Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 93 > pp. 255-274


By E. C. Slob and K. Wapenaar

Full Article PDF (592 KB)

Development of theory and experiments to retrieve Green's functions from cross correlations of recorded wave fields between two receivers has grown rapidly in the last seven years. The theory includes situations with flow, mechanical and electromagnetic disturbances and their mutual coupling. Here an electromagnetic theory is presented for Green's function retrieval from cross correlations that incorporates general bianisotropic media, which is the most general class of linear media. In the presence of dispersive non-reciprocal media, the Green's function is obtained by cross correlating the recordings at two locations of fields generated by sources on a boundary. The only condition for this relation to be valid is that the medium is non-dissipative. The principle of bianisotropic Green's function retrieval by cross correlation is illustrated with a numerical example.

E. C. Slob and K. Wapenaar, " retrieving the green ' s function from cross correlation in a bianisotropic medium ," Progress In Electromagnetics Research, Vol. 93, 255-274, 2009.

1. Scherbaum, F., "Seismic imaging of the site response using microearthquake recordings: Part I. Method," Bull. Seism. Soc. Am., Vol. 77, No. 6, 1905-1923, 1987.

2. Scherbaum, F., "Seismic imaging of the site response using microearthquake recordings: Part I. Application to the Swabian Jura, southwest Germany, seismic network," Bull. Seism. Soc. Am., Vol. 77, No. 6, 1924-1944, 1987.

3. Buckingham, M. J., B. V. Berkhout, and S. A. L. Glegg, "Imaging the ocean with ambient noise," Nature, Vol. 356, No. 6367, 327-329, London, March 1992.

4. Weaver, R. and O. Lobkis, "Ultrasonics without a source: Thermal fluctuation correlations at MHz frequencies," Phys. Rev. Lett., Vol. 87, No. 13, 134301-1-134301-4, 2001.

5. Campillo, M. and A. Paul, "Long-range correlations in the diffuse seismic coda waves," Science, Vol. 299, No. 5606, 547-549, 2003.

6. Shapiro, N., M. Campillo, L. Stehly, and M. Ritzwoller, "High-resolution surface-wave tomography from ambient seismic noise," Science, Vol. 307, No. 5715, 1615-1618, 2005.

7. Draganov, D., K. Wapenaar, W. Mulder, J. Singer, and A. Verdel, "Retrieval of reflections from seismic background-noise measurements," Geoph. Res. Lett., Vol. 34, No. 4, L04305, 2007.

8. Schuster, G., J. Yu, J. Sheng, and J. Rickett, "Interferomet-ric/daylight seismic imaging," Geoph. J. Int., Vol. 157, No. 2, 838-852, 2004.

9. Snieder, R., "Extracting the Green's function from the correlation of coda waves: A derivation based on stationary phase," Phys. Rev. E, Vol. 69, No. 4, 046610-1-046610-8, 2004.

10. Wapenaar, K., "Retrieving the elastodynamic Green's function of an arbitrary inhomogeneous medium by cross correlation," Phys. Rev. Lett., Vol. 93, No. 25, 254301-1-254301-4, 2004.

11. Lerosey, G., J. De Rosny, A. Tourin, A. Derode, G. Montaldo, and M. Fink, "Time reversal of electromagnetic waves," Phys. Rev. Lett., Vol. 92, No. 19, 193904-1-193904-3, 2004.

12. Corbella, I., N. Duffo, M. Vall-llossera, A. Camps, and F. Torres, "The visibility function in interferometric aperture synthesis radiometry," IEEE Trans. on Geoscience and Remote Sensing, Vol. 42, No. 8, 1677-1682, 2004.

13. Oestges, C., A. Kim, G. Papanicolaou, and A. Paulraj, "Characterization of space-time focusing in time-reversed random fields," IEEE Trans. Ant. and Prop., Vol. 53, No. 1, 283-293, 2005.

14. Snieder, R., "Retrieving the Green's function of the diffusion equation from the response to a random forcing ," Phys. Rev. E, Vol. 74, No. 4, 046620-1-046620-9, 2006.

15. Slob, E., D. Draganov, and K. Wapenaar, GPR without a source, Proceedings of the 11th International Conf. on GPR, ANT. 6, Ohio State University, Columbus, Ohio, , 2006.

16. Wapenaar, K., E. Slob, and R. Snieder, "United Green's function retrieval by cross correlation ," Phys. Rev. Lett., Vol. 97, No. 23, 234301-1-234301-4, 2006.

17. Slob, E., D. Draganov, and K. Wapenaar, "Interferometric electromagnetic Green's functions representations using propagation invariants," Geoph. J. Int., Vol. 169, No. 1, 60-80, 2007.

18. Slob, E. and K. Wapenaar, "GPR without a source: Cross-correlation and cross-convolution methods," IEEE Trans. Geoscience and Remote Sensing, Vol. 45, No. 8, 2501-2510, 2007.

19. Slob, E. and K. Wapenaar, "Electromagnetic Green's functions retrieval by cross-correlation and cross-convolution in media with losses," Geoph. Res. Lett., Vol. 34, No. 5, L05307, 2007.

20. Weaver, R., "Ward identities and the retrieval of Green's functions in the correlations of a diffuse field," Wave Motion, Vol. 45, No. 5, 596-604, 2008.

21. Ruigrok, E., D. Draganov, and K. Wapenaar, "Global-scale seismic interferometry: Theory and numerical examples," Geophysical Prospecting, Vol. 56, No. 3, 395-417, May 2008.

22. Kong, J., Theorems of bianisotropic media, Proceedings of the IEEE, Vol. 60, No. 9, 1036-1046, 1972.

23. Chow, W. W., J. G.-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, "The ring laser gyro," Rev. Mod. Phys., Vol. 57, No. 1, 61-104, January 1985.

24. Sihvola, A., "Metamaterials in electromagnetics," Metamaterials, Vol. 1, No. 1, 2-11, 2007.

25. Caloz, C. and T. Itoh, Electromagnetic Metamaterials, John Wiley & Sons, Inc., Hoboken, New Jersey, 2006.

26. Pitarch, J., J. M. C.-Civera, F. L. P.-Foix, and M. A. Solano, "Efficient modal analysis of bianisotropic waveguides by the coupled mode method," IEEE Trans. on Microwave Theory and Techniques, Vol. 55, No. 1, 108-116, 2007.

27. Cui, T.-J., H.-F. Ma, R. P. Liu, B. Zhao, Q. Cheng, and J. Y. Chin, "A symmetrical circuit model describing all kinds of circuit metamaterials," Progress In Electromagnetics Research B, Vol. 5, 63-76, 2008.

28. Huang, R., Z.-W. Li, L. B. Kong, L. Liu, and S. Matitsine, "Analysis and design of an ultra-thin metamaterial absorber," Progress In Electromagnetics Research B, Vol. 14, 407-429, 2009.

29. Weng, Z.-B., Y.-C. Jiao, F.-S. Zhang, Y. Song, and G. Zhao, "A multi-band patch antenna on metamaterial substrate," J. of Electromagn. Waves and Appl., Vol. 22, No. 2/3, 445-452, 2008.

30. Wongkasem, N., A. Akyurtlu, K. A. Marx, Q. Dong, J. Li, and W. D. Goodhue, "Development of chiral negative refractive index metamaterials for the terahertz frequency regime," IEEE Trans. Antennas and Propagation, Vol. 55, No. 11, 3052-3062, 2007.

31. Meiners, C. and A. F. Jacob, "Numerical and experimental parameter study of helix layers," Trans. Antennas and Propagation, Vol. 56, No. 5, 1321-1328, 2008.

32. Silveirinha, M. G., "Design of linear-to-circular polarization transformers made of long densely packed metallic helices," IEEE Trans. Antennas and Propagation, Vol. 56, No. 2, 390-401, 2008.

33. Santagata, N. M., P. Luo, A. M. Lakhani, D. J. De Witt, B. S. Day, M. L. Norton, and T. P. Pearl, "Organizational structure and electronic decoupling of surface bound chiral domains and biomolecules," IEEE Sensors Journal, Vol. 8, No. 6, 758-766, 2008.

34. Tajitsu, Y., "Piezoelectricity of chiral polymeric fiber and its application in biomedical engineering," IEEE Trans. on Ultrasonics, Ferroelectrics and Frequency Control, Vol. 55, No. 5, 1000-1008, 2008.

35. Yang, X. M., J. Y. Chin, Q. Cheng, X. Q. Lin, and T. J. Cui, "Realization and experimental verification of chiral cascaded circuit," IEEE Microwave and Wireless Components Letters, Vol. 18, No. 5, 308-310, 2008.

36. Dong, J. and C. Xu, "Characteristics of guided modes in planar chiral nihility meta-material waveguides," Progress In Electromagnetics Research B, Vol. 14, 107-126, 2009.

37. Lindell, I., A. Sihvola, and K. Suchy, "Six-vector formalism in electromagnetics of bi-anisotropic media," Journal of Electromagnetic Waves and Applications, Vol. 9, No. 7-8, 887-903, 1995.

38. Wapenaar, K. and J. Fokkema, "Reciprocity theorems for diffusion, flow and waves," A.S.M.E. Journal of Applied Mechanics, Vol. 71, No. 1, 145-150, 2004.

39. Tai, C., A study of electrodynamics of moving media, Proceedings of the IEEE, Vol. 52, No. 6, 685-689, 1964.

40. Harrington, R. and A. Villeneuve, "Reciprocity relationships for gyrotropic media," IRE Trans. on Microwave Theory and Techn., Vol. 6, No. 3, 308-310, 1958.

41. Altman, C. and K. Suchy, Reciprocity, Spatial Mapping and Time Reversal in Electromagnetics, Kluwer, Dordrecht, 1991.

42. Lindell, I., A. Sihvola, S. Tretyakov, and A. Viitanen, Electromagnetic Waves and Bi-Isotropic Media, Artech House, Boston, 1994.

43. Melrose, D. and R. McPhedran, Electromagnetic Processes in Dispersive Media, Cambridge University Press, Cambridge, 1991.

44. Landau, L. and E. Lifshitz, Electrodynamics of Continuous Media, Pergamon Press, New York, 1994.

45. Van Manen, D.-J., J. Robertsson, and A. Curtis, "Modeling of wave propagation in inhomogeneous media," Phys. Rev. Lett., Vol. 94, No. 16, 164301-1-164301-4, 2005.

46. Wapenaar, K., "General wave field representations for seismic modeling and inversion ," Geophysics, Vol. 72, No. 5, SM5-SM17, 2007.

47. Shen, J., "Negative refractive index in gyrotropically magnetoelectric media," Phys. Rev. B, Vol. 73, No. 4, 045113, 2006.

48. Kiehn, R., G. Kiehn, and J. Roberds, "Parity and time-reversal symmetry breaking, singular solitons, and Fresnel surfaces," Phys. Rev. A, Vol. 43, No. 10, 5665-5671, 1991.

© Copyright 2014 EMW Publishing. All Rights Reserved