Vol. 94
Latest Volume
All Volumes
PIERB 105 [2024] PIERB 104 [2024] PIERB 103 [2023] PIERB 102 [2023] PIERB 101 [2023] PIERB 100 [2023] PIERB 99 [2023] PIERB 98 [2023] PIERB 97 [2022] PIERB 96 [2022] PIERB 95 [2022] PIERB 94 [2021] PIERB 93 [2021] PIERB 92 [2021] PIERB 91 [2021] PIERB 90 [2021] PIERB 89 [2020] PIERB 88 [2020] PIERB 87 [2020] PIERB 86 [2020] PIERB 85 [2019] PIERB 84 [2019] PIERB 83 [2019] PIERB 82 [2018] PIERB 81 [2018] PIERB 80 [2018] PIERB 79 [2017] PIERB 78 [2017] PIERB 77 [2017] PIERB 76 [2017] PIERB 75 [2017] PIERB 74 [2017] PIERB 73 [2017] PIERB 72 [2017] PIERB 71 [2016] PIERB 70 [2016] PIERB 69 [2016] PIERB 68 [2016] PIERB 67 [2016] PIERB 66 [2016] PIERB 65 [2016] PIERB 64 [2015] PIERB 63 [2015] PIERB 62 [2015] PIERB 61 [2014] PIERB 60 [2014] PIERB 59 [2014] PIERB 58 [2014] PIERB 57 [2014] PIERB 56 [2013] PIERB 55 [2013] PIERB 54 [2013] PIERB 53 [2013] PIERB 52 [2013] PIERB 51 [2013] PIERB 50 [2013] PIERB 49 [2013] PIERB 48 [2013] PIERB 47 [2013] PIERB 46 [2013] PIERB 45 [2012] PIERB 44 [2012] PIERB 43 [2012] PIERB 42 [2012] PIERB 41 [2012] PIERB 40 [2012] PIERB 39 [2012] PIERB 38 [2012] PIERB 37 [2012] PIERB 36 [2012] PIERB 35 [2011] PIERB 34 [2011] PIERB 33 [2011] PIERB 32 [2011] PIERB 31 [2011] PIERB 30 [2011] PIERB 29 [2011] PIERB 28 [2011] PIERB 27 [2011] PIERB 26 [2010] PIERB 25 [2010] PIERB 24 [2010] PIERB 23 [2010] PIERB 22 [2010] PIERB 21 [2010] PIERB 20 [2010] PIERB 19 [2010] PIERB 18 [2009] PIERB 17 [2009] PIERB 16 [2009] PIERB 15 [2009] PIERB 14 [2009] PIERB 13 [2009] PIERB 12 [2009] PIERB 11 [2009] PIERB 10 [2008] PIERB 9 [2008] PIERB 8 [2008] PIERB 7 [2008] PIERB 6 [2008] PIERB 5 [2008] PIERB 4 [2008] PIERB 3 [2008] PIERB 2 [2008] PIERB 1 [2008]
2021-10-10
Inversion of Electrical and Geometrical Parameters of a Stratified Medium from Data Derived from the Small Perturbation Method and the Small Slope Approximation
By
Progress In Electromagnetics Research B, Vol. 94, 19-36, 2021
Abstract
The goal of the present paper is on retrieving the electrical and geometrical parameters of a stratified medium with two rough interfaces. The inversion problem is formulated as a cost function optimization problem, and it is solved using the simulated annealing algorithm. The cost function consists in the integrated squared deviation between the co-polarized incoherent intensities obtained from the Small Slope Approximation and those obtained from the Small Perturbation Method. The inversion scheme is applied to the electrical and geometrical parameters involved into the analytical expressions of the incoherent intensities given by the SPM. We study the influence of the shape of the autocorrelation function and the isotropy factor upon the estimation of parameters. We test the sensitivity of the inversion scheme to noisy synthetic data. The study is applied to snow-covered soils in L-band. For the configurations under study, we show that the inverse method is efficient for eight-parameter or ten-parameter predicting problems.
Citation
Nada Djedouani, Saddek Afifi, and Richard Dusséaux, "Inversion of Electrical and Geometrical Parameters of a Stratified Medium from Data Derived from the Small Perturbation Method and the Small Slope Approximation," Progress In Electromagnetics Research B, Vol. 94, 19-36, 2021.
doi:10.2528/PIERB21071305
References

1. Tabatabaeenejad, A. and M. Moghaddam, "Study of validity region of small perturbation method for two-layer rough surfaces," IEEE Geosci. Remote Sens. Lett., Vol. 7, No. 2, 319-323, Apr. 2010.
doi:10.1109/LGRS.2009.2034543

2. Imperatore, P., A. Iodice, M. Pastorino, and N. Pinel, "Modelling scattering of electromagnetic waves in layered media: An up-to-date perspective," Int. J. Antennas Propag., Vol. 2017, 1-14, 2017.
doi:10.1155/2017/7513239

3. Amra, C., M. Lequime, and M. Zerrad, Electromagnetic Optics of Thin-film Coatings: Light Scattering, Giant Field Enhancement, and Planar Microcavities, Cambridge University Press, 2021.

4. El-Shenawee, M., "Polarimetric scattering from two-layered two dimensional random rough surfaces with and without buried objects," IEEE Trans. Geosci. Remote Sens., Vol. 42, No. 1, 67-76, Jan. 2001.
doi:10.1109/TGRS.2003.815675

5. Dechamps, N., N. de Beaucoudrey, C. Bourlier, and S. Toutain, "Fast numerical method for electromagnetic scattering by rough layered interfaces: Propagation-inside-layer expansion method," J. Opt. Soc. Amer. A, Vol. 23, No. 2, 359, Feb. 2006.
doi:10.1364/JOSAA.23.000359

6. Dechamps, N. and C. Bourlier, "Electromagnetic scattering from a rough layer: Propagation-inside-layer expansion method combined to the forward-backward novel spectral acceleration," IEEE Trans. Antennas Propag., Vol. 55, No. 12, 3576-3586, Dec. 2007.
doi:10.1109/TAP.2007.910360

7. Zamani, H., A. Tavakoli, and M. Dehmollaian, "Scattering from layered rough surfaces: Analytical and numerical investigations," IEEE Trans. Geosci. Rem. Sens., Vol. 54, No. 6, 3685-3696, Jun. 2016.
doi:10.1109/TGRS.2016.2524639

8. Yang, Y. and K.-S. Chen, "Full-polarization bistatic scattering from an inhomogeneous rough surface," IEEE Trans. Geosci. Remote Sens., Vol. 57, No. 9, 6434-6446, Sep. 2019.
doi:10.1109/TGRS.2019.2906079

9. Jonard, F., F. Ande, N. Pinel, C. Warren, H. Vereecken, and S. Lambot, "Modeling of multilayered media Green's functions with rough interfaces," IEEE Trans. Geosci. Remote Sens., Vol. 57, No. 10, 7671-7681, Oct. 2019.
doi:10.1109/TGRS.2019.2915676

10. Tijhuis, A. G., Electromagnetic Inverse Profiling: Theory and Numerical Implementation, VNU, Utrecht, The Netherlands, 1987.

11. Ghosh Roy, D. N. and L. S. Couchman, Inverse Problems and Inverse Scattering of Plane Waves, Academic Press, London, 1996.

12. Afifi, S. and M. Diaf, "Scattering by random rough surfaces: Study of direct and inverse problem," Optics Comm., Vol. 265, 11-17, 2006.
doi:10.1016/j.optcom.2006.02.044

13. Tabatabaeenejad, A. and M. Moghaddam, "Inversion of subsurface properties of layered dielectric structures with random slightly rough interfaces using the method of simulated annealing," IEEE Trans. Geosci. Remote Sensing, Vol. 47, No. 7, 2035-2046, Jul. 2009.
doi:10.1109/TGRS.2008.2011982

14. Elson, J. M., "Infrared light scattering from surfaces covered with multiple dielectric overlayers," Appl. Opt., Vol. 16, No. 11, 2873-2881, Nov. 1977.

15. Elson, J. M., J. P. Rahn, and J. M. Bennett, "Relationship of the total integrated scattering from multilayer-coated optics to angle of incidence, polarization, correlation length, and roughness cross-correlation properties," Appl. Opt., Vol. 22, No. 20, 3207-3219, Oct. 1983.
doi:10.1364/AO.22.003207

16. Fuks, I. M., "Wave diffraction by a rough boundary of an arbitrary plane-layered medium," IEEE Trans. Antennas Propag., Vol. 49, No. 4, 630-639, Apr. 2001.
doi:10.1109/8.923325

17. Tabatabaeenejad, A. and M. Moghaddam, "Bistatic scattering from three-dimensional layered rough surfaces," IEEE Trans. Geosci. Remote Sens., Vol. 44, No. 8, 2102-2114, Aug. 2006.
doi:10.1109/TGRS.2006.872140

18. Imperatore, P., A. Iodiceand, and D. Riccio, "Electromagnetic wave scattering from layered structures with an arbitrary number of rough interfaces," IEEE Trans. Geosci. Remote Sens., Vol. 47, No. 4, 1056-1072, Apr. 2009.
doi:10.1109/TGRS.2008.2007804

19. Afifi, S., R. Duseaux, and R. de Oliveira, "Statistical distribution of the field scattered by rough layered interfaces: Formulae derived from the small perturbation method," Waves Random Complex Media, Vol. 20, No. 1, 1-22, Feb. 2010.
doi:10.1080/17455030903329374

20. Afifi, S. and R. Dusseaux, "Scattering by anisotropic rough layered 2D interfaces," IEEE Trans. Antenna Propagat., Vol. 60, No. 11, 5315-5328, Nov. 2012.
doi:10.1109/TAP.2012.2207671

21. Zamani, H., A. Tavakoli, and M. Dehmollaian, "Scattering from two rough surfaces with inhomogeneous dielectric profiles," IEEE Trans. Antenna. Propag., Vol. 63, No. 12, 5753-5766, Dec. 2015.
doi:10.1109/TAP.2015.2490668

22. Van Laarhoven, P. J. M. and E. H. L. Aarts, Simulated Annealing: Theory and Applications, Reidel, Dordrecht, The Netherlands, 1987.
doi:10.1007/978-94-015-7744-1

23. Kirkpatrick, S., C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing," Science, Vol. 220, No. 4598, 671-680, May 1983.
doi:10.1126/science.220.4598.671

24. Kirkpatrick, S., "Optimization by simulated annealing: Quantitative studies," J. Stat. Phys., Vol. 34, No. 5/6, 975-986, Mar. 1984.
doi:10.1007/BF01009452

25. Corana, A., M. Marchesi, C. Martini, and S. Ridella, "Minimizing multimodal functions of continuous variables with the "simulated annealin" algorithm," ACM Trans. Math. Soft., Vol. 13, No. 3, 262-280, Sep. 1987.
doi:10.1145/29380.29864

26. Lee, K.-C., "Frequency-domain analyses of non-linearly loaded antenna arrays using simulated annealing algorithms," Progress In Electromagnetics Research, Vol. 53, 271-281, 2005.
doi:10.2528/PIER04101501

27. Voronovich, G., Wave Scattering from Rough Surfaces, Springer, Berlin, 1994.
doi:10.1007/978-3-642-97544-8

28. Voronovich, G., "Small-slope approximation for electromagnetic wave scattering at a rough interface of two dielectric half-spaces," Wave Random Media, Vol. 4, 337-367, 1994.
doi:10.1088/0959-7174/4/3/008

29. Berrouk, A., R. Duseaux, and S. Afifi, "Electromagnetic wave scattering from rough layered interfaces: Analysis with the small perturbation method and the small slope approximation," Progress In Electromagnetics Research B, Vol. 57, 177-190, 2014.
doi:10.2528/PIERB13101802

30. Afifi, S., R. Dusseaux, and A. Berrouk, "Electromagnetic scattering from 3D layered structures with randomly rough interfaces: Analysis with the small perturbation method and the small slope approximation," IEEE Trans. Ant. Prop., Vol. 62, No. 10, 5200-5208, Oct. 2014.
doi:10.1109/TAP.2014.2341704

31. Duseaux, R., S. Afifi, and M. Dechambre, "Scattering properties of a stratified air/snow/sea ice medium. Small slope approximation," Comptes Rendus Physique, Vol. 17, No. 9, 995-1002, Elsevier Masson, 2016.
doi:10.1016/j.crhy.2016.07.017

32. Jackson, D. R. and D. R. Olson, "The small-slope approximation for layered, fluid seafloors," J. Acoust. Soc. Am., Vol. 147, 56-73, 2020.
doi:10.1121/10.0000470

33. Beckmann, P. and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces, Pergamon Press, Oxford, UK, 1963.

34. Chen, Q., D. Won, and D. M. Akos, "Snow depth estimation accuracy using a dual-interface GPS-IR model with experimental results," GPS Solut., Vol. 21, 211-223, 2017.
doi:10.1007/s10291-016-0517-1

35. Lemmetyinen, J., M. Schwank, K. Rautiainen, A. Kontu, T. Parkkinen, C. Matzler, A. Wiesmann, U. Weguller, C. Derksen, and P. Toose, "Snow density and ground permittivity retrieved from L-band radiometry: Application to experimental data," Remote Sensing of Environment, Vol. 180, 377-391, 2016.
doi:10.1016/j.rse.2016.02.002

36. Frolov, A. D. and Y. Y. Macheret, "On dielectric properties of dry and wet snow," Hydrol. Process., Vol. 13, 1755-1760, 1999.
doi:10.1002/(SICI)1099-1085(199909)13:12/13<1755::AID-HYP854>3.0.CO;2-T

37. Kennedy, J. and R. Eberhart, "Particle swarm optimization," Proc. IEEE of International Conference on Neural Networks, 1942-1948, 1995.
doi:10.1109/ICNN.1995.488968

38. Holland, J. H., Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Arbor, MI, 1975.

39. Tso, B. C. K. and P. M. Mather, "Classification of multisource remote sensing imagery using a genetic algorithm and Markov random fields," IEEE Trans. Geosci. Remote Sens., Vol. 37, No. 3, 1255-1260, May 1999.
doi:10.1109/36.763284