AC Resistance vs DC Resistance

There's a difference between resistivity and resistance. Resistivity has units of resistance times length and is a property of a material. You might measure resistivity of the ground, for example.

The units are ohms times length because resistance of a given material is proportional to length and inversely proportional to cross-sectional area.

Consider a resistor of fixed cross-section area A and length L made of material of resistivity ρ:

R = ρL/A or ρ = RA/L, units of ρ are ohms x length² / length = ohms x length.

If you are measuring earth resistivity, AC would used because there may be a dc potential due to galvanic action between the electrodes and the ground which would act like a battery and give erroneous readings. I would assume that you would also want to avoid power frequencies (50/60 hz) because ground fault currents would also interfere.

Rixter explains it all pretty well.

I would add that the 128Hz is known as a high frequency measurement, but it has disadvantages in that, whilst cheaper than its low frequency counterpart, it tends to induce noise in the potential leads which can be difficult to filter, and can often eclipse the original signal, and this is further exacerbated by increasing distance between the probes and decreasing soil resistivity.

Low frequency meters, working in the order of one or two second pulses are far more accurate and can read over much larger distances, but are also far more expensive, and therefore not as commonly used.

A rule of thumb is that high frequency can be used reasonably accurately up to about 30 metres probe spacing, but for larger, or deep soil readings then low frequency is required.

It is vitally important to closely follow the instructions for probe placement and depth as these can dramatically affect resulting readings, particularly if there is any buried conductive structure nearby.