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Volume 21 Number 2
  • E-ISSN: 1365-2478

Abstract

A

In a previous paper it has been shown that we can relate the transient electric field , existing in a rock after a step wave of polarizing current, with the steady‐state current density during the current step wave as follows: =ρ'.

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

Supposing =— U and applying the divergence condition div = o, one can, for a layered earth, obtain a general expression for the depolarization potential U as a solution of Laplace's equation ∇2U= 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' (defined as the product of the apparent resistivity ρ with the apparent chargeability ) as a new parameter for the interpretations of soundings carried out over layered structures with a common electrode array.

The most general expression of ρ' as a function of the electrode distance turns out to be mathematically identical to the general expression of ρ'. Therefore it is possible to interpret a ρ' 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 graphs for the interpretation of soundings, as it has been done up to now.

Finally some field examples are reported.

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2006-04-27
2024-04-18

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References

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