GNGTS 2013 - Atti del 32° Convegno Nazionale

The complex physical and chemical fluid-metal-rock interactions may produce induced polarization effects, which are related to the dispersion in rocks. This is manifested on the MT response either in recognizable or in subtle forms, in both cases creating a distortion on the experimental curves. Disregarding the distortion effect may lead to misleading interpretation of the surveyed structures. We performed MT synthetic responses adopting 1D and 2D models in order to illustrate the dispersion effect on a geometrical structure typical of a volcano- geothermal environment. The dispersion model. A generalized physical model was examined by Patella (2003), by solving in the FD the following electrodynamic equation of a charge carrier subject to an external electrical field e (ω) (1) In Eq. (1), q and m 2 are the electrical charge and mass of the carrier, m 0 is an elastic-like parameter explaining recall effects, m 1 is a friction-like parameter accounting for dissipative losses due to collisions and r ( ω ) is the Fourier transform of the trajectory of the charge. Assuming, for simplicity, only one species of charge carriers and putting with K their number per unit of volume, the following elementary expression was derived for the impedivity ρ ( ω ) (Patella, 2003), (2) Eq. (2) is a simple physical model, describing the behavior of a tuned circuit-like cell, i.e., a resistor–inductor–capacitor (RLC) series link. It is the equivalent of Lorentz’s solution to the 2nd-order differential equation of harmonic oscillation (Balanis, 1989). We can distinguish different type of models, the positive non-resonant model, the negative non-resonant model and the resonant model, both positive and negative. For the purpose of this work we will consider the positive non-resonant model since positive dispersion effects in MT were experimentally recognized in volcanic and geothermal areas (Coppola et al. , 1993, Di Maio et al. , 1997, 2000; Giammetti et al. , 1996; Mauriello et al , 2000, 2004; Patella et al. , 1991). The positive model. By the generalized scheme reported above, a positive dispersion model was derived, assuming a dispersive rock equivalent to a serial chain of N two-branch parallel circuits. Each two-branch parallel circuit simulates the behavior of two different ionic species, which are both assumed to have negligible inertia, i.e., m 2 , jω 2 ≈ 0, where the index j = 1, 2 indicates the ionic species. One species ( j = 1) is also assumed unbound, i.e., with m 0,1 negligible, and the other ( j = 2) bound. In other words, one branch is a single R, in order to represent the path the unbound light ions can run through, with constant speed, under the action of an external exciting field. The other branch is, instead, an RC series link, in order to represent the path the bound light ions can move through, under the action of the same external field and against the decelerating recall forces (Patella, 2003). This assumption was proved to lead to the following dispersion formula (Patella, 2003, 2008) (3) which describes a typical positive dispersion model. In Eq. (3), i = √− 1, ω is the angular frequency, ρ 0 is the DC resistivity and m [0, 1], known in mining geophysics as chargeability, is the dispersion amplitude defined as m =( ρ 0 – ρ ∞ )/ ρ 0 , where ρ ∞ [0, ρ 0 ] is the real impedivity at infinite frequency. Moreover, c [0, 1] is the decay spectrum flatting factor and τ ≥0 is the main time constant. The Cole-Cole model was used to study the distortion on 1D (Di Maio et al. , 1991) and 2D (Mauriello et al. , 1996) MT models created by the dispersion of the resistivity. 119 GNGTS 2013 S essione 3.2