File : itrf93.txt ITRF93 DATA ANALYSIS The ITRF93 global combined solution is divided into three parts: - a set of station coordinates at epoch 1988.0 - a set of station coordinates at epoch 1993.0 - a velocity field consistent with the above two sets. All of these three parts are estimated, using least square adjustment, by combination of individual terrestrial reference frames provided by the analysis centers participating in the IERS activities. These individual terrestrial reference frames are derived fromVLBI, GPS and SLR observations. We have only used solutions which should bring a significant contribution to the combination. Solutions of weaker quality or with unsufficient information were only compared a posteriori. In this analysis, we have constrained the orientation of the ITRF93 and its rate of change with time to be consistent with the IERS series of Earth Orientation Parameters (EOP). This is different from what was done in the past, where a no-net-rotation condition at 1988.0 with respect to the previous ITRF was applied and where a no-net-rotation condition was applied to the velocity field through NNR-NUVEL1. ITRF93 station coordinates -------------------------- ITRF93 station coordinates at 1988.0 ------------------------------------ The ITRF93 station coordinates at epoch 1988.0 are estimated by combination of selected individual terrestrial reference frames among those submitted by the IERS analysis centers. The combination at 1988.0 is performed in two steps: - in the first step, a global adjustment is done, holding to zero the seven transfomation parameters of the SLR solution SSC(CSR) 94 L 01 (labeled hereafter LC). The three rotations R1, R2 and R3 obtained from this combination for two VLBI solutions ( SSC(GSFC) 94 R 01 and SSC(NOAA) 94 R 01, labeled hereafter RG and RN respectively) have been compared to their corresponding EOP bias relative to the EOP of CSR solution: EOP(CSR) 94 L 01. Table 1 lists these values as the following: *) the rotation angles of RG and RN wrt LC, *) the corresponding EOP bias, *) the differences between the rotation angles and the corresponding EOP bias, *) the average of the above differences *) the EOP bias of LC wrt to the IERS series (EOP(IERS) 94 C 01) Table 1 : Rotation angles and their corresponding EOP bias with respect to LC _____________________________________________________________________________ Solution R1/y pole R2/x pole A3-R3/f.dUT1 0.001" 0.001" 0.001" ------------ --------- --------- ------------ RG wrt LC 2.06 1.20 -1.97 +/- 0.22 0.19 0.14 EOP bias 2.20 0.26 -0.62 +/- 0.03 0.03 0.01 ----- ----- ----- diff. 0.14 -0.94 1.35 RN wrt LC 1.43 0.31 -2.24 +/- 0.22 0.19 0.14 EOP bias 1.69 -0.49 -0.97 +/- 0.03 0.03 0.01 ----- ----- ----- diff. 0.26 -0.80 1.27 mean diff. 0.20 -0.87 1.31 LC EOP wrt EOP(IERS) 94 C 01 -0.55 -0.12 0.0 Values fixed for LC in the 1988.0 combination R1 = -0.35 R2 = -0.99 R3 = -1.31 _____________________________________________________________________________ - in the second step, the terrestrial frame is rotated so that the average rotation angles of two the VLBI solutions (RG and RN) relative to the resulting frame match the biases of the corresponding series of EOP relative to EOP(IERS) 94 C 01 at epoch 1988.0. On other words the three rotations of LC have been fixed to those values given in the last line of Table 1. ITRF93 station coordinates at 1993.0 ------------------------------------ The ITRF93 station coordinates at epoch 1993.0 are also estimated in two steps: - in the first step, a global adjustment is done, holding to zero the seven transfomation parameters of LC solution. From this first step adjustment and the 1988.0 first step adjustment, the rates of change of the . . . transformation parameters have been computed. The three rotation rates R1,R2,R3 for the two VLBI solutions (RG and RN) have been compared to their corresponding EOP rates relative to the EOP rates of the CSR solution. Table 2 lists these values as the following: *) the rotation rates of RG and RN wrt LC, *) the corresponding EOP rates, *) the differences between the rotation rates and the corresponding EOP rates, *) the average of the above differences, *) the EOP rates of LC wrt to the IERS series (EOP(IERS) 94 C 01), *) the adopted values for LC rates. Table 2 : Rotation rates and their corresponding EOP rates with respect to LC _____________________________________________________________________________ . . . . . . Solution R1/y pole R2/x pole -R3/f.dUT1 0.001"/y 0.001"/y 0.001"/y -------- --------- --------- ---------- RG wrt LC -0.09 -0.10 -0.01 +/- 0.06 0.06 0.04 EOP rates -0.12 0.14 0.06 +/- 0.01 0.01 0.01 ----- ----- ----- diff. -0.03 0.24 0.07 RN wrt LC -0.12 -0.12 -0.02 +/- 0.06 0.06 0.04 EOP rates -0.17 0.10 0.06 +/- 0.01 0.01 0.01 ----- ----- ----- diff. -0.05 0.22 0.08 mean diff. -0.04 0.23 0.07 LC EOP rates wrt EOP(IERS) 94 C 01 0.16 0.07 0.0 Adopted rotation rates . . . for LC R1 = 0.12 R2 = 0.30 R3 = -0.07 _____________________________________________________________________________ - in the second step, the three rotation angles of LC solution were fixed to their values of the 1988.0 combined solution to which was added the rotation rate effect over 5 years. These three rotation angle values fixed for LC solution in the 1993.0 combination are (in 0.001"): R1 = 0.25, R2 = 0.51 and R3 = -1.66. The two adjustments were performed using the SSCMIX software developped by IGN. The options used were: - least square estimation of station coordinates and 7 transformation parameters for each solution, - local surveys used with a priori variances (see file IERS.ECC) - station coordinates used with a priori variances In summary, the consistency of the ITRF93 with the IERS series of EOP at the two epochs (88.0 and 93.0) defines the orientation and time evolution of the ITRF93. The origin and the scale of the ITRF93 are defined by holding to zero the three translations and the scale factor of the SLR solution, SSC(CSR) 94 L 01 in the two adjustments at the two epochs. Velocity field -------------- Geophysical reference motion model ---------------------------------- We used as geophysical reference motion model the more recent one; NNR-NUVEL1A (DeMets et al, 1994) instead of the previous NNR-NUVEL1. The new model differ from the old one by a factor of 0.9562 due to recent recalibration of the geomagnetic time scale. A velocity field was constructed using the NNR-NUVEL1A model containing all the ITRF93 sites. NNR-NUVEL1A is a horizontal motion model. For the consistency of the three-dimensional we used it as three-dimensional model with zero vertical velocity and assumed an error of 3mm/year for the horizontal components and 1 cm/year for the vertical one. NNR-NUVEL1A velocities were deweighted in the combination (with 10 cm/year as a priori standard deviation) for sites whose motion may differ from NNR-NUVEL1A, such as sites in California, Japan, the Mediterranean area and for all sites located on plate boundaries. Consequently, the condition of no-net-rotation is practically applied to those sites which are located on the rigid part of the tectonic plates and whose motion are consistent with that predicted by NNR-NUVEL1A. ITRF93 velocity field --------------------- For a consistency check, we first estimated a provisional velocity field by differenciating ITRF93 coordiantes at the two epochs; 88.0 and 93.0. This provisional velocity field was then compared to the constructed NNR-NUVEL1A velocity field described above. This comparison indicated that there is a small rotation rate between the two, which means that the time evolution of the EOP derived from the two VLBI solutions RG and RN does not follow the NNR-NUVEL1A model. The three rotation rates between the provisional velocity field and NNR-NUVEL1A are listed in Table 3. Table 3 : Rates of the rotation angles from the provisional velocity field to NNR-NUVEL1A __________________________________________________________________________ . . . R1 R2 R3 0.001"/y 0.001"/y 0.001"/y -------- -------- -------- 0.12 0.29 -0.02 +/- 0.01 0.01 0.01 __________________________________________________________________________ The ITRF93 velocity field has been obtained by combination of ten site velocity fields estimated by SLR, VLBI AND GPS analysis centers. These ten velocity fields have been estimated together with ten SSCs among those incorporated in the two ITRF93 station coordinates combined solutions. The method for combining velocities is equivalent to and consistent with the method for combining SSCs into the ITRF93 station coordinates. The consistency between the ITRF93 velocity field and the two epoch station coordinates sets is insured by the following way: - the rates of change of the transformation parameters were computed, from the transformation parameters of these solutions obtained in the two station coordinates combinations (epochs 88.0 and 93.0), - these rates of change were then held fixed for the corresponding solutions in the combination of the velocity fields. On the other hand, the constructed NNR-NUVEL1A velocity field was also incorporated in the combination of the velocity fields. The rates of change of the rotation angles of of this NNR-NUVEL1A velocity field were fixed to the values given in Table 3. ITRF93N velocity field ---------------------- Another velocity field labeled ITRF93N was also estimated and allowed to follow NNR-NUVEL1A as the following: - the data included are the same as for the ITRF93 velocity field, - the rates of change of the transformation parameters were computed, from the transformation parameters of these solutions obtained in the two station coordinates combinations (epochs 88.0 and 93.0), - these rates of change from which the values given in Table 3 were substracted, were then held fixed for the corresponding solutions in the combination of the velocity fields, - the rates of change of the constructed NNR-NUVEL1A velocity field were fixed to zero. Table 4 summarizes the different velocity fields used in the ITRF93 computations. Table 4. The different velocity fields used in the ITRF93 computations _______________________________________________________________________________ Label| Velocity field| Time evolution | Source -----|---------------|----------------|---------------------------------------- NA | NNR-NUVEL1A | NNR-NUVEL1A | Constructed velocity field using | | | NNR-NUVEL1A model for all ITRF93 sites. | | | NAR | NNR-NUVEL1A | Follows the RG | NA velocity field rotated by the | Rotated | and RN EOP time| values given in Table 3 | | evolution | | | | CI1 | Provisional | Follows the RG | Computed from the two SSC | ITRF93 | and RN EOP time| combinatations at epochs 88.0 and 93.0 | | evolution | | | | CI2 | ITRF93 | Follows the RG | Combination of VLBI, GPS, SLR and NAR | | and RN EOP time| velocity fields | | evolution | | | | CIN | ITRF93N | Follows | Combination of VLBI, GPS, SLR and | | NNR-NUVEL1A | NNR-NUVEL1A velocity fields _______________________________________________________________________________ RESULTS ------- We have adjusted combined coordinates in the ITRF93 solution for two epochs; 1988.0 and 1993.0. In total, 290 stations located in 157 sites have been independently adjusted. These coordinates are given in File ITRF93.SSC under the label SSC(IERS) 94 C 01 for epoch 1993.0 File ITRF93.SSC contains also the ITRF93 combined velocity field. These velocities should be used to refer the ITRF93 coordinates from 1993.0 epoch to another desired epoch. This Table gives for each site its DOMES number, name, the individual solutions in which its velocities are available, the cartesian velocities and their standard deviations, the plate and a code : CN for Combined Velocities with NAR velocities, C for Combined velocities with NAR velocities deweighted, and N for NAR velocities. The adjusted transformation parameters were published in Tables T-2 and T-3 of the 1993 IERS Annual Report. They are also available in File ITRF93.TP for epochs 1988.0 and 1993.0. File ITRF93.TP contains also the rate of change of the transformation parameters. These values have to be considered as annual variations to the transformation parameters. So for a given transformation parameter T at an epoch t in years, we have: . T (t) = T(t0) + T. (t - t0) Where t0 is the reference epoch of the used transformation parameters; . . 1988.0 or 1993.0. When T is not given one can assume T = 0. File ITRF93.SSC contains also the ITRF93N velocity field.