The magnetotelluric response over 2D media with resistivity frequency dispersion¹

Abstract

We investigate the magnetotelluric response of two-dimensional bodies, characterized by the presence of low-frequency dispersion phenomena of the electrical parameters. The Cole-Cole dispersion model is assumed to represent the frequency dependence of the 'impedivity' complex function, defined as the inverse of Stoyer's 'admittivity' complex parameter. To simulate real geological situations, we consider three structural models, representing a sedimentary basin, a geothermal system and a magma chamber, assumed to be partially or totally dispersive. From a detailed study of the frequency and space behaviours of the magnetotelluric parameters, taking known non-dispersive results as reference, we outline the main peculiarities of the local distortion effects, caused b-v the presence of dispersion in the target media. Finally, we discuss the interpretative errors which can be made by neglecting the dispersion phenomena. The apparent dispersion function, which was defined in a previous paper to describe similar effects in the one-dimensional case, is again used as a reliable indicator of location, shape and spatial extent of the dispersive bodies. The general result of this study is a marked improvement in the resolution por'ver of the magnetotelluric method. lntroduction A great variety of laboratory and field experiments, carried out in different physical and geological conditions, have clearly revealed that the electrical properties ofrocks very often depend, to a greater or lesser extent, on the time and frequencl, behaviour of the exciting (natural or artificial) electromagnetic (EM) fields. Resistivity, which is the chief parameter in most conventional EM prospecting methods, and, for the purpose of this article, variable-frequency input fields, are both usually included in the categor-v of dispersion phenomena.

Modeling electrical dispersion phenomena in Earth materials

“…Following the theory developed by Patella (1987Patella ( , 1993, the CC model has been included in the magnetotelluric (MT) method to study the distortions provoked by IP on 1D (Di Maio et al, 1991) and 2D (Mauriello et al, 1996) synthetic responses. IP effects in MT have been experimentally recognized in volcanic and geothermal areas (Patella et al, 1991;Coppola et al, 1993;Giammetti et al, 1996;Di Maio et al, 1997Mauriello et al, 2000Mauriello et al, , 2004.…”

The Role of the Impedivity in the Magnetotelluric Response

“…This a slightly different representation compared with that used in classical not dispersive MT, where the phase curves of the wave impedance are generally drawn, e.g., [42]. Using the well known relationship between apparent impedivity and wave impedance, e.g., [19,24,42], it can be easily demonstrated that the apparent impedivity phase function is equal to two times the impedance phase function minus 90 • .…”

“…Following the theory developed by [23,24], the Cole-Cole model was included in MT to study the distortions provoked by dispersion on 1D [8] and 2D [19] synthetic responses. Positive dispersion effects in MT were experimentally recognized in volcanic and geothermal areas [6,9,10,12,20,21,27].…”

Transient Electromagnetic Method in the Keritis basin (Crete, Greece): Evidence of hierarchy in a complex geological structure in view of Tsallis distribution.

“…A generalized Ohm's law J(t)=σ*e(t) has been used in geophysics to model electromagnetic induction in a polarizable medium [Esposito et al 2017, Mauriello et al 1996, Patella 2008, Smith et al 1988. Typically, modelling EM induction in such a medium is performed in the frequency domain, in which case Ohm's law becomes the product J(ω)=σ(ω)E(ω), and the governing Maxwell equations are solved for a given frequency assuming a time-harmonic source excitation.…”