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Transient electromagnetic response of a layered conducting medium at asymptotically late times

Published online by Cambridge University Press:  17 February 2009

D. M. O'Brien  and
R. S. Smith
D. M. O'Brien
Affiliation:
CSIRO Division of Atmospheric Research, Private Bag 1, Mordialloc, Vic. 3195, Australia.
R. S. Smith
Affiliation:
Department of Physics, Univerisity of Toronto, Toronto, Ontario, CanadaM5S 1A7.
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Abstract

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In this paper we consider a pair of horizontal conducting loops in the air above a horizontally layered ground. The transmitting loop is driven by a current source which rises from zero at time zero to a final constant value at time τ. We first compute the e.m.f. induced in the receiving loop and derive an asymptotic series for the e.m.f. at late times. Secondly, we estimate the error in truncating the asymptotic series at N terms and design a reliable numerical algorithm for summing the asymptotic series.

Type
Research Article
Information
The ANZIAM Journal , Volume 27 , Issue 1 , July 1985 , pp. 1 - 30
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Abramowitz, M. and Stegun, I. A., Handbook of mathematical functions (Dover, New York, 1965).Google Scholar
[2]Anderson, W. L., “Numerical integration of related Hankel transforms of orders 0 and 1 by adaptive digital filtering”, Geophysics 44 (1979), 1287–1305.Google Scholar
[3]Buselli, G. and O'Neill, B., “SIROTEM: A new portable instrument for multichannel transient electromagnetic measurements”, ASEG Bull. 8 (1977), 82–87.Google Scholar
[4]Copson, E. T., Asymptotic expansions (Cambridge University Press, Cambridge, 1971).Google Scholar
[5]Crone, J. D., “Ground pulse EM—examples of survey results in the search for massive sulphides and new developments with the Crone PEM equipment”, Paper presented by the author at the 25th international geological congress, Sydney, Australia (08, 1976).Google Scholar
[6]Gaver, D. P. Jr, “Observing stochastic processes and approximate transform inversion”, Oper. Res. 14 (1966), 444–459.CrossRefGoogle Scholar
[7]Kamenetski, F. M., “Transient processes using combined loops for a two layer section with a nonconducting base”, Izu. Vuzov. Section Geology Prosp. 6 (1969), 108–113.Google Scholar
[8]Kaufman, A. A., “Harmonic and transient fields on the surface of a two layered medium”, Geophysics 44 (1979), 1208–1217.CrossRefGoogle Scholar
[9]Knight, J. H. and Raiche, A. P., “Transient electromagnetic calculations using the Gaver-Stehfest inverse Laplace transform method”, Geophysics 47 (1982), 47–50.CrossRefGoogle Scholar
[10]Koefoed, O., Ghosh, D. P. and Polman, G. J., “Computation of type curves for electromagnetic depth sounding with a horizontal coil by means of a digital linear filter”, Geophys. Prosp. 20 (1972), 403–420.CrossRefGoogle Scholar
[11]Krylov, V. J., Lugin, V. V. and Yanovich, L. A., Tables for integration of functions with power singularities (Izdat. Akad. Nauk BSSR, Minsk, 1963).Google Scholar
[12]Lamontagne, Y. L., Lodha, G. S., Macnae, J. C. and West, G. F., “UTEM: Wideband time domain EM project 1976–78, reports 1–5”, Research in applied geophysics #11, Geophysics laboratory, Department of Physics, University of Toronto (1980).Google Scholar
[13]Lee, T., ‘Asymptotic expansions for transient electromagnetic fields”, Geophysics 47 (1982), 38–46.CrossRefGoogle Scholar
[14]Lee, T. and Lewis, R., “Transient EM response of a large loop on a layered ground”, Geophys. Prosp. 22 (1974), 430–444.Google Scholar
[15]Mallick, K. and Verma, R. K., “Time domain electromagnetic sounding with horizontal and vertical coplanar loops on a multilayered earth”, Geoexploration 16 (1978), 291–302.CrossRefGoogle Scholar
[16]Morrison, H. F., Phillips, R. J. and O'Brien, D. P., “Quantitative interpretation of transient electromagnetic fields over a layered half space”, Geophys. Prosp. 17 (1968), 82–101.CrossRefGoogle Scholar
[17]Patterson, T. N. L., “Algorithm for automatic numerical integration over a finite interval”, Comm. ACM 16 (1973), 694–699.Google Scholar
[18]Schechter, M., Operator methods in quantum mechanics (North-Holland, New York, 1981).Google Scholar
[19]Stehfest, H., “Algorithm 368. Numerical inversion of Laplace transforms”, Comm. ACM 13 (1970), 47–49.CrossRefGoogle Scholar
[20]Stehfest, H., “Remark on algorithm 368”, Comm. ACM 13 (1970), 624.CrossRefGoogle Scholar
[21]Stroud, A. H. and Secrest, D., Gaussian quadrature formulas (Prentice-Hall, Englewood Cliffs, N.J., 1966).Google Scholar
[22]Wait, J. R., Geoelectromagnetism (Academic Press, New York, 1982).Google Scholar