[SAC-HELP] Calculation of AZ and BAZ in SAC

[Brian Savage]

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

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://www.iris.washington.edu/pipermail/sac-help/attachments/20131118/07e632a5/attachment.html>