Technical description of solution gsf2007d 1. Purpose of the solution: a) Obtain baseline length series; b) Provide intermediary information, such as covariance matrix, matrix of constraints equaiton, decomposed normal matrix, for individuals who are investigating in study of a feasibility and usefulness of attempts to combine solutions from different space geodesy techniques. c) Generate daily SINEX file output 2. Analysis center: GSF (NASA Goddard Space Flight Center) 3. Short narrative description of solution: Solution gsf2007d estimates position of all stations, coordinates of some unstable or infrequently observed sources, UT1, polar motion and their rates, daily nutation offsets for each session independently. No-net-rotation, no-net-translation constraints are imposed on the estimates of the station positions. Clock function for all stations except the reference one and atmosphere zenith path delay are modeled by a linear spline with the time span 60 and 20 minutes respectively. Parameters of these spline are estimated as well together with other parameters. NB: although UT1 and pole coordinates are adjusted in the solution, these estimates should not be used in scientific analysis, since they heavily depend on apriori EOP values. 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]. 4. Estimated parameters: a. Celestial frame: Right Ascension, Declination of about 400 sources for each 24 hour session when they were observed. This includes all sources NOT estimated as global parameters. These were estimated as local parameters in each individual session since they were not observed very frequently. These sources usually are a small fraction of the sources observed in a session. b. Terrestrial frame: X, Y, Z of all sites for each 24 hour session independently. c. Earth orientation: x, y, UT1-TAI, xdot, ydot, UT1dot, dpsi, deps. 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: East and North gradients as well of the rate of their change was estimated for all stations. Offset and rate constraints with reciprocal weights 0.5 mm and 2.0 mm/day were applied (local). 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) 5. Celestial reference frame: a. A priori source positions: 2007d_apr.src catalogue b. Source positions adjusted in solution: yes, positions for infrequently observed sources were estimated. If yes, c. Definition of orientation: no-net-rotation tie to the ICRF using only the 212 ICRF defining sources. d. Source position estimation: 611 global sources, Appendix A. 6. Terrestrial reference frame: a. A priori station positions: 2007d_apr.sit b. A priori station velocities: 2007d_apr.vel c. Reference epoch: 1997.0 d. Station positions/velocities adjusted in solution: yes, positions only. e. Definition of origin, orientation, and their time evolution: No-net-translation and no-net-rotation of position with respect to 2007d_apr.sit. All stations participate in equations of constraints. Equations of constraints are equally weighted. f. Station parameter estimation: X, Y, Z, locally for all stations g. Stations with constraints: NO! h. Stations with discontinuous positions and date of discontinuity: No 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 modeled, 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/nutation model: IAU2000A nutation/precision model using the non-rotating origin b. A priori short-period tidal variations in x, y, UT1 were taken into account in accordance with the model presented in Appendix B. c. 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. 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 2003, chapter 7, page 9, step 1 and step 2. 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 only. 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 10.0, SOLVE revision date 2006.04.28 14. Other information: Mean pole coordinates used for computation of pole tide deformation were set to the mean pole expression given in the IERS2003 Conventions. Axis offsets were fixed to either measured offsets or to offsets estimated in a solution (2007c_axis) run by Leonid Petrov. The corresponding axis offset file is to be used by all IVS ACs as of June 30, 2007. 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. 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. ---------------------------------------------------------------------------- Appendix A. ~~~~~~~~~~~ List of 611 sources with right ascension and declination estimated as global parameters in solution gsf2007d. 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 0332-403 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+171 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. ~~~~~~~~~~~ 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 -----------------------------------------