We propose an approach to characterize the AC underwater radiation produced by a ship over a shallow water medium using dipole sources distributed over an interior surface to the ship. The proposed approach relies in the accurate and efficient representation of dipole sources over the shallow water medium that characterize the behavior of the electric or magnetic field. The approach is reduced to the solution of the resultant matrix system from the dipole representation. These systems are ill-posed, i.e., if the matrix systems are not solved by special regularization methods, the resultant solution will amplify the measurement noise. The regularization method applied is the least squares QR iterations combined with a new stopping rule that uses a numerical estimate of the measurement noise. Numerically generated data is used to study the validity of the different dipole representations. Finally we validate our methodology using magnetic measurements that result from degaussing coils of a mid-size vessel.
2. Holmes, J. J., Exploitation of A Ship's Magnetic Field Signatures. Synthesis Lectures on Computational Electromagnetics, 1st Ed., 9, Morgan & Claypool, 2006.
3. Bradley Nelson, J., T. C. Richards, M. Bisan, C. Greene, R. Dewey, F. Ludwar, K. Hofener, J. Rhebergen, and F. de Wolf, "Rimpasse 2011 electromagnetic trials quick-look report," Technical Report, Defence R&D Canada-Atlantic, November 2011.
4. Stratton, J. A. and L. J. Chu, "Diffraction theory of electromagnetic waves," Physical Review, Vol. 56, 99-107, 1939.
5. Stratton, J. A., "Electromagnetic Theory," IEEE Press Series on Electromagnetic Wave Theory, John Wiley and Sons, 1941.
6. Guo, Y., H. W. Ko, and D. M. White, "3-D localization of buried objects by nearfield electromagnetic holography," Geophysics, Vol. 63, No. 3, 880-889, 1998.
7. Harms, P., J. Maloney, M. P. Kesler, E. J. Kuster, and G. S. Smith, "A system for unobstrusive measurement of surface currents," IEEE Transactions on Antennas and Propagation, Vol. 49, No. 2, 174-184, 2001.
8. Morgan, M. A., "Electromagnetic holography on cylindrical surfaces using k-space transformations," Progress In Electromagnetics Research, Vol. 42, 303-337, 2003.
9. Williams, E. G. and N. Valdivia, "Near-field electromagnetic holography in conductive media," IEEE Transactions on Antennas and Propagation, Vol. 58, No. 4, 1181-1192, 2010.
10. Guler, M. G. and E. B. Joy, "High resolution spherical microwave holography," IEEE Transactions on Antennas and Propagation, Vol. 43, No. 5, 464-472, 1995.
11. Valdivia, N. and E. G. Williams, "The reconstruction of surface tangential components of the electromagnetic field from near-field measurements," Inverse Problems, Vol. 23, 785-798, March 2007.
12. Valdivia, N. and E. G. Williams, "Study of the comparison of the methods of equivalent sources and boundary element methods for near-field acoustic holography," Journal of the Acoustical Society of America, Vol. 120, No. 6, 3694-3705, December 2006.
13. Alqadah, H. F., N. P. Valdivia, and E. G. Williams, "A super-resolving near-field electromagnetic holographic method," IEEE Transactions on Antennas and Propagation, Vol. 62, No. 7, 3679-3692, 2014.
14. Colton, D. and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Vol. 93 of Applied Mathematical Sciences, 3rd Ed., Springer, Berlin, 2013.
15. Paige, C. C. and M. A. Saunders, "LSQR: An algorithm for sparse linear equations and sparse least squares," ACM Transactions on Mathematical Software, Vol. 8, No. 1, 43-71, 1982.
16. Hanke, M., Conjugate Gradient Methods for Ill-posed Problems, Kluwer Academic Publishers, Boston, 1995.
17. Hansen, P. C., Rank-deficient and Discrete Ill-posed Problems, SIAM, Philadelphia, PA, 1998.
18. Hanke, M. and T. Raus, "A general heuristic for choosing the regularization parameter in ill-posed problems," SIAM Journal on Scientific Computing, Vol. 17, No. 4, 956-972, 1996.
19. Hansen, P. C. and D. P. O’Leary, "The use of the L-curve in the regularization of discrete ill-posed problems," SIAM Journal on Scientific Computation, Vol. 14, No. 6, 341-373, 1993.
20. Valdivia, N., E. G. Williams, P. C. Herdic, and B. Houston, "Surface decomposition method for near-field acoustic holography," Journal of the Acoustical Society of America, Vol. 132, No. 1, 186-196, 2012.
21. Le Dorze, F., J. P. Bongiraud, J. L. Coulomb, P. Labie, and X. Brunotte, "Modeling of degaussing coils effects in ships by the method of reduced scalar potential jump," IEEE Transactions on Magnetics, Vol. 34, No. 5, 2477-2480, September 1998.
22. Nguyen, T. S., J. M. Guichon, O. Chadebec, P. Labie, and J. L. Coulomb, "Ship magnetic anomaly computation with integral equation and fast multipole method," IEEE Transactions on Magnetics, Vol. 47, No. 5, 1414-1417, May 2011.
23. Nguyen, T. T., G. Meunier, J. M. Guichon, and T. S. Nguyen, "An integral formulation for the computation of 3-D eddy current using facet elements," IEEE Transactions on Magnetics, Vol. 50, No. 2, 7013504-7013508, 2014.
24. Sommerfeld, A., Partial Differential Equations in Physics, Volume VI of Lectures on Theoretical Physics, Academic Press, 1949.
25. Arutaki, A. and J. Chiba, "Communication in a three-layered conducting media with a vertical magnetic dipole," IEEE Transactions on Antennas and Propagation, Vol. 28, No. 4, 551-556, 1980.