UNIVERSITÀ DEGLI STUDI DI PISA
Corso di Laurea Magistrale in Geofisica di Esplorazione ed Applicata
Tesi di laurea magistrale
Polarizzazione indotta implementazione e verifica di algoritmi per la stima dei
parametri spettrali e per il calcolo dell'EM-Coupling
Candidato: Nenci Alessandro
Relatore: Professor Paolo Costantini
ANNO ACCADEMICO
2012/2013
ABSTRACT
Induced Polarisation is a geophysical methodology that is mainly employed in the mining exploration activities, where it is probably the principal ground-based exploration technique: it consists in measuring and modelling the low-frequency dispersion phenomena affecting artificially generated time-varying electric fields. The measurements can be effected either in the time and the frequency domain (fig.1) (Telford et al., 1990). In the mining applications, the intensity of the dispersion is a direct function of the concentration of polarisable metallic particles (sulphides) and it depends, almost exclusively, on electrode polarisation. In the last years this methodology was increasingly used in applications other than mining exploration, like hydrogeology, mapping of contaminants, geothermal and
hydrocarbon exploration. In these cases, the polarisation effects can be due to a variety of phenomena, among which the most important are: interfacial (surface) phenomena, membrane polarisation, variations of porosity, transformations induced by chemically active fluids on the host rock. In all these cases the intensity of the measured dispersion responses (synthesised through the integral chargeability in TD and Percent Frequency Effect PFE in FD) is generally much lower, at least one order of magnitude, than the one observed in mining exploration settings.
The small intensity of the response gives rise to detectability problems, the final estimated parameters being eventually non distinguishable from the background effects. The picture is worsened by the fact that, in the above described environments more than in typical mining
Figure 1. Left: Complex Resistivity Spectrum; Amplitude
(continuous line) and Phase (dashed line) – Frequency Domain; right: Decay Curve – Time Domain.
prospects, the half-space and/or the cover formations are conductive and hence the Voltage signals measured at the receiver's electrodes are very small; when exploring for geothermal or hydrocarbon resources, there is another drawback: the depths of interest are generally large and then require very long wire layouts which, especially in conductive half-spaces, give rise to EM-coupling effects which mask the IP response (Wynn and Zonge, 1975). In this thesis two significant problems in IP prospecting were then treated: the spectral response synthesis, which would enable a better signal recovery and possibly a source discrimination, and the analytical computation of the EM-coupling effects, whose removal would enhance the reliability of the spectral estimates and at the same time allow to explore
at greater depth.
With respect to the Spectral Analysis, two different approaches were implemented and analysed:
1. Cole-Cole Synthesis (and derived models) 2. Multi-Exponential Synthesis
In general, the former is commonly used in applied geophysics and gives the possibility, within the limits imposed by the usual bandwidth, to discriminate between different mineral species (or contaminants) using three fundamental parameters: time constant (Tau), Seigel's Chargeability (M) and Frequency Dependence (c) (Pelton and al., 1978). Being a well
Figure 2: Multi-Exponential Inversion. Left: Measured (red points) and inverse (blue line) Amplitude spectra; right: Phase spectra. The graphs shows the results obtained truncating at XX (top) and YY (bottom) values.
established procedure, it has been used as reference model for evaluating the results obtained via Multi-exponential inversion. The latter, although its mathematical formulation dates back to the Eighteenth Century, is a relatively new approach which recently has seen an increased use. Its application is mainly in laboratory measurements (Nordsiek and Weller, 2008), but the use of its synthesis parameters (comparable to the Cole-Cole ones) is proposed, in literature, also for field surveying, especially in the hydrogeological sector. An inversion routine, written in Fortran 90, has then been implemented with the aim of evaluating the results of the Multi-Exponential approach on synthetic and real datasets, with the final scope of adding this step in a robust inversion procedure possibly applicable to a more general field than that of the laboratory determinations. However, the work has shown that, given the typical field records (either classic and full-wave), a stable inversion
procedure is almost impossible: the problem is severely under-determined and its solution would involve a sampling of the waveform tighter (one order of magnitude smaller) than what is normally available on the existent instrumentation and to use energising waveforms with a fundamental frequency which makes field acquisition infeasible (fig.2).The second subject, EM-coupling, concerns what can be considered, at least in certain situations, the
Figure 3:EM-Coupling. From top to bottom: Synthetic Resistivity/Chargeability Model; IP Chargeability Pseudosection, EM Chargeability Pseudosection; IP+EM Chargeability Pseudosection. The pseudosections are calculated using a pole-dipole array: the left ones with a “a” value of 25 m and the right with “a”=200 m.
main noise source affecting the IP measurements. It derives from inductive phenomena generated by the time-varying current which circulates in the energising circuit and whose effects manifest themselves, on the receiving circuit, with voltage signal that have the same characteristics of the IP. The EM-coupling intensity is directly, but not linearly, proportional to the array's wires length and to the half-space conductivity: this reduces the possibilities of the IP method when searching for deep targets or for target underlying conductive covers.The existing methods used for decoupling EM-contaminated data exploit the fact that its time constant is very short (compared with IP's one) and then significantly different from the usal targets. These methods, more or less sophisticated, are normally based on quite heavy assumptions (e.g. the phase spectrum is assumed to be linear within a certain frequency range). Hence, it has been decided to implement, in Fortran 90, a program library, adapted from the FORTRAN IV EMCUPL package (Kauahikaua and Anderson, 1979) and expanded to calculate the time-domain synthesis via convolution with the Current waveform. The library allows to compute, given the conductivity of the half-space and the array configuration, the EM effect and to subtract it from the measured signal (fig.3). The algorithm appears stable and reliable either with synthetic and real datasets and then its application opens the possibility of applying the IP method to deeper tergets and/or low-resistivity half-spaces.
Bibliografia
Telford et al.,1990: W. M. Telford L. P. Geldart R. E. Sheriff, Applied geophysics, 1990 J. C. Wynn and K. L. Zonge, EM- Coupling, it's intrinsic value, it's removal and the cultural couplin, 1975;Geophysics
W. H. Pelton, S. H. Ward, P.G. Hallof, W. R. Sill, P. H. Nelson, Mineral discrimination and removal of inductive coupling, 1978;Geophysics
S. Nordsiek et A. Weller, A new approach to fitting induced polarization spectra, 2008;Geophysics Sunde, 1968: E. D. Sunde, Earth conduction effects in trasmission system, 1968
Kauahikaua and Anderson, 1979: J. Kauahikaua W. L Anderson, Programs EMCUPL and SCHOPL, 1979
