The concept of generalized functions and universal properties of the Green's functions associated with the wave equation in bounded piece-wise homogeneous domains

2020 ◽  
pp. 119-144
Author(s):  
Mithat Idemen
Keyword(s):  
Wave Equation ◽  
Green's Functions ◽  
Green’S Functions ◽  
Generalized Functions ◽  
Universal Properties ◽  
Homogeneous Domains

Parabolic Representations of Scattering Green’s Functions

1999 ◽  
Author(s):  
Paul E. Barbone
Keyword(s):  
Asymptotic Expansion ◽  
Wave Equation ◽  
Green’S Function ◽  
Inhomogeneous Medium ◽  
Green's Function ◽  
Free Space ◽  
Green's Functions ◽  
Green’S Functions

Abstract We derive a one-way wave equation representation of the “free space” Green’s function for an inhomogeneous medium. Our representation results from an asymptotic expansion in inverse powers of the wavenumber. Our representation takes account of losses due to scattering in all directions, even though only one-way operators are used.

The K-Space Green’s Functions for Decoupled Constant-Q Wave Equation and its Adjoint Equation

2017 ◽  
Author(s):  
Y.F. Wang ◽  
H. Zhou ◽  
X.Z. Zhao ◽  
M.M. Xia ◽  
X.L. Cai
Keyword(s):  
Wave Equation ◽  
Green's Functions ◽  
Green’S Functions ◽  
Adjoint Equation ◽  
Q Wave

On: “Green's function implementation of common‐offset wave equation migration,” (A. Ehinger, P. Lailly and K. J. Marfurt, November‐December 1996 GEOPHYSICS, 61, p. 1813–1821)

Geophysics ◽  
1997 ◽  
Vol 62 (4) ◽  
pp. 1333-1335
Author(s):  
Kees Wapenaar
Keyword(s):  
Wave Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Complex Media

The paper by Ehinger and co‐authors deals with migration in complex media in which severe multi‐pathing may occur. I wholeheartedly agree with their remark that the use of complete Green's functions is preferred over approximate Green's functions containing first arrivals only.

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