Representation theorems and Green’s function retrieval for scattering in acoustic media

2009 ◽  
Vol 80 (3) ◽  
Author(s):  
Ivan Vasconcelos ◽  
Roel Snieder ◽  
Huub Douma
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Representation Theorems ◽  
Acoustic Media

Composite boundary‐valued solution of the 2.5-D Green’s function for arbitrary acoustic media

Geophysics ◽  
1998 ◽  
Vol 63 (5) ◽  
pp. 1813-1823 ◽  
Author(s):  
Bing Zhou ◽  
Stewart A. Greenhalgh
Keyword(s):  
Boundary Condition ◽  
Green’S Function ◽  
Frequency Domain ◽  
Green's Function ◽  
Mixed Boundary ◽  
Waveform Inversion ◽  
Acoustic Medium ◽  
Model Parameters ◽  
Low Velocity ◽  
Acoustic Media

Theoretically, the Green’s function can be used to calculate the wavefield response of a specified source and the Fréchet derivative with respect to the model parameters for crosshole seismic full‐waveform inversion. In this paper, we apply the finite‐element method to numerically compute the 2.5-D Green’s function for an arbitrary acoustic medium by solving a composite boundary‐valued problem in the wavenumber‐frequency domain. The composite boundary condition consists of a 2.5-D absorbing boundary condition for the propagating wave field and a mixed boundary condition for the evanescent field in inhomogeneous media modeling. A numerical experiment performed for a uniform earth (having a known exact solution) shows the accuracy of the computation in the frequency and time domain. An inhomogeneous medium test, involving an embedded low‐velocity layer, demonstrates that the permissible range of [Formula: see text] at each frequency can be determined rationally from the critical wavenumber value of the medium around the source. Furthermore, it shows that the frequency‐domain solution is not improved continuously by increasing the number of [Formula: see text] samples because of the complicated nature of the wavefield. Both experiments show that the proposed method is effective and flexible for computing the 2.5-D Green’s function for arbitrary acoustic media.

On a method to obtain a Green's function for a multi-layered half space

1964 ◽  
Vol 54 (4) ◽  
pp. 1087-1096
Author(s):  
I. Herrera
Keyword(s):  
Surface Wave ◽  
Integral Representation ◽  
Green’S Function ◽  
Surface Waves ◽  
Half Space ◽  
Green's Function ◽  
Rayleigh Waves ◽  
Two Dimensional ◽  
Representation Theorems ◽  
Layered Half Space

Abstract In this paper the surface wave terms of the Green's function for a two-dimensional multilayered half space are obtained. The method used is new and remarkable by its simplicity. It is based on the integral representation theorems for elastodynamics. The orthogonality properties of surface waves are generalized to include not only Love waves but Rayleigh waves as well.

GREEN'S FUNCTION MATCHING METHOD FOR REALISTIC CALCULATIONS OF INTERFACES

1985 ◽  
Vol 46 (C4) ◽  
pp. C4-321-C4-329 ◽  
Author(s):  
E. Molinari ◽  
G. B. Bachelet ◽  
M. Altarelli
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Matching Method

THE ATOMISTIC GREEN'S FUNCTION METHOD FOR INTERFACIAL PHONON TRANSPORT

2014 ◽  
Vol 17 (N/A) ◽  
pp. 89-145 ◽  
Author(s):  
Sridhar Sadasivam ◽  
Yuhang Che ◽  
Zhen Huang ◽  
Liang Chen ◽  
Satish Kumar ◽  
...  
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Phonon Transport ◽  
Green’S Function Method
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