volume | PIER Journals

Abstract

A novel image solution for the canonical electrostatic problem of a point charge in an anisotropic half-space bounded by an anisotropic surface is presented. The image source is obtained in operator form by using Fourier-transformed Maxwell equations and transmission line theory. After applying methods from Heaviside operator calculus, the image operator can be interpreted as a combination of a point charge and a line-charge-bounded sector of planar charge density. The new theory is shown to coincide with the previously known image solutions of less general anisotropic media. In addition to being applicable to any physically feasible anisotropic medium of electrostatics, the method can be used for steady-current conductivity problems via a duality transformation.

1. Lindell, I. V., M. E. Ermutlu, K. I. Nikoskinen, and E. H. Eloranta, "Static image principle for anisotropic-conducting half-space problems: PEC and PMC boundaries," Geophysics, Vol. 59, No. 12, 1861-1864, 1993.
doi:10.1190/1.1443401

2. Lindell, I. V.J. J. HÃ¤nninen, and K. I. Nikoskinen, "Electrostatic image theory for the anisotropic boundary," IEEE Proceedings â€” Science.

3. Lindell, I. V., M. E. Ermutlu, K. I. Nikoskinen, and E. H. Eloranta, "Static image principle for anisotropic conducting half-space problems: impedance boundary," Geophysics, Vol. 59, No. 12, 1773-1778, 1993.
doi:10.1190/1.1443391

4. Negi, J. G. and P. D. Saraf, Methods in Geochemistry and Geophysics: Anisotropy in Geoelectromagnetism, Vol. 28, Elsevier Science Publishers, 1989.

5. Smythe, W. R., Static and Dynamic Electricity, 2 Ed., McGraw-Hill Book Company, 1950.

6. Kobayashi, M. and R. Terakado, "New view on an anisotropic medium and its application to transformation from anisotropic to isotropic problems," IEEE Transactions on Microwave Theory and Techniques, Vol. 27, No. 9, 769-775, 1979.
doi:10.1109/TMTT.1979.1129726

7. Eloranta, E. H., "The modeling of mise-`a-la-masse anomalies in an anisotropic half-space by the integral equation method," Geoexploration, Vol. 25, 93-101, 1988.
doi:10.1016/0016-7142(88)90007-5

8. Eskola, L., Geophysical Interpretation usingInte gral Equations, Chapman and Hall, 1992.

9. Wait, J. R., Geo-electromagnetism, Academic Press, 1982.

10. Landau, L. D., E. M. Lifshitz, and L. P. Pitaevskii, Landau and Lifshitz Course on Theoretical Physics: Electrodynamics of Continuous Media, 2 Ed., Vol. 8, Pergamon Press, 1984.

11. Lindell, I. V., Methods for Electromagnetic Field Analysis, 2 Ed., IEEE Press, Piscataway, , 1995.

12. Prudnikov, A. P., Yu. A. Brychkov, and O. I. Marichev, Integrals and Series: Special Functions, 2 Ed., Vol. 2, Gordon and Breach Science Publishers, 1986.

Dr. J. Hanninen

Prof. Ismo Veikko Lindell

Dr. K. Nikoskinen