On Green's functions for the reduced wave equation in a circular annular domain with dirichlet, Neumann and radiation type boundary conditions

1966 ◽  
Vol 16 (1) ◽  
pp. 5-12 ◽  
Author(s):  
Johann Martinek ◽  
Henry P. Thielman
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Green's Functions ◽  
Green’S Functions ◽  
Annular Domain ◽  
Type Boundary ◽  
Radiation Type

On seismic deghosting using integral representation for the wave equation: Use of Green’s functions with Neumann or Dirichlet boundary conditions

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. T89-T98 ◽  
Author(s):  
Lasse Amundsen ◽  
Arthur B. Weglein ◽  
Arne Reitan
Keyword(s):  
Wave Equation ◽  
Integral Representation ◽  
Boundary Conditions ◽  
Representation Theorem ◽  
Green's Functions ◽  
Dirichlet Boundary ◽  
Green’S Functions ◽  
Dirichlet Boundary Conditions ◽  
Sea Surface ◽  
Receiver Side

The recent interest in broadband seismic technology has spurred research into new and improved seismic deghosting solutions. One starting point for deriving deghosting methods is the representation theorem, which is an integral representation for the wave equation. Recent research results show that by using Green’s functions with Dirichlet boundary conditions in the representation theorem, source-side deghosting of already receiver-side deghosted wavefields can be achieved. We found that the choice of Green’s functions with Neumann boundary conditions on the sea surface and the plane that contains the sources leads to an identical but simpler solution with fewer processing steps. In addition, we found that pressure data can be receiver-side deghosted by introducing Green’s functions with Dirichlet boundary conditions on the sea surface and the plane containing the receivers into a modified representation theorem. The deghosting methods derived from the representation theorem are wave-theoretic algorithms defined in the frequency-space domain and can accommodate streamers of any shape (e.g., slanted). Our theoretical analysis of deghosting is performed in the frequency-wavenumber domain where analytical deghosting solutions are well known and thus are available for verifying the solutions. A simple numerical example can be used to show how source-side deghosting can be performed in the space domain by convolving data with Green’s functions.

Boundary conditions for Green's functions of spatially inhomogeneous superconducting systems

1988 ◽  
Vol 74 (3) ◽  
pp. 306-311 ◽  
Author(s):  
B. P. Leskov ◽  
A. N. Makeev ◽  
A. V. Svidzinskii
Keyword(s):  
Boundary Conditions ◽  
Green's Functions ◽  
Green’S Functions ◽  
Spatially Inhomogeneous

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.

Sign Properties of Green's Functions For Two Classes of Boundary Value Problems

1987 ◽  
Vol 30 (1) ◽  
pp. 28-35 ◽  
Author(s):  
P. W. Eloe
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Green’S Function ◽  
Boundary Value Problems ◽  
Green's Function ◽  
Difference Equations ◽  
Green's Functions ◽  
Green’S Functions ◽  
Boundary Value ◽  
Partial Derivatives

AbstractLet G(x,s) be the Green's function for the boundary value problem y(n) = 0, Ty = 0, where Ty = 0 represents boundary conditions at two points. The signs of G(x,s) and certain of its partial derivatives with respect to x are determined for two classes of boundary value problems. The results are also carried over to analogous classes of boundary value problems for difference equations.

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