I'm thinking that an enemy would have a fair idea of the maximum speed of a collins class boat and endurance related at that speed. Taking into account the known range of the cruise missile in question, wouldn't one be able to work out the maximum distance the boat could have traveled in what time frame? Would not the enemy work a circular patrol area and work this to the centre. I would think that would be a reasonable search pattern. At the very least you would not waste time looking in dead space. Stand to be corrected as always by the learned gentlemen here though.
You seem to be missing (or perhaps forgetting) a few of the key factors behind a TLAM launch. At present, it seems likely that a TLAM in RAN service would be a member of the Tomahawk family of missiles. Those have a max range of ~900 n miles, 1,000 miles, or 1,600 km, and it can take ~2 hours between TLAM launch striking a target at max range. This in turn also means that unless the ADF/RAN is trying to strike a target that is very far inland, a RAN sub (or surface vessel for that matter) can be well away from a coastline during the launch.
Unless the targeted group or nation had surveillance assets in place which detected the TLAM at launch, at the point of launch, and can get then ASW assets to the launch site quickly, trying to backtrack to find the launch site is IMO largely an exercise in futility.
Now, let us use the coastline nation of Turaqistan, and to simplify the problem, a single RAN sub launching a TLAM strike on a single target 300km inland, without any allied support or strike missions being launched by allies (esp the UK and US), and the RAN is launching a TLAM Block IV (max range ~1,600 km).
Unless Turaqistan had a vessel or aircraft in the vicinity of the launch site, during the launch, then Turaqistani forces will not detect in the inbound TLAM until it is ~40km from the coast. Assuming that Turaqistani forces are able to track the TLAM all the way to the target but not successfully engage/intercept, then Turaqistan will have track data for about 23 minutes/340km out of a max flight of ~108 minutes/1,600km.
For those interested in drawing range rings, that means starting from the first known detection of the inbound TLAM, and from there drawing a circle with a radius of ~1,260km, and then eliminating from that areas where the launch would have been detected. There is also the little matter of Turaqistan not knowing what the max range could be, until the TLAM strikes the target, which is a minimum of 23 minutes after launch, which means that the sub would have had between 23-108 minutes to move, before the target nation could determine a range distance for potential launch sites. That time could allow a
Collins-class sub to travel up to ~36 n miles from the launch site, or an additional ~66 km. If you look at those numbers, you can see it is an enormous area where the launching sub could potentially be.
To muddle things even further, the targeted nation will most likely not be able to tell the type of inbound missile, which means that guestimates on what the max launch range, location of launch, or even launching platform getting even fuzzier. Was it a TLAM, or a JASSM-ER? How about a SLAM-ER or Scalp? Was the launch platform a sub, surface vessel, or aircraft? Realistically, unless the launch itself was detected or other assets detect the sub, not much can be done to prosecute an attack, simply because of the number of variables involved and the sheer potential volume of air/sea which would need to be searched.
-Cheers