Phase delay solution of geodetic VLBI experiments at baseline HART15M/HARTRAO

Phase delay solution of geodetic VLBI experiments at baseline HART15M/HARTRAO

There were five very short baseline radio interferometry experiments at 113 m long baseline HARTRAO/HART15M. I took visibility data that the Bonn geodesy group provided to me, and processed the data. At baseline that short, propagation effects in atmosphere do not affect our ability to resolve phase delay ambiguities. I resolved phase delay ambiguities and compared geodetic solutions that uses X band group delays and X band phase delays. Here is the table of results of determination of baseline length:

                                         Baseline length (mm)
                                         X-band Phase-del      X-band Group-del
r1598  2013.08.12  HART15M / HARTRAO     113096.77 -+  0.47    113093.94 -+ 0.82  
r1600  2013.08.26  HART15M / HARTRAO     113096.39 -+  1.06    113096.09 -+ 1.12
r1602  2013.09.09  HART15M / HARTRAO     113096.82 -+  0.35    113095.59 -+ 0.09  
r1604  2013.09.24  HART15M / HARTRAO     113094.47 -+  1.67    113094.99 -+ 6.63   6 hours
r1607  2013.10.15  HART15M / HARTRAO     113096.79 -+  0.48    113096.30 -+ 1.56

NB: experiment on 2013.09.24 had only 6 hours of data. If to discard this experiment, the scatter in four experiments has peak-to-peak variations 400 microns. Of course, I am well aware that 4 points are not sufficient to draw a statistical inference, but nevertheless results are encouraging. Similar, sub-mm scatter was found in processing 10 experiments at the 67 meter long baseline TIGOWTZL/WETTZELL.

I estimated coordinates of HART15M, axis offsets of both stations, clock function modeled with B-spline of the 1st degree, and the atmosphere path delay for HART15M, constant over an experiment. Here are estimates of the atmosphere path delay.

                                          Estimate   Uncertainty   Theor pred
HART15M  AT 0 2013.08.12-16:59:25.416     9.005 ps      1.406 ps   9.61 ps
HART15M  AT 0 2013.08.26-16:59:51.336     8.538 ps      3.284 ps   9.53 ps
HART15M  AT 0 2013.09.09-17:00:43.176     8.041 ps      1.180 ps   9.23 ps
HART15M  AT 0 2013.09.24-16:59:34.056    -5.177 ps     19.981 ps   9.27 ps
HART15M  AT 0 2013.10.15-16:59:34.056    11.217 ps      2.065 ps   9.41 ps

We see significant(except experiment r1604) positive path delay that is scaled as a mapping function. What is its origin? Radio waves from the sources propagate parallel to HART15M and HARTRAO. The mapping function is the same for both stations. Checking the height of the reference point, we see that the reference point if HARTRAO is 6.304 meter higher. At barometric pressure 86000 Pa, the refractivity index, defined as (c-v)/c, is 2.35 · 10^-4. Radio wave traveling distance 6.304 meter in a medium with refractivity 2.35 · 10^-4 delays at 4.9 ps. We have correct sign (HART15M is lower than HARTRAO, therefore radio waves coming from the sky have a longer distance to travel), but we explain only 60% of the estimate.

Thinking a little bit further, I recollected that both antenna have a significant axis offset. HART15M has azimuth mounting, and the height of the elevation axis is the same as the height of the reference point. But HARTRAO has equatorial mounting. Its declination axis is 6.6907 · cos φ meter above the reference point. This effect closes the gap between the estimated value of the path delay and theoretical. We can compute the path delay due to differences in height between movable axes of two HART antennas using numerical weather models. I used GEOS-FP model. Theoretical predictions are given in the last column. The agreement is within 1–2 ps for all experiments, except a 6 hour long r1604.

Happy end? Not, well. Phase delays have a potential to provide much more precise solutions. Their uncertainties are at a level of 0.1—0.3ps. But we see the scatter has peak-to-peak variations at a level of ± 20 ps: The residuals versus time, elevation angle, azimuth, parallactic angle do not show any recognizable pattern. I can only speculate what may cause scatter with rms 6–8 ps: a) jitter in clock (H-maser, distributor, cables, and other parts of VLBI hardware); c) polarization leakage; d) geometrical effects. Sampoilenko noted that analysis of the entire dataset of his survey measurements of Simeiz antenna suggests that antenna azimuth antenna move along a cone. Antenna motion at sub-millimeter accuracies may be more complicated than we used to think.

Back to Leonid Petrov's discussion page.

Last update: 2013.11.19_21:40:48