Technical description of solution gsi2023a Last update: 31 March, 2023 1. Purpose of solution: TRF 2. Analysis Center: Geospatial Information Authority of Japan (GSI) 3. Short narrative description of solution: Solution gsi2023a estimates station position and velocity parameters in order to obtain a terrestrial reference frame (TRF). The TRF is defined by no-net-translation and rotation constraints for positions and velocities of 21 stations with respect to the ITRF2014 [1]. The solution also estimated EOP time series and source positions. VLBI data from 1980.04.11 to 2022.12.27, totally 7413 sessions were used for this solution. The wrms postfit residual was 24.294 psec and Chi/ndg was 1.01. The estimated parameters are split into three groups. 1) Global parameters estimated overall sessions; station positions and velocities, source positions, and antenna axis offset 2) Local parameters estimated for each 24-hour session individually; EOP 3) Segmented parameters estimated over 20 minute, 1 hr, or 6 hr; zenith troposphere, station clock, troposphere gradient 4. Estimated parameters: a. celestial frame: Right ascension and declination as global parameters. b. terrestrial frame: X, Y, Z, Xdot, Ydot, Zdot (global) c. earth orientation: X-pol, Y-pole, UT1-TAI, Xdot, Ydot, UT1dot, X-nutation, Y-nutation (local) d. zenith troposphere: Linear spline 20-min interval; rate constraint with 50 ps/hour; VMF3 wet partial derivative (segmented). e. troposphere gradient: 6-hour East and North linear splines using offset and rate constraints with reciprocal weights of 0.5 mm and 2.0 mm/day (segmented). f. station clocks: Linear spline with 1-hr interval (segmented); rate constraint with reciprocal weights, generally 5.0E-14. g. baseline clocks: As set in initial analysis usually used (local). h. other: Global antenna axis offsets for a set of stations listed in Appendix A. (global). 5. Celestial reference frame: a. a priori source positions: ICRF3 b. source positions adjusted in solution: Yes c. definition of orientation: no-net-rotation tie to the ICRF3 using the 303 ICRF3 defining sources. 6. Terrestrial reference frame: a. a priori station positions: gsi_sitmod_20220307, which is from ITRF2014. b. a priori station velocities: gsi_velmod_20220127, which is from ITRF2014. c. reference epoch: 2010.01.01 d. station positions/velocities adjusted in solution: Yes e. definition of origin, orientation, and their time evolution: no-net-translation and no-net-rotation of position with respect to gsi_sitmod_20220307 and gsi_velmod_20220127 for 21 stations: BADARY BR-VLBA FD-VLBA FORTLEZA GILCREEK HARTRAO HOBART26 KASHIMA KATH12M KOKEE NL-VLBA NOTO NYALES20 ONSALA60 OV-VLBA RICHMOND SC-VLBA SESHAN25 WARK12M WESTFORD WETTZELL f. station parameter estimation: X, Y, Z, Xdot, Ydot, Zdot - globally for all stations, some with constraint g. stations with constraints: A priori velocities for U, E, and N components of 36 stations listed in Appendix B. were constrained to their gsi_velmod_20220127 velocities with reciprocal weights 0.1, 3.0, and 3.0 mm/yr respectively, because these stations have very short historyies of observations. Many are mobile sites occupies only once. The velocities of the 29 groups of stations listed in Appendix C. were constrained to be the same. h. stations with discontinuous positions and date of discontinuity: Appendix D. i. stations with nonlinear velocities: Spline functions were used to model the motion at the following stations, due to non-linear behavior for all or past of their observing histories. HRAS_085 PIETOWN GILCREEK j. postseismic deformation: Postseismic model parameters are from ITRF2014. 7. Earth orientation: a. a priori precession model: IAU2006/2000 Precession/Nutation b. a priori short-period tidal variations in Xpol, Ypol and UT1 due to short period tidal and nutation effects were applied. These were computed by Calc 11, as recommended in the IERS 2010 Conventions [2]. c. a priori UT1 and polar motion: usno_finals.erp High frequency variations in polar motion and UT1, as computed by Calc 11, were added to the a priori EOP during the Solve/Global solution. The reported values of polar motion and UT1 are the sum of the adjustments and the apriori EOP without the contribution due to high frequency variations. Thus, the final series of polar motion and UT1 do not contain contributions due to high frequency variations. The EOPs were not estimated for sessions consisting of one baseline. d. EOP estimation: X-pol, Y-pol, UT1-TAI, Xdot, Ydot, UT1dot, X-nutation, Y-nutation (local) 8. A priori geophysical models: a. troposphere: VMF3 total (dry+wet) mapping function b. solid Earth tide: IERS Conventions 2010 c. ocean loading: IERS 2010 Conventions (implemented in Calc 11) d. pole tides: IERS 2010 Conventions (implemented in Calc 11) e. ocean pole tide loading: IERS 2010 Conventions (implemented in Calc11) f. antenna thermal deformation: IVS antenna thermal deformation model [3] g. axis offsets: Values of the official list of VLBI antenna axis offsets issued by the IVS Analysis Coordinator based on 2019a.axo h. a priori gradients: GSFC Data Assimilation Office (DAO) model 9. Data type: Group delays 10. Data editing : 5 deg elevation cutoff 11. Data weighting: Observations are weighted using std reported in observational files; re-weighting iteration for each session to achieve the chi-square unity. 12. Standard errors reported: Reported formal errors are derived from least-squares estimation propagated from data uncertainties and weighted as discussed in #11 13. Software: CALC Version: 11.0 SOLVE release: 2019.11.21 SOLVE revision: 2020.01.23 References [1] Altamimi, Z., P. Rebischung, L. Metivier, and X. Collilieux, "ITRF2014: A new release of the International Terrestrial Reference Frame modeling nonlinear station motions", J. Geophys. Res. Solid Earth, vol. 121 Issue #8, pp. 6109-6131, 2016. doi: 10.1002/2016JB013098. [2] IERS Technical Note 35, "The Second Realization of the International Celestial Reference Frame by Very Long Baseline Interferometry"; A.L. Fey, D.Gordon, C.S. Jacobs, editors; 2009. https://www.iers.org/IERS/EN/Publications/TechnicalNotes/tn35.html [3] Nothnagel, A., "Short Note: Conventions on Thermal Expansion Modelling of Radio Telescopes for Geodetic and Astrometric VLBI", Jornal of Geodesy, vol.83 Issue #8, pp. 787-792, 2009. doi: 10.1007/s00190-008-0284-z. Appendix A. List of 81 stations with axis offsets estimated as global parameters: AGGO AIRA ALGOPARK BADARY BR-VLBA CHICHI10 CRIMEA CTVASTJ DSS13 DSS15 DSS45 DSS65 DSS65A EFLSBERG FD-VLBA FORTLEZA GGAO7108 GILCREEK HART15M HARTRAO HATCREEK HAYSTACK HN-VLBA HOBART12 HOBART26 HRAS_085 ISHIOKA KASHIM11 KASHIM34 KASHIMA KATH12M KAUAI KOGANEI KOKEE KP-VLBA KUNMING LA-VLBA MARPOINT MATERA MEDICINA METSAHOV MK-VLBA MOJAVE12 MON_PEAK NL-VLBA NOTO NRAO20 NRAO85_3 NYALE13S NYALES20 OHIGGINS ONSALA60 OV-VLBA OVRO_130 PARKES PIETOWN RAEGSMAR RICHMOND SANTIA12 SC-VLBA SEJONG SESHAN25 SINTOTU3 SVETLOE SYOWA TIANMA65 TIGOCONC TSUKUB32 URUMQI VERAISGK VERAMZSW VNDNBERG WARK12M WESTFORD WETTZ13N WETTZELL YARRA12M YEBES YEBES40M YLOW7296 ZELENCHK Appendix B. List of 36 stations with constraints on velocity: AUSTINTX AZORES BERMUDA BLOOMIND BREST CARNUSTY CARROLGA CHLBOLTN CTVASBAY DAITO DEADMANL DSS26 DSS56 GRASSE HOFN HOHENFRG HOHNBERG KAINAN KANOZAN KARLBURG KIRSBERG LEONRDOK MAMMOTHL MILESMON NOBEY_6M OCOTILLO SAGARA SEATTLE1 SEST SUWON TOMAKO11 TOULOUSE TRYSILNO VICTORIA WHTHORSE YAKATAGA Appendix C. Velocities of these 29 pairs, triplets or quadrets of stations were constrainted to be the same: CHICHI10 TITIJIMA DSS15 DSS13 GOLDMARS GOLDVENU MOJAVE12 MOJ_7288 DSS34 DSS36 DSS45 TIDBIN64 DSS65 DSS65A ROBLED32 MADRID64 FORT_ORD FORTORDS GGAO7108 GORF7102 GGAO12M GIFU11 GIFU3 HARTRAO HART15M HRAS_085 FTD_7900 MCD_7850 HOBART26 HOBART12 KASHIM34 KASHIM11 KASHIMA KAUAI HALEAKAL KOKEE KOKEE12M KOGANEI KOGANEI3 MACGO12M FD-VLBA METSAHOV METSHOVI MIZNAO10 VERAMZSW MIZUSGSI NRAO20 NRAO_140 NRAO85_1 NRAO85_3 GBT-VLBA NYALES20 NYALE13S ONSALA60 MV2ONSLA ONSALA85 ONSA13NE ONSA13SW OVRO_130 OVR_7853 RICHMOND MIAMI20 SESHAN25 SHANGHAI TIANMA65 TIANMA13 SESHAN13 SINTOTU SINTOTU3 TSUKUB32 TSUKU3 TSUKUBA PIETOWN VLA VLA-N8 WETTZELL TIGOWTZL WETTZ13N WETTZ13S YLOW7296 YELLOWKN YEBES YEBES40M RAEGYEB Appendix D. List of stations with discontinuous positions SOURDOGH 871201 * EQ M7.9 Alaska WHTHORSE 871201 * EQ M7.9 Alaska YAKATAGA 871201 * EQ M7.9 Alaska FORTORDS 891018 * EQ M6.9 Loma Prieta, California PRESIDIO 891018 * EQ M6.9 Loma Prieta, California NRAO85 3 901201 * Unknown DSS15 920627 * EQ M7.3 Landers, California MOJAVE12 920627 * EQ M7.3 Landers, California MEDICINA 960701 * Rail reparing EFLSBERG 961001 * Rail reparing DSS65 970415 * Rail reparing DSS15 991016 * EQ M7.1 Hector Mine, California GGAO7108 030101 * Station relocation MIZNAO10 030526 * EQ M7.0 Miyagi-oki VERAMZSW 030526 * EQ M7.0 Miyagi-oki SINTOTU3 030926 * EQ M8.3 Tokachi-oki MIZNAO10 050816 * EQ M7.2 Miyagi-oki VERAMZSW 050816 * EQ M7.2 Miyagi-oki MK-VLBA 060712 * Unknown ZELENCHK 070701 * Rail reparing KASHIM34 080507 * EQ M6.9 Ibaraki-oki VERAMZSW 080613 * EQ M6.9 Iwate-nairiku OHIGGINS 100203 * Unknown CHICHI10 101221 * EQ M7.4 Chichijima TIGOCONC 100305 * EQ M6.6 WNW of Talcahuano, Chile TIGOCONC 110211 * EQ M6.9 N of Tome, Chile KASHIM11 110311 * EQ M9.0 off the Pacific coast of Tohoku KASHIM34 110311 * EQ M9.0 off the Pacific coast of Tohoku KOGANEI 110311 * EQ M9.0 off the Pacific coast of Tohoku SINTOTU3 110311 * EQ M9.0 off the Pacific coast of Tohoku TSUKUB32 110311 * EQ M9.0 off the Pacific coast of Tohoku USUDA64 110311 * EQ M9.0 off the Pacific coast of Tohoku VERAMZSW 110311 * EQ M9.0 off the Pacific coast of Tohoku YEBES40M 111111 * Readjustment of the sub-reflector ---- Tsukuba VLBI Analysis Center Contact: Yu Takagi (gsi-oper@gxb.mlit.go.jp)