File : ITRF94.REPORT
ITRF94 DATA ANALYSIS
CONTENTS:
-INTRODUCTION
-ANALYSIS PER TECHNIQUE OF CLASS I SOLUTIONS
-THE ITRF94 SOLUTION
-STATION CLASSIFICATION
-ITRF94 RESULTS
-CONSISTENCY OF EOP WITH TERRESTRIAL AND CELESTIAL REFERENCE FRAMES
-ANALYSIS OF THE ITRF94 RESULTS
INTRODUCTION
------------
As a new step for improving the ITRF products, we used in the ITRF94
computation full covariance information of the individual solutions.
The ITRF94 solution is based on a combination of a selected sets
of individual solutions (class I) submitted to the IERS Central Bureau. This
combination includes VLBI, GPS, SLR and DORIS solutions. Notice that DORIS
solutions are included for the first time in the ITRF computations.
All the selected individual solutions contain estimated station
positions and velocities, and they are provided with full covariance
information in ISEF1 format (a subset of the new SINEX format).
ANALYSIS PER TECHNIQUE OF CLASS I SOLUTIONS
-------------------------------------------
Several specific analyses within each technique have been undertaken in
order to assess the relative quality of the different solutions and their
behaviour with respect to each other. Moreover these analyses lead to the
estimation of the Matrix Scaling Factor.
Many comparisons and combinations of solutions per technique were
performed. For each comparison/combination, we concentrated our analysis on
two specific (among other) parameters:
- the Factor of Unit Variances (SIG0: sigmas zero) of the entire
comparison/combination, and
- the Factor of Unit Variances per solution (labeled NSX2, see below),
computed by taking into account the correlations between the estimated
parameters.
In theory, the SIG0 should be 1 and the values of NSX2 of the solutions
incorporated in the comparison/combination should be equal and not far from the
unity. Practically, these two conditions could be easily satisfied in case of
two solutions, by repeating the comparison and varying the Matrix Scaling
Factors till we have identical NSX2 for the two solutions. But the two
conditions are more difficult to satisfy in case of 3 or more solutions.
In this second case, two types of analysis per pair of solutions have been
performed:
- comparisons per pair of solutions over all common points.
- comparisons per pair of solutions over common points of the 3 solutions.
Based on these two types of analysis, one combination per technique
has been adopted as optimal combination, yielding so the Matrix Scaling Factor
for each individual solution. Table 1 to 4 list the statistical numbers for
each optimal combination per technique. Note that all these combinations were
performed at epoch 1993.0. The captions of these tables are:
N : Number of common points
SP : 2-D unweighted RMS
SU : Vertical unweighted RMS
SX : 3-D unweighted RMS
WSP : 2-D Weighted RMS
WSU : Vertical Weighted RMS
WSX : 3-D Weighted RMS
NSX1 : Factor of Unit Variances per solution, without taking into
account the correlations between the estimated parameters
NSX2 : Factor of Unit Variances per solution, taking into
account the correlations between the estimated parameters
F : Matrix Scaling Factor
Table 1 : Global Residuals of the VLBI Combinaison at 93.0
SIG0 = .9159
N SP SU SX WSP WSU WSX NSX1 NSX2 F
cm cm cm cm cm cm
--------------------------------------------------------------------
(USNO) 95 R 04 80 2.4 4.1 3.1 .3 .4 .3 .87 .94 2.2845
(GSFC) 95 R 01 116 1.4 5.7 3.5 .4 .5 .4 .63 .84 3.6546
(NOAA) 95 R 01 111 .9 4.1 2.5 .7 1.1 .8 .61 1.19 4.8444
(JPL) 95 R 01 6 .5 1.5 .9 .4 1.1 .7 .82 .83 1.5000
Table 2 : Global Residuals of the GPS Combinaison at 93.0
SIG0 = .9690
N SP SU SX WSP WSU WSX NSX1 NSX2 F
cm cm cm cm cm cm
--------------------------------------------------------------------
(JPL) 95 P 02 38 .3 1.2 .7 .2 .8 .5 1.11 1.01 7.9736
(EMR) 95 P 02 25 4.4 5.3 4.7 1.5 3.7 1.6 .86 1.16 20.4648
(CODE) 95 P 02 40 .9 .6 .8 .6 .4 .5 .92 .88 .0577
Table 3 : Global Residuals of the SLR Combinaison at 93.0
SIG0 = 1.0000
N SP SU SX WSP WSU WSX NSX1 NSX2 F
cm cm cm cm cm cm
--------------------------------------------------------------------
(CSR) 95 L 01 76 3.1 9.3 5.9 .8 1.2 1.2 1.00 1.00 1.6071
(DUT) 95 C 02 76 3.2 1.1 2.7 .5 1.0 .7 1.00 1.00 1.6071
Table 4 : Global Residuals of the DORIS Combinaison at 93.0
SIG0 = 1.0000
N SP SU SX WSP WSU WSX NSX1 NSX2 F
cm cm cm cm cm cm
--------------------------------------------------------------------
(IGN) 95 D 01 49 2.5 1.9 2.3 1.7 1.5 1.7 .67 .85 6.2906
(CSR) 95 D 01 47 2.8 2.8 2.8 1.9 1.5 1.7 .62 .85 1.7474
(GRGS) 95 D 01 47 3.3 2.6 3.1 2.1 2.1 2.2 1.14 1.25 15.7266
THE ITRF94 SOLUTION
-------------------
The ITRF94 computations consist on station postion combinations
at two different epochs: 1988.0 and 1993.0. Each individual covariance matrix,
scalled by the F factor (see Tables 1 to 4 above ), was computed for these two
epochs using the full covariance matrix between positions and velocities. Some
positions have been rejected from some individual solutions if they:
- have their velocities fixed, and
- the observation epochs occur before 1991.0 for the 93.0 combination, or
- the observation epochs occur before 1986.0 and after 91.0 for the 88.0
combination.
In the two combinations at 88.0 and 93.0, local ties have been
introduced with proper variances (see file iers.ecc). We selected one or more
reference points per site to which other points are tied, yielding so one or
more local tie sets: A, B, C, etc. All these sets were included in the
combination providing that at least one point of each set is available in at
least one spatial individual solution.
The datum definition of the ITRF94 is ensured by the following:
- the origin is a weighted average of a selection of SLR and GPS
solutions
- the scale is a weighted average of a selection of VLBI, SLR and GPS
solutions.
- the orientation is consistent with the ITRF92 (not the ITRF93) at
1988.0 epoch,
- the time evolution is consistent with the geophysical model
NNR-NUVEL1A.
The ITRF94 solution was performed using the following steps:
1- A global combination at epoch 1993.0 has been done, holding to
zero the seven transfomation parameters of the SLR solution
SSC(CSR) 95 L 01 (labeled hereafter LC);
2- The same combination as in step 1 has been done at epoch 1988.0;
3- A Provisonal Velocity Field has been derived from the above two
combinations;
4- The solution obtained in step 2 has been compared to the ITRF92
at epoch 1988.0 considering only one point per site;
5- The Provisional Velocity Field obtained in step 3 was then compared
to the geophysical model NNR-NUVEL1A in order to estimate the 7 rates
of the transformation parameters between the two, which are:
FROM (ITRF94 Provisional Velocity Field) TO NNR-NUVEL1A
. . . . . . .
T1 T2 T3 D R1 R2 R3
cm cm cm 10**-8 0.001" 0.001" 0.001" /y
---------------------------------------------------
.10 -.12 .14 -.053 -.138 -.222 .032
+/- .03 .03 .03 .009 .011 .011 .009
6- The combination at epoch 88.0 has been repeated, holding for LC:
- the 3 translations and scale factor to zero;
- the 3 rotations to the values determined in step 4 which are:
R1(88.0) = -.15 (0.001")
R2(88.0) = 1.30
R3(88.0) = -.87
7- The combination at epoch 93.0 has been repeated, holding for LC:
- the 3 translations and the scale factor to zero to which we added
the corresponding rates determined in step 5 over 5 years;
- the 3 rotations to the values determined in step 4 to which
we added the rotation rates determined in step 5 over 5 years.
8- Weighted averages for the origin and the scale have been estimated
based on the following solutions:
- for the origin and scale: SSC(JPL) 95 P 02, SSC(CODE) 95 P 02 and
SSC(DUT) 95 C 02;
- for the scale: SSC(GSFC) 95 R 01, SSC(NOAA) 95 R 01 and
SSC(USNO) 95 R 04
9- The two combinations at epochs 88.0 and 93.0 (steps 6 and 7) were
finally repeated, but correcting the translations and the scale
factor fixed for LC by the values obtained in step 8. The scale
factor was also corrected by (0.7 x 10**-9) in order to be
consistent with IUGG/IAU resolutions.
10- The ITRF94 velocity field was finally estimated from the two
combinations of step 9.
STATION CLASSIFICATION
----------------------
An effort has been made to classify the ITRF94 stations in order to
help users for estimating the quality of station coordinates they may be use.
For this analysis, we tried to distinguish four classes: A, B, C and Z (see
file ITRF94CLA).
ITRF94 RESULTS
--------------
The ITRF94 adjusted coordinates at epoch 1993.0 were split into four
tables according to their calsses. They are available in the files:
ITRF94.SSCA, ITRF94.SSCB, ITRF94.SSCC and ITRF94.SSCZ. Velocities are available
for all stations of class A as well as for most os stations of class B and C.
These velocities have to be used to refer the ITRF94 coordinates from
1993.0 epoch to another desired epoch.
File ITRF94.TI contains the adjusted transformation parameters at
epoch 1993.0 as well as the rates of class I solutions . The rates 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 - 1993.0) (1)
File ITRF94.TII contains the transformation parameters from the ITRF94
to the individual solutions of class II. These parameters were obtained by
comparison of the ITRF94 and each solution at the epoch of the latter one.
File ITRF94.TX contains transformation parameters from ITRF94 to
previous ITRF's and other frames.
CONSISTENCY OF EOP WITH TERRESTRIAL AND CELESTIAL REFERENCE FRAMES
------------------------------------------------------------------
Let us consider two series of EOP, each of which is referred to
a celestial frame defined by the adopted Radio Source Coordinates (RSC)
and to a terrestrial frame defined by the adopted Set of Station
Coordinates (SSC). The systematic differences in the pole coordinates
(dPsi, dEps), in universal time (dUT1), and in the celestial pole offsets
(Ddy, Dde) due to the rotations (A1, A2, A3) between the two celestial
frames and (R1, R2, R3) between the two terrestrial frames are given
by the relationships (Zhu and Mueller, 1983) :
dx = R2 - A1 sin q + A2 cos q
dy = R1 + A1 cos q + A2 sin q
f.dUT1 = -R3 + A3 (2)
DdPsi = A2/sin e
DdEps = -A1
where q is the sidereal time, f is the conversion factor from universal
time to sidereal time, and e is the obliquity of the ecliptic. The
dependence of dx, dy on the celestial frames angles A1, A2 are
diurnal terms which are not accessible to the present analysis.
The relationships (2), applied to the comparison of the data sets
described in Table II-1 of the 1994 IERS Annual Report, p. II-14,
with EOP(IERS) C 01 on the one hand, and the comparisons of the
related reference frames to RSC/SSC(IERS) 95 C 01 on the other hand
can be used to characterize the internal consistency of the set
of IERS results, time series and reference frames.
When considering two terrestrial frames, each one having its own
velocity field, and the corresponding series of EOP, the relative drifts
dx', dy', dUT1' between the series of EOP can be predicted by
relationships (3), obtained as the time derivatives for the first three
relationships (2):
dx' = R'2 ; dy' = R'1 ; dUT1' = -R'3 (3)
where R'1, R'2, R'3 are the rates of change of the rotation angles
between the two terrestrial reference frames. These relationships are used
to compare the drifts of the EOP series relative to EOP(IERS) C 01 are
compared with their predicted values derived from the rates of
change of their rotation angles relative to the ITRF94 velocity field.
Tables ITRF94_EOP CONSISTENCY (a) and (b) give the evaluations
of internal consistency for the Class I individual terrestrial frames using
relationships (2) and (3). The celestial frames angles are those in
Table C-2, p. II-26 of the 1994 IERS Annual Report. The terrestrial
frames angles and their rates of change with time come from
Table ITRF94.TI. The closures for x, y, UT1-UTC are computed at 1993.0.
Based on these closures for the earth-rotation series used to derive
EOP(IERS) C 01 in 1984-1994, an estimation of the inconsistency
of EOP(IERS) with the IERS reference frames is given in Table 5 and
plotted on Figures 1 and 2.
Table 5.CONSISTENCY OF THE IERS EOP SERIES WITH THE IERS REFERENCE FRAMES:
the value to add to EOP(IERS) time series in order to make them
consistent with the 1994 realizations of the IERS terrestrial and
celestial reference systems is A+A' (t-1993.0), t in Besselian years.
(@ stands for + or -).
-------------------------------------------------------------------------
Cor x y UT1 dPsi dEps
0.001" 0.001" 0.0001s 0.001" 0.001"
-------------------------------------------------------------------------
A -0.05 @0.28 +0.76 @0.29 -0.42 @0.16 -0.01 @0.07 0.00 @0.03
A' +0.12 @0.07 +0.11 @0.07 0.04 @0.05 - -
-------------------------------------------------------------------------
For Class II individual terrestrial frames, comparisons based on
equations (2) are given in Table ITRF94_EOP.CONSISTENCY (c), for the
epochs of the terrestrial frames.
ANALYSIS OF THE ITRF94 RESULTS
------------------------------
The quality analysis of the ITRF94 results was based more specifically
on global residuals per solution (Table 6) as well as per site. All residuals
on a site-by-site basis resulting from the combination at 93.0 are available
in file ITRF94.RESIDUALS. For sites of calss A and B, position and velocity
residuals are ploted in figures: files in gif format are available under the
form:IERSDxxxxxA.gif where xxxxx is the DOMES number.
Table 6: Global ITRF94 residuals per solution at epochs 88.0 and 93.0
Positions at 88.0 Positions at 93.0
SSC LABEL N(88) WSP WSU WSX N(93) WSP WSU WSX
cm cm cm cm cm cm
----------------------------------------------------------------------------
(GSFC) 95 R 01 RG 110 0.4 0.8 0.6 109 0.4 0.7 0.6
(JPL) 95 R 01 RJ 8 1.0 3.7 2.1 8 0.8 3.2 1.9
(NOAA) 95 R 01 RN 98 0.5 1.1 0.8 94 0.6 0.9 0.7
(USNO) 95 R 04 RO 68 0.9 1.1 0.7 72 0.3 0.6 0.4
(CODE) 95 P 02 PB 41 1.7 0.8 1.4 55 0.6 0.8 0.7
(EMR) 95 P 02 PE 11 5.3 14.5 8.0 25 2.0 4.7 2.0
(JPL) 95 P 02 PJ 44 1.4 3.5 2.3 45 0.3 0.8 0.5
(CSR) 95 L 01 LC 67 0.9 2.2 1.4 71 0.8 1.2 1.1
(DUT) 95 C 02 CU 78 0.8 1.4 1.0 85 1.0 1.8 1.3
(CSR) 95 D 01 DC 47 6.4 7.0 6.7 47 1.8 2.0 1.8
(GRGS) 95 D 01 DR 42 4.7 4.2 4.7 49 2.8 2.8 2.8
(IGN) 95 D 02 DH 52 7.0 7.3 7.1 52 1.9 2.0 1.9