Genuinely curious here, why is the travelled distance important?
The second thing you might want to do: "filter" neutrinos ... well that just doesn't work at all. Nothing stops (a decent amount of) neutrinos. So you can't filter them and create a known point with, say, only electron neutrinos like you can with light. There are also no known astronomical objects that filter neutrinos. They fly right through a star, so that's no good either.
Third you could filter observations. But again you hit the filter problem. You can focus neutrinos measurements (even if you can't focus the neutrinos themselves), but that lowers the amount of neutrinos you measure further. And you're only measuring like maybe 50 per cubic meter of water, so you don't have much to work with.
I guess you could wait for things to get especially good for your measurement but you'll be waiting a long time.
> the three types of neutrino-flavors mix into each other. That means, if you start with, say, only electron-neutrinos, they’ll convert into muon-neutrinos as they travel. And then they’ll convert back into electron neutrinos. So, depending on what distance from a source you make a measurement, you’ll get more electron neutrinos or more muon neutrinos.
Neutrinos are not directly detected. What happens is that they interact with matter in a medium and produce muons or electrons that are moving faster than the speed of light in that medium. That's only possible because the speed of light in said medium is less than the speed of light in vaccuum by the way. These fast-moving, charged particles lead to the generation of a cone of cherenkov radiation, not unlike a supersonic object is producing a mach cone. From that cone, the direction of the particle motion can be inferred.
One could also keep the detector running while switching the source on and off to establish a baseline and calculate the excess of detected particles while the source was switched on.
Indeed it’s the child-particles of the interactions that are observed, so, electrons muons and Tau particles. Depending how you are measuring, (many approaches) these interactions are generally separable - and usually you can get some directionality out of your measured event - so you know the direction it came from.
Combining the direction with timing - with an accelerator you know exactly when the pulse of neutrinos were produced - this means you can exclude a very large amount of background.
Some background does get through, but you can measure it with e.g. the source turned off as you suggest, or the times when you know the source isn’t otherwise producing (like in between pulses) to get a background rate. You then generate enough data from the source to effectively “drown out” the background.
Much the same can be done with reactor sources - very often when building an experiment with a reactor as a source, there will be some government-level agreement to allow knowledge of what power the reactor is being run at, as well as shutdowns.
Along with Cherenkov, there are and have been scintillator, chemical-energy-deposition, Photographic film and even ocean-audio based methods of detection. Probably some more exotic ones I am forgetting also.
(I did a PHD in neutrino physics, although been out of the field a few years)
I did not know that "ocean-audio based methods of detection" for neutrinos are even possible and will certainly look that up later.
It always seemed a neat idea, that you could instrument absolutely gigantic volumes with.