Assuming that I am interpreting your questions correctly:

1) The discrete Fourier transformation (https://en.wikipedia.org/wiki/Fourier_transform) says that:

* Sampling interval dt is related to the maximum frequency resolved DF as DF=1/dt;

* Duration/length of observation/recording/sampling DT is related to the frequency resolution df as df=1/DT.

From these general relationships, I would say that the ability to resolve the switch time would mainly depend on maximizing the sampling frequency used.

2) From the name of the institute you work for, it seems the current is used to send a signal through the ground. I would then assume that the lower frequency has less attenuation and permits to penetrate deeper depth. If I am not mistaken, you probably send a transient wave modulated by these frequencies (32Hz, 16Hz etc) and receive and try to interpret a response. If so, then in theory, the switch off time should not depend on the frequency. In practice, however, the switch off time will likely have most dependency on the electronics (e.g. if the currents or voltage is high) or the transducer used to send the signals into the ground. The higher the modulation frequency, the more difficult it may be to push the signal into the ground. This is however a very big assumption as I do not really know your field well.

The topic seems interesting and I would be happy to try to assist more but will need better understanding of the problem / more information. For example, please clarify

- if the above is correct and

- if subject of the question is in trying to characterise the transmitter or transponder?

- more info on what you do, how it is done, and what you are looking for.

If you are asking for the relation between the highest frequency component in a signal and the rise-time, the usual accepted rule is that the time for a "square wave" signal to rise from 10% to 90% is 0.35/(highest frequency in the signal), i.e. just over a third of a cycle at the highest frequency.