[Difx-users] On delay modelling

Mon Apr 24 11:26:33 EDT 2017

Hi Mugundhan,

Maybe I can add a little to what Adam has said. I recommend you download
the IERS Conventions (2010) technical note
(https://www.iers.org/TN36) for more details. But briefly, the calc
programs compute a terrestrial-to-celestial rotation matrix
at the desired epoch using the value of UT1 at that epoch and smaller
rotations for polar motion and precession/nutation.
It also computes the first and second time derivatives of that rotation
matrix. The X,Y, Z site positions, velocities and accelerations
are then rotated into the J2000 celestial reference frame. Then some
elastic and other corrections are computed and applied at
each station - such as the solid earth tide, the ocean loading, the pole
tide, short period UT1 and polar motion corrections, etc.
An atmosphere delay is also computed. We use the 'concensus' delay model,
described in chapter 11 of the conventions.
The source vector used is the un-abberrated direction to the source as seen
from the solar system barycenter. Corrections for
aberration and the retarded baseline are contained in the concensus model.
The 'geocenter'  is just the (0,0,0) point in the
VLBI reference frame (which we try to align with the ITRF), but does not
strictly represent the earth's center of mass. It only
needs to be the same point for all the antennas in a correlation.

Cheers,
David (David.Gordon-1 at nasa.gov)

On Mon, Apr 24, 2017 at 3:19 AM, Mugundhan vijayaraghavan <
v.vaishnav151190 at gmail.com> wrote:

> Hi Adam,
>
> Thank you so much for the clarifications.
>
> Regards,
>
> Mugundhan
>
> On Mon, Apr 24, 2017 at 12:44 PM, Adam Deller <adeller at astro.swin.edu.au>
> wrote:
>
>> Hi Mugundhan,
>>
>> Since the x axis of the ITRF is nominally aligned with longitude 0 on the
>> Earth, if you want to think of things in terms of hour angles then yes the
>> hour angle will be GMST.  You don't then make any further adjustment for
>> the latitude and longitude of the observing stations.  To be properly
>> precise, though, you will have to take into account precession and nutation
>> as well as polar offset (orientation of the Earth in space c.f. the best
>> model including precession and nutation) and UT1-UTC (Earth's rotational
>> phase c.f. "average").  They are changing the tilt and rotation of the xyz
>> ITRF frame with respect to the J2000 positions, which you can "undo" by
>> offsetting the hour angle and declination of the source very slightly.
>>
>> Cheers,
>> Adam
>>
>> On 24 April 2017 at 14:41, Mugundhan vijayaraghavan <
>> v.vaishnav151190 at gmail.com> wrote:
>>
>>> Dear Adam,
>>>
>>> Thank you for your clarifications.
>>>
>>> One more question:
>>> The unit vector \hat(s) originates from the center of the earth, in this
>>> case, the hour angles of the sources will have to be calculated as GMST-RA
>>> ? In this case, do we have to offset the obtained hour angles and the
>>> declination by the lat and long of the observing stations ?
>>>
>>> Thank you,
>>>
>>> Mugundhan
>>>
>>> On Mon, Apr 24, 2017 at 6:10 AM, Adam Deller <adeller at astro.swin.edu.au>
>>> wrote:
>>>
>>>> Hi Mugundhan,
>>>>
>>>> On 21 April 2017 at 15:30, Mugundhan vijayaraghavan <
>>>> v.vaishnav151190 at gmail.com> wrote:
>>>>
>>>>> Dear All,
>>>>>
>>>>> I have a few queries about how delay modelling is carried out in VLBI
>>>>> for compensating the same.
>>>>>
>>>>> 1.) The geometric delay is calculated as tg=*b.s*, where *b *is the
>>>>> baseline vector and *s *is the source vector. Lets say I have two
>>>>> antennas, both located about 100 kms apart. How do standard VLBI delay
>>>>> modelling software calculate this delay ? Based on some preliminary reading
>>>>> I understood that the baseline distance are first calculated referenced to
>>>>> the earth center, if this is done, are delays estimated assuming the earth
>>>>> center to be the phase reference ? How is this earth centered reference
>>>>> then transformed to the celestial frame ? because both *b *and *s *must
>>>>> be in the same coordinate system for carrying out a dot product operation,
>>>>> right ?
>>>>>
>>>>
>>>> VLBI delay modeling is very complicated, involving considerably more
>>>> than just a *b.s* operation.  Other propagation effects are taken into
>>>> account too, and the length of the baseline *b* is changing with time
>>>> due to tidal forces and what-not, plus the whole system is wobbling around
>>>> due to the changing earth orientation.
>>>>
>>>> But stripping it back to the minimum: yes, the Earth centre is usually
>>>> used as the reference.  Look up the International Terrestrial Reference
>>>> Frame (ITRF) to see the definition of the axes.  Then you obviously need to
>>>> know the *time* (and the Earth orientation parameters) to figure out
>>>> where the unit vector \hat(s) that points at the direction of the source is
>>>> pointing in this reference frame.  For each telescope, we then compute the
>>>> station-based delay from the telescope back to the geocentre at the desired
>>>> instant of time, and each telescope's data stream is delayed by the
>>>> computed amount (rather than shifting only one data stream by the
>>>> difference between \tau_a and \tau_b).  That's what it means to use the
>>>> geocentre as the reference.
>>>>
>>>>
>>>>>
>>>>> 2.) In some books/articles i find a reference to a RA and Dec of
>>>>> Baseline ? What does this physically mean ? I'm not able to visualize this
>>>>> clearly. any help will be greatly appreciated !
>>>>>
>>>>
>>>> Like I said above, it makes more sense to figure out where the source
>>>> unit vector is pointing relative to a telescope coordinate system.  You can
>>>> equivalently rotate the telescope coordinates and keep the source unit
>>>> vector fixed, but that is (I think) less intuitive.
>>>>
>>>>
>>>>>
>>>>> 3.) In the complete delay model, tm, which is the sum of geometric
>>>>> delay+clock delay+ionospheric/atmospheric delay+fixed delays due to analog
>>>>> component, the fastest varying component will be geometric delay only, once
>>>>> this is compensated, if the other quantities are contributing to some
>>>>> excess time varying delay, this will be seen as a residual fringe. Now, for
>>>>> clock delay, is this estimated using the allan deviation of the clock being
>>>>> used? Lets say my clock loses 10^-9 seconds in 30 minutes, and if I sample
>>>>> my signal at 16 MHz which is ~ 62.5 ns, will I be able to integrate the
>>>>> data without any degradation due to clock upto 30 minutes ?
>>>>>
>>>>>
>>>> The sampling time is irrelevant.  It's the sky frequency that
>>>> determines the visibility phase.  Your signal might only be 16 MHz wide,
>>>> but if you were observing at 100 GHz then a change of 1 nanosecond
>>>> translates to 100 turns of phase.  So in that example you could only
>>>> integrate for maximally a fraction of a second.  Normally VLBI clock drifts
>>>> are monitored to a level of at worst a few ns/day or so. If they are
>>>> unknown then a test correlation is performed to determine the clock offset
>>>> and drift, and then the observation is recorrelated having applied the best
>>>> available clock model.
>>>>
>>>>
>>>>> 4.) There is also an associated baseline velocity component which will
>>>>> lead to a time difference between the wavefronts received at both the
>>>>> antennas. Is this baseline velocity the same as the orbital velocity of the
>>>>> earth ? Or is this modelled differently ?
>>>>>
>>>>>
>>>> By delay tracking to the geocentre, this problem is naturally taken
>>>> into account. When you use the geocentre, you are automatically forced to
>>>> account for the rotation of the reference frame between the time the signal
>>>> is received at the antenna and the time that it would pass through the
>>>> geocentre.  So you've corrected for the velocity of both of the stations,
>>>> rather than their difference.  The process is known as retarded baseline
>>>> correction.
>>>>
>>>> Unfortunately the documentation for VLBI delay packages is not
>>>> extensive.  You can look up CALC (https://lupus.gsfc.nasa.gov/s
>>>> oftware_calc_solve.htm) or VTD (http://astrogeo.org/vtd/) but neither
>>>> have an excellent explanation of the theory.
>>>>
>>>> Cheers,
>>>> Adam
>>>>
>>>>
>>>>> I would greatly appreciate if the experts here clarify my doubts.
>>>>> Kindly do point me to references that may lead to clarification of these
>>>>> doubts too !
>>>>>
>>>>> Thanking you,
>>>>> With best regards,
>>>>>
>>>>> Mugundhan V.
>>>>>
>>>>>
>>>>> _______________________________________________
>>>>> Difx-users mailing list
>>>>> Difx-users at listmgr.nrao.edu
>>>>> https://listmgr.nrao.edu/mailman/listinfo/difx-users
>>>>>
>>>>>
>>>>
>>>>
>>>> --
>>>> !=============================================================!
>>>> Dr. Adam Deller
>>>> ARC Future Fellow, Senior Lecturer
>>>> Centre for Astrophysics & Supercomputing
>>>> Swinburne University of Technology
>>>> John St, Hawthorn VIC 3122 Australia
>>>> phone: +61 3 9214 5307 <+61%203%209214%205307>
>>>> fax: +61 3 9214 8797 <+61%203%209214%208797>
>>>>
>>>> office days (usually): Mon-Thu
>>>> !=============================================================!
>>>>
>>>
>>>
>>>
>>> --
>>> the giver of moksha
>>>
>>
>>
>>
>> --
>> !=============================================================!
>> Dr. Adam Deller
>> ARC Future Fellow, Senior Lecturer
>> Centre for Astrophysics & Supercomputing
>> Swinburne University of Technology
>> John St, Hawthorn VIC 3122 Australia
>> phone: +61 3 9214 5307 <+61%203%209214%205307>
>> fax: +61 3 9214 8797 <+61%203%209214%208797>
>>
>> office days (usually): Mon-Thu
>> !=============================================================!
>>
>
>
>
> --
> the giver of moksha
>
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