Dang it, I wish I didn't have real architecture design work to do today, because this seems like it'd be a lot of fun to research.
Pure horizontal scaling would be trucks with survey counters. Pure vertical would be getting the US to retask one of those radiation-sensing satellites they use to characterize stuff like the Urals trace. (Not that that'd be likely to happen - national security, etc. But have the embassy in DC call NASA anyway, just in case they do have something.) Both would be GA aircraft doing a broad survey while trucks retrace the route. In any case the logistics would be critical, and speed as ever would be costly - good thing we have government-scale resources to work with.
And, yes, the system in this case would be implemented on a human substrate, not a silicon one. This isn't Chernobyl; we don't need robots to do this job, the problem is of limited enough scope to be safely handled by properly trained and equipped humans - finding whom would be an early logistical concern. (The surveyors would be safe enough barring a forced landing or breakdown very near the source, which is unlikely but we still want to get rescue services on standby, or hire a couple of civil helicopters from the oil industry or similar, for fast recovery just in case.) And for a one-off job like this that needs to be done as fast as possible, there isn't time to design, build, and debug robots that can do it.
> The surveyors would be safe enough barring a forced landing or breakdown very near the source
Weird assumption. Forced landings anywhere are unsafe. They are also very rare, because aircraft are quite reliable. The chances of the surveyors having a forced landing near the capsule must be minuscule (tiny danger zone compared to the extent of full search area, small probability of an aircraft having a forced landing at all).
If you are counting such minuscule dangers then you are ignoring much bigger (but still relatively small) dangers to the surveyors: they might trip during the survey, they might get into a traffic accident as they search or their aircraft might crash injuring them (irrespective of distance from the source). They might have a wildlife encounter as they are verifying a signal (false or true positive). They might suffer from heat stroke, or get sunburnt.
My intuition says that if you send out teams of people scurrying around the countryside these listed dangers are all more likely than having a forced landing right on top of the source. I also assume that you ignored them because they are all “everyday risks”, and you had tunnel vision concentrating on the radiation hazard.
Great catch, and you're right: lots of things can go wrong in a desert whether there's radiation involved or not, so we'd have needed those helicopters either way. This is why we work in teams - don't be shy about anything else you see me missing.
> don't be shy about anything else you see me missing
I would think we need to clarify the theoretical and practical limits of the detectors.
Depending on how the sensors work the search might look very different.
If you can get some expensive lab gear and distinguish the radiation of this source from the background from hundreds of kilometers then you only need to measure at a few strategic locations to triangulate it.
If you need to get a sensor within ten meters from the source before it can be detected then you need to lug the sensor around on the ground. That would be too low for a manned aircraft to fly at.
How fast does the sensor detect? If the sensor can detect up to 100 meters but need 5 second to measure that will make the search much different than if it can measure with 500hz for the same distance.
Do we think we can sense only the source or also the places the source has been at? Does it leave a detectable trace?
What of these is hard limit by physics (nobody, for no amount of money can build a better detector) vs limit of resources (it would be very expensive to do x)? If it is a limit of resources how does detector quality scales with resources spent?
Without having solid answers to these it would be foolish to jump at designing a search method.
Certainly there would be significant engineering problems involved if we had to develop the survey technology and methodology from scratch, and more problems still if we first needed to confirm that such engineering is even achievable.
Fortunately for us in this case, aerial radiological surveying has long since been reduced to practice. [1] [2] The detection equipment described in those references is on the order of tens of thousand times more sensitive than consumer-grade G-M counters, and is commercially available. [3]
Not as such, no. On further research, it looks like the understanding that led me to surmise the existence of such a survey capability was significantly incomplete.