My guess is basic lines being drawn on a physical map using observations spaced over time, and then humans trying to spot the pattern. I think these sort of sound mirrors are fairly directional, so with a bunch pointing in various slightly different directions you might be able to find the "sweet spot" and at least get an idea of where the enemy is, even if it is not precise.
From my own personal half-forgotten memories of seeing these as a kid in the 90s, they always seemed to be aligned with the coast, e.g. facing directly out to sea, not at an angle. This I guess would get you a lot of subtlety different directions to take a sounding from.
Very interesting.
The chap mentioned here, Tucke, was active in developing sound artillery ranging, which survived well after WW2. Artillery didn't have the speed issues that killed off sound mirrors before they ever really got going.
Watson Watt and his team fortunately gave us workable radar with height and direction finding by war's outbreak. Just.
The waveguide was rotatable so that sound direction could be roughly determined. This was done by slowly turning the guide until the sound was at its loudest and then reading off the angle.