Technical description of solution gsf2003c 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 gsf2003c 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, 2003.07.01]. 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 2003.06.30, except 12 VCS1 and VCS2 sessions and 3 gravity sessions, 3607 sessions with duration 18 hours and longer, 4 099 155 group delays, were used in a single solution. The wrms of postfit residuals is 22.694 psec and chi-sq/ndg = 1.021 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 605 sources (Appendix A) were estimated as global parameters. Positions of 133 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 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: 2003c.sou -- catalogue of 605 sources estimated as global parameters; 2003c_lso.sou -- catalogue of 133 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 gsf2003b solutions: 1) Stations VERAMZSW and GIFU11 were added to the solution. 2) Bias of EOP series with repsect to USNO finals series is significantly reduced. 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: 2003c_apr.src catalogue. This catalogue was created in the preliminary solution similar to gsf2003c. 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: 605 global and 133 local 6 - Terrestrial reference frame: a. a priori station positions: 2003c_apr.sit . This catalogue was created in the preliminary solution similar to gsf2003c. However, positions of 35 strong stations were replaced with the values from the ITRF2000 catalogue. b. a priori station velocities: 2003c_apr.vel . This catalogue was created in the preliminary solution similar to gsf2003c. However, velocities of 35 strong stations were replaced with the values from the ITRF2000 catalogue. c. reference epoch: 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 0.04543120 0.07630656 0.06161934 NO EXCEPT \ * nnt_pos RIGHT_PART -0.13563202 0.04536970 0.05194841 NO EXCEPT \ * nnr_pos RIGHT_PART 0.01632479 0.00473411 0.00620421 NO EXCEPT \ * nnt_vel RIGHT_PART -0.00932911 0.01975589 0.01354300 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 GILCREEK 021103 ! Earthquake GGAO7108 030101 ! Station relocation 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: no 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 1996 b. a priori nutation model: IERS 1996 c. a priori short-period tidal variations in x, y, UT1 were taken into account in accordance with the model presented in Appendix G. 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 specified in the Appendix G 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 gsf2003c.eops . The pole coordinates and UT1 from singular networks were substantially affected by weak constraints. They were removed from the output file gsf2003c.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. 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 9.12, SOLVE revision date 2003.05.15 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. 25-MAR-2003 09:27:06 ---------------------------------------------------------------------------- Appendix A. ~~~~~~~~~~~ * * --- 605 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 0019+058 0026+346 0035+413 0039+230 0047-579 0048-097 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 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 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 0335-364 0338-214 0341+158 0342+147 0400+258 0400-319 \ 0402-362 0403-132 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 0451-282 0454+844 0454-234 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 0516-621 0521-365 0524-460 0528+134 0528-250 0529+075 \ 0530-727 0536+145 0537-158 0537-286 0537-441 0539-057 0544+273 0552+398 \ 0554+242 0556+238 0600+177 0602+405 0602+673 0605-085 0607-157 0609+607 \ 0610+260 0611+131 0615+820 0620+389 0629+160 0636+680 0637-752 0642+449 \ 0646-306 0648-165 0650+371 0651+410 0656+082 0657+172 0707+476 0710+439 \ 0711+356 0716+714 0718+793 0722+145 0723-008 0727-115 0733-174 0735+178 \ 0736+017 0738+313 0738+491 0738-674 0742+103 0743+259 0743-006 0745+241 \ 0748+126 0749+540 0754+100 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+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 1014+615 1020+400 1021-006 1022+194 1023+131 1030+074 \ 1030+415 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 1101-536 1104+728 1104-445 1105-680 1111+149 1116-462 1116+128 \ 1123+264 1124-186 1125+596 1127-145 1128+385 1128-047 1130+009 1143-245 \ 1144+402 1144-379 1145-071 1147+245 1148-001 1148-671 1150+497 1150+812 \ 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 \ 1240+381 1243-072 1244-255 1251-713 1252+119 1254+571 1255-316 1257+145 \ 1300+580 1302-102 1307+121 1308+326 1308+328 1313-333 1323+321 1324+224 \ 1327+321 1330+476 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 1413+349 1416+067 1417+273 1417+385 \ 1418+546 1420+326 1424+240 1424+366 1424-418 1427+543 1428+422 1430-178 \ 1432+200 1433+304 1435+638 1435-218 1436+373 1437+331 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 1510-089 1511-100 1514+197 1514-241 \ 1519-273 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 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 1705+018 1705+456 1706-174 1717+178 1718-649 1725+044 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+159 \ 1758+388 1758-651 1800+440 1803+784 1806-458 1806+456 1815-553 1817-254 \ 1821+107 1823+568 1826+796 1830+139 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 \ 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+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 \ 2143-156 2144+092 2145+067 2145+082 2149+056 2149-306 2150+173 2155-152 \ 2155-304 2201+171 2201+315 2204-540 2209+236 2210-257 2214+350 2216-038 \ 2227-088 2227-399 2229+695 2232-488 2233-148 2234+282 2235+731 2243-123 \ 2245-328 2250+194 2252-089 2253+417 2254+024 2254+074 2255-282 2309+454 \ 2312-319 2318+049 2319+272 2320+506 2320-035 2325-150 2326-477 2328+107 \ 2329-162 2329-384 2331-240 2335-027 2337+264 2344+09A 2345-167 2351+456 \ 2351-154 2352+495 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 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 NGC5675 NGC6251 NGC6454 \ NRAO140 NRAO150 NRAO190 NRAO512 NRAO530 OJ287 OK290 OP326 \ OQ172 OQ208 OW-015 SN1993J VR422201 Appendix B. ~~~~~~~~~~~ List of 133 sources with right ascension and declination estimated as local parameters: 0008-421 0022-423 0032+612 0037+139 0048-427 0056-572 0116+319 0119+247 \ 0127+084 0131-522 0147-076 0150-334 0153-410 0201+088 0202-765 0206+136 \ 0207-078 0253+133 0307+380 0312-770 0331+022 0334-546 0355-483 0407-658 \ 0423+233 0431-512 0450-743 0454-463 0503-608 0509+152 0517-726 0522-611 \ 0534-340 0534-611 0600+219 0610+171 0615-365 0622-441 0629-418 0637-337 \ 0700-465 0736-332 0743-673 0759+183 0823-223 0823-500 0836+290 0842-754 \ 0936-853 0937+262 0952+581 1012-448 1016-311 1026-084 1043+066 1058+726 \ 1101-325 1117+146 1119+183 1144+352 1204+124 1215-457 1217+023 1228-113 \ 1234-504 1236-684 1239+606 1251-407 1320-446 1325-558 1334-649 1352-632 \ 1355-416 1412-368 1423+146 1522+155 1535+004 1540-828 1600+43A 1600+43B \ 1600-445 1606-398 1628+216 1705+135 1725+123 1733-565 1740-517 1748-253 \ 1754+155 1814-637 1815+531 1822-173 1829-718 1843+400 1848+283 1852-534 \ 1901+155 1903-802 1910+052 1919+086 1928+154 1932+106 1934-638 1936-623 \ 1950-613 1952+138 2058-425 2100+468 2115-305 2142-758 2146-783 2147+077 \ 2152-699 2205+166 2211-388 2244-372 2258+166 2300-307 2311-452 2314-340 \ 2321-375 2333-528 2358+189 4C55.17 M104 NGC5141 NGC7720 UG01841 \ UGC02748 VELA VELA-G Appendix C. ~~~~~~~~~~~ List of 86 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 GIFU3 GOLDVENU \ GORF7102 GRASSE HALEAKAL HOFN HOHENFRG \ HOHNBERG JPL_MV1 KANOZAN KARLBURG KASHIM11 \ KIRSBERG KODIAK KOGANEI KOGANEI3 KWAJAL26 \ LEONRDOK MAMMOTHL MARCUS MARPOINT MCD_7850 \ METSHOVI MIAMI20 MILESMON MIURA MIYAZAKI \ MIZNAO10 VERAMZSW 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 TOULOUSE TROMSONO TRYSILNO \ TIDBIN64 TIGOCONC TIGOWTZL TSUKUBA TSUKU3 \ URUMQI USSURISK USUDA64 VERNAL VICTORIA \ VLA WHTHORSE YAKATAGA YEBES YELLOWKN \ YLOW7296 YUMA GIFU11 Appendix D. ~~~~~~~~~~~ List of 41 stations with axis offsets estimated as global parameters: ALGOPARK BR-VLBA DSS45 DSS65 EFLSBERG FD-VLBA FORTLEZA GILCREEK HARTRAO HATCREEK HAYSTACK HN-VLBA HOBART26 HRAS 085 KASHIM34 KASHIMA KAUAI KOKEE KP-VLBA LA-VLBA MATERA MEDICINA MK-VLBA MOJAVE12 NL-VLBA NOTO NRAO 140 NRAO20 NRAO85 3 NYALES20 ONSALA60 OV-VLBA OVRO 130 PIETOWN RICHMOND SANTIA12 SC-VLBA TSUKUB32 VNDNBERG WESTFORD WETTZELL Appendix E. ~~~~~~~~~~~ 40 stations with constraints on velocity: AUSTINTX AZORES BERMUDA BLOOMIND BREST CARNUSTY CARROLGA CHLBOLTN CTVASBAY CTVASTJ DAITO FTD_7900 GIFU3 GRASSE HOFN HOHENFRG HOHNBERG KANOZAN KARLBURG KIRSBERG LEONRDOK MCD_7850 METSHOVI MILESMON VERAMZSW MIYAZAKI NOBEY_6M OCOTILLO SAGARA SEST SUWON TIDBIN64 TIGOCONC TITIJIMA TOULOUSE USSURISK USUDA64 VICTORIA VLA GIFU11 Appendix F. ~~~~~~~~~~~ Velocities of these pairs of stations were constrainted to be the same: DSS15 GOLDMARS AND DSS45 TIDBIN64 AND DSS65 ROBLED32 MADRID64 AND FORT_ORD FORTORDS AND GBT-VLBA NRAO20 AND GGAO7108 GORF7102 AND KASHIM34 KASHIM11 AND KAUAI HALEAKAL AND KOGANEI KOGANEI3 AND MIZNAO10 MIZUSGSI AND MOJAVE12 MOJ_7288 AND NRAO_140 NRAO85_1 AND ONSALA60 MV2ONSLA ONSALA85 AND OVRO_130 OVR_7853 AND RICHMOND MIAMI20 AND SESHAN25 SHANGHAI AND SINTOTU3 SINTOTU AND TSUKUB32 TSUKU3 AND WETTZELL TIGOWTZL AND YLOW7296 YELLOWKN Appendix G. ~~~~~~~~~~~ Expansion of short-period variations in polar motion and UT1. UT1 tidal terms (microseconds) l l' F D Om GST | Cos | Sin | +pi | | | ----------------------------------------- 2 0 2 0 2 -1 -.13 -1.24 0 0 2 2 2 -1 .19 -.82 1 0 2 0 1 -1 -.50 -.92 1 0 2 0 2 -1 -2.64 -4.90 -1 0 2 2 2 -1 -1.10 -.77 0 0 2 0 1 -1 -2.51 -3.34 0 0 2 0 2 -1 -13.31 -17.72 -1 0 2 0 2 -1 .34 .63 1 0 0 0 0 -1 .48 .77 0 1 2 -2 2 -1 -.21 -.43 0 0 2 -2 2 -1 -3.20 -5.32 0 1 0 0 0 -1 .50 1.89 0 0 0 0 -1 -1 -.19 -.33 0 0 0 0 0 -1 9.83 16.45 0 0 0 0 1 -1 1.33 2.23 0 -1 0 0 0 -1 -.17 .41 0 0 -2 2 -2 -1 .08 -.04 -1 0 0 0 0 -1 .13 1.25 0 0 -2 0 -2 -1 .68 .33 0 0 -2 0 -1 -1 .44 .21 -1 0 -2 0 -2 -1 .18 .75 -1 0 -2 0 -1 -1 .12 .48 2 0 2 0 2 -2 -.30 .61 0 0 2 2 2 -2 -.83 .47 1 0 2 0 2 -2 -1.94 3.13 -1 0 2 2 2 -2 -.19 .67 0 0 2 0 1 -2 .37 -.57 0 0 2 0 2 -2 -9.88 15.37 -1 0 2 0 2 -2 .12 -.34 0 1 2 -2 2 -2 -.06 .17 0 0 2 -2 2 -2 -1.25 7.73 0 1 0 0 0 -2 .24 .27 0 0 0 0 0 -2 .28 2.48 0 0 0 0 1 -2 .08 .74 0 0 3 0 3 -3 .24 .03 0 0 0 4 1 -1 .26 .10 1 0 4 -2 2 -1 .43 -.52 0 0 0 1 0 -1 -.29 -.23 3 -1 2 0 2 -2 .14 .00 1 1 2 0 1 -2 -.26 -.40 0 0 0 -2 2 -2 .23 .09 ----------------------------------------- Polar motion tidal terms (microarcseconds) l l' F D Om GST | Cos | Sin | +pi | | | ----------------------------------------- -2 0 -2 0 -2 1 -6.90 5.52 0 0 -2 -2 -2 1 -8.63 3.00 -1 0 -2 0 -1 1 -5.58 1.48 -1 0 -2 0 -2 1 -29.56 7.83 1 0 -2 -2 -2 1 -7.86 3.64 0 0 -2 0 -1 1 -25.03 8.53 0 0 -2 0 -2 1 -132.70 45.21 1 0 -2 0 -2 1 2.59 .60 -1 0 0 0 0 1 3.26 -8.76 0 -1 -2 2 -2 1 1.25 9.68 0 0 -2 2 -2 1 -49.40 19.23 0 -1 0 0 0 1 25.06 6.71 0 0 0 0 1 1 -3.09 1.76 0 0 0 0 0 1 156.21 -88.75 0 0 0 0 -1 1 21.18 -12.04 0 1 0 0 0 1 4.99 .50 0 0 2 -2 2 1 3.25 2.62 1 0 0 0 0 1 .51 -4.99 0 0 2 0 2 1 5.93 -10.38 0 0 2 0 1 1 3.80 -6.65 1 0 2 0 2 1 .46 .59 1 0 2 0 1 1 .30 .37 -2 0 -2 0 -2 2 4.13 -.28 0 0 -2 -2 -2 2 -1.37 .40 -1 0 -2 0 -2 2 10.48 -12.69 1 0 -2 -2 -2 2 4.33 1.81 0 0 -2 0 -1 2 -1.06 2.12 0 0 -2 0 -2 2 28.34 -56.83 1 0 -2 0 -2 2 1.92 .54 0 -1 -2 2 -2 2 5.42 -4.28 0 0 -2 2 -2 2 -.48 -20.16 0 -1 0 0 0 2 2.61 1.85 0 0 0 0 0 2 -.83 -18.26 0 0 0 0 -1 2 -.25 -5.44 0 0 -3 0 -3 3 1.92 -1.16 0 0 0 -4 -1 1 5.23 -1.47 -1 0 -4 2 -2 1 -1.28 -3.62 0 0 0 -1 0 1 2.33 -2.61 -3 1 -2 0 -2 2 -.88 -1.13 -1 -1 -2 0 -1 2 .24 .00 0 0 0 2 -2 2 .05 -1.31 2 0 2 0 2 -2 2.33 7.19 0 0 2 2 2 -2 2.87 7.66 1 0 2 0 2 -2 .59 43.62 -1 0 2 2 2 -2 -3.07 8.30 0 0 2 0 1 -2 .50 -9.59 0 0 2 0 2 -2 -13.37 257.07 -1 0 2 0 2 -2 1.83 -7.67 0 1 2 -2 2 -2 -7.08 .33 0 0 2 -2 2 -2 -72.53 106.95 0 1 0 0 0 -2 .34 -4.29 0 0 0 0 0 -2 -18.74 12.64 0 0 0 0 1 -2 -5.59 3.77 0 0 3 0 3 -3 -.56 -1.57 3 -1 2 0 2 -2 -.98 4.60 1 1 2 0 1 -2 -.62 4.28 0 0 0 -2 2 -2 -.83 2.72 -----------------------------------------