Do you understand that measuring the derivative of gravity will be noisy as hell, right? The measure we are looking for is, instead, the delta. Measuring the potential at several diferent points in altitude, filter noise, and average them out to get the m/s^2 per metre. If the discontinuity is, as you seem to say, spatial, then we can aproximate the range via bisection.
Gravity is just one example, though it would be easier: refraction would increase as you look through more air (and so increase with altitude), in addition to the effect of aether.
There will be noise in any scientific experiment. Also handy would be repetitions, to average out noise. With an average of the gravity at each altitude, we can plot and see if it's a smooth curve, or if there are any sudden jumps.
What I meant is that measuring the derivative of gravity is possible, but unfortunate, since derivatives are usually noisier. Measuring g at various points makes more sense, which is what I suggested, and what I think you also accept.
Technically it's still just measuring the derivative, only doing so indirectly. Even so, until the resources are available, I'm not wasting too much time on detailed planning.
There is a diference from measuring the delta,and measuring the derivative. In any case, deltas are more than enough for this. I could try and move some connections to the guys at arquitechture's faculty for them to let me use a gravimeter, but I doubt it. I think I will have to instead use public gravimetric surveys.