Turning off (collapsing the field) of large inductors
I want to point out one thing that the other answers are ignoring, or at least glossing over.

In this measurement, we stop the flow of current in our inductor, and this causes current to flow in the earth below it. That means we're effectively using the earth itself as the secondary coil of a flyback transformer.  

In a flyback transformer, the primary current can indeed be shut off very quickly, precisely because the magnetic flux is able to couple to the secondary and produce a current there, and we don't need to absorb the stored magnetic energy in the primary side circuit to quench the current.

The typical waveforms for a typical flyback transformer (with a copper wire secondary rather than soil) look like 



(image source)

To the extent that the experiment works, and we do generate a current in the earth, we won't need any voltage limiting device on the primary to ensure we can quench the current. The resistance of the earth will eventually absorb the energy that was stored in the magnetic field.

It may be a good idea to include a spark gap or other voltage limiting device, to protect the primary side circuit from damage in case the earth resistance is very high, or the device is accidentally operated in air instead of near the ground. But if this voltage limiter actually operates, it will likely disturb the measurement so that we don't get a result usable for determining the properites of the earth being studied.

You should also notice this paragraph in the page you referred to:


  In figure 4 and in this discussion, it was assumed that the transmitter current is turned off instantaneously.  To actually accomplish this with a large loop of transmitter wire is impossible, and modern transmitters shut the current down using a very fast linear ramp.  The duration of this ramp is maintained as short as possible (it can be shown to have an effect similar to that of broadening the measurement gate widths) particularly for shallow sounding where the transient decays very rapidly at early times.  The duration of the transmitter turn-off ramp (which can also be included in modern inversion programs) is usually controlled by transmitter loop size and/or loop current.