Vol. 111
Latest Volume
All Volumes
PIER 180 [2024] PIER 179 [2024] PIER 178 [2023] PIER 177 [2023] PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2010-12-01
Fast Computation of the Forward Solution in Controlled-Source Electromagnetic Sounding Problems
By
Progress In Electromagnetics Research, Vol. 111, 119-139, 2011
Abstract
The forward problem of calculating the electromagnetic (EM) field of a circular current loop in presence of a layered earth structure, given the geometrical and EM parameters of the layers, is solved fast. Efficient computation is obtained through a quasi-analytical procedure that allows to transform the field integrals into expressions involving only a known Sommerfeld Integral. The final explicit forms of the fields are in terms of modified Bessel functions. To validate the method, the magnitudes of the EM field components versus induction number and versus frequency are calculated assuming two- and three-layer earth models. The achieved results are in good agreement with the ones provided by the commonly used digital filter algorithms. The computational time taken by the application of this technique is shown to be much less than that required by both digital filters and other recently developed integration techniques for similar problems. This paper is an extension of an earlier conference paper.
Citation
Mauro Parise, "Fast Computation of the Forward Solution in Controlled-Source Electromagnetic Sounding Problems," Progress In Electromagnetics Research, Vol. 111, 119-139, 2011.
doi:10.2528/PIER10101409
References

1. Boerner, D. E., "Controlled source electromagnetic deep sounding: Theory, results and correlation with natural source results," Surveys in Geophysics, Vol. 13, No. 4-5, 435-488, 1992.

2. Zhdanov, M. S., Geophysical Electromagnetic Theory and Methods, Elsevier, Amsterdam, 2009.

3. Singh, N. P. and T. Mogi, "EMLCLLER-A program for computing the EM response of a large loop source over a layered earth model," Computer and Geosciences, Vol. 29, No. 10, 1301-1307, 2003.

4. Kong, F. N., S. E. Johnstad, and J. Park, "Wavenumber of the guided wave supported by a thin resistive layer in marine controlled-source electromagnetics," Geophysical Prospecting, Vol. 29, No. 10, 1301-1307, 2003.

5. Shastri, N. L. and H. P. Patra, "Multifrequency sounding results of laboratory simulated homogeneous and two-Layer earth models," IEEE Trans. Geosci. Remote Sensing, Vol. 26, No. 6, 749-752, 1988.

6. Kong, J. A., L. Tsang, and G. Simmons, "Geophysical subsurface probing with radio-frequency interferometry," IEEE Trans. Antennas Propagat., Vol. 22, No. 4, 616-620, 1974.

7. Singh, N. P. and T. Mogi, "Inversion of large loop transient electromagnetic data over layered earth models," Jour. Fac. Sci. Hokkaido Univ. Ser. VII, Vol. 12, No. 1, 41-54, 2003.

8. Farquharson, C. G., D. W. Oldenburg, and P. S. Routh, "Simultaneous 1D inversion of loop-loop electromagnetic data for magnetic susceptibility and electrical conductivity," Geophysics, Vol. 68, No. 6, 1857-1869, 2003.

9. Wait, J. R., "Mutual electromagnetic coupling of loops over a homogeneous ground," Geophysics, Vol. 20, No. 3, 630-637, 1955.

10. Constable, S. C., R. L. Parker, and C. G. Constable, "Occams inversion: A practical algorithm for generatlng smooth models from electromagnetic sounding data," Geophysics, Vol. 52, No. 3, 289-300, 1987.

11. Beard, L. P. and J. E. Nyquist, "Simultaneous inversion of airborne electromagnetic data for resistivity and magnetic permeability," Geophysics, Vol. 63, No. 5, 1556-1564, 1998.

12. Singh, N. P. and T. Mogi, "Electromagnetic response of a large circular loop source on a layered earth: A new computation method," Pure and Applied Geophysics, Vol. 162, No. 1, 181-200, 2005.

13. Guptasarma, D. and B. Singh, "New digital linear filters for Hankel J0 and J1 transforms," Geophysical Prospecting, Vol. 45, No. 5, 745-762, 1997.

14. Kong, F. N., "Hankel transform filters for dipole antenna radiation in a conductive medium," Geophysical Prospecting, Vol. 55, No. 1, 83-89, 2007.

15. Parise, M. and S. Cristina, "High-order electromagnetic modeling of shortwave inductive diathermy effects," Progress In Electromagnetics Research, Vol. 92, 235-253, 2009.

16. Alpak, F. O. and C. Torres-Verdin, "Data-adaptive resolution method for the parametric three-dimensional inversion of triaxial borehole electromagnetic measurements," Progress In Electromagnetics Research B, Vol. 25, 93-111, 2010.

17. Soleimani, M., "Simultaneous reconstruction of permeability and conductivity in magnetic induction tomography," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 5-6, 785-798, 2009.

18. Prasad, R., R. Kumar, and D. Singh, "A radial basis function approach to retrieve soil moisture and crop variables from x-band scatterometer observations," Progress In Electromagnetics Research B, Vol. 12, 201-217, 2009.

19. Nordebo, S. and M. Gustafsson, "A priori modeling for gradient based inverse scattering algorithms," Progress In Electromagnetics Research B, Vol. 16, 407-432, 2009.

20. Caramanica, F. and G. Oliveri, "An innovative multi-source strategy for enhancing the reconstruction capabilities of inverse scattering techniques," Progress In Electromagnetics Research, Vol. 101, 349-374, 2010.

21. Goharian, M., M. Soleimani, and G. R. Moran, "A trust region subproblem for 3D electrical impedance tomography inverse problem using experimental data," Progress In Electromagnetics Research, Vol. 94, 19-32, 2009.

22. Zheng, H., M.-Z. Wang, Z. Zhao, and L. Li, "A novel linear EM reconstruction algorithm with phaseless data," Progress In Electromagnetics Research Letters, Vol. 14, 133-146, 2010.

23. Chen, X.-D., "Subspace-based optimization method in electric impedance tomography," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 11-12, 1397-1406, 2009.

24. Banasiak, R., R. Wajman, D. Sankowski, and M. Soleimani, "Three-dimensional nonlinear inversion of electrical capacitance tomography data using a complete sensor model," Progress In Electromagnetics Research, Vol. 100, 219-234, 2010.

25. Mauriello, P. and D. Patella, "A data-adaptive probability-based fast ERT inversion method," Progress In Electromagnetics Research, Vol. 97, 275-290, 2009.

26. Cristina, S. and M. Parise, "Fast calculation of theoretical response curves for induction depth sounding," Proc. of the 39th European Microwave Conference, Sep. 29-Oct. 1, 2009, 1567-1570, Rome, Italy, 2009.

27. Ward, S. H. and G. W. Hohmann, "Electromagnetic theory for geophysical applications," Electromagnetic Methods in Applied Geophysics, Theory --- Volume 1, M. N. Nabighian Ed., 131-308, SEG, Tulsa, Oklahoma, 1988.

28. Ryu, J., H. F. Morrison, and S. H. Ward, "Electromagnetic fields about a loop source of current," Geophysics, Vol. 35, No. 5, 862-896, 1970.

29. Kong, J. A., Electromagnetic Wave Theory, John Wiley & Sons, New York, 1986.

30. Lin, Z., X. Zhang, and G. Fang, "Theoretical model of electromagnetic scattering from 3D multi-layer dielectric media with slightly rough surfaces," Progress In Electromagnetics Research, Vol. 96, 37-62, 2009.

31. Gennarelli, G. and G. Riccio, "Diffraction by a lossy double-negative metamaterial layer: a uniform asymptotic solution," Progress In Electromagnetics Research Letters, Vol. 13, 173-180, 2010.

32. Dai, S.-Y., C. Zhang, and Z.-S. Wu, "Electromagnetic scattering of objects above ground using MRTD/FDTD hybrid method," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 16, 2187-2196, 2009.

33. Gustavsen, B. and A. Semlyen, "Rational approximation of frequency domain responses by vector fitting," IEEE Trans. Power Delivery, Vol. 14, No. 3, 1052-1061, 1999.

34. Gustavsen, B., "Improving the pole relocating properties of vector fitting," IEEE Trans. Power Delivery, Vol. 21, No. 3, 1587-1592, 2006.

35. Deschrijver, D., M. Mrozowski, T. Dhaene, and D. de Zutter, "Macromodeling of multiport systems using a fast implementation of the vector fitting method," IEEE Microwave Wireless Comp. Lett., Vol. 18, No. 6, 383-385, 2008.

36. Gustavsen, B. and C. Heitz, "Modal vector fitting: A tool for generating rational models of high accuracy with arbitrary terminal conditions," IEEE Trans. Adv. Packaging, Vol. 31, No. 4, 664-672, 2008.

37. Watson, G. N., A Treatise on the Theory of Bessel Functions, Cambridge University Press, 1944.

38. Eroglu, A. and J. K. Lee, "Far field radiation from an arbitrarily oriented hertzian dipole in an unbounded electricaly gyrotropic medium," Progress In Electromagnetics Research, Vol. 89, 291-310, 2009.

39. Kudrin, A. V., E. Y. Petrov, G. A. Kyriacou, and T. M. Zaboronkova, "Electromagnetic radiation from sources embedded in a cylindrically stratified unbounded gyrotropic medium," Progress In Electromagnetics Research B, Vol. 12, 297-331, 2009.

40. Ruppin, R., "Scattering of electromagnetic radiation by a coated perfect electromagnetic conductor sphere," Progress In Electromagnetics Research Letters, Vol. 8, 53-62, 2009.

41. Lamultree, S., C. Phongcharoenpanich, S. Kosulvit, and M. Krairiksh, "Analysis of radiation characteristics of a probe-excited rectangular ring antenna by the dyadic green's function approach," Progress In Electromagnetics Research B, Vol. 11, 79-101, 2009.

42. Mushref, M. A., "Radiation from an eccentric coated cylinder with slots of arbitrary sizes and positions," Progress In Electromagnetics Research B, Vol. 11, 55-78, 2009.

43. Boriraksantikul, N., P. Kirawanich, and N. E. Islam, "Near-field radiation from commercial cellular phones using a TEM cell," Progress In Electromagnetics Research B, Vol. 11, 15-28, 2009.

44. LaComb, J. A., "Spoke top antenna for transient radiation," Progress In Electromagnetics Research Letters, Vol. 11, 1-9, 2009.

45. Simons, N. R. S., A. Sebak, and G. E. Bridges, "Application of the TLM method to half-space and remote-sensing problems," IEEE Trans. Geosci. Remote Sensing, Vol. 33, No. 3, 759-767, 1995.

46. Parise, M., "Exact electromagnetic field excited by a vertical magnetic dipole on the surface of a lossy half-space," Progress In Electromagnetics Research B, Vol. 23, 69-82, 2010.

47. Tiwari, K. C., D. Singh, and M. K. Arora, "Development of a model for detection and estimation of depth of shallow buried non-metallic landmine at microwave x-band frequency," Progress In Electromagnetics Research, Vol. 79, 225-250, 2008.

48. Singh, D., N. K. Choudhary, K. C. Tiwari, and R. Prasad, "Shape recognition of shallow buried metallic objects at x-band using ann and image analysis techniques," Progress In Electromagnetics Research B, Vol. 13, 257-273, 2009.

49. Kalaee, P. and J. Rashed-Mohassel, "Investigation of dipole radiation pattern above a chiral media using 3D BI-FDTD approach," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 1, 75-86, 2009.

50. Lu, Y. L., Y.-L. Wang, Y. H. Xu, and K. Li, "Electromagnetic field of a horizontal electric dipole buried in a four-layered region," Progress In Electromagnetics Research B, Vol. 16, 247-275, 2009.

51. Attiya, A. M., "Lower frequency limit of carbon nanotube antenna," Progress In Electromagnetics Research, Vol. 94, 419-433, 2009.

52. Muoz-Barrutia, A., X. Artaechevarria, and C. Ortiz-de-Solorzano, "Spatially variant convolution with scaled B-splines," IEEE Trans. Image Processing, Vol. 19, No. 1, 11-24, 2010.

53. Higham, N. J., Accuracy and Stability of Numerical Algorithms, SIAM, Philadelphia, PA, 2002.

54. Dongarra, J. J., "Performance of various computers using standard linear equations software,", Technical report CS-89-85, Department of Computer Science, University of Tennessee, Knoxville, 2008.

55. Telford, W. M., L. P. Geldart, and R. E. Sheriff, Applied Geophysics, Cambridge University Press, New York, 1990.