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Two dimensional inverse scattering from buried magnetic anomalies
Issued date
February 2008
Issue/vol(year)
1/51 (2008)
Language
English
Abstract
This paper deals with the problem of the electromagnetic linear inverse scattering from magnetic anomalies
buried in a lossy half space, for a scalar and two dimensional case. First, the formulation of the exact model of
the electromagnetic scattering is given. Then, the linear inverse problem is solved by resorting to the well assessed
Singular Value Decomposition tool. The reliability of the solution procedure is tested with synthetic data
achieved by a FDTD code.
buried in a lossy half space, for a scalar and two dimensional case. First, the formulation of the exact model of
the electromagnetic scattering is given. Then, the linear inverse problem is solved by resorting to the well assessed
Singular Value Decomposition tool. The reliability of the solution procedure is tested with synthetic data
achieved by a FDTD code.
References
ABUBAKAR, A. and P.M. VAN DEN BERG (2004): Iterative forward
and inverse algorithms based on domain integral
equations for three-dimensional electric and magnetic
objects, J. Comput. Phys., 195, 236-262.
BERTERO, M. and P. BOCCACCI (1998): Introduction to Inverse
Problems in Imaging (IOP, Bristol, U.K.).
CHEW, W.C. (1995): Waves and Fields in Inhomogeneous
Media (IEEE Ppress, Piscataway, N.J.).
CHEN, P., R.X. WU, T. ZHAO, F. YANG and J.Q. XIAO (2005):
Complex permittivity and permeability of metallic
magnetic granular composites at microwave frequencies,
J. Phys. D Appl. Phys., 38, 2302-2305.
COLLIN, R.E. (1985): Antennas and Radiowave Propagation
(McGraw-Hill).
COLTON, D. and R. KRESS (1992): Inverse Acoustic and
Electromagnetic Scattering Theory (Springer Verlag).
CROCCO, L. and F. SOLDOVIERI (2003): A microwave tomographic
approach for imaging targets buried in a layered
medium, Ann. Geophys., 46 (3), 559-572.
DURAL, D. and M.I. AKSUN (1995): Closed-Form Green’s
Functions for General Sources and Stratified Media,
IEEE Trans. Microwave Theory Techniques, 43 (7),
1545-1552.
GIANNOPULOS, A. (2003): GprMax2D V 1.5 (Electromagnetic
Simulator for Ground Probing Radar).
GUSTAFSSON, M. and S. HE (2000): An optimization approach
to two-dimensional time domain electromagnetic
inverse problems, Radio Sci., 35 (2), 525-536.
JARVIS, J.B., M.D. JANEZIC, B.F. RIDDLE, R.T. JOHNK, P. KABOS,
C.L. HOLLOWAY, R.G. GEYER and C.A. GROSVENOVER
(2004): Measuring the permittivity and permeability
of lossy materials: solids, liquids, metals, buildings
materials, and negative-index materials, NIST
Technical Note 1536.
NABIGHIAN, M. (1987): Electromagnetic Methods in Applied
Geophysics-Theory (Society of Exploration Geophysics),
vol. 1.
NIE, X.C., N. YUAN, L.W. LI, Y.B. GAN and T.S. YEO
(2006): A fast combined field volume integral equation
solution to EM scattering by 3D dielectric objects of arbitrary permittivity and permeability, IEEE Trans.
Antennas Prop., 54 (3), 961-969.
PISCITELLI, S., E. RIZZO, F. CRISTALLO, V. LAPENNA, L.
CROCCO, R. PERSICO and F. SOLDOVIERI (2007): GPR
and microwave tomography for detecting shallow cavities
in the historical area of Sassi of Matera (Southern
italy), Near Surface Geophysics (accepted).
SOLDOVIERI, F., R. PERSICO and G. LEONE (2006): A microwave
tomographic imaging approach for multibistatic
configuration: the choice of frequency step, IEEE
Trans. Instrumentation Measurements, 55 (6), 1926-
1934.
SOLDOVIERI, F., J. HUGENSCHMIDT, R. PERSICO and G. LEONE
(2007): A linear inverse scattering algorithm for realistic GPR applications, Near Surface Geophys., 5 (1),
29-42.
STILLMAN, D.E. and G.R. OLHOEFT (2004): GPR and magnetic
minerals at Mars temperatures, in Tenth International
Conference on Ground Penetrating Radar, 735-
738.
STILLMAN, D.E. and G.R. OLHOEFT (2006): Electromagnetic
properties of martian analog minerals at radar frequencies
and martian temperatures, in Proceedings of
the 37th Lunar and Planetary Science Conference.
YOUNG, J.L. and C.M. JOHNSON (2004): A Compact Recursive
Trans-Impedance Green’s Function for the Inhomogeneous
Ferrite Microwave Circulator, IEEE Trans.
Microwave Theory Techniques, 52 (7), 1751-1759.
and inverse algorithms based on domain integral
equations for three-dimensional electric and magnetic
objects, J. Comput. Phys., 195, 236-262.
BERTERO, M. and P. BOCCACCI (1998): Introduction to Inverse
Problems in Imaging (IOP, Bristol, U.K.).
CHEW, W.C. (1995): Waves and Fields in Inhomogeneous
Media (IEEE Ppress, Piscataway, N.J.).
CHEN, P., R.X. WU, T. ZHAO, F. YANG and J.Q. XIAO (2005):
Complex permittivity and permeability of metallic
magnetic granular composites at microwave frequencies,
J. Phys. D Appl. Phys., 38, 2302-2305.
COLLIN, R.E. (1985): Antennas and Radiowave Propagation
(McGraw-Hill).
COLTON, D. and R. KRESS (1992): Inverse Acoustic and
Electromagnetic Scattering Theory (Springer Verlag).
CROCCO, L. and F. SOLDOVIERI (2003): A microwave tomographic
approach for imaging targets buried in a layered
medium, Ann. Geophys., 46 (3), 559-572.
DURAL, D. and M.I. AKSUN (1995): Closed-Form Green’s
Functions for General Sources and Stratified Media,
IEEE Trans. Microwave Theory Techniques, 43 (7),
1545-1552.
GIANNOPULOS, A. (2003): GprMax2D V 1.5 (Electromagnetic
Simulator for Ground Probing Radar).
GUSTAFSSON, M. and S. HE (2000): An optimization approach
to two-dimensional time domain electromagnetic
inverse problems, Radio Sci., 35 (2), 525-536.
JARVIS, J.B., M.D. JANEZIC, B.F. RIDDLE, R.T. JOHNK, P. KABOS,
C.L. HOLLOWAY, R.G. GEYER and C.A. GROSVENOVER
(2004): Measuring the permittivity and permeability
of lossy materials: solids, liquids, metals, buildings
materials, and negative-index materials, NIST
Technical Note 1536.
NABIGHIAN, M. (1987): Electromagnetic Methods in Applied
Geophysics-Theory (Society of Exploration Geophysics),
vol. 1.
NIE, X.C., N. YUAN, L.W. LI, Y.B. GAN and T.S. YEO
(2006): A fast combined field volume integral equation
solution to EM scattering by 3D dielectric objects of arbitrary permittivity and permeability, IEEE Trans.
Antennas Prop., 54 (3), 961-969.
PISCITELLI, S., E. RIZZO, F. CRISTALLO, V. LAPENNA, L.
CROCCO, R. PERSICO and F. SOLDOVIERI (2007): GPR
and microwave tomography for detecting shallow cavities
in the historical area of Sassi of Matera (Southern
italy), Near Surface Geophysics (accepted).
SOLDOVIERI, F., R. PERSICO and G. LEONE (2006): A microwave
tomographic imaging approach for multibistatic
configuration: the choice of frequency step, IEEE
Trans. Instrumentation Measurements, 55 (6), 1926-
1934.
SOLDOVIERI, F., J. HUGENSCHMIDT, R. PERSICO and G. LEONE
(2007): A linear inverse scattering algorithm for realistic GPR applications, Near Surface Geophys., 5 (1),
29-42.
STILLMAN, D.E. and G.R. OLHOEFT (2004): GPR and magnetic
minerals at Mars temperatures, in Tenth International
Conference on Ground Penetrating Radar, 735-
738.
STILLMAN, D.E. and G.R. OLHOEFT (2006): Electromagnetic
properties of martian analog minerals at radar frequencies
and martian temperatures, in Proceedings of
the 37th Lunar and Planetary Science Conference.
YOUNG, J.L. and C.M. JOHNSON (2004): A Compact Recursive
Trans-Impedance Green’s Function for the Inhomogeneous
Ferrite Microwave Circulator, IEEE Trans.
Microwave Theory Techniques, 52 (7), 1751-1759.
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