Rocks containing disseminated metallics or clay particles in natural environment where electrolytic solutions fill the pore spaces, show a certain type of polarization at low frequencies known as induced electrical polarization. In this thesis, a new model to describe the electrical polarization on rocks was developed, not only for low frequencies, but spanning the entire electromagnetic spectrum used in geolectric prospection. This new model encompasses most of the other commonly used models as special cases, and overcomes some of the known limitations. The proposed circuit analog includes a non-linear impedance r(iwtf)-1 which simulates the effects of the rough surface of the interfaces between the blocking grains (metallic or clay particles) and the electrolyte. This generalized Warburg impedance is in series with the resistance of the blocking grains and both are shunted by the double layer capacitance. This combination is in series with the resistance of the electrolyte in the blocked pore passages. The unblocked pore paths are represented by a. resistance which corresponds to the normal DC resistivity of the rock. The parallel combination of this resistance with the "bulk" sample capacitance is finally connected in parallel to the rest of the above-mentioned circuit. The parameters of this model include the DC resistivity (p0), the chargeability (m), three relaxation times (T, Tf and T0), a grain resistivity factor (δr) and the frequency exponent (η). The fractal relaxation time (Tf) and the frequency exponent (η) are related to the fractal geometry of the rough pore interfaces between the conductive grains (metallic or clay minerals which are blocking the pore paths) and the electrolyte. The relaxation time T is a result of the low-frequency relaxation of the electrical double layers formed between the electrolyte and the crystals, whereas T0 is a macroscopic relaxation time of the "bulk" sample. The grain resistivity factor (δr) relates the resistivity of the conductive grains with the DC resistivity value of the rock. The DC resistivity of the rock and δr are related to the porosity, the electrolyte conductivity and the volumetric ratios between the matrix and the conductive grains. The model was tested over a wide range of frequencies against experimental data obtained for amplitude and phase of resistivity or conductivity as well as for the complex dielectric constant. The data used in this work were obtained from digitizing published experimental data, obtained by several authors from sedimentary, metamorphic and igneous rocks. The results show that the parameters of this model are related to textural and mineralogical aspects of the rocks. This model was introduced firstly as the intrinsic electric property of a homogeneous and polarizable half-space, and it was demonstrated, in this thesis, that the response observed at the surface is equivalent to the intrinsic property of the polarizable medium, been the electromagnetic coupling irrelevant to frequencies lower than 104 Hz. Next, the polarizable medium was embedded as an intermediate layer between two non-polarizable layers with the same De resistivity. The response obtained shows that the frequency exponent of the fractal medium could be determined even when the polarizable medium is at a considerable depth in relation to the dipole-dipole length. This justifies the use of simple models developed to explain the response of laboratory samples to fit field data, and that is being used without a right justification. These results shows the importance of the proposed model to the geoelectric prospection.
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