Technical description of solution gsf2006d 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 gsf2006d 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 catalogue and the resulting series of the Earth orientation parameters has zero shift and drift with respect to the USNO Finals series at the range [1997.01.01, 2006.09.15]. The CRF is defined in such a way that positions of 212 sources, marked as defining source in the ICRF catalogue [1], do not have net rotation with respect to the coordinates reported in this catalogue. All available dual-band Mark-3/Mark-4/Mark-5 VLBI observations from 1979.08.03 through 2006.09.14 (except 25 VCS1, VCS2, VCS3, VCS4, VCS5, NPCS sessions, 3 gravity sessions and 8 K/Q band experiments ) -- 4190 sessions with duration 18 hours and longer, 5178194 group delays -- were used in a single solution. The wrms of postfit residuals is 21.648 psec and chi-sq/ndg = 1.029 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 686 sources (Appendix A) were estimated as global parameters. Positions of 192 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. Observations of only 25% of sources observed with VLBI in astrometric or geodetic mode were used in this solution. The sources that A) were observed in two or more sessions and had 40 or more good observations or B) were observed only in one session and had 25 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 catalogues are provided: 2006d.sou -- catalogue of 686 sources estimated as global parameters; 2006d_lso.sou -- catalogue of 192 sources estimated in each session individually. 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 gsf2006b solutions: MHB2000 nutations and spurious terms in UT1 according to N. Capitaine suggestion. 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: 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: 2006d_apr.src catalogue. This catalogue was created in the preliminary solution similar to gsf2006d. However, positions of 212 ICRF defining sources were replaced with the values taken from the ICRF catalogue. b. source positions adjusted in solution: yes If yes, c. definition of orientation: no-net-rotation tie to the ICRF using only the 212 ICRF defining sources d. source position estimation: 686 global and 192 local 6. Terrestrial reference frame: a. a priori station positions: 2006d_apr.sit . This catalogue was created in the preliminary solution similar to gsf2006d. However, positions of 35 strong stations were replaced with the values from the ITRF2000 catalogue. b. a priori station velocities: 2006d_apr.vel . This catalogue was created in the preliminary solution similar to gsf2006d. However, velocities of 35 strong stations were replaced with the values from the ITRF2000 catalogue. 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 no-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-roatation/net-translation constraints: RIGHT_PART 0.02838002 0.08872961 0.06734085 NO EXCEPT \ * nnt_pos RIGHT_PART -0.15877348 0.01567920 0.05407551 NO EXCEPT \ * nnr_pos RIGHT_PART 0.01884230 0.00108192 0.00408223 NO EXCEPT \ * nnt_vel RIGHT_PART -0.00312889 0.02353162 0.01452231 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 velocity for U, E, and N components of the stations listed in Appendix E were constrained to the ITRF2000 velocities with reciprocal weights 0.1, 3.0, and 3.0 mm/yr respectively because the stations have a very short history of observations, in many cases only one occupation. The velocities of the 20 groups of stations listed in Appendix F are 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 to (-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 results of geodetic surveys [4]. Changes in the eccentricity vector are caused by repairing of 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 IAU 2000 RESOLUTIONS! k. permanent tide correction: yes "Yes" means that both the permanent and the periodic tides have been included in the model, so that the output station position is for after the removal of both the permanent and the periodic tidal effect. The model used includes tide displacements for zero frequency with Love numbers h2(freq=0) = 0.6074, l2(freq=0) = 0.0852 7. Earth orientation: a. a priori precession model: IERS 2003 b. a priori nutation model: MHB2000 c. a priori short-period tidal variations in x, y, UT1 were taken into account in accordance with the model hf1002 d. EOP estimation: X, Y, UT1, Xdot, Ydot, UT1dot, deps, dpsi each day 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 EOP series is the middle epoch of the observing session. The model of high frequency variations in polar motion and UT1 hf1102 was added to the apriori 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 the high frequency variations. A network of each individual session falls 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 applying strong constraints. The records related to these experiments were eliminated from the output EOP file. EOP from other series were put in file gsf2006d.eops . The pole coordinates and UT1 from singular networks were substantially affected by weak constraints. They were removed from the output file gsf2006d.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, temperature; a priori mean gradients from DAO weather model. b. solid Earth tide: IERS Conventions 1996, p.56-65, step 1 and step 2, anelasticity variant, including tides of the 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. atmosphere loading: 3D displacements computed by convolving global surface pressure field on 2.5x2.5 degrees grid with 6 hour temporal resolution using the NCEP Reanalysis model [5]. 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 2006.06.08 14. Other information: Mean pole coordinates used for computation of pole tide deformation were set to 0.0, 0.0 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. Petrov, L. and J.-P. Boy, "Study of the atmospheric pressure loading signal in VLBI observations", J. Geophys. Res., 10.1029/2003JB002500, vol. 109, No. B03405, 2004. 2006.06.29_17:52:51 ---------------------------------------------------------------------------- Appendix A. ~~~~~~~~~~~ * * --- 686 sources were considered as good (i.e. eligible for estimation * --- as global parameters). They passed the following tests: * --- either a) participation in 2 or more sessions AND 40 or more * --- good observations; or * --- b) participation in 1 session AND 25 or more good observations * --- Sessions where sources had less than 2 good observations were not * --- counted for. * 0002-478 0003+380 0003-066 0007+171 0008-264 0010+405 0013-005 0014+813 \ 0016+731 0017+200 0019+058 0021+243 0026+346 0035+413 0037+139 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 0131-522 0133+476 0134+311 0135-247 0138-097 0146+056 \ 0148+274 0149+218 0150-334 0151+474 0153+744 0159+723 0159-062 0201+113 \ 0202+149 0202+319 0202-172 0206-048 0208-512 0210-075 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 0235-618 0237+040 0237-027 0237-233 \ 0239+108 0241+622 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 \ 0332-403 0334-546 0335-364 0338-214 0341+158 0342+147 0358+040 0358+210 \ 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 0423+233 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 0454-463 0454-810 0457+024 0458+138 0458-020 0459+060 \ 0459+135 0500+019 0502+049 0506+101 0506-612 0507+179 0508+138 0511-220 \ 0515+208 0516-621 0521-365 0522-611 0524-460 0524-485 0528+134 0528-250 \ 0529+075 0530-727 0534-340 0534-611 0536+145 0537-158 0537-286 0537-441 \ 0539-057 0544+273 0547+234 0549+192 0549-575 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 0637-337 0637-752 \ 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+046 0805+410 0805-077 0808+019 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+290 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 1004-500 1011+250 \ 1012+232 1012-448 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 1038+52B 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+728 \ 1104-445 1105-680 1111+149 1116+128 1116-462 1119+183 1123+264 1124-186 \ 1125+596 1127-145 1128+385 1128-047 1129-580 1130+009 1143-245 1143-696 \ 1144+402 1144-379 1145-071 1147+245 1148-001 1148-671 1150+497 1150+812 \ 1155+169 1155+251 1156+295 1156-094 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 1239+606 1240+381 1243-072 1244-255 1245-454 1251-713 1252+119 \ 1254+571 1255-316 1257+145 1257-326 1300+580 1302-102 1307+121 1308+326 \ 1308+328 1313-333 1318+225 1323+321 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 1412-368 1413+135 1413+349 1416+067 1417+273 1417+385 \ 1418+546 1420+326 1420-679 1423+146 1424+240 1424+366 1424-418 1427+543 \ 1428+422 1430-178 1432+200 1433+304 1434+235 1435+638 1435-218 1436+373 \ 1437+331 1441+522 1443-162 1444+175 1445-161 1448+762 1451+270 1451-375 \ 1451-400 1459+480 1502+036 1502+106 1504+377 1504-166 1508+572 1508-055 \ 1509+022 1510-089 1511-100 1511-476 1514+197 1514-241 1519-273 1522+155 \ 1532+016 1538+149 1546+027 1547+507 1548+056 1549-790 1551+130 1555+001 \ 1555-140 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 1636+473 \ 1637+574 1639+230 1642+690 1647-296 1655+077 1656+053 1656+348 1656+477 \ 1657-261 1657-562 1659-621 1705+018 1705+135 1705+456 1706-174 1717+178 \ 1718-649 1725+044 1725-795 1726+455 1727+502 1732+389 1734+363 1734+508 \ 1738+476 1738+499 1739+522 1741-038 1743+173 1745+624 1746+470 1749+096 \ 1749+701 1751+288 1751+441 1754+155 1754+159 1758+388 1758-651 1800+440 \ 1803+784 1806+456 1806-458 1815-553 1817-254 1821+107 1823+568 1826+796 \ 1827-272 1829-207 1830+139 1830+285 1831-711 1842+681 1843+400 1849+670 \ 1856+736 1903-802 1908-201 1920-211 1921-293 1922+155 1923+210 1925-610 \ 1926+087 1928+154 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+148 2000+472 2000-330 2005+403 2005+642 2005-489 2007+777 2008-159 \ 2013+163 2017+743 2021+317 2021+614 2022+171 2023+336 2029+022 2029+121 \ 2030+547 2037-253 2051+745 2052-474 2054-377 2059+034 2059-786 2106+143 \ 2106-413 2109-811 2113+293 2120+099 2121+053 2126-158 2128+048 2128-123 \ 2131-021 2134+00 2136+141 2142+110 2142-758 2143-156 2144+092 2145+067 \ 2145+082 2146-783 2149+056 2149-306 2150+173 2155-152 2155-304 2201+171 \ 2201+315 2204-540 2209+236 2210-257 2214+350 2216-038 2223+210 2227-088 \ 2227-399 2229+695 2232-488 2233-148 2234+282 2235+731 2243-123 2244-372 \ 2245-328 2246+208 2250+194 2252-089 2253+417 2254+024 2254+074 2255-282 \ 2300-683 2302+232 2309+454 2312-319 2318+049 2319+272 2320+506 2320-035 \ 2321-375 2325-150 2326-477 2328+107 2329-162 2329-384 2331-240 2335-027 \ 2337+264 2344+09A 2344-514 2345-167 2351+456 2351-154 2352+495 2353-686 \ 2355-106 2355-534 2356+385 2358+189 3C120 3C138 3C147 3C166 \ 3C245 3C273B 3C274 3C279 3C286 3C309.1 3C345 3C371 \ 3C390.3 3C395 3C418 3C446 3C454.3 3C48 3C84 4C39.25 \ 4C67.05 CEN-A CL4 CTA102 CTA26 CTD93 DA426 IIIZW2 \ LSI61303 M81 M84 MRK180 NGC0262 NGC0315 NGC1052 NGC1218 \ NGC2484 NGC3862 NGC3894 NGC4261 NGC5675 NGC6251 NGC6454 NGC7720 \ NRAO140 NRAO150 NRAO190 NRAO512 NRAO530 OJ287 OK290 OP326 \ OQ172 OQ208 OW-015 SN1993J UG01841 VR422201 Appendix B. ~~~~~~~~~~~ List of 192 sources with right ascension and declination estimated as local parameters: 0002+200 0008-421 0022-423 0025+197 0032+612 0037-593 0056-572 0107-610 \ 0110-668 0116+319 0116-219 0119+247 0122-514 0127+084 0147-076 0153-410 \ 0201+088 0202-765 0206+136 0207-078 0214-522 0234-301 0252-712 0253+133 \ 0254-334 0307+380 0312-770 0331+022 0334+014 0354+231 0355-483 0355-669 \ 0407-658 0431-512 0450-743 0503-608 0509+152 0517-726 0542-735 0600+219 \ 0610+171 0614-349 0615-365 0622-441 0628-627 0647-475 0700-465 0728+249 \ 0736-332 0741+214 0744-691 0809-493 0823-223 0823-500 0842-754 0844+387 \ 0903-573 0936-853 0937+262 0952+581 0959-443 1005-739 1026-084 1034-374 \ 1040+244 1043+066 1045-620 1049-650 1055-301 1056+212 1058+726 1109-567 \ 1117+146 1121+238 1133-739 1143-287 1144+352 1156-663 1204+124 1215-457 \ 1217+023 1228-113 1234-504 1236-684 1241+176 1251-407 1303-827 1320-446 \ 1334-649 1343-601 1352-632 1355-416 1417-782 1448-648 1454-354 1455+247 \ 1505-496 1508-656 1519-294 1535+004 1540-828 1554-643 1556-245 1600+43A \ 1600+43B 1600-445 1600-489 1606-398 1608+243 1611-710 1624-617 1628+216 \ 1633-810 1634+213 1637-771 1645+224 1646-506 1708+433 1725+123 1729-373 \ 1733-565 1740-517 1748-253 1756+237 1814-637 1815+531 1822-173 1824-582 \ 1829-106 1829-718 1848+283 1852-534 1901+155 1910+052 1919+086 1928-698 \ 1929-457 1932+106 1934-638 1936-623 1950-613 1952+138 2002-375 2005-044 \ 2030-689 2058-297 2058-425 2100+468 2102-659 2115-305 2117-614 2117-642 \ 2123-463 2138-377 2147+077 2152+226 2152-699 2205+166 2205-636 2211-388 \ 2214+241 2215-508 2220-351 2229-172 2236-572 2239-631 2254-367 2258+166 \ 2300-307 2306-312 2311-452 2311-477 2314-340 2324-023 2333-415 2333-528 \ 2340+233 2351-309 4C55.17 CYGNUS-A HR1099 M104 NGC4278 NGC5077 \ NGC5141 NGC6034 NGC6500 TON202 UG03927 UGC02748 VELA VELA-G Appendix C. ~~~~~~~~~~~ List of 111 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 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 VERAMZSW VERNAL VICTORIA VLA VLA-N8 WHTHORSE YAKATAGA YEBES YELLOWKN YLOW7296 YUMA Appendix D. ~~~~~~~~~~~ List of 61 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 Appendix E. ~~~~~~~~~~~ 37 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 USUDA64 VERAISGK \ VICTORIA ZELENCHK Appendix F. ~~~~~~~~~~~ Velocities of these 23 pairs, triplets or quadrets of stations were constrainted to be the same: DSS15 GOLDMARS \ DSS45 TIDBIN64 \ DSS65 DSS64 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