Thread: Calculation of AZ and BAZ in SAC

Started: 2013-11-18 16:01:33
Last activity: 2013-11-18 22:24:45
Topics: SAC Help
Fiona Darbyshire
2013-11-18 16:01:33
Hello,

Could someone tell me a bit more about how AZ and BAZ are calculated in SAC?

Up to now, e.g. when binning receiver functions, I have used BAZ and
GCARC to group them together, and that's always seemed to work, so
I've always assumed that the BAZ/GCARC (or DIST, I imagine) pair gives
you a unique position from the point of interest (the station).

This time, I have some data output that is expressed in AZ and DIST. I
assumed (perhaps naively?) that this would also allow successful
spatial grouping, but it turns out not to be the case; one can have
the same forward azimuth for several different locations.

Here's the example where I found the issue:
Station lat, lon: 82.5033, -62.35 (ALE)

Event1: lat 80.205, lon -1.091
Event 2: lat 86.876, lon 54.373
The two events are almost 1000km apart.

Event 1: AZ 313, BAZ 72, GCARC 9, DIST 1006
Event 2: AZ 314, BAZ 17, GCARC 9, DIST 1042

I'd like to know more about the calculation, in particular because (i)
I'd like to reassure myself that BAZ/distance does indeed give a
unique location, and (ii) I don't understand how AZ is calculated. One
website I looked at (Matlab) talks about rhumb lines vs great-circles;
is that the issue? Will an AZ/distance pair always be non-unique?
(Also most websites define back-azimuth as simply 180 opposite to
azimuth, but I guess they aren't talking about spherical geometry
then...)

Thanks for any insight.

Fiona Darbyshire.

Centre de recherche GEOTOP, Université du Québec à Montréal


  • Brian Savage
    2013-11-18 19:38:44
    Fiona,

    The implementation of the computation of Great Circle Distance (degrees), Azimuth, Back Azimuth, and Distance (km) is based off of Rudoe's formula found in Geodesy by R.Bomford (1980). It assumes a Radius of 6378.160 km and a flattening of 1/298.2466081. I can send you the appropriate pages from R. Bomford (1980) if you would like.

    The azimuth and back-azimuth will generally not be offset by180 degrees, and some pairs of point will have "odd-looking" (not event close to 180 degrees) azimuth/back azimuth pairs.

    Note: There are more robust methods of calculating these quantities and the current implementation in SAC as well as many other implementations, up until recently [1], have trouble with particular pairs of points. For over ~ 99% of point pairs SAC's implementation produces the correct result, but that last 1% can be incorrect (sometimes badly).

    I hope this helps.

    Brian Savage

    [1] Karney, C. F. F. (2013). "Algorithms for geodesics". Journal of Geodesy 87 (1): 43–42. arXiv:1109.4448. Bibcode:2013JGeod..87...43K. doi:10.1007/s00190-012-0578-z (open access). Addenda.


    On Nov 18, 2013, at 8:01 AM, Fiona Darbyshire wrote:

    Hello,

    Could someone tell me a bit more about how AZ and BAZ are calculated in SAC?

    Up to now, e.g. when binning receiver functions, I have used BAZ and
    GCARC to group them together, and that's always seemed to work, so
    I've always assumed that the BAZ/GCARC (or DIST, I imagine) pair gives
    you a unique position from the point of interest (the station).

    This time, I have some data output that is expressed in AZ and DIST. I
    assumed (perhaps naively?) that this would also allow successful
    spatial grouping, but it turns out not to be the case; one can have
    the same forward azimuth for several different locations.

    Here's the example where I found the issue:
    Station lat, lon: 82.5033, -62.35 (ALE)

    Event1: lat 80.205, lon -1.091
    Event 2: lat 86.876, lon 54.373
    The two events are almost 1000km apart.

    Event 1: AZ 313, BAZ 72, GCARC 9, DIST 1006
    Event 2: AZ 314, BAZ 17, GCARC 9, DIST 1042

    I'd like to know more about the calculation, in particular because (i)
    I'd like to reassure myself that BAZ/distance does indeed give a
    unique location, and (ii) I don't understand how AZ is calculated. One
    website I looked at (Matlab) talks about rhumb lines vs great-circles;
    is that the issue? Will an AZ/distance pair always be non-unique?
    (Also most websites define back-azimuth as simply 180 opposite to
    azimuth, but I guess they aren't talking about spherical geometry
    then...)

    Thanks for any insight.

    Fiona Darbyshire.

    Centre de recherche GEOTOP, Université du Québec à Montréal

    _______________________________________________
    sac-help mailing list
    sac-help<at>iris.washington.edu
    http://www.iris.washington.edu/mailman/listinfo/sac-help


  • Arthur Snoke
    2013-11-18 22:24:45
    Fiona,

    Brian May have given an adequate answer to your question, but perhaps you
    are asking when one should use BAZ and when one should use AZ. Here are a
    few comments on that.

    In SAC, BAZ is defined as "Station to event azimuth (degrees)", and AZ is
    defined as "Event to station azimuth (degrees)." For receiver-fuction
    work, as for surface-wave analyses, BAZ is the one to use because it can
    be used to transfer the NS and EW horizontal components into Radial and
    Transverse -- the transformaiton should be made at the station. For
    focal-mechanism studies, AZ shoud be used, as one wants to know the
    direction rays leave the source. For practical purposes, the difference
    between DOST and GCARC probably is too small to worry about, but DIST is
    probably est for receiver functions.

    On Mon, 18 Nov 2013, Fiona Darbyshire wrote:

    Hello,

    Could someone tell me a bit more about how AZ and BAZ are calculated in SAC?

    Up to now, e.g. when binning receiver functions, I have used BAZ and
    GCARC to group them together, and that's always seemed to work, so
    I've always assumed that the BAZ/GCARC (or DIST, I imagine) pair gives
    you a unique position from the point of interest (the station).

    This time, I have some data output that is expressed in AZ and DIST. I
    assumed (perhaps naively?) that this would also allow successful
    spatial grouping, but it turns out not to be the case; one can have
    the same forward azimuth for several different locations.

    Here's the example where I found the issue:
    Station lat, lon: 82.5033, -62.35 (ALE)

    Event1: lat 80.205, lon -1.091
    Event 2: lat 86.876, lon 54.373
    The two events are almost 1000km apart.

    Event 1: AZ 313, BAZ 72, GCARC 9, DIST 1006
    Event 2: AZ 314, BAZ 17, GCARC 9, DIST 1042

    I'd like to know more about the calculation, in particular because (i)
    I'd like to reassure myself that BAZ/distance does indeed give a
    unique location, and (ii) I don't understand how AZ is calculated. One
    website I looked at (Matlab) talks about rhumb lines vs great-circles;
    is that the issue? Will an AZ/distance pair always be non-unique?
    (Also most websites define back-azimuth as simply 180 opposite to
    azimuth, but I guess they aren't talking about spherical geometry
    then...)

    Thanks for any insight.

    Fiona Darbyshire.

    Centre de recherche GEOTOP, Université du Québec à Montréal

    _______________________________________________
    sac-help mailing list
    sac-help<at>iris.washington.edu
    http://www.iris.washington.edu/mailman/listinfo/sac-help

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