Technical description of solution gsfd0001 1. Purpose of the solution: a) obtain baseline length series; b) provide intermediary information, such as decomposed normal matrix, covariance matrix, for individuals who are combining different space geodesy techniques. 2. Analysis center: GSF ( NASA Goddard Space Flight Center ) 3. Short narrative description of solution: Solution gsfd001 estimates position of all stations, coordinates of some unstable 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. All available dual-band Mark-3/Mark-4 VLBI observations from 03-AUG-1979 through 23-MAY-2002, except 10 VCS1 sessions and 38 other sessions not listed in the master files, 3346 sessions with duration 18 hours and longer, about 3.5 millions group delays, were used in this solution. 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 159 sources for each 24 hour session independently. These were estimated as arc sources in the 2002b TRF solution. Refer to Appendix A. These sources are a minor 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: 2002b_apr.src catalogue b. source positions adjusted in solution: yes, some of them. Refer to Appendix A. If yes, c. definition of orientation: no-net-rotation tie to the ICRF using only the 212 ICRF defining sources d. source position estimation: 159 local 6. Terrestrial reference frame: a. a priori station positions: 2002b_apr.sit b. a priori station velocities: 2002b_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 2002b_apr.sit. 2002b_apr.sit coincides with the ITRF2000 positions for the following 40 stations: ALGOPARK BR-VLBA DSS45 DSS65 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 NRAO20 NRAO85_3 NYALES20 ONSALA60 OV-VLBA OVRO_130 PIETOWN RICHMOND SANTIA12 SC-VLBA SESHAN25 TSUKUB32 VNDNBERG WESTFORD WETTZELL 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 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 B. 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. 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: IERS Conventions 1996, 11 tidal waves in accordance with Schwiderski model, no nodal correction, no interpolation within the band. d. atmosphere loading: VLBI estimates of site local pressure admittances from VLBI [4] were used for the most frequently observed sites: GILCREEK HATCREEK HAYSTACK HRAS 085 (FD-VLBA,MCD 7850,FTD 7900) MOJAVE12 (MOJ 7288, DSS15) ONSALA60 (MV2ONSLA) RICHMOND (MIAMI20) WESTFORD (HAYSTACK) WETTZELL For the remaining stations we used values derived theoretically from convolution of a loading Green's function with meteorological surface pressure data by regression against local pressure. These values are from T. van Dam (personal communication) for all other sites except KASHIMA KASHIM34 KAUAI for which values from S. Manabe [5] were used. The estimates of station positions are related to the reference pressure at the station (Appendix C). Reference pressures were determined from a solution run in 1997. These reference pressures were chosen in such a way that the globally estimated vertical station positions would not change in that TRF solution when the pressure loading contribution was applied. For some stations atmosphere pressure loading contributiuon was not used at all: AIRA CHICHI10 GIFU KANOZAN KOGANEI KOGANEI3 SINTOTU3 TIGOCONC TSUKU3 9. Data type: group delays 10. Data editing: 7 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 2002.07.09 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. MacMillan, D.S. and J.M. Gipson, Atmospheric pressure loading parameters from very long baseline interferometry observations, J. Geophys. Res., 99, 18081-18087, 1994. 5. Manabe, S., T. Sato, S. Sakai, and K. Yokoyama, Atmospheric loading effect on VLBI observations, in Proceedings of the AGU Chapman Conference on Geodetic VLBI: Monitoring Global Change, NOAA Tech. Rep. NOS 137 NGS 49, 111-122, 1991. 18-JUL-2002 12:03:15 ---------------------------------------------------------------------------- Appendix A. ~~~~~~~~~~~ List of 159 sources with right ascension and declination estimated: 0002-478 0008-421 0022-423 0037+139 0056-572 0116+319 0118-272 0119+247 0127+084 0131-522 0147-076 0150-334 0153-410 0201+088 0202-765 0206+136 0241+622 0252-549 0252-712 0307+380 0312-770 0331+022 0334+014 0334-546 0335-364 0355-483 0407-658 0423+233 0431-512 0450-743 0454-463 0503-608 0517-726 0522-611 0534-611 0600+219 0614-349 0615-365 0622-441 0629+160 0629-418 0637-337 0647-475 0656+082 0700-465 0736-332 0743-673 0809-493 0823-223 0823-500 0834-201 0836+290 0842-754 0844+387 0936-853 0937+262 0952+581 0959-443 1004-500 1020-103 1026-084 1043+066 1058+726 1101-325 1105-680 1116-462 1117+146 1129-580 1144+352 1148-671 1206-399 1215-457 1217+023 1221-829 1228-113 1234-504 1236-684 1239+376 1239+606 1251-407 1320-446 1334-649 1349-439 1352-632 1354-174 1355-416 1444+175 1535+004 1540-828 1600+43A 1600+43B 1604-333 1628+216 1647-296 1718-649 1729-373 1733-565 1740-517 1748-253 1806-458 1814-637 1815+531 1822-173 1829-718 1830+139 1843+400 1848+283 1852-534 1901+155 1903-802 1910+052 1919+086 1920+154 1925-610 1932+106 1934-638 1936-623 1950-613 2037-253 2054-377 2058-425 2100+468 2115-305 2142-758 2146-783 2147+077 2152-699 2201+171 2209+184 2211-388 2227-399 2229-172 2300-307 2309+454 2311-452 2329-384 2333-528 2353-686 4C55.17 CYGNUS-A HD32918 HR1099 M104 NGC2110 NGC2146 NGC2484 NGC4151 NGC4278 NGC5077 NGC5141 NGC6034 NGC6166 NGC7720 UG01841 UG03927 UGC01651 UGC02748 VELA VELA-G 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 ----------------------------------------- Appendix C. ~~~~~~~~~~~ Reference station pressure (in mbar): ALGOPARK 987.7269 AUSTINTX 987.8843 AZORES 980.0000 BERMUDA 1032.0591 BLKBUTTE 958.2020 BLOOMIND 986.2808 BR-VLBA 991.1151 BREST 1018.2115 CARNUSTY 1006.7997 CARROLGA 983.5973 CHLBOLTN 1004.2083 CRIMEA 1022.2811 DAITO 1004.8062 DEADMANL 921.1954 DSS15 903.3864 DSS45 940.8996 DSS65 927.3283 EFLSBERG 973.3153 ELY 818.4020 FD-VLBA 840.9660 FLAGSTAF 780.6606 FORT ORD 1026.5164 FORTLEZA 1008.8414 FORTORDS 996.2424 FTD 7900 843.6926 GGAO7108 1009.1006 GILCREEK 973.5949 GOLDVENU 907.6266 GORF7102 1013.7940 GRASSE 880.8029 HALEAKAL 980.0000 HARTRAO 872.2941 HATCREEK 903.4485 HAYSTACK 1004.2732 HN-VLBA 974.3740 HOBART26 1015.8087 HOFN 1008.1025 HOHENFRG 1006.0411 HOHNBERG 914.8175 HRAS 085 841.6975 JPL MV1 968.8810 KARLBURG 1024.5398 KASHIM34 1011.8796 KASHIMA 1011.6565 KAUAI 893.1727 KIRSBERG 999.8500 KODIAK 1019.8853 KOKEE 897.6151 KP-VLBA 809.7043 KWAJAL26 1010.4768 LA-VLBA 805.6143 LEONRDOK 987.2458 MAMMOTHL 788.4177 MARCUS 980.0000 MARPOINT 1015.3604 MATERA 957.6935 MCD 7850 804.4337 MEDICINA 1015.4830 METSHOVI 1007.9857 MIAMI20 1015.2756 MILESMON 929.2285 MIYAZAKI 1010.7844 MIZNAO10 1005.5121 MIZUSGSI 1001.3473 MK-VLBA 980.0000 MOJ 7288 904.4807 MOJAVE12 910.8149 MON PEAK 817.6861 MV2ONSLA 1018.9158 NL-VLBA 992.0599 NOBEY 6M 888.1540 NOME 979.4225 NOTO 1004.8668 NRAO 140 924.2388 NRAO20 921.1600 NRAO85 1 925.3710 NRAO85 3 925.6830 NYALES20 999.8049 OCOTILLO 1018.0067 OHIGGINS 995.1413 ONSALA60 1008.6664 OV-VLBA 884.1696 OVR 7853 888.0806 OVRO 130 885.8806 PARKES 967.9925 PBLOSSOM 913.4080 PENTICTN 966.3524 PIETOWN 766.7355 PINFLATS 888.9036 PLATTVIL 854.2665 PRESIDIO 1025.0298 PT REYES 1027.5281 PVERDES 1020.2778 QUINCY 897.4122 RICHMOND 1017.6532 ROBLED32 1007.4550 SAGARA 1002.6400 SANPAULA 1010.2264 SANTIA12 937.0019 SC-VLBA 994.8800 SEATTLE1 1043.2625 SESHAN25 1013.3407 SEST 774.8864 SHANGHAI 1012.1340 SINTOTU 1003.8890 SNDPOINT 1011.2705 SOURDOGH 952.7302 TIDBIN64 937.1552 TITIJIMA 1012.7039 TOULOUSE 1013.0025 TROMSONO 1001.7485 TRYSILNO 932.2366 TSUKUBA 1011.0706 URUMQI 798.9826 USSURISK 993.4937 USUDA64 847.8439 VERNAL 851.8669 VICTORIA 1025.1324 VLA 788.5615 VNDNBERG 1008.3600 WESTFORD 1005.9516 WETTZELL 946.1236 WHTHORSE 931.0909 YAKATAGA 1018.9455 YEBES 907.5895 YELLOWKN 986.8436 YLOW7296 987.1935 YUMA 979.1090 SYOWA 921.6600