Inverse scattering of 2-D dielectric objects buried in multilayer media using complex images Green's function in Born iteration method

Abstract Green's theorem plays a fundamental role in a diverse range of wavefield imaging applications, such as holographic imaging, inverse scattering, time-reversal acoustics and interferometric Green's function retrieval. In many of those applications, the homogeneous Green's function (i.e. the Green's function of the wave equation without a singularity on the right-hand side) is represented by a closed boundary integral. In practical applications, sources and/or receivers are usually present only on an open surface, which implies that a significant part of the closed boundary integral is by necessity ignored. Here we derive a homogeneous Green's function representation for the common situation that sources and/or receivers are present on an open surface only. We modify the integrand in such a way that it vanishes on the part of the boundary where no sources and receivers are present. As a consequence, the remaining integral along the open surface is an accurate single-sided representation of the homogeneous Green's function. This single-sided representation accounts for all orders of multiple scattering. The new representation significantly improves the aforementioned wavefield imaging applications, particularly in situations where the first-order scattering approximation breaks down.

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A new representation for the Green's function of a multilayer media

IEEE Antennas and Propagation Society International Symposium (IEEE Cat. No.02CH37313) ◽

10.1109/aps.2002.1016766 ◽

2003 ◽

Cited By ~ 3

Author(s):

M. Ayatollahi ◽

S. Safavi-Naeini

Keyword(s):

Green’S Function ◽

Green's Function ◽

Multilayer Media

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Simulating composite metallic and dielectric objects by an improved multilevel Green's function interpolation method

2013 IEEE International Workshop on Electromagnetics, Applications and Student Innovation Competition ◽

10.1109/iwem.2013.6888779 ◽

2013 ◽

Author(s):

Peng Zhao ◽

Chi-Hou Chan

Keyword(s):

Green’S Function ◽

Green's Function ◽

Interpolation Method ◽

Dielectric Objects

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Marchenko imaging

Geophysics ◽

10.1190/geo2013-0302.1 ◽

2014 ◽

Vol 79 (3) ◽

pp. WA39-WA57 ◽

Cited By ~ 169

Author(s):

Kees Wapenaar ◽

Jan Thorbecke ◽

Joost van der Neut ◽

Filippo Broggini ◽

Evert Slob ◽

...

Keyword(s):

Green’S Function ◽

Inverse Scattering ◽

Green's Function ◽

Seismic Interferometry ◽

Virtual Source ◽

Target Zone ◽

Scattering Problems ◽

Inverse Scattering Problems ◽

Marchenko Equation ◽

Internal Multiples

Traditionally, the Marchenko equation forms a basis for 1D inverse scattering problems. A 3D extension of the Marchenko equation enables the retrieval of the Green’s response to a virtual source in the subsurface from reflection measurements at the earth’s surface. This constitutes an important step beyond seismic interferometry. Whereas seismic interferometry requires a receiver at the position of the virtual source, for the Marchenko scheme it suffices to have sources and receivers at the surface only. The underlying assumptions are that the medium is lossless and that an estimate of the direct arrivals of the Green’s function is available. The Green’s function retrieved with the 3D Marchenko scheme contains accurate internal multiples of the inhomogeneous subsurface. Using source-receiver reciprocity, the retrieved Green’s function can be interpreted as the response to sources at the surface, observed by a virtual receiver in the subsurface. By decomposing the 3D Marchenko equation, the response at the virtual receiver can be decomposed into a downgoing field and an upgoing field. By deconvolving the retrieved upgoing field with the downgoing field, a reflection response is obtained, with virtual sources and virtual receivers in the subsurface. This redatumed reflection response is free of spurious events related to internal multiples in the overburden. The redatumed reflection response forms the basis for obtaining an image of a target zone. An important feature is that spurious reflections in the target zone are suppressed, without the need to resolve first the reflection properties of the overburden.

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