It sounds like you may have made the assumption that the impedance measurement has to be done by a special procedure. While this is possible, it is impractical as the power required from a test unit would be pretty massive for a transmission line in the grid.
The neat thing about those relays you're studying is that they can resolve all voltages and currents as phasors, and determine all other parameters mathematically, on the fly.
Characteristic impedance does have to be assumed prior to actual installation, but this is tested at the factory and is highly reliable. So, a high impedance fault is either a tree limb to ground, or very distant. A low impedance fault current is very near, or so catastrophic that the instantaneous function has to trip anyway, without delay. Substation engineering then consists of laying out current transformers and potential transformers so that the math makes sense, and all parameters can be provided to the functions that require them. Well, besides sizing all the components, selecting trip times, installing communication for carrier signals etc, etc.
Edit: to be clear, voltage and current waveforms are known at both ends of every major conductor, and modern relays timestamp it by GPS. Getting the characteristic impedance of the line is pretty much what these relays do, and when it changes, something is wrong.