Technical description of solution gsf2007d 2007.11.09 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 gsf2007d estimates station position and velocity parameters in order to obtain a terrestrial reference frame (TRF) for computing 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 35 strong stations have no net translation with respect to positions and velocities of these stations reported in the ITRF2000 catalog and the resulting series of the Earth orientation parameters has zero shift and drift with respect to the USNO Finals series over the range [1997.01.01, 2007.10.04]. The CRF is defined in such a way that the positions of 212 sources, marked as defining source in the ICRF catalog [1], do not have any net rotation with respect to the coordinates reported in the ICRF catalog. All available dual-band Mark-3/Mark-4/Mark-5/K3/K4/VERA VLBI observations from 1979.08.03 through 2007.10.18 (except 26 VCS1, VCS2, VCS3, VCS4, VCS5, VCS6, NPCS sessions, 3 gravity sessions and 10 K/Q band experiments ) -- 4383 sessions with duration 18 hours and longer, 5707934 group delays -- were used in a single solution. The wrms postfit residual is 22.211 ps, Chi/ndg is 0.923. 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 time spans. Positions and velocities of all stations were estimated as global parameters. Positions of 609 sources (Appendix A) were estimated as global parameters. Positions of 427 other sources (Appendix B) were estimated in each session individually. In order to determine to which group a source belonged, two scores were computed: the number of sessions in which the source had at least two good observations, and the total number of observations excluding the sessions in which the source had only one good observation. The sources that A) were observed in two or more sessions and had 100 or more good observations or B) were observed only in one session and had 40 or more good observations were included in the group of sources whose positions were estimated as global parameters. The sources which had only one good observation as well as two gravitational lenses, 0218+35A/0218+35B and 1830-21A/1830-21B, were excluded from the dataset. Position of all other sources were estimated in each session individually. Two source catalogs are provided: 2007d.sou -- catalog of 609 sources estimated as global parameters. 2007d_lso.sou -- catalog of 427 sources estimated in each session individually. NB: Observations of only 25% of the sources observed with VLBI in astrometric or geodetic mode were used in this solution. Mean site gradients 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 [2] and [3]. 3a. Differences with respect to gsf2007c solutions: Mean pole coordinates used for computation of the pole tide deformation were set to the IERS 2003 Conventions [5] recommended values (Chapter 7, p. 15). 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, y, UT1-TAI, xdot, ydot, UT1dot, Dpsi, Deps (local). d. Zenith Troposphere: Linear spline 20-min interval; rate constraint with reciprocal weights generally 50 ps/hr; NMF wet partial derivative (segmented). e. Troposphere Gradient: 6-hour East and North linear spline at all stations, except a set of 84 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: 2007d_apr.src catalog. This catalog was created from solution 2007a_astro. However, positions of 212 so-called ICRF defining sources were replaced with the values taken from the ICRF catalog. b. Source positions adjusted in solution: Yes. Orientation defined by a no-net-rotation tie to the ICRF using only the 212 ICRF defining sources. 609 global and 427 local sources. 6. Terrestrial Reference Frame: a. A priori station positions: 2007d_apr.sit. This catalog was copied from the 2007c final solution. b. A priori station velocities: 2007d_apr.vel. This catalog was copied from the 2007c final solution. c. Reference epoch for site positions: 1997.0. d. Station positions/velocities adjusted in solution: Yes. e. Definition of origin, orientation, and their time evolution: Net-translation and net-rotation of position with respect to ITRF2000 for 35 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 Net-translation and net-rotation of velocity with respect to ITRF2000 for the same 35 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 Values of right-hand side of net-rotation/net-translation constraints: RIGHT_PART 0.04004014 -0.03064922 -0.01447310 NO EXCEPT \ * nnt_pos RIGHT_PART 0.04521636 0.04233687 0.04784906 NO EXCEPT \ * nnr_pos RIGHT_PART 0.00901793 0.00017483 0.00171279 NO EXCEPT \ * nnt_vel RIGHT_PART 0.00001816 0.01348665 0.00268893 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 40 stations listed in Appendix E were constrained to their ITRF2000 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 24 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 Besides, 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 [4]. Changes in the eccentricity vector were caused by repairs to the concrete foundation slab. i. Stations with nonlinear velocities: HRAS_085, GILCREEK, PIETOWN 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. 7. Earth orientation: a. A priori precession model: IAU2000A Precession-Nutation, IERS 2003 [5] implementation. b. A priori nutation model: IAU2000A Precession-Nutation, IERS 2003 [5] implementation. c. A priori short-period tidal variations in X, Y, UT1 were computed using the model GSFC hf1102. [These are used in place of the short period tidal and nutation polar motion and UT1 terms recommended in the IERS 2003 Conventions [5], chapter 5, p. 5.] d. EOP estimation: X, Y, UT1, Xdot, Ydot, UT1dot, Deps, Dpsi each session with 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; Deps and Dpsi are relative to IAU 1976 precession and IAU 1980 nutation models. Time tag of the EOP series is the middle epoch of the observing session. {Internally, Calc/Solve estimates classical nutation corrections relative to the IAU2000A nutation model, using the IERS 2003 Conventions [5] implementation. These are then converted to the IAU 1976/1980 precession/nutation 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. The user is referred to reference [6].} High frequency variations in polar motion and UT1, as computed by the GSFC hf1102 model were added to the a priori EOP during data reduction. 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 file gsf2007d.eops. The pole coordinates and UT1 from singular networks were substantially affected by weak constraints. They were removed from the output file gsf2007d.eops 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: NMF dry 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 [5], 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 [5] recommended values (Chapter 7, p. 15). 9. Data type: Group delays. 10. Data editing: 5 deg elevation cutoff. 11. Data weighting: Weights are defined as follows: 1/sqrt ( f**2 + a**2 ) where "f" is formal uncertainty of the ionosphere free linear combination of group delays at X- and S-band obtained by fringe fitting on the base of achieved signal to noise ratio. The station-dependent parameter "a" was computed for each session by an iterative procedure such that the ratio of the sum of squares of weighted residuals to the estimate of their mathematical expectation is about unity. 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, SOLVE revision date 2007.10.04. References: 1. Coordinates of the defining sources in ICRF: http://hpiers.obspm.fr/webiers/results/icrf/icrfdef.html 2. MacMillan, D.S. and C. Ma, "Atmospheric gradients from very long baseline interferometry observations", Geophys. Res. Lett., 22, 1041-1044, 1995. 3. MacMillan, D.S. and C. Ma, "Atmospheric gradients and the VLBI terrestrial and celestial reference frames", Geophys. Res. Lett., 24, 453-456, 1997. 4. 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. 5. McCarthy, D.D., Petit, G., IERS Technical Note 32, IERS Conventions (2003), 2003. 6. Gordon, D., MacMillan, D., and Baver, K., "Calc 10 Implementation", in IVS General Meeting Proceedings, 2006, p. 291-295. ---------------------------------------------------------------------------- Appendix A. ~~~~~~~~~~~ List of 609 sources considered as good (i.e. eligible for estimation as global parameters). They passed the following tests: a) participation in 2 or more sessions AND 100 or more good observations; OR b) participation in 1 session AND 40 or more good observations. [Sessions where sources had less than 2 good observations were not counted.] 0002-478 0003+380 0003-066 0007+171 0008-264 0009+081 0010+405 0013-005 \ 0014+813 0016+731 0017+200 0019+058 0026+346 0035+413 0035-024 0039+230 \ 0047-579 0048-097 0048-427 0056-001 0059+581 0104-408 0106+013 0108+388 \ 0109+224 0110+495 0111+021 0112-017 0113-118 0118-272 0119+041 0119+115 \ 0123+257 0130-171 0133+476 0134+311 0135-247 0138-097 0146+056 0148+274 \ 0149+218 0151+474 0153+744 0159+723 0159-062 0201+113 0202+149 0202+319 \ 0202-172 0206-048 0208-512 0212+735 0212-039 0213-013 0213-015 0215+015 \ 0215-015 0219+428 0220-023 0220-349 0221+067 0229+131 0230-790 0234+285 \ 0235+164 0237+040 0237-027 0237-233 0239+108 0248+430 0252-549 0256+075 \ 0259+121 0300+470 0302+625 0302-623 0306+102 0308-611 0309+411 0317+188 \ 0319+121 0322+222 0326+278 0338-214 0340+362 0341+158 0342+147 0350+465 \ 0400+258 0400-319 0402-362 0403-132 0403-179 0405+305 0405-123 0405-385 \ 0406+121 0406-127 0409+229 0414-189 0415+379 0420+210 0420+417 0420-014 \ 0422+004 0422-380 0423+051 0425+048 0426+273 0426-380 0430+289 0434-188 \ 0437-454 0438-436 0440+345 0444+634 0446+112 0446+595 0451-282 0454+844 \ 0454-234 0454-810 0456+060 0457+024 0458+138 0458-020 0459+060 0459+135 \ 0459+252 0500+019 0502+049 0506+101 0506-612 0507+179 0516-621 0521-365 \ 0524-460 0528+134 0528-250 0530-727 0536+145 0537-158 0537-286 0537-441 \ 0539-057 0544+273 0547+234 0552+398 0554+242 0556+238 0600+177 0601+245 \ 0602+405 0602+673 0605-085 0607-157 0609+607 0610+260 0611+131 0615+820 \ 0620+389 0629+160 0629-418 0636+680 0637-752 0639-032 0642+449 0646-306 \ 0648-165 0649-209 0650+371 0651+410 0656+082 0657+172 0707+476 0710+439 \ 0711+356 0716+714 0718+793 0722+145 0723-008 0725+219 0727-115 0733-174 \ 0735+178 0736+017 0738+313 0738+491 0738-674 0742+103 0743+259 0743-006 \ 0743-673 0745+241 0748+126 0749+540 0754+100 0759+183 0804+499 0805+410 \ 0805-077 0808+019 0812+020 0812+367 0814+425 0818-128 0820+560 0821+394 \ 0821+621 0822+137 0823+033 0826-373 0827+243 0828+493 0829+046 0831+557 \ 0833+585 0834+250 0834-201 0836+182 0836+710 0839+187 0850+581 0854+213 \ 0859+470 0859-140 0906+015 0912+029 0912+297 0917+449 0917+624 0919-260 \ 0920+390 0920-397 0925-203 0942+358 0945+408 0949+354 0952+179 0954+658 \ 0955+326 0955+476 1004+141 1011+250 1012+232 1013+208 1014+615 1016-311 \ 1020+400 1021-006 1022+194 1022-665 1023+131 1030+074 1030+415 1031+567 \ 1032-199 1034-293 1038+064 1038+52A 1039+811 1042+071 1044+719 1045-188 \ 1048-313 1049+215 1053+704 1053+815 1055+018 1057-797 1101+384 1101-325 \ 1101-536 1104-445 1105-680 1111+149 1116+128 1116-462 1119+183 1123+264 \ 1124-186 1125+596 1127-145 1128+385 1128-047 1130+009 1142+052 1143-245 \ 1144+402 1144-379 1145-071 1147+245 1148-001 1150+497 1150+812 1155+251 \ 1156+295 1156-094 1200+045 1213+350 1213-172 1215+303 1216+487 1219+044 \ 1219+285 1221+809 1222+037 1226+373 1226-028 1236+077 1237-101 1239+376 \ 1240+381 1243-072 1244-255 1251-713 1252+119 1255-316 1256-220 1257+145 \ 1257-326 1300+580 1302-102 1307+121 1308+326 1308+328 1313-333 1324+224 \ 1325-558 1327+321 1330+476 1331+170 1334-127 1338+381 1342+662 1342+663 \ 1345+125 1347+539 1349-439 1351-018 1352-104 1354+195 1354-152 1354-174 \ 1357+769 1402+044 1402-012 1406-076 1409+218 1413+135 1416+067 1417+273 \ 1417+385 1418+546 1420+326 1423+146 1424+240 1424+366 1424-418 1427+543 \ 1428+422 1430-178 1432+200 1433+304 1435+638 1435-218 1436+373 1443-162 \ 1445-161 1448+762 1451+270 1451-375 1451-400 1459+480 1502+036 1502+106 \ 1504+377 1504-166 1505+428 1508+572 1508-055 1510-089 1511-100 1511-476 \ 1514+004 1514+197 1514-241 1519-273 1522+155 1532+016 1538+149 1546+027 \ 1547+507 1548+056 1549-790 1555+001 1557+032 1600+335 1604-333 1606+106 \ 1610-771 1611+343 1614+051 1616+063 1617+229 1619-680 1622-253 1622-297 \ 1624+416 1633+38 1637+574 1639+230 1642+690 1647-296 1655+077 1656+053 \ 1656+348 1656+477 1657-261 1657-562 1705+018 1705+456 1706-174 1708+433 \ 1717+178 1725+044 1726+455 1727+502 1732+389 1734+363 1738+476 1738+499 \ 1739+522 1741-038 1743+173 1745+624 1746+470 1749+096 1749+701 1751+288 \ 1751+441 1758+388 1758-651 1800+440 1803+784 1806+456 1806-458 1815-553 \ 1821+107 1823+568 1826+796 1827-272 1829-207 1830+285 1831-711 1842+681 \ 1849+670 1856+736 1908-201 1920-211 1921-293 1922+155 1923+210 1925-610 \ 1926+087 1928+738 1929+226 1932+204 1933-400 1935-692 1936-155 1937-101 \ 1943+228 1947+079 1951+355 1954+513 1954-388 1955+335 1958-179 2000-330 \ 2005+403 2005+642 2005-489 2007+777 2008-159 2017+743 2021+317 2021+614 \ 2023+336 2029+022 2029+121 2030+547 2037-253 2051+745 2052-474 2059+034 \ 2106+143 2106-413 2109-811 2113+293 2121+053 2126-158 2128-123 2131-021 \ 2134+00 2136+141 2142+110 2143-156 2144+092 2145+067 2149+056 2149-306 \ 2150+173 2155-152 2155-304 2201+315 2204-540 2209+236 2210-257 2214+350 \ 2216-038 2227-088 2229+695 2232-488 2233-148 2234+282 2235+731 2239+096 \ 2243-123 2244-372 2245-328 2250+194 2252-089 2253+417 2254+024 2254+074 \ 2255-282 2312-319 2318+049 2319+272 2320+506 2320-035 2325+093 2325-150 \ 2326-477 2328+107 2329-162 2329-384 2335-027 2337+264 2344+09A 2345-167 \ 2351+456 2351-154 2352+495 2353+816 2353-686 2355-106 2355-534 2356+385 \ 3C120 3C138 3C147 3C166 3C245 3C273B 3C274 3C279 \ 3C286 3C309.1 3C345 3C371 3C390.3 3C395 3C418 3C446 \ 3C454.3 3C84 4C39.25 4C67.05 CL4 CTA102 CTA26 CTD93 \ DA426 IIIZW2 M81 M84 MRK180 NGC0262 NGC0315 NGC1052 \ NGC1218 NGC3862 NGC3894 NGC6251 NGC6454 NRAO140 NRAO150 NRAO190 \ NRAO512 NRAO530 OJ287 OK290 OP326 OQ172 OQ208 OW-015 \ VR422201 Appendix B. ~~~~~~~~~~~ List of 427 sources with Right Ascension and Declination estimated as local parameters: 0002+200 0008-421 0021+243 0022-423 0025+197 0032+612 0035+238 0035-252 0037+139 0037-593 0047+023 0054+161 0056-572 0102+511 0103+127 0107-610 0110-668 0111+131 0115-214 0116+319 0116-219 0119+247 0122-003 0122-514 0125+628 0127+084 0131-522 0137+012 0137+467 0147-076 0150-334 0153-410 0159-117 0201+088 0202-765 0206+136 0207-078 0209+168 0210-075 0211+171 0214-522 0234-301 0235-618 0239+175 0241+622 0248+560 0252-712 0253+133 0254-334 0256-005 0307+380 0312+100 0312-770 0325+395 0331+022 0332+078 0332-403 0334+014 0334-546 0335-364 0345+460 0347-211 0354+231 0354+559 0355-483 0355-669 0358+040 0358+210 0407-658 0410+110 0411+054 0415+398 0423+233 0423+237 0431-512 0436-129 0442+389 0450-743 0454-463 0503-608 0508+138 0509+152 0511-220 0515+208 0517-726 0519+142 0522-611 0524+034 0524-485 0529+075 0534-340 0534-611 0542-735 0548+378 0549+192 0549-575 0600+219 0606-223 0610+171 0614-349 0615-365 0622-441 0627-199 0628-627 0637-337 0641+392 0645+209 0647-475 0654+244 0700-465 0721-071 0723+219 0728+249 0729+259 0736-332 0741+214 0741-063 0743+277 0744-691 0746+483 0747+185 0805+046 0809-493 0816+054 0821+248 0823-223 0823-500 0835-339 0836+290 0838+133 0842-754 0844+387 0903-573 0906-048 0925+504 0927+469 0928+144 0936-853 0937+262 0938+119 0943+105 0951+268 0952+581 0958+346 0959-443 1003+351 1004-217 1004-500 1005-739 1010+495 1012-448 1013+054 1013+127 1015+057 1015+359 1019+416 1026-084 1027-186 1034-374 1038+52B 1040+244 1043+066 1045-620 1049-650 1054+004 1055-242 1055-301 1056+212 1058+726 1059+282 1100+122 1104+728 1107+485 1109-567 1117+146 1121+238 1125+062 1125+366 1129-580 1133-032 1133-739 1143-287 1143-332 1143-696 1144+352 1145+268 1148-671 1149-084 1155+169 1156-663 1159+148 1200+468 1204+124 1212+171 1215-457 1217+023 1218+339 1222+216 1228-113 1234-504 1236-684 1239+606 1241+166 1241+176 1243-160 1245-454 1246+489 1251-407 1254+571 1303-827 1306+360 1308+554 1318+225 1320-446 1323+321 1330+022 1334-649 1337-033 1339-287 1343-601 1348+308 1352-632 1355-416 1406-267 1412+461 1412-368 1413+349 1417-782 1420-679 1421+122 1434+235 1437+331 1441+252 1441+522 1444+175 1448-648 1454-354 1455+247 1456+044 1505-496 1508-656 1509+022 1519-294 1520+319 1535+004 1540-828 1541+050 1551+130 1554-643 1555-140 1556-245 1600+43A 1600+43B 1600-445 1600-489 1601+112 1603+573 1606-398 1608+243 1611-710 1615+029 1624-617 1627+476 1628+216 1633-810 1634+213 1636+473 1637-771 1639-062 1640-231 1645+174 1645+224 1645+271 1646-506 1648+084 1651+391 1656-075 1659-621 1705+135 1718-649 1721+343 1721+589 1722+330 1725+123 1725-795 1729-373 1733-565 1734+508 1736+324 1740-517 1742-078 1745+670 1748-253 1754+155 1754+159 1756+237 1759-396 1814-637 1815+531 1817-254 1822+033 1822-173 1824-582 1825-055 1829-106 1829-718 1830+139 1843+400 1846+322 1848+283 1852-534 1855+031 1901+155 1903-802 1908+484 1909+161 1910+052 1919+086 1928+154 1928-698 1929-457 1932+106 1934-638 1936-623 1950-613 1952+138 1954+282 2000+148 2000+472 2002-375 2005-044 2013+163 2013+508 2018+282 2022+171 2022+542 2029+024 2030-689 2046+429 2054-377 2058-297 2058-425 2059-786 2100+468 2102-659 2115-305 2117-614 2117-642 2120+099 2123-463 2127-096 2128+048 2135-184 2138-377 2141+175 2142-758 2145+082 2146-783 2147+077 2152+226 2152-699 2155+312 2201+044 2201+171 2203-188 2205+166 2205+743 2205-636 2211-388 2214+241 2215+020 2215-508 2216+178 2220-351 2223+210 2227-399 2229-172 2236-572 2239-631 2243+047 2246+208 2254-367 2258+166 2300-307 2300-683 2302+232 2304+377 2306-312 2307+106 2309+454 2311-452 2311-477 2314-340 2319+317 2321-375 2324-023 2331-240 2333-415 2333-528 2340+233 2344-514 2349-014 2351-309 2358+189 3C48 4C55.17 CEN-A CYGNUS-A HR1099 LSI61303 M104 NGC2484 NGC4261 NGC4278 NGC5077 NGC5141 NGC5675 NGC6034 NGC6500 NGC7720 SN1993J TON202 UG01841 UG03927 UGC02748 VELA VELA-G Appendix C. ~~~~~~~~~~ List of 110 stations for which troposphere gradients were not estimated: AIRA AUSTINTX AZORES BERMUDA BLKBUTTE \ BLOOMIND BREST CARNUSTY CARROLGA CHICHI10 \ CHLBOLTN CTVASBAY CTVASTJ DAITO DEADMANL \ DSS15 ELY FLAGSTAF FORTORDS FORT_ORD \ FTD_7900 GBT-VLBA GGAO7108 GIFU11 GIFU3 \ GOLDVENU GORF7102 GRASSE HALEAKAL HOFN \ HOHENFRG HOHNBERG JPL_MV1 KAINAN KANOZAN \ KARLBURG KASHIM11 KIRSBERG KODIAK KOGANEI \ KOGANEI3 KWAJAL26 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 OHIGGINS ONSALA85 OVR_7853 \ PARKES PBLOSSOM PENTICTN PINFLATS PLATTVIL \ PRESIDIO PT_REYES PVERDES QUINCY ROBLED32 \ SAGARA SANPAULA SEATTLE1 SESHAN25 SEST \ SHANGHAI SINTOTU SINTOTU3 SNDPOINT SOURDOGH \ SUWON SYOWA TATEYAMA TITIJIMA TOMAKO11 \ TOULOUSE TROMSONO TRYSILNO TIDBIN64 TIGOWTZL \ TSUKUBA TSUKU3 URUMQI USSURISK USUDA64 \ VERNAL VICTORIA VLA VLA-N8 WHTHORSE YAKATAGA YEBES YELLOWKN YLOW7296 YUMA Appendix D. ~~~~~~~~~~~ List of 64 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 \ YUMA VERAISGK VERAMZSW ZELENCHK \ Appendix E. ~~~~~~~~~~~ List of 40 stations with constraints on velocity: AUSTINTX AZORES BADARY 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 ZELENCHK Appendix F. ~~~~~~~~~~~ Velocities of these 24 pairs, triplets or quadrets of stations were constrainted to be the same: DSS15 DSS13 \ DSS15 GOLDMARS \ DSS45 TIDBIN64 \ DSS65 DSS65A ROBLED32 MADRID64 \ FORTORDS FORT_ORD FTD_7900 \ GIFU11 GIFU3 \ GGAO7108 GORF7102 \ 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