>>> SOLUTION DESCRIPTION <<< #################### Technical description of solution gsfd0003 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 usefullness of attempts to combinie solutions from different space geodesy techniques. 2. Analysis center: GSF ( NASA Goddard Space Flight Center ) 3. Short narrative description of solution: Solution gsfd0003 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 estiamted as well togeather 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 295 sources for each 24 hour session when they were observed. This includes all sources NOT estimated as global parameters in TRF solutions gsf2006a and gsf2006b (674 sources listed in control file). These were estimated as local parameters for each individual sessions independently in the gsf2006a solution since they were not observed very frequently. Refer to Appendix A. 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: 2006b_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: 295 local 6. Terrestrial reference frame: a. a priori station positions: 2006b_apr.sit b. a priori station velocities: 2006b_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 2006b_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 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: 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 10.0, SOLVE revision date 2006.04.28 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. 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. 31-MAY-2006 10:07:00 ---------------------------------------------------------------------------- Appendix A. ~~~~~~~~~~~ List of 295 sources with right ascension and declination estimated as local parameters in solution gsf2006a since they were observed infrequently (were not observed in 1) 2 or more sessions with at least 40 good observations or 2) at least 1 session with at least 25 good observations): 0002+200 0008-421 0022-423 0025+197 0032+612 0036-216 0037-593 0043+246 0056-572 0107-610 0110-668 0116+319 0116-219 0119+247 0122-514 0127+084 0147-076 0153-410 0201+088 0201-440 0202-765 0206+136 0207-078 0214-522 0218+357 0218+35A 0218+35B 0234-301 0248+560 0252-712 0253+133 0254-334 0307+380 0312-770 0331+022 0334+014 0335-122 0336-017 0340+044 0354+231 0354+559 0355-483 0355-669 0407-658 0420-625 0428+205 0431-512 0450-743 0454-463 0503-608 0509+152 0512+249 0515-674 0517-726 0524-485 0532+506 0534-611 0537-692 0542-735 0558-504 0600+219 0610+171 0614-349 0615-365 0622-441 0628-627 0647-475 0700-465 0710+196 0727-365 0728+249 0731-465 0736-332 0741+214 0744-691 0802-276 0806-710 0809-493 0823-223 0823-500 0842-754 0844+387 0902+343 0903-573 0925+504 0936-853 0937+262 0941-080 0952+581 0959-443 1004-500 1005-739 1015-314 1017+109 1020-103 1026-084 1034-374 1039-474 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 1206-399 1215-457 1217+023 1221-829 1222+216 1225-023 1228-113 1234-504 1236-684 1239-044 1251-407 1303-827 1305-241 1320-446 1328+254 1329-665 1334-649 1343-601 1352-632 1355-416 1417-782 1421-490 1422+268 1439+327 1448-648 1454-354 1455+247 1505+428 1505-496 1508-656 1511+238 1519-294 1535+004 1540-828 1554-643 1556-245 1600+43A 1600+43B 1600-445 1600-489 1603+573 1606-398 1608+243 1611-710 1622+238 1624-617 1628+216 1633-810 1634+213 1637-771 1645+224 1646-506 1713+218 1721+589 1725+123 1729-373 1733-565 1740-517 1742-283 1748-253 1756+237 1756-663 1809+170 1813-241 1814-637 1815+531 1822-173 1824-582 1827-360 1829-106 1829-718 1830-211 1830-21A 1830-21B 1848+283 1848+333 1852-534 1855+031 1901+155 1910+052 1919+086 1920+154 1928-698 1929-457 1932+106 1934+207 1934-638 1936-623 1950-613 1952+138 1954+282 1955+343 2002-375 2022+542 2027+383 2030-689 2044-168 2058-297 2058-425 2100+468 2101-715 2102-659 2115-305 2117-614 2117-642 2123-463 2134-470 2138-377 2141+175 2146-783 2147+077 2152+226 2152-699 2155+312 2205+166 2205-636 2209+184 2211-388 2214+241 2215-508 2220-351 2226-411 2229-172 2236-572 2239-631 2254-367 2258+166 2259-375 2300-307 2306-312 2310-417 2311-452 2311-477 2314-340 2322-411 2333-415 2333-528 2340+233 2344-514 2351-309 2353+816 3C343 3C343.1 4C+00.02 4C+32.26 4C55.17 CYGNUS-A HD132742 HD32918 HR1099 M104 M106 M77 M82 MRK003 NAQL93 NGC0253 NGC1167 NGC2110 NGC2146 NGC3079 NGC3690 NGC4151 NGC4278 NGC5077 NGC5141 NGC6034 NGC6166 NGC6240 NGC6500 NGC6946 OB338 SGR-A SIGCRB TON202 UG00192 UG03927 UGC01651 UGC02748 UXARI 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 -----------------------------------------