Let's start with the Falkland Islands, South Georgia and the South Sandwich Islands, and the British Antarctic Territory:
Per fess azure and barry wavy argent and azure, in chief a ram proper upon a grassy mount issuant from the division vert, and in base a galley proper, its mainsail charged with four torts in cross.
South Georgia & the South Sandwich Islands:
The rather amateurish emblazonment assumes that the field is argent and bleu celeste which it isn't. The azure should be the same tint as in the mantling. (The arms of the Falkland Islands also suggest the use of bleu celeste rather than azure as specified in the blazon, but in this case I suspect the use of a lighter blue was deliberate to make the arms more visible when used on the Falklands' blue ensign.)
British Antarctic Territory: