q1 2.772800D+00 6.495854110023D-05 GOT00 q1-a 4.955240D+00 6.494784413786D-05 GOT00 admittance mtm-a 4.652212D+00 7.973314413516D-06 NAO99.l admittance mtm 5.514660D-01 7.962617451151D-06 NAO99.l mf-a 2.296657D+00 5.334111360775D-06 NAO99.l admittance mf 4.479096D+00 5.323414398410D-06 NAO99.l msf 9.721550D-01 4.925201628510D-06 NAO99.l mm 5.497148D+00 2.639203052741D-06 NAO99.l msm 4.899785D+00 2.285998575769D-06 NAO99.l ssa 3.653480D-01 3.982127698995D-07 NAO99.l paw 5.012885D+00 1.991063797295D-07 equilibrium sa 3.098467D+00 1.990968752920D-07 NAO99.l pcw 2.003605D+00 1.671771314171D-07 equilibrium 18.6 4.100746D+00 1.069696236521D-08 equilibrium d. Pole tide: Mean pole coordinates used for computation of pole tide deformation were set to the IERS 2003 Conventions [6] recommended values (Chapter 7, p. 15). e. Antenna thermal deformation: Antenna heights were adjusted, based on the average daily temperatures, using the IVS antennae 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 10.00/10.01/10.02, SOLVE revision date 2011.02.05. References: 1. Altimimi, Z., X. Collilieux, and L. Metivier, " ITRF2008: an improved solution of the international terrestrial reference frame", Journal of Geodesy, 2011, DOI 10.1007/s00190-011-0444-4. 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. McCarthy, D.D., Petit, G., IERS Technical Note 32, IERS Conventions (2003), 2003. 7. Gordon, D., MacMillan, D., and Baver, K., "Calc 10 Implementation", in IVS General Meeting Proceedings, 2006, p. 291-295. 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 1340 sources estimated as global parameters: 2358+189 2359-221 0002-478 0002+200 0003+380 0003-066 0005-239 0007-325 IIIZW2 0007+171 0008-421 0008-264 0009+081 0010+405 0013-005 0017+200 0016+731 0019+058 0021+243 0022-423 0024+224 0025+197 0026+346 0027+056 0027-426 0032+612 0035+238 0035-252 0035-024 0035+413 0037+139 0037-593 0038+319 0039+230 0039+568 0043-392 0043-268 NGC0262 0047+023 0047-579 0048-097 0048-427 0046+861 0054+161 NGC0315 0055-059 0056-572 0056-001 0057-338 0059+581 0102+511 0104-275 0103+127 0104-408 0107-610 0108+388 0109+224 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+247 0121+560 0122-514 0122-003 0124-155 0123+257 0125+628 0127+084 0130-171 0130-447 0131-522 0132-097 0133+476 0134+311 0135-247 3C48 0136+176 0137+012 0137+467 0138-097 0144+209 0146+056 0147-076 0148+274 0149-175 0149+218 0150-144 0150-334 0151+474 0153-410 0155-549 0153+744 0159-117 0159-062 0202-765 0157+808 0159+723 0201+113 0201+088 0202-172 0202+319 0206-689 0206-178 0206-048 0206+136 0207-078 0209+168 0210-180 0210-075 0211+171 0212-039 0214-522 0213-015 0213-013 0215+015 0215-015 0216+011 0219+428 0220-349 UG01841 0220-023 0221+067 0222-234 0224-189 0226-559 4C67.05 0227-369 0230-790 0227+403 0229+131 0229+230 0230-288 0234-301 0235-618 0234+285 0237-027 0237+040 0237-233 LSI61303 0239+175 0239+108 0241+622 0244-452 0246+061 0248+430 0252-712 0250-001 0252-549 0253+133 0254-334 0256+075 0256-005 0258-184 0258+011 0259+121 0301-243 0300+470 0302-623 0302-437 0302+625 NGC1218 0306+102 0308-611 0307+380 0312-770 0309+411 0312+100 0315-282 0316-444 0316-164 0317+188 0318-172 0319+121 0322-230 0322+222 0325-182 UGC02748 0325+395 0326+278 0329-404 0331+022 0332-403 0332-375 0332+078 0334-546 NRAO140 0335-364 0334+014 0335-122 0336-017 CTA26 0338-214 0340+362 0341+158 0342+147 0346-279 0345+460 0347-211 0350+465 0355-669 0354+231 0355-483 0355+055 0354+559 NRAO150 0357-263 0358+040 0358+210 0400-319 0400+258 0402-362 0403-132 0403-179 0404-240 0405-385 0405-123 0405+305 0407-658 0406-127 0406+121 0407-199 0409-280 0409+229 0410+110 0414-189 0415+379 0415+398 0417-302 0418+532 0420+022 0420+210 0420-014 0420+417 0421+023 0421+145 0422-389 0422-380 0422+004 0423+051 0423+233 0423+237 0425+048 0425+174 0426-380 0426+273 0431-512 0432-606 0430+289 0434-188 0436-129 0437-454 NRAO190 0440+345 0442+389 0445-221 0446-265 0450-743 0446+112 0444+634 0454-810 0446+462 0446+595 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 0454+844 0506+101 0507+179 0508+138 0509+152 0511-220 0510+559 0514-459 0514-161 0517-726 0516-621 0514+074 0515+208 3C138 0522-611 0519+142 0521-403 0521-365 0524-460 0524-485 0524-237 0525-231 0524+034 0530-727 0527-253 0528-250 0529+075 0531-397 0529+483 0532-378 0534-611 0534-340 0537-441 0537-158 0536+145 0537-286 0539-057 0542-735 0540-270 3C147 0540+529 0544+273 0549-575 0547+234 0548+378 0549+192 0552+398 0552+393 0554+242 0557-454 0556+238 0558-396 0600+177 0600+219 0601-172 0601+245 0602+405 0602+673 0605-085 0606-223 0604+728 0609-284 0610+171 0610+260 0611+131 0609+607 0614-349 0613+570 0615-365 0616-244 0621-787 0622-441 0620+389 0615+820 0625-354 0628-671 0628-627 0627-199 0629-418 0630-261 0629+160 0630+367 0632-235 0632-183 0633-26B 0633-26A 0634-584 0635-296 0627+814 0637-337 0639+098 0639-032 0636+680 0641+392 3C166 0642+449 0646-306 0645+209 0647-475 0647-410 0648-165 0648-287 0649-209 0650+371 0651+410 0654+244 0656-062 0656+082 0657+172 0700-465 0700-197 0704-231 0705-412 0707+476 0710+439 0714+457 0713+669 0717-393 0718-154 0716+714 0720-305 0721-071 0722+145 0723-008 0718+793 0723+219 0725-381 0725+219 0727-365 0727-115 0727+409 0728+249 0729+259 0733-174 0733-187 0735+178 0736-332 0738-674 0736+017 0738+491 0743-673 0741-444 0744-691 0741-063 0741+214 0742+103 0743-006 0743+259 0743+277 0745-291 0745+241 0747+185 0746+483 0748+126 0749+540 0750+633 0753-425 0754+100 NGC2484 0759+183 0802-170 0800+618 0806-710 0804-153 0805+046 0805-077 0804+499 0805+410 0806-153 0809-493 0808+019 0811-179 0812+020 0812+367 0814+425 0818-128 0820-578 0821+248 0820+560 0822-152 0821+394 0822+137 0823-500 0821+621 0823+033 0823-223 0826-373 0826+180 0827+243 0828-222 0829+046 0828+493 VELA-G 0831+557 0833-450 0834-201 0835-339 0833+585 0834+250 0836+290 0836+182 0838+133 0836+710 0842-754 0839+187 0843-336 0843-371 0847-120 0850+581 OJ287 0855-716 0854-108 0854+213 0855+143 0857-329 0859-140 0859+470 0859+681 0902-350 0903-573 0906+015 0906-048 0907+022 0910-414 0912-330 0912+029 0912+297 0913+079 0913+657 0915-118 0918-297 0917+449 0917+624 0920-397 0920+390 0925-203 0925+504 0936-853 0927+469 0928+008 0937+262 0938+119 0939+620 0942+358 0943+105 0945+408 0949+354 0951+268 0952+179 SN1993J M81 0952+581 4C55.17 0955+476 0955+326 0954+658 0958+346 1003+351 1005-739 1004-500 1004+054 1004-217 1004+141 1009-041 1009-321 1010+495 1011+250 1012+232 1012-448 1013+127 1013+054 1013+208 1014+615 1015+359 1015+057 1016-311 1019+416 1020+400 1022-665 1022+194 1023+131 1026-084 1027-186 1030+415 1030+074 1032-199 1031+567 1034-374 1034-293 1038+064 1038+52A 1038+52B 3C245 1040+244 1039+811 1042+071 1043+066 1045-620 1045-188 1046-409 1046-222 1047+147 1048-526 1049-726 1048-313 1049-650 1049+215 1053+704 1054+004 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+384 1104-445 1105-680 1104+728 1106+084 1107+485 1109-567 1111+149 1116-462 1116+128 1117-248 1117-270 1117+146 1119+183 1121+238 1123+264 1124-056 1124-186 1124+571 1125+366 1125+596 1127-443 1127-145 1128+385 1128-047 1129-580 1130-741 1130+009 1131+730 1133-739 1133-032 MRK180 1137+660 NGC3862 1142+052 1142-225 1143-696 1143-245 1143-287 1143+590 1143-332 1144+402 1144-379 1144+352 1145-071 1145+268 NGC3894 1147+245 1147-192 1148-001 1148-671 1149-084 1150+812 1150+497 1155+169 1155+251 1156+101 1156-094 1156-663 1156-214 1156+295 1200+068 1200+045 1200+468 1204+399 1204+124 1206-238 1210+197 1212+087 1212+171 1213-172 1213+350 1215+303 1215-457 1216+487 NGC4261 1217+023 1218+339 1218-341 1219+285 1219+044 1221+809 1222+037 1221-829 1222+216 M84 1223-188 1226-028 1226+373 3C274 1228-113 1232-338 1232+366 1234-504 1236+077 1237-101 1236-684 M104 1239+552 1239+606 1239+376 1240+381 1241+166 1241+176 1243-160 1243-072 1244-255 1245-454 1246+489 1247-442 1247+139 1251-407 1251-197 1252+119 1251-713 1254+571 1256+802 1255-316 1255-177 1256-220 1257+145 1257-326 1300+580 1302-208 1302-102 1304-318 1306+360 1303-827 1307+121 1308+328 1308+554 1313-333 OP326 1317+520 1317+019 1318+225 1318-434 1318-263 1320-446 1320-303 1323+799 NGC5141 CEN-A 1323+321 1323-527 1324+224 1325-558 1327+504 1327+321 1326-698 1328+254 3C286 1330+476 1330+022 1331+170 1333-152 1333-337 1335+658 1334-127 1335+552 1334-649 1336-260 1337-033 1338+381 1339-287 1342+662 1342+663 1343-601 1345+125 1346-306 1347+539 1348+308 1349-439 1351-018 1352-104 1352-632 1354+195 1354-174 1354-152 1357+769 1355-416 1356+022 1402-012 1402+044 1404-342 1406+564 1406-076 1406-267 1409+218 1412+461 1412+087 1412-368 1413+135 1413+349 1416+067 1418+546 1417+385 1417+273 1418-192 1420+326 1421+122 1417-782 1420-725 1420-679 1423+146 1424+366 1424+240 1424-418 1427+543 1428+422 1428+370 NGC5675 1430-178 1432+200 1433+304 1434+235 1435+638 1435-218 1436+373 1437+331 1437+061 1441+522 1441-058 1441+252 1442+637 OQ172 1442-245 1443-162 1444+175 1445-161 1448-648 1451+270 1451-375 1452+301 1451-400 1454-354 1455+247 1455+348 1456+044 1459+480 1502+106 1501-343 1502+036 1504+377 1505+428 1504-166 1505-496 1508+572 1508-055 1508-325 1509+022 1510-089 1508-656 1510-319 1510-421 1511-100 1511-476 1511-360 1514+004 1514+197 1514-241 1520+437 1520+319 1519-294 1519-273 1522+155 1526+670 1532+016 1531-352 1533-653 1535+004 1538+149 1541+050 1547+507 1546+027 1548+056 1540-828 1550-242 1551+130 1550-269 1551-416 1549-790 1555+001 1555-140 1554-643 1557+032 1556-245 1600+43A 1600+43B 1600+335 1600-294 1601+112 1600-445 1603+573 1602-115 1604-333 1606+106 CTD93 1606-398 1608+243 1611-710 1614+051 1613-350 1614-255 1615+029 1616+063 1617+229 1619+491 1618-399 1621+078 1619-680 1621-351 1623+578 1621-321 1622-253 1622-310 1624+416 1622-297 1627+476 1624-617 1628+216 NGC6251 1633+38 1634+213 1633-409 1636+473 1637+574 NRAO512 1638+118 1639+230 1639-062 1639-200 1642+690 1633-810 1640-231 1637-771 1647+744 1645+271 1645+174 1645+224 1645-329 1648+084 1647-296 1651+391 1650-157 DA426 1653-329 1656+348 1656+477 1655+077 1656+053 1656-075 1657-261 1659+399 1657-562 1659-621 1705+456 1705+018 1705+135 1705-353 1706-174 1708+433 1710-323 1711-209 1717+178 1718-259 1721+589 1721+343 1722+526 1718-649 1722+330 1726+455 1725+123 1727+502 1725+044 NRAO530 1725-795 1732+389 1734+363 1734+508 1734+063 1733-565 1736+324 1738+499 1738+476 1741-038 1740-517 NGC6454 1742-078 1743+173 1745+670 1745+624 1746+470 1749+701 1749+096 1748-253 1750-187 1751+441 1751+288 1753+204 1755+626 1755+578 1754+292 1753-144 1754+159 1754+155 1753-418 1756+237 1758+388 1803+784 1800+440 1759-396 1800-045 1758-651 1801+036 3C371 1806+456 1806-458 1812+412 1815+531 1815-111 1814-637 1817+157 1815-553 1817-254 1826+796 1823+689 1821+107 1823+568 1822+033 1822-173 1822-076 1825-214 1825-055 1824-582 1826-447 1827-272 1829-207 1832+687 1830+139 1830+285 1831-030 1828-733 1832-113 1829-718 1831-693 1831-711 1839+389 3C390.3 1842+681 1843+400 1843-001 1846+322 1845-273 1849+670 1848+283 1851+488 1851-162 1856+736 1853+027 1854+061 1852-534 1855+031 1856-252 3C395 1901+016 1901+155 1904+013 1905-297 1906-217 1908+484 1907-224 1908-201 1909+161 1903-802 1910+052 1913-272 1917-248 1919+086 1918-634 1920-211 1922+155 1921-293 1922-224 1923+210 1928+738 1925-206 1926+087 1927+090 1925-610 1928+154 1929+226 1929-457 1928-698 1932+106 1932+204 1936+714 1934+226 1933-400 1936+095 1934-638 1936-155 1937-101 1935-692 1936-623 1942-313 1943+228 1945-325 1948+505 1947+079 1946-582 1951+355 1950-613 1952+138 1954+513 1954+282 1955+343 1955+335 1954-388 CYGNUS-A 1958-179 2000+472 2000+148 2000-330 2007+777 2002-375 2005+642 2005+403 2005+372 2005-044 2005-489 OW-015 2008-159 2013+508 2013+163 2017+743 2018+282 2021+614 2021+317 2022+542 2022+171 2022+031 2023+336 2025-538 2027-035 2029+024 2030+547 2029+121 2030-689 2033-286 3C418 2037-253 2039+037 2044-168 2046+429 2045-405 CL4 2051+745 2052-474 2054-075 2054-377 2056-369 2058-297 2059+034 2058-425 2100+468 2059-786 2102-659 2105-293 2106+143 2106-413 2113+293 2109-811 2115-305 2117-614 2117-642 2120+099 2120-309 2122-238 2123-463 2126-158 2127-096 2128+048 2136+824 2131-021 2131-340 2135-184 2136+141 2136-251 2138-377 2141+175 2142+110 2143-156 2144+092 2142-758 2145+082 2146+019 2147+077 2149+056 2149-306 2146-783 2150+173 2152+226 2152-699 2155+312 2155-152 2155-304 2157-255 2159+505 VR422201 2201+171 2201+044 2205+743 2203-188 2204-007 2204-540 2205+166 2206+650 2205-636 2207+374 2207+356 2208-137 2209+236 2210-257 2211-388 2211-256 2214+350 2214+241 2215+020 2215+150 2215-508 2216-038 2216+178 2220-351 2220-318 2221-387 2223+210 3C446 2227-088 2229+695 2227-399 2227-445 2229-172 CTA102 2232-488 2233-186 2233-148 2235+731 2236+678 2236-572 2238-362 2239+096 2239-631 2243+047 2244-372 2245-328 2246+208 2250+194 2252+618 2252-089 2253+417 2254-367 2254+074 2254+024 2255-282 2258+166 2259+058 2300-307 2300-683 2301+060 2302+232 2304+377 2306-312 2307+106 2309+454 2311-477 2311-373 2311-452 2312-319 2314-340 2314-409 2318+049 2319+317 2319+272 2319+444 2320+506 2320-035 2321-375 2321-215 2322-411 2322+396 2324-023 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 2337+264 2338+191 2340+233 2344+09A 2344-514 2344+429 2345-167 2348-432 2349-014 2350-280 2351-309 2351+456 2351-154 2352+495 2353-686 2353+816 2355-534 2355-106 2356+196 2356+385 2357-318 Appendix C. ~~~~~~~~~~ List of 98 stations for which troposphere gradients were not estimated: AUSTINTX AZORES BERMUDA BLKBUTTE BLOOMIND BREST CARNUSTY CARROLGA CHLBOLTN CTVASBAY CTVASTJ DAITO DEADMANL ELY FLAGSTAF FORTORDS FORT_ORD FTD_7900 GBT-VLBA GGAO7108 GIFU11 GIFU3 GORF7102 GRASSE HALEAKAL HOFN HOHENFRG HOHNBERG JPL_MV1 KAINAN KANOZAN KARLBURG KASHIM11 KIRSBERG KODIAK KOGANEI KOGANEI3 LEONRDOK MAMMOTHL MARCUS MARPOINT MCD_7850 METSAHOV METSHOVI MIAMI20 MILESMON MIURA MIYAZAKI MIZNAO10 MIZUSGSI MOJ_7288 MON_PEAK MV2ONSLA NOBEY_6M NOME NRAO85_1 OCOTILLO ONSALA85 OVR_7853 PBLOSSOM PENTICTN PINFLATS PLATTVIL PRESIDIO PT_REYES PVERDES QUINCY ROBLED32 SAGARA SANPAULA SEATTLE1 SHANGHAI SINTOTU SINTOTU3 SNDPOINT SOURDOGH SUWON TATEYAMA TITIJIMA TOMAKO11 TOULOUSE TROMSONO TRYSILNO TIDBIN64 TIGOWTZL TSUKUBA TSUKU3 USSURISK USUDA64 VERNAL VICTORIA VLA VLA-N8 WHTHORSE YAKATAGA YEBES YELLOWKN YUMA Appendix D. ~~~~~~~~~~~ List of 83 stations with axis offsets estimated as global parameters: AIRA ALGOPARK BR-VLBA CHICHI10 DSS15 DSS45 DSS65 FD-VLBA FORTLEZA GBT-VLBA GGAO7108 GIFU11 GILCREEK GOLDVENU HARTRAO HATCREEK HAYSTACK HN-VLBA HRAS_085 KASHIM11 KASHIM34 KASHIMA KAUAI KOGANEI KOKEE KP-VLBA LA-VLBA MARPOINT MATERA MIAMI20 MIURA MIZNAO10 MK-VLBA MOJAVE12 NL-VLBA NOTO NRAO_140 NRAO20 NRAO85_1 NRAO85_3 OHIGGINS OV-VLBA OVRO_130 PIETOWN RICHMOND SANTIA12 SC-VLBA SESHAN25 SINTOTU3 SVETLOE TATEYAMA TIGOCONC TIGOWTZL TOMAKO11 TSUKUB32 URUMQI VNDNBERG WESTFORD YEBES YLOW7296 VERAISGK VERAMZSW ZELENCHK BADARY CRIMEA DSS65A EFLSBERG HOBART26 MEDICINA NYALES20 ONSALA60 PARKES YEBES40M WETTZELL KWAJAL26 METSAHOV SEST SYOWA TIDBIN64 DSS13 MARCUS TSUKUBA HOBART12 Appendix E. ~~~~~~~~~~~ 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 TIDBIN64 TITIJIMA TOMAKO11 TOULOUSE USSURISK VERAIRIK VERAISGK VERAOGSW USUDA64 VICTORIA Appendix F. ~~~~~~~~~~~ Velocities of these 25 pairs, triplets or quadrets of stations were constrainted to be the same: DSS15 DSS13 GOLDMARS DSS45 TIDBIN64 DSS65 DSS65A ROBLED32 MADRID64 FORTORDS FORT_ORD GIFU11 GIFU3 GGAO7108 GORF7102 HRAS_085 FTD_7900 HOBART26 HOBART12 KASHIM34 KASHIM11 KAUAI HALEAKAL KOGANEI KOGANEI3 METSAHOV METSHOVI MIZNAO10 MIZUSGSI VERAMZSW MOJAVE12 MOJ_7288 NRAO20 GBT-VLBA NRAO_140 NRAO85_1 ONSALA60 MV2ONSLA ONSALA85 OVRO_130 OVR_7853 RICHMOND MIAMI20 SESHAN25 SHANGHAI SINTOTU SINTOTU3 TSUKUB32 TSUKU3 TSUKUBA PIETOWN VLA VLA-N8 WETTZELL TIGOWTZL YLOW7296 YELLOWKN