Some key points are:
Large range of resistivity variations will occur in the order of mega ohms.
Drastic variations may occur due to the uneven structural phenomenon.
To my understand, it's possible to assess the thickness of ice layers using electrical resistivity. Some researches have already been conducted:
http://www.sciencedirect.com/science/article/pii/S0165232X07001012
http://www.sciencedirect.com/science/article/pii/S0165232X1200225X
http://www.sciencedirect.com/science/article/pii/0165232X86900418
http://www.sciencedirect.com/science/article/pii/S1359431104003308
The most practical approach for the determination of the thickness of an ice layer appears to be Ground Penetrating Radar. Depth estimates derived from electrical resistance surveys have to be taken with a large pinch of salt.
In 1979 I have published paper in Doklady of Russian academy of science magazine called Linear inverse problem of electrical deep sounding. Some integral parameters of resistivity could be detected. Many things depends of dence of reaciving network, distance between feeding and reaciving dipols,
Well, if you want to get the thickness of sea ice (which some of your listed publications indicate) you are far better off with frequency-domain electromagnetic inductions sounding (5-10 kHz) like an EM31 or similar.
there is many geophysical method for identify the underground, but the ERT (electrical resistivity tomography) DC is most used. especially the VES (Vertical Electrical sounding), is technical for present the number of layers and the thickness.
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