GNGTS 2014 - Atti del 33° Convegno Nazionale

GNGTS 2014 S essione 3.2 163 equations. We can use the well-known Cole-Cole model (Pelton et al. , 1978), as expressed in eq. 81): (1) (Where, ρ : is the frequency-dependent resistivity, ρ 0 : the resistivity at zero frequency, ω : the angular frequency, η : the chargeability at 0 time after current switch-off, τ : the relaxation time and 0< c <= 1 a suitable exponent) and implement its Fourier transform in the time-domain into a suitable computer program. �� ��� �� ���� ��������� �� ���� ������ ��� �������� ��� �� If c=1 in this equation, in time domain the function can be expressed as in eq. 2): (2) where σ : indicates the electrical conductivity σ=1/ρ . Using a proprietary Matlab code, written by Zadorozhnaya and described by Zadorozhnaya and Lepyoshkin (1998), we obtain reasonable model parameters (i.e. solution) when we invert soundings 4, 5 and 6 (Tab. 1), while we obtain a similar solution for soundings 1, 2 and 3 only if we invert the data pertaining to the repeating frequency of 32 Hz (Tab. 2, model on left). If we try to invert, with the same algorithm, data pertaining to the repeating frequency of 4 Hz, we obtain nonrealistic low resistivity at depth. As an example we show, in Tab. 2, both models obtained for TEM-3. How to explain both the time-dependent behavior and the obtained very low resistivity values? If we are successful to explain and model it, we should obtain coherent TEM inverted models throughout. Perhaps we could be so lucky to find second order parameters linked to hydrogeology. Moreover, is this time-dependent behavior correlated with observed time- and current-dependence of resistivity in the (more usual) geo-electrical method? In both reported cases geology suggests the presence of membrane polarization linked to saturated sandstone, which is more abundant in the FAA formation, i.e. below soundings 1, 2 and 3. We remember that sandstone is the same rock type where these phenomena were clearly observed in the lab. Non linearity of DC and TEM data: preliminary common model. The foundation of membrane polarization caused by constrictivity of pores is as follows: when the electrical current flows through a porous channel with pores of different radii (transfer numbers), an excess/loss of ions accumulates at the boundaries (Marshall and Madden, 1959). Obviously �������� ���� captions have higher mobility (transfer more electrical charges) when in a large capillary because �� ������ in narrow capillaries some of the anions are absorbed by the double electric layers (DEL) hence they become immobile. When a steady state current is applied, concentration of ions at one side of a Tab. 2 - Model parameters obtained. Layer ρ Thickness η τ Layer ρ Thickness η τ No. Ohmm m s No. Ohmm m s 1 90 15 - - 1 30 30 - - 2 12 25 - - 2 8 45 - - 3 2.3 19 - - 3 0.92 45 0.25 3°-3 4 0.5 20 0.25 3.5°-3 4 0.05 45 0.99 3.5°-3 5 0.5 25 0.25 3°-3 5 0.05 45 0.99 3°-3 6 0.6 24 0.25 3°-3 6 0.05 45 0.99 3°-3 1D petrophysical model parameters of sounding 3 using the Cole-Cole formula at 32 Hz repetition rate 1D petrophysical model parameters of sounding 3 using the Cole-Cole formula at 4 Hz repetition rate