Hi Seden,
When a High voltage Tesla coil discharges, it creates broadband radio noise of frequencies that are greatly influenced by the choice of capacitors and inductors, as well as the construction methods. The kind of coil used in this patent would be expected to generate radio noise far in excess of what is allowed by the FCC in the USA and most other radio regulating agencies around the world. So I would suspect this device is illegal for anyone who doesn't have a government permit to operate it. I expect that some governments would issue permits for the purpose of locating UXO under controlled conditions.
But assuming that it was permitted, here are some thoughts:
1. If you are intrested in studying the frequency spectrum of EM noise generated by the high voltage, it is not necessary to use the gross amount of power needed to see large sparks up to 2 meters long. A small, battery / inverter powered coil could probably do the job just as well. This does not necessarily need to be a Tesla coil, but a Tesla coil generally is more efficient. At lower power levels, the device may be within radio noise regulations.
2. When a spark discharges into the ground, one phenomenon that occurs is that molecules in the air and on substances at the nearby ground can become ionized, and possibly objects under the ground depending on the electrical properties of the object and the surrounding ground.
3. Another phenomenon that occurs is you have certainly created an artificial electric field anomaly in the air where the high voltage probe is located. There is a natural voltage gradient in the atmosphere approximately 100 v/meter that becomes more positive as you increase the altitude. This gradient is upset by the very existence of the high voltage coil and probe. And the high voltage will influence much more than the immediate location of the coil. A 50,000 volt probe may make a distortion in the natural atmospheric voltage gradient that extends as much as a mile. While this is probably not of interest to you, those who are interested in static fields and detecting ionization may be concerned.
4. When the sparks discharge into the ground, you can expect ground currents to flow from the location where the spark hits the ground to the ground lead on the high voltage coil. (This ground lead would probably be connected to a dragging strap conductor, or possibly a conductor rigged to the wheel of the vehicle to always make contact with the ground). In any case there would be some current flow through the ground to the coil ground lead. The path of this current flow Would be expected to be concentrated in a line, but could be spread and angled to several directions depending on the composition of the ground materials. The currents flowing in the ground would have some influence on your equipment to detect the spectrum, as it may provide a stronger signal when your sensor is closer to where the current is flowing, and aligned in a plane to best capture the magnetic component (I presume) of the noise.
5. There are 2 sources of radio noise, from the primary Tesla coil circuit and associated spark gap, and from the secondary coil circuit which sends sparks to the ground. Each of these circuits can be expected to emit broadband noise with several frequencies and harmonics to be very pronounced. When you are measuring the spectrum, you may decide to make corrections for known frequencies and their strengths. ie: you may want to use noise canceling methods such as subtracting the spectrum components known to exist when there is no target in the path.
Personally, I doubt you will find any correlation between the spectrum you measure and the presence of treasures. For one, the broadband noise of an arcing Tesla coil is enough to smother your ability to sense the minute signals that LRL operators are usually looking for. Secondly, some of the prerequisites for LRL-style frequency discrimination have been destroyed by the presence of the high voltage equipment and lightning bolts. If you are successful in canceling the non-target related noise, then I would think you have a chance of testing to see if the sensed spectrum correlates to buried targets.
But I may be wrong. I have never measured the broadband spectrum under high voltage discharge conditions near a buried target. And some LRL proponents may argue that a high voltage positive charge from a Tesla coil actually helps locate buried targets if the coil is not sparking.
It would be interesting to see what you find out.