Improving convergence in scattering problems by smoothing discrete constraints using an approximate convolution with a smoothed composite Green’s function

1998 ◽  
Vol 103 (5) ◽  
pp. 3056-3056
Author(s):  
Rickard C. Loftman ◽  
Donald B. Bliss
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Scattering Problems

Green’s Function Integral Equation Methods for Electromagnetic Scattering Problems

2018 ◽  
pp. 197-250
Author(s):  
Andrei V. Lavrinenko ◽  
Jesper Lægsgaard ◽  
Niels Gregersen ◽  
Frank Schmidt ◽  
Thomas Søndergaard
Keyword(s):  
Integral Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Electromagnetic Scattering ◽  
Scattering Problems ◽  
Integral Equation Methods

scholarly journals Marchenko imaging

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. WA39-WA57 ◽  
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.

scholarly journals Dyadic Green's function of an ideal hard surface circular waveguide with application to excitation and scattering problems

Radio Science ◽  
2005 ◽  
Vol 40 (3) ◽  
pp. n/a-n/a ◽  
Author(s):  
Victor A. Klymko ◽  
Alexander B. Yakovlev ◽  
Islam A. Eshrah ◽  
Ahmed A. Kishk ◽  
Allen W. Glisson
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Circular Waveguide ◽  
Scattering Problems ◽  
Hard Surface ◽  
Dyadic Green’S Function ◽  
Dyadic Green's Function

The efficient implementation of IE-FFT algorithm with combined field integral equation for solving electromagnetic scattering problems

2020 ◽  
pp. 1-7
Author(s):  
Seung Mo Seo
Keyword(s):  
Integral Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Electromagnetic Scattering ◽  
Cartesian Grid ◽  
Memory Storage ◽  
Scattering Problems ◽  
Cpu Time ◽  
Interaction Terms ◽  
Field Integral

Abstract An integral equation-fast Fourier transform (IE-FFT) algorithm is applied to the electromagnetic solutions of the combined field integral equation (CFIE) for scattering problems by an arbitrary-shaped three-dimensional perfect electric conducting object. The IE-FFT with CFIE uses a Cartesian grid for known Green's function to considerably reduce memory storage and speed up CPU time for both matrix fill-in and matrix vector multiplication when used with a generalized minimal residual method. The uniform interpolation of the Green's function on an equally spaced Cartesian grid allows a global FFT for field interaction terms. However, the near interaction terms do not take care for the singularity of the Green's function and should be adequately corrected. The IE-FFT with CFIE does not always require a suitable preconditioner for electrically large problems. It is shown that the complexity of the IE-FFT with CFIE is found to be approximately O(N1.5) and O(N1.5log N) for memory and CPU time, respectively.

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