Application of transforms to accelerate the summation of periodic free-space Green's functions

1990 ◽  
Vol 38 (11) ◽  
pp. 1746-1748 ◽  
Author(s):  
S. Singh ◽  
R. Singh
Keyword(s):  
Free Space ◽  
Green's Functions ◽  
Green’S Functions

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.

WEIGHTING FACTORS IN THE CONSTRUCTION AND RECONSTRUCTION OF ACOUSTICAL WAVE FIELDS

Geophysics ◽  
1977 ◽  
Vol 42 (6) ◽  
pp. 1183-1198 ◽  
Author(s):  
Milos J. Kuhn ◽  
Khalid A. Alhilali
Keyword(s):  
Free Space ◽  
Green's Functions ◽  
Green’S Functions ◽  
Diffraction Theory ◽  
Weighting Factor ◽  
Total Response ◽  
Wave Fields ◽  
Seismic Migration ◽  
Weighting Factors ◽  
The Fourier Transform

The numerical solution of the Helmholtz equation is examined for a separated source and receiver over a model having a single planar interface. Expressions describing the construction and reconstruction of acoustical wave fields are derived in terms of Green’s functions. Their relation to the Fourier transform is briefly discussed. Three simple Green’s functions—free space, free surface, and rigid surface—are used to test the relative accuracy of the respective weighting factors by comparing the numerically calculated field for a simple model to a field obtained analytically by application of rigorous diffraction theory. The main purpose of this paper is to study the behavior of the total response (amplitude and phase) for models in which the aperture is not sufficiently sampled (e.g., close to half the wavelength). The degree of distortion in the response due to spatial undersampling is unacceptable for all three Green’s functions. A modified weighting factor relative to the free‐space Green’s function is introduced, which effectively reduces the degree of distortion in the total response under the same sampling condition. The importance of this finding to exploration geophysics in the construction of the synthetic seismograms by application of the Huygen’s principle and in seismic migration will be demonstrated.

The Anisotropic Truncated Kernel Method for Convolution with Free-Space Green's Functions

2018 ◽  
Vol 40 (6) ◽  
pp. A3733-A3754 ◽  
Author(s):  
Leslie Greengard ◽  
Shidong Jiang ◽  
Yong Zhang
Keyword(s):  
Free Space ◽  
Green's Functions ◽  
Green’S Functions ◽  
Kernel Method

scholarly journals Fast convolution with free-space Green's functions

2016 ◽  
Vol 323 ◽  
pp. 191-203 ◽  
Author(s):  
Felipe Vico ◽  
Leslie Greengard ◽  
Miguel Ferrando
Keyword(s):  
Free Space ◽  
Green's Functions ◽  
Green’S Functions ◽  
Fast Convolution
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