Some satellite visibility plots and satellite antenna pattern plots here:
BGAN Coverage Map & Details
Spot beam footprints:
http://www.groundcontrol.com/images/GC-Map33.jpg
More on INMARSAT 4:
ESA Telecommunications:BGAN Extension Phase 1
and another footprint map:
http://telecom.esa.int/telecom/media...-Obj4-hres.jpg
The spot beams might be dedicated to higher bandwidth communications, and might not be used for ACARS data. Without knowing more, it is risky to assume that a received "ping" could be located within a single spot beam. See comments by TelcoAUS #3862.
Snowfalcon2 #3849 and rh200 #3809 comment on poor accuracy of using signal strength for location. Agreed, and uncertainty in the aircraft's antenna gain degrades it even more.
Current satellite locations:
INMARSAT 4-F1
143.5 E
LIVE REAL TIME SATELLITE TRACKING AND PREDICTIONS: INMARSAT 4-F1
INMARSAT 3-F1
64.55 E
LIVE REAL TIME SATELLITE TRACKING AND PREDICTIONS: INMARSAT 3-F1
INMARSAT 5-F1
62.58 E
LIVE REAL TIME SATELLITE TRACKING AND PREDICTIONS: INMARSAT 5-F1