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

[Fiona Darbyshire]

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