That is "nice" questions. I was thinking to consider the "true" relative coordinate of the infinite electrode with respect to the coordinates of the surveyed area. If the distance is at least "ten" times greater than the size of the investigated area, it should work. In the past I did it for cross-hole pole-pole investigation. Sincerely

The definition of infinite electrodes in a 3D inversion of pol-dipole data requires specifying the locations of the electrodes in the x, y, and z coordinates. The pol-dipole data that you have is typically collected along parallel lines, and the infinite electrodes are defined as points at infinity along each line.

One way to define these infinite electrodes is to extend the line of the electrodes to a large distance (e.g., several kilometers) beyond the area of interest. The exact location of the infinite electrodes would depend on the specific study area and data, but it is typically far enough away that it can be considered as a true "infinity" point. In this way, the inversion algorithm can use the pol-dipole data from the finite electrodes and the infinite electrodes to estimate the subsurface resistivity distribution.

Another way is to use a mathematical approach called "null-point" electrode. This method consists in placing a pair of electrodes (A,B) with a large enough distance so that the potential difference between them is negligible. The potential on the null-point electrodes (A,B) is considered to be the same, and it is treated as the same point, allowing an infinite electrode to be defined.

It is important to note that the electrode configuration, both finite and infinite, can influence the results of the inversion, so it's important to choose an electrode configuration that is appropriate for the specific study area and data. Additionally, it's also important to have a good understanding of the inversion algorithm and its assumptions, in order to ensure that the results are physically meaningful.

n 3D inversion of pol-dipole data, the infinite electrode is typically defined as an electrode that is located far away from the area of interest and is not expected to have any significant electrical influence on the measurements. In practice, this can be achieved by placing electrodes at a large distance from the survey area or by using a reference electrode placed in a known non-conductive medium, such as a borehole filled with a non-conductive grout.

The exact location and configuration of the infinite electrode will depend on the specific survey design and the type of inversion algorithm being used. It is important to consult the documentation for the specific inversion software being used for details on how to define the infinite electrode in the protocol file. Also, it is important to check that the selected infinite electrodes are not affected by resistivity changes due to the presence of nearby conductive or resistive structures.