[Difx-users] On delay modelling

Tue Apr 25 00:42:22 EDT 2017

Dear David,

Thank you so much for the reference. I'll go through it first and come back
with more questions (if any) :)

Thanks,
Best regards,
Mugundhan

On Mon, Apr 24, 2017 at 8:56 PM, David Gordon <geovlbi at gmail.com> wrote:

> 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.
>>>>>>
>>>>>>
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>>>>>> Difx-users at listmgr.nrao.edu
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>>>>>>
>>>>>>
>>>>>
>>>>>
>>>>> --
>>>>> !=============================================================!
>>>>> 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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>

-- 
the giver of moksha
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