How we can choose the vertical extension of the discretized model in the inversion of large scale potential field data? and how it affects the results of the inversion?
Potential fields are typically not very sensitive to the "depth to bottom" of vertically extensive source bodies, so the vertical extension is often badly constrained in simple inversion. Longer wavelength components contain most of that information, so the result is very sensitive to the way you treat the regional.
If you're working with gravity, you can sometime exploit the excess mass theorem.
Of course you should try very hard to get independent geological information to help. But failing that, try a range of vertical extensions and do a sensitivity analysis.