Modeling electrical dispersion phenomena in Earth materials

It is illustrated that IP phenomena in rocks can be described using conductivity dispersion models deduced as
solutions to a 2nd-order linear differential equation describing the motion of a charged particle immersed in an
external electrical field. Five dispersion laws are discussed, namely: the non-resonant positive IP model, which
leads to the classical Debye-type dispersion law and by extension to the Cole-Cole model, largely used in current
practice; the non-resonant negative IP model, which allows negative chargeability values, known in metals
at high frequencies, to be explained as an intrinsic physical property of earth materials in specific field cases; the
resonant flat, positive or negative IP models, which can explain the presence of peak effects at specific frequencies
superimposed on flat, positive or negative dispersion spectra.

AGEEV, V.V. and B.S. SVETOV (1999): The influence of rock
polarizability on electromagnetic soundings, Izvestia
RAS, Physics of the Solid Earth, 35, 16-24.
BALANIS, C.A. (1989): Advanced Engineering Electromagnetics
(J. Wiley & Sons, New York).
BERTIN, J. and J. LOEB (1976): Experimental and Theoretical
Aspects of Induced polarization (Gebrüder-Bornträger,
Berlin), 2 vols.
COLE, K.S. and R.H. COLE (1941): Dispersion and Absorption
in dielectrics, J. Chem. Phys., 9, 341-351.
COPPOLA, B., R. DI MAIO, I. MARINI, A. MERLA, D. PATELLA,
G. PULELLI, F.M. ROSSI and A. SINISCALCHI (1993):
Study of the Simplon area geothermal anomaly in the frame of a transalpine deep railway tunnel feasibility
projectin, in Underground Transportation Infrastructures,
Proc. of an Intern. Conf. of the Association
Française des Travaux en Souterrain, edited by J.L.
REITH (Balkema, Rotterdam), Toulon, 1993, 93-102.
DEBYE , P. (1928): Polar Molecules (Chemical Catalogue
Company, New York).
DI MAIO, R., D. PATELLA and A. SINISCALCHI (1991: Sul
problema del riconoscimento di uno strato elettricamente
polarizzabile mediante misure magnetotelluriche
(in Italian), in Atti del II Convegno di Geomagnetismo
ed Aeronomia, edited by A. MELONI and B.
ZOLESI (Istituto Nazionale di Geofisica e Vulcanologia,
Roma), 239-250.
DI MAIO, R., P. MAURIELLO, D. PATELLA, Z. PETRILLO, S.
PISCITELLI, A. SINISCALCHI and M. VENERUSO (1997):
Self-potential, geoelectric and magnetotelluric studies
in Italian active volcanic areas, Ann. Geofis., XL (2),
519-537.
DI MAIO, R., D. PATELLA, Z. PETRILLO, A. SINISCALCHI, G.
CECERE and P. DEMARTINO (2000): Application of electric
and electromagnetic methods to the study of the
Phlegrean Fields caldera, Ann. Geofis., 43 (2), 375-390.
FINK, J.B., E.O. MCALISTER, B.K. STERNBERG, W.G.
WIEDUWILT and S.H. WARD (Editors) (1990): Induced
polarization: applications and case histories, in Investigations
in Geophysics, Society of Exploration Geophysicists,
Tulsa, Oklahoma, vol. 4, pp. 414.
GIAMMETTI, S., D. PATELLA, A. SINISCALCHI and A. TRAMACERE
(1996): The Siena Graben: Combined interpretation
of DES and MT soundings, Ann. Geofis.,
XXXIX (1), 189-200.
MADDEN, T.R. and T. CANTWELL (1967): Induced polarization,
a review, in Mining Geophysics, Society of Exploration
Geophysicists, Tulsa, Oklahoma, vol. 2, 373-400.
MAURIELLO, P., D. PATELLA and A. SINISCALCHI (1996): The
magnetotelluric response over two-dimensional media
with resistivity frequency dispersion, Geophys. Prosp.,
44, 789-818.
MAURIELLO, P., D. PATELLA, Z. PETRILLO and A. SINISCALCHI
(2000): An integrated magnetotelluric study of
the Mt. Etna volcanic structure, Ann. Geofis., 43 (2),
325-342.
MAURIELLO, P., D. PATELLA, Z. PETRILLO, A. SINISCALCHI, T.
IULIANO and C. DEL NEGRO (2004): A geophysical
study of the Mt. Etna volcanic area, in Mt. Etna: Volcano
Laboratory, edited by A. BONACCORSO, S. CALVARI,
M. COLTELLI, C. DEL NEGRO and S. FALSAPERLA,
American Geophysical Union, Geophysical Monograph
Series, 143, 273-291.
NABIGHIAN, M.N., and C.L. ELLIOT (1976): Negative induced
polarization effects from layered media, Geophysics,
41, 1235-1255.
PATELLA, D. (1987): Tutorial: Interpretation of magnetotelluric
measurements over an electrically dispersive onedimensional
earth, Geophys. Prosp., 35, 1-11.
PATELLA, D. (1993): I principi metodologici della magnetotellurica
su mezzi generalmente dispersivi (in Italian),
Ann. Geofis., XXXVI (5/6), 147-160.
PATELLA, D. (2003): On the role of the J-E constitutive relationship
in applied geoelectromagnetism, Ann. Geophys.,
46, 589-597.
PATELLA, D. and R. DI MAIO (1989): On the analysis of
Cole-Cole relaxations transients in the induced polarization
prospecting method, in Inverse Modeling in
Exploration Geophysics, edited by A. VOGEL, R.
GORENFLO, B. KUMMER and C.O. OFOEGBU (F. Vieweg
& Sohn, Braunschweig/Wiesbaden), 205-219.
PATELLA, D., A. TRAMACERE, R. DI MAIO and A. SINISCALCHI
(1991): Experimental evidence of resistivity
frequency-dispersion in magnetotellurics in the Newberry
(Oregon), Snake River Plain (Idaho) and Campi
Flegrei (Italy) volcano-geothermal areas, J. Volcanol.
Geoth. Res., 48, 61-75.
PELTON, W.H., S.H. WARD, P.G. HALLOF, W.R. SILL and P.H.
NELSON (1978): Mineral discrimination and removal of
inductive coupling with multi-frequency IP, Geophysics,
43, 588-603.
PELTON, W.H., W.R. SILL and B.D. SMITH (1983): Interpretation
of complex resistivity and dielectric data. Part I,
Geophys. Trans., 29, 297-330.
SAFONOV, A.S., I.A. MUSHIN, E.S. KISELEV and A.S.
GORYUNOV (1996): A structural-formation model as the
physical-geological basis for high-resolution electroprospecting,
Geofizika, 2, 12-23.
SEIGEL, H.O. (1959): Mathematical formulation and type
curves for induced polarization, Geophysics, 24, 547-
565.
STOYER, C.H. (1976): Consequences of induced polarization
in magnetotelluric interpretation, Pure Appl. Geophys.,
114, 435-449.
STRATTON, J. (1941): Electromagnetic Theory (McGraw-
Hill, New York).
SUMNER, J.S. (1967): The problem of negative IP anomalies,
in Proc. of the Symposium on Induced Electrical Polarization,
Engineering Geoscience, Department of Mineral,
Technical University of California, Berkeley, 32-50.
SUMNER, J.S. (1976): Principles of Induced Polarization for
Geophysical Exploration (Elsevier, Amsterdam).
SVETOV, B.S. and V.V. AGEEV, (1999): High resolution electromagnetic
methods and low fequency dispersion of
rock conductivity, Ann. Geofis., 42 (4), 699-713.
WAIT, J.R. (Editor) (1959): Overvoltage Research and Geophysical
Applications (Pergamon, Oxford).
WAIT, J.R. (1982): Geo-electromagnetism (Academic Press,
New York).