Very long baseline interferometry observations made with a 3900 km baseline interferometer (Haystack Observatory in Massachusetts to Owens Valley Observation in California) were used to estimate changes in the X-component of the position of the Earth's pole and in UT1. These estimates are compared with corresponding ones from lunar laser ranging, satellite laser ranging, satellite Doppler, and stellar observations

Clark, T. A.

Coates, R. J.

Corey, B. E.

Counselman, C. C., III

Hinteregger, H. F.

King, R. W.

Ma, C.

Robertson, D. S.

Ryan, J. W.

Shapiro, I. I.

English

NASA Technical Reports Server

POLAR MOTION AND UTl: COMPARISON OF VLBI, LUNAR LASER, 
SATELLITE LASER, SATELLITE DOPPLER, AND 
CONVENTIONAL ASTROMETRIC DETERMINATIONS 
D. S. Robertson 
National Geodetic Survey, NOS, NOAA 
T. A. Clark, R. J. Coates, C. Ma, J. W. Ryan 
NASA, Goddard Space Flight Center 
B. E. Corey, C. C. Counsehuan, R. W. King, I. I. Shapiro 
Department of Earth and Planetary Sciences 
and Department of Physics, 
Massachusetts Institute of Technology 
H. F. Hinteregger, C. A. Knight, A. E. E. Rogers, A. R. Whitney 
Hays tat k Observatory 
J. C. Pigg, B. R. Schupler 
Computer Sciences Corporation 
ABSTRACT 
Very-long-baseline interferometry (VLBI) observations made with a 3900 km baseline interferom- 
eter (Haystack Observatory in Massachusetts to Owens Valley Observatory in California) have been 
used to estimate changes in the X-component of the position of the Earth’s pole and in UTl. These 
estimates are compared with corresponding ones from lunar laser ranging, satellite laser ranging, 
satellite Doppler, and stellar observations. 
33 
https://ntrs.nasa.gov/search.jsp?R=19800020301 2020-03-21T17:50:46+00:00Z
34 RADIO INTERFEROMETRY 
INTRODUCTION 
Significant progress is being made in the technology of measuring the motion of the Earth’s pole 
and the irregularities in the Earth’s rotation. Very-long-baseline interferometry (VLBI), lunar laser 
ranging, satellite laser ranging, and satellite Doppler observations all have the potential of measuring 
the Earth’s orientation with a precision far better than than obtainable with classical techniques. In 
this paper we compare the VLBI determinations of polar motion and Earth rotation with the cor- 
responding results from other techniques and attempt to assess the current state of the art of such 
measurements. 
SENSITIVITY OF VLBI MEASUREMENTS TO 
POLAR MOTION AND UT1 
VLBI delay observations of extra-galactic radio sources are insensitive to translations of the VLBI 
baseline, but are sensitive to some changes in the orientation of that baseline with respect to the 
(planar) radio wavefronts. To specify orientation in space, three angles are generally required; how- 
ever, a baseline is one-dimensional and its orientation in space is specified by two angles. A rotation 
about an axis parallel to the baseline does not change the orientation of the baseline, but rather pro- 
duces at most a translation of that baseline. VLBI observations are therefore insensitive to rotations 
about any axis parallel to the baseline. This result can be expressed analytically as follows: Define 
a Cartesian coordinate system fixed to the rigid Earth, with the Z-axis in the direction of the refer- 
ence pole, the X axis perpendicular to Z in the direction of the Greenwich meridian, and the Y axis 
completing a right-hand triad. The changes in the coordinates of the baseline vector caused by polar 
motion and variations in UT1 can be written as: 
AX = -BY-xz 
AY = ex+yz 
AZ = xX-yY 
where 8 is UTl-UTC in radians, and x and y are the coordinates of the instantaneous pole, also in 
radians. Non-zero values for AX and AY will introduce a sinusoidal signature in the delays observed 
for a non-polar source because of the rotation of the Earth. A non-zero value for AZ will introduce 
a time-independent change in the delays, whose magnitude will depend on the declination of the 
source being observed. For the case of a polar baseline (X = 0, Y = 0) the sensitivity to 0 vanishes, 
and a change in pole position introduces a sinusoid in the delay observations whose amplitude and 
phase can be used to estimate the components of this change in pole position. For the case of an 
equatorial baseline oriented parallel to the plane of the Greenwich meridian (Y = 0, Z = 0) the sen- 
sitivity to the y component of the pole position vanishes. 6’ will introduce a sinusoidal variation in 
the observed delays, and x will introduce a constant offset in those delays. For Y # 0, the VLBI 
observations will be sensitive to a change in the component of the pole that is in the direction of the 
SURVEYS OF THE SEVENTIES 35 
meridian whose plane is parallel to the baseline, and insensitive to a change in the component per- 
pendicular to that plane. Thus for an equatorial baseline, the effects of polar motion and UT1 are 
separable. 
The VLBI measurements discussed in this paper were obtained in 14 separate experiments spread 
between September 1976 and May 1978. These experiments utilized the 37-meter-diameter an- 
tenna at the Haystack Observatory in Massachusetts, and the 40-meter-diameter antenna at the 
Owens Valley Radio Observatory in California. This baseline is nearly parallel to the Earth’s equa- 
torial plane, having a declination of less than 7”, and is even closer to parallel to the plane of the 
Greenwich meridian, making an angle of less than 0?5 with that plane. The interferometric obser- 
vations are therefore sensitive to changes in the X-component of the position of the pole and to 
changes in UT1 and are practically insensitive to changes in the Y-component of the pole. 
POLAR MOTION 
VLBI determinations of the X-component of the pole are shown in figure 1, displayed as differences 
from the corresponding values determined by the Bureau International de 1’Heure (BIH). The VLBI 
values show peak-to-valley excursions from the BIH values of about 80 msec of arc, or a little more 
than two meters. The error bars shown are the formal standard errors, based on an adjustment of 
the measurement errors to yield an rms value of unity for the posttit residuals. Further analysis of 
these data, including detailed studies of effects of clock and atmosphere errors, as well as inclusion 
of some additional data from NRA0 and Onsala (Sweden), may change these values by amounts up 
to a few times the formal standard errors. 
VLBI measurements alone are sensitive only to changes in the pole position and therefore the zero 
point of figure 1 is necessarily arbitrary. It was set by fixing the value of the X-component of the 
pole position at the BIH value for the experiment of October 4-5, 1976. 
Figure 2 shows the two-day average values of the X-component of the pole position determined 
from satellite Doppler observations by the Defense Mapping Agency Hydrographic and Topographic 
Control (DMAHTC). Again, the values are differenced from those of the BIH and are plotted on 
the same scale as before. A clear systematic trend is present which appears to have an annual period 
with an amplitude of about 30 msec of arc; the point-to-point (short-period) scatter has an RMS of 
about 25 msec. In order to better exhibit the systematic trend, we smoothed these data by convolu- 
tion with a Gaussian function whose full-width at half-maximum was 10 days. The result is shown 
in figure 3. 
Figure 4 shows the corresponding determinations of the X-component of the position of the pole 
from laser ranging observations of the LAGEOS satellite. These values were supplied to us by 
D. Smith of NASA’s Goddard Space Flight Center. Figure 5 shows these values smoothed by the 
same filter used to produce figure 3. Again, an annual trend seems to be present. 
36 RADIO INTERFEROMETRY 
+ 
t 
+ 4 
.+-i, .---._- __..__._.. -  _ ..^.._. ._._.__. - __._ ._ ? ....._: .--..-_. _..._..._ .__ --.._. __ 
; I$ . ..--. J -..- ---A- .-...- ‘--.--- ..,. -.. _-.. .I--- 
1 NOY JAN tlRR mr JUL 
lB76 1377 
Figure 1 . 
t 
t 
Ft 
t 
I 
-1 
3 
-. --I-.- - ._.. c. - _ -.I. . -.I - .--A. 
SW NlW Jflfl ntls nflr 
lI7U 
1376 
Figure 2. 
SURVEYS OF THE SEVENTIES 37 
, 
? 6EP -.NOV 
.J --C-L--L- 
JflN tlm tlRY JUL 6EP NOV JRN tlfw IIAY 
1976 1977 197B 
Figure 3. 
-AI IL--- 
1377 
Figure 4. 
1370 
38 RADIO INTERFEROMETRY 
“RR bnr 
Figure 5. 
Figure 6 shows the corresponding determination of the X-component of the position of the pole as 
determined by the International Polar Motion Service (IPMS) in Misuzawa, Japan. The IPMS em- 
ploys only classical optical observations (PZT, VZT, etc.). Even here, the annual trend away from 
the BIH is clear. 
Each of the figures of differences in estimates of pole position has a different bias. This bias can be 
removed by redefining the “zero point.” (In fact, this procedure was used /for the Doppler, satellite 
laser, and IPMS values, but for different spans of data.) Shifting each set of differences shown in 
our figures by the mean value of its difference from the corresponding values from the Doppler set 
yields figure 7. The consistency of the amplitudes and phases of the annual terms is quite clear. 
In order to evaluate quantitatively the short-term differences between the results from the different 
techniques, we can calculate the RMS deviation about the mean of the differences between the cor- 
responding members of each pair of results, for the dates in common. The results of these calcula- 
tions are tabulated in matrix form in table 1. The first value in the matrix indicates a 9 msec RMS 
difference between the VLBI and the Doppler estimates of the position of the pole. Since the ex- 
pected standard error in the Doppler estimates of - 10 msec, and the average formal standard error 
of the VLBI estimates is -3 msec, the RMS difference is about what one would expect. Although, 
admittedly, there are only 13 VLBI estimates, this RMS difference does indicate that the systematic 
errors in the Doppler estimates are not contributing significantly to the total errors. The other 
values in the table are consistent with the errors in the satellite laser ranging estimates of the pole 
position being - 12 msec, the corresponding IPMS errors - 15 msec, and the BIH errors -25 msec. 
SURVEYS OF THE SEVENTIES 39 
----L.----.~-.L---L.----l- A---_ L-d.-.-.-.,--.--. L--- 
IP NOV JAN nm my JUL CEP NW JRN nm nflr 
Figure 6. 
-I 1 
JRN man nnr - 
1976 1977 197D 
Figure 7. 
40 RADIO INTEREEROMETRY 
The anomalously large RMS difference between the VLBI and the BIH estimates is due to the dis- 
tribution of the VLBI values in time. The epochs of most of the VLBI observations were close to 
the extrema of the annual error in the BIH estimates. 
Table 1 
RMS Deviations about the Mean of the Differences between the Determinations 
of the X-Component of the Pole by Various Monitoring Techniques 
VLBI Doppler 
Satellite 
Laser IPMS BIH 
VLBI 
Doppler 
Satellite Laser 
IPMS 
BIH 
Corrected BIH 
- 
9 ms - 
12ms 14ms 
16ms 15ms 18ms - 
30 ms 23 ms 24 ms 27 ms - 
16 ms 11 ms 17nns 19 ms 15ms 
In May 1979, the BIH altered this picture by announcing that it would introduce an ad hoc correc- 
tion to its X-component values in the form of an annual term and a semi-annual term. The form of 
the correction is displayed in figure 8. After application of this correction, the RMS difference 
between the BIH estimates and those from the other techniques are displayed in the last line of 
table 1. The errors in the BIH estimates of the X-component of the position of the pole appear to 
have been reduced by the correction to about the level of the errors in the IPMS values. 
UT1 
Figure 9 displays the differences between the VLBI determinations of (UTl-UTC) and the BIH de- 
terminations. As with the values of pole position, completion of a more detailed analysis of the 
VLBI observations may lead to changes in these estimates of (UTl-UTC) by amounts up to several 
times the formal standard errors. Nonetheless, the general trends in the differences from the BIH 
estimates are probably significant. 
Lunar laser ranging data have also been employed to determine variations in UTl. The UT1 varia- 
tions were modeled as a piece-wise linear function, as described by King et al. (1978). To compare 
the lunar laser ranging values with the VLBI values, the laser values were converted to UT1 from 
UT0 at the McDonald Observatory by using the estimate of the position of the Earth’s pole as deter- 
mined from the Doppler observations. Figure 10 shows the lunar laser values compared to the 
VLBI values which have been adjusted to allow for a different value used for the precession con- 
stant in the lunar laser program. 
SURVEYS OF THE SEVENTIES 
0 , 0 -..-. - ~..--. 
2 
4 
=: 
0 - LA. I 
i?~ 6EP NOV JRN tlRR nflv JUL SEP NOV JRN HRR my 
n 
r; t t 
t 
CJ 
f 
w T 
1976 1977 
Figure 8. 
19711 
cl 
LA _ -. _. --.-- 
CJ 
-i t 
t 
k- 
= -t c) LL: 0 
t: 
t t 
rm 9 --- =ce. 1 
ti 
. -----.I----------- ---__----..- ._._._. - 
t t 4- 
7 
CI , .I I -A- -A-. --A ----I.- -I-_ L-.--I--1 ____ A--- 
7 6EP NOV JRN HRR nar JUL 6EP NOV JRN MN? nar 
1976 1977 1170 
Figure 9. 
41 
42 
, 
, 
L 
RADIO INTERFEROMETRY 
I I I -- .I ..A-I.-- 
7 6EP NOV JAN tlRR HRY JUL SEP NOV JRN tlm URY 
1976 lB77 1970 
Figure 10. 
The RMS differences between the lunar laser and the BIH values and between the VLBI and the 
BIH values are both 1.6 msec, but the difference between the VLBI and the lunar laser values is only 
0.8 msec. 
Although the general agreement between the VLBI and the lunar laser values is good, more regular 
monitoring of Earth rotation with VLBI is necessary to establish the significance of any small 
(>2 msec) differences between the BIH values and those from VLBI and lunar laser ranging. 
The BIH has also published an annual and a semi-annual correction term for its UT1 values. The 
form of this correction is shown in figure 11. With this correction included, the RMS differences 
between the BIH and the VLBI and lunar laser results are 1.3 msec and 1.1 msec, respectively, still 
larger than the corresponding difference between the VLBI and the lunar laser ranging estimates of 
UTl. 
- 
SURVEYS OF THE SEVENTIES 43 
c) I I I L I II- 
7 6EP NW JRN tlflR IIRY JUL 6EP NOV JRN tlRR IlflY 
1976 1977 1sis 
Figure 11. 
CONCLUSIONS 
The determination of the position of the Earth’s pole from satellite Doppler and satellite laser 
ranging observations are approaching an accuracy of - 10 msec of arc (30 cm). The VLBI determi- 
nations may have better accuracy, although a determination of whether the VLBI accuracy is 
indeed better, and by how much, must await the collection and analysis of a far larger set of VLBI 
data. 
The comparison of lunar laser ranging and VLBI determinations of UT1 suggests that the RMS of 
the uncertainties in each set are under 1 msec. 
All of these comparisons have been hampered by the paucity of VLBI data. To rectify this prob- 
lem, the National Geodetic Survey has undertaken Project POLARIS whose object is to obtain 
VLBI data at least several times per week, starting in 1982. 
44 RADIO INTERFEROMETRY 
REFERENCE 
King, R. W., C. C. Counselman, and I. I. Shapiro, Universal Time: Results from Lunar Laser Rang- 
ing, J. Geophys. Res., 83, 3377-3381, 1978. - 
A REVIEW OF CONNECTED ELEMENT RADIO INTERFEROMETRY 
DIRECTED AT ESTABLISHING 
AN ALMOST INERTIAL REFERENCE FRAME 
K. J. Johnston 
E. 0. Hulburt Center for Space Research 
Naval Research Laboratory 
ABSTRACT 
The present status of connected element radio interferometry towards establishing an accurate grid 
of positions of extragalactic radio sources is reviewed. Many of the problems being encountered are, 
in general, also faced by very long baseline interferometry (VLBI). 
45 


Polar motion and UT1:  Comparison of VLBI, lunar laser, satellite laser, satellite Doppler, and conventional astrometric determinations

Polar motion and UT1: Comparison of VLBI, lunar laser, satellite laser, satellite Doppler, and conventional astrometric determinations

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server