Fractal Geometry, porosity and complex resistivity: from hand specimen to field data

• Published in: Development in Petrophysics Vol. 122; no. 1; pp. 287 - 297
• Main Authors: Da Rocha, Brígida Ramati P., Habashy, Tarek M.
• Format: Book Chapter Journal Article
• Language: English
• Published: The Geological Society of London 1997; The Geological Society, London; Geological Society of London
• Series: Geological Society, London, Special Publications
• Subjects: Geology, Exploration & Drilling; Oil & Gas Engineering
• ISBN: 1897799810; 9781897799819
• ISSN: 0305-8719; 2041-4927
• DOI: 10.1144/GSL.SP.1997.122.01.17

In the induced polarization (IP) method of geophysical prospecting, the frequency dependence of the constitutive parameters (conductivity and permittivity) of rocks is exploited to distinguish between different types of rocks with different types of mineralization. Unavoidably, the field data measured using either a four electrode array or an inductive type setup employing ungrounded loops will not directly provide the induced polarization properties of the geological medium to the exclusion of the ‘electromagnetic coupling’. In fact one can not measure one effect without the other. Inference of the medium constitutive parameters from field data is often masked and confused by the purely electromagnetic effects that would be present even when the medium is non-dispersive. In this paper we present a framework by which one can separate the electrochemical effects from the electromagnetic effects which are usually intertwined in a complicated manner in the measured field data. We formulate the problem in a fairly general way without introducing the customary quasi-static approximation. The model we use is that of a layered earth with one of the layers representing a polarizable medium and the rest of the layers are non-polarizable. The effective complex resistivity of the polarizable medium, which is described in a companion paper, is given by a generalized Cole-Cole type resistive network.