We study the influence of the resistivity frequency dispersion effects on the magnetotelluric (MT) response. Impedivity is the term used to indicate the frequency dependent resistivity in rocks. The impedivity functions, used in this paper, have been derived from the general solution of the motion equation of a charge carrier, discussed in a previous paper. A 1D three-layered earth section, with the second layer assumed to be dispersive, is considered to analyze the distortions due to dispersion on the modulus and phase of the MT responses on the earth's free surface. The MT responses of the section, where the dispersive layer is attributed an impedivity function describing at first a positive, then a negative and finally a resonant dispersion model, are computed for various combines of the dispersion parameters. A general conclusion is that the dispersion effects can strongly influence the MT response either in recognizable or in subtle forms. In the former case, the distortions appear as either steeply rising and/or descending curve branches or spike-like deltas, not compatible with a dispersion-free section. In the latter case, instead, the MT curves preserve the typical behavior for a dispersion-free section, and may thus erroneously be modeled by a section, where the dispersive layer is totally suppressed. In both case, disregarding the distortion effects may lead to misleading conclusions as to the physical properties of the surveyed structures.
"The Role of the Impedivity in the Magnetotelluric Response," Progress In Electromagnetics Research,
Vol. 89, 225-253, 2009. doi:10.2528/PIER08121203
1. Ageev, V. V. and B. S. Svetov, "The influence of rock polarizability on electromagnetic soundings," Izvestia RAS, Physics of the Solid Earth, Vol. 35, 16-24, 1999.
2. Avdeev, D. B. and A. D. Avdeeva, "A rigorous three-dimensional magnetotelluric inversion," Progress In Electromagnetics Research, Vol. 62, 41-48, 2006. doi:10.2528/PIER06041205
3. Balanis, C. A., Advanced Engineering Electromagnetics, J. Wiley & Sons, New York, 1989.
4. Bertin, J. and J. Loeb, Experimental and Theoretical Aspects of Induced Polarization, Gebruder-Borntrager, Berlin, 1976.
5. Cole, K. S. and R. H. Cole, "Dispersion and absorption in dielectrics," J. Chem. Phys., Vol. 9, 341-351, 1941. doi:10.1063/1.1750906
6. Coppola, B., R. Di Maio, I. Marini, A. Merla, D. Patella, G. Pulelli, F. M. Rossi, and A. Siniscalchi, "Study of the Simplon area geothermal anomaly in the frame of a transalpine deep railway tunnel feasibility project," Underground Transportation Infrastructures, J. L. Reith (ed.), 93-102, Balkema, Rotterdam, 1993.
7. Debye, P., Polar Molecules, Chemical Catalogue Company, New York, 1928.
8. Di Maio, R., D. Patella, and A. Siniscalchi, "Sul problema del riconoscimento di uno strato elettricamente polarizzabile mediante misure magnetotelluriche," Atti del II Convegno di Geomagnetismo ed Aeronomia, A. Meloni and B. Zolesi (ed.), 239-250, 1991.
9. Di Maio, R., P. Mauriello, D. Patella, Z. Petrillo, S. Piscitelli, A. Siniscalchi, and M. Veneruso, "Self-potential, geoelectric and magnetotelluric studies in Italian active volcanic areas," Ann. Geofis., Vol. 40, 519-537, 1997.
10. Di Maio, R., D. Patella, Z. Petrillo, A. Siniscalchi, G. Cecere, and P. de Martino, "Application of electric and electromagnetic methods to the study of the Phlegrean Fields caldera," Ann. Geofis., Vol. 43, 375-390, 2000.
11. Fink, J. B., E. O. McAlister, B. K. Sternberg, W. G. Wieduwilt, and S. H. Ward, Induced Polarization: Applications and Case Histories, Investigations in Geophysics, Vol. 4, Society of Exploration Geophysicists, Tulsa, Oklahoma, 1990.
12. Giammetti, S., D. Patella, A. Siniscalchi, and A. Tramacere, "The Siena Graben: Combined interpretation of DES and MT soundings," Ann. Geofis., Vol. 39, 189-200, 1996.
13. Ivashov, S. I., I. A. Vasiliev, T. D. Bechtel, and C. Snapp, "Comparison between impulse and holographic subsurface radar for NDT of space vehicle structural materials," PIERS Online, Vol. 3, 658-661, 2007. doi:10.2529/PIERS061004045944
14. Kaufman, A. A. and G. V. Keller, The Magnetotelluric Sounding Method, Elsevier, Amsterdam, 1981.
15. Manzanares-Martinez, J. and J. Gaspar-Armenta, "Direct integration of the constitutive relations for modelling dispersive metamaterials using the finite difference time-domain technique," Journal of Electromagnetic Waves and Applications, Vol. 21, 2297-2310, 2007. doi:10.1163/156939307783134452
16. Mauriello, P. and D. Patella, "Localization of magnetic sources underground by a probability tomography approach," Progress In Electromagnetics Research M, Vol. 3, 27-56, 2008. doi:10.2528/PIERM08050504
17. Mauriello, P. and D. Patella, "Resistivity tensor probability tomography," Progress In Electromagnetics Research B, Vol. 8, 129-146, 2008. doi:10.2528/PIERB08051604
18. Mauriello, P. and D. Patella, "Geoelectrical anomalies imaged by polar and dipolar probability tomography," Progress In Electromagnetics Research, Vol. 87, 63-88, 2008. doi:10.2528/PIER08092201
19. Mauriello, P., D. Patella, and A. Siniscalchi, "The magnetotelluric response over two-dimensional media with resistivity frequency dispersion," Geophys. Prosp., Vol. 44, 789-818, 1996. doi:10.1111/j.1365-2478.1996.tb00174.x
20. Mauriello, P., D. Patella, Z. Petrillo, and A. Siniscalchi, "An integrated magnetotelluric study of the Mt. Etna volcanic structur," Ann. Geofis., Vol. 43, 325-342, 2000.
21. Mauriello, P., D. Patella, Z. Petrillo, A. Siniscalchi, T. Iuliano, and C. Del Negro, "A geophysical study of the Mount Etna volcanic area," Mt. Etna: Volcano Laboratory, Vol. 143, A. Bonaccorso, S. Calvari, M. Coltelli, C. Del Negro, and S. Falsaperla (eds.), 273-291, American Geophysical Union, Geophysical Monograph Series, 2004.
22. Nishimoto, M., S. Ueno, and Y. Kimura, "Feature extraction from GPR data for identification of landmine-like objects under rough ground surface," Journal of Electromagnetic Waves and Applications, Vol. 20, 1577-1586, 2006. doi:10.1163/156939306779292318
23. Patella, D., "Tutorial: Interpretation of magnetotelluric measurements over an electrically dispersive one-dimensional earth," Geophys. Prosp., Vol. 35, 1-11, 1987. doi:10.1111/j.1365-2478.1987.tb00799.x
24. Patella, D., "I principi metodologici della magnetotellurica su mezzi generalmente dispersivi," Ann. Geofis., Vol. 36, 147-160, 1993.
25. Patella, D., "On the role of the J-E constitutive relationship in applied geoelectromagnetism," Ann. Geophys., Vol. 46, 589-597, 2003.
26. Patella, D., "Modelling electrical dispersion phenomena in earth materials," Ann. Geophys., Vol. 51, 2008.
27. Patella, D., A. Tramacere, R. Di Maio, and A. Siniscalchi, "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., Vol. 48, 61-75, 1991. doi:10.1016/0377-0273(91)90033-V
28. Pellerin, L., J. M. Johnston, and G. W. Hohmann, "A numerical evaluation of electromagnetic methods in geothermal exploration," Geophysics, Vol. 61, 121-137, 1996. doi:10.1190/1.1443931
29. Pelton, W. H., S. H. Ward, P. G. Hallof, W. R. Sill, and P. H. Nelson, "Mineral discrimination and removal of inductive coupling with multi-frequency IP," Geophysics, Vol. 43, 588-603, 1978. doi:10.1190/1.1440839
30. Pelton, W. H., W. R. Sill, and B. D. Smith, "Interpretation of complex resistivity and dielectric data, Part I," Geophys. Trans., Vol. 29, 297-330, 1983.
31. Prosvirnin, S. L. and S. Zouhdi, "On the effective constitutive parameters of metal-dielectric arrays of complex-shaped particles," Journal of Electromagnetic Waves and Applications, Vol. 20, 583-598, 2006. doi:10.1163/156939306776137818
32. Razevig, V. V., S. I. Ivashov, A. P. Sheyko, I. A. Vasilyev, and A. V. Zhuravlev, "An example of holographic radar using at restoration works of historical building," Progress In Electromagnetics Research Letters, Vol. 1, 173-179, 2008. doi:10.2528/PIERL07120603
33. Seigel, H. O., "Mathematical formulation and type curves for induced polarization," Geophysics, Vol. 24, 547-565, 1959. doi:10.1190/1.1438625
34. Sjoberg, D., "Exact and asymptotic dispersion relations for homogenization of stratified media with two phases," Journal of Electromagnetic Waves and Applications, Vol. 20, 781-792, 2006. doi:10.1163/156939306776143460
35. Stoyer, C. H., "Consequences of induced polarization in magnetotelluric interpretation," Pure and Appl. Geophys., Vol. 114, 435-449, 1976. doi:10.1007/BF00876943
36. Sumner, J. S., Principles of Induced Polarization for Geophysical Exploration, Elsevier, Amsterdam, 1976.
37. Svetov, B. S. and V. V. Ageev, "High resolution electromagnetic methods and low frequency dispersion of rock conductivity," Ann. Geofis., Vol. 42, 699-713, 1999.
38. Uduwawala, D., "Modeling and investigation of planar parabolic dipoles for GPR applications: A comparison with bow-tie using FDTD," Journal of Electromagnetic Waves and Applications, Vol. 20, 227-236, 2006. doi:10.1163/156939306775777224
39. Van den Bosch, I., S. Lambot, M. Acheroy, I. Huynen, and P. Druyts, "Accurate and efficient modelling of monostatic GPR signal of dielectric targets buried in stratified media," Journal of Electromagnetic Waves and Applications, Vol. 20, 283-290, 2006. doi:10.1163/156939306775701704
40. Wait, J. R., Overvoltage Research and Geophysical Applications, Pergamon, Oxford, 1959.
41. Wait, J. R., Geo-electromagnetism, Academic Press, New York, 1982.
42. Zhdanov, M. S. and G. V. Keller, The Geoelectrical Methods in Geophysical Exploration, Elsevier, Amsterdam, 1994.