Which method is best suitable for VLF-EM inversion? Upto now I've generated apparent current density depth sections using Karous-Hjelt filter and surfer.
See if the following paper helps you. It is an extension to the Karous-Hjelt filter.
Sampaio E E S (2009) VLF-EM Anomalies Simulation by Underground Line Sources of Alternating Current, In: Resumos Expandidos, 11th. Congr. Intern. daSBGf, Salvador, SBGf.
You can use various inversion programme developed for RMT method with slight modification. There could be many literature but these two can be useful to look first hand.