Electromagnetic subsurface prospecting by a fully nonlinear multifocusing inexact Newton method

Marco Salucci; Giacomo Oliveri; Andrea Randazzo; Matteo Pastorino; Andrea Massa

doi:10.1364/JOSAA.31.002618

Journal of the Optical Society of America A
Vol. 31,
Issue 12,
pp. 2618-2629
(2014)
•https://doi.org/10.1364/JOSAA.31.002618

Electromagnetic subsurface prospecting by a fully nonlinear multifocusing inexact Newton method

Marco Salucci, Giacomo Oliveri, Andrea Randazzo, Matteo Pastorino, and Andrea Massa

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Marco Salucci, Giacomo Oliveri, Andrea Randazzo, Matteo Pastorino, and Andrea Massa, "Electromagnetic subsurface prospecting by a fully nonlinear multifocusing inexact Newton method," J. Opt. Soc. Am. A 31, 2618-2629 (2014)

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Abstract

An electromagnetic inverse scattering procedure for the reconstruction of shallow buried objects in a homogeneous half-space is proposed. The approach is based on the numerical solution of the integral equations that model inverse scattering relationships, and it extends to strong scatterers the imaging capabilities of a previously proposed approach relying on approximated formulations. The inversion is based on the synergic application of a multifocusing strategy based on the iterative multiscaling approach along with an efficient regularization scheme based on the inexact Newton method. Numerical results corroborate the mathematical description to assess capabilities and current limitations of the proposed fully nonlinear technique.

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SNR	$I_{tot}$	$ϕ^{final}$	$Ξ_{tot}$	$Ξ_{int}$	$Ξ_{ext}$	$Δ t$ [s]
BARE
$\infty$ (Noiseless)	600	$1.28 \times 10^{- 3}$	$9.46 \times 10^{- 2}$	$2.17 \times 10^{- 1}$	$6.94 \times 10^{- 2}$	4041
30 [dB]	600	$1.80 \times 10^{- 3}$	$9.44 \times 10^{- 2}$	$2.17 \times 10^{- 1}$	$7.04 \times 10^{- 2}$	4045
20 [dB]	600	$4.07 \times 10^{- 3}$	$9.83 \times 10^{- 2}$	$2.21 \times 10^{- 1}$	$7.25 \times 10^{- 2}$	4042
10 [dB]	600	$1.25 \times 10^{- 2}$	$1.35 \times 10^{- 1}$	$2.17 \times 10^{- 1}$	$1.00 \times 10^{- 1}$	4038
5 [dB]	600	$2.20 \times 10^{- 2}$	$1.91 \times 10^{- 1}$	$2.31 \times 10^{- 1}$	$1.37 \times 10^{- 1}$	4023
IMSA
$\infty$ (Noiseless)	450	$4.45 \times 10^{- 3}$	$5.61 \times 10^{- 3}$	$1.36 \times 10^{- 1}$	0.00	211
30 [dB]	461	$4.53 \times 10^{- 3}$	$5.60 \times 10^{- 3}$	$1.36 \times 10^{- 1}$	0.00	212
20 [dB]	827	$5.39 \times 10^{- 3}$	$2.89 \times 10^{- 3}$	$6.87 \times 10^{- 2}$	0.00	288
10 [dB]	3020	$1.41 \times 10^{- 2}$	$5.21 \times 10^{- 3}$	$1.17 \times 10^{- 1}$	0.00	795
5 [dB]	3020	$2.43 \times 10^{- 2}$	$1.46 \times 10^{- 2}$	$1.97 \times 10^{- 1}$	$5.96 \times 10^{- 3}$	776

SNR	$Ξ_{tot} BARE$	$Ξ_{tot} IMSA$
$\infty$ (Noiseless)	$3.07 \times 10^{- 1}$	$4.01 \times 10^{- 2}$
30 [dB]	$3.07 \times 10^{- 1}$	$3.98 \times 10^{- 2}$
20 [dB]	$3.14 \times 10^{- 1}$	$1.61 \times 10^{- 2}$
10 [dB]	$3.60 \times 10^{- 1}$	$2.26 \times 10^{- 2}$
5 [dB]	$4.21 \times 10^{- 1}$	$3.97 \times 10^{- 2}$

SNR	$I_{tot}$	$ϕ^{final}$	$Ξ_{tot}$	$Ξ_{int}$	$Ξ_{ext}$	$Δ t$ [s]
BARE
$\infty$ (Noiseless)	600	$1.28 \times 10^{- 3}$	$9.46 \times 10^{- 2}$	$2.17 \times 10^{- 1}$	$6.94 \times 10^{- 2}$	4041
30 [dB]	600	$1.80 \times 10^{- 3}$	$9.44 \times 10^{- 2}$	$2.17 \times 10^{- 1}$	$7.04 \times 10^{- 2}$	4045
20 [dB]	600	$4.07 \times 10^{- 3}$	$9.83 \times 10^{- 2}$	$2.21 \times 10^{- 1}$	$7.25 \times 10^{- 2}$	4042
10 [dB]	600	$1.25 \times 10^{- 2}$	$1.35 \times 10^{- 1}$	$2.17 \times 10^{- 1}$	$1.00 \times 10^{- 1}$	4038
5 [dB]	600	$2.20 \times 10^{- 2}$	$1.91 \times 10^{- 1}$	$2.31 \times 10^{- 1}$	$1.37 \times 10^{- 1}$	4023
IMSA
$\infty$ (Noiseless)	450	$4.45 \times 10^{- 3}$	$5.61 \times 10^{- 3}$	$1.36 \times 10^{- 1}$	0.00	211
30 [dB]	461	$4.53 \times 10^{- 3}$	$5.60 \times 10^{- 3}$	$1.36 \times 10^{- 1}$	0.00	212
20 [dB]	827	$5.39 \times 10^{- 3}$	$2.89 \times 10^{- 3}$	$6.87 \times 10^{- 2}$	0.00	288
10 [dB]	3020	$1.41 \times 10^{- 2}$	$5.21 \times 10^{- 3}$	$1.17 \times 10^{- 1}$	0.00	795
5 [dB]	3020	$2.43 \times 10^{- 2}$	$1.46 \times 10^{- 2}$	$1.97 \times 10^{- 1}$	$5.96 \times 10^{- 3}$	776

SNR	$Ξ_{tot} BARE$	$Ξ_{tot} IMSA$
$\infty$ (Noiseless)	$3.07 \times 10^{- 1}$	$4.01 \times 10^{- 2}$
30 [dB]	$3.07 \times 10^{- 1}$	$3.98 \times 10^{- 2}$
20 [dB]	$3.14 \times 10^{- 1}$	$1.61 \times 10^{- 2}$
10 [dB]	$3.60 \times 10^{- 1}$	$2.26 \times 10^{- 2}$
5 [dB]	$4.21 \times 10^{- 1}$	$3.97 \times 10^{- 2}$

Abstract

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Equations (19)

Journal of the Optical Society of America A