| Abstract: | In a previous paper it has been shown that we can relate the transient IP electric field Ep , existing in a rock after a step wave of polarizing current, with the steady-state current density Jss during the current step wave as follows: Ep =ρ' Jss . This relation may be interpreted as a generalized Ohm's law, valid in linear cases, in which ρ’(fictitious resistivity) is defined as the product of the true resistivity ρ with the chargeability m. Supposing E p=— grad Up and applying the divergence condition div Jss = o, one can, for a layered earth, obtain a general expression for the depolarization potential Up as a solution of Laplace's equation ?2Up= o. Since the mathematical procedure for the solution of this last equation is identical to that used in resistivity problems, we propose now the introduction of an apparent fictitious resistivity ρ'a (defined as the product of the apparent resistivity ρa with the apparent chargeability ma) as a new parameter for the interpretations of IP soundings carried out over layered structures with a common electrode array. The most general expression of ρ'a as a function of the electrode distance turns out to be mathematically identical to the general expression of ρ'a. Therefore it is possible to interpret a ρ'a field curve using the same standard graphs for resistivity prospecting with the usual method of complete curve matching. In this manner a great deal of work is saved since there is no need to construct proper ma graphs for the interpretation of IP soundings, as it has been done up to now. Finally some field examples are reported. |
