scholarly journals Dynamic Green's functions for layered media by using 3 dimensional Cartesian coordinates and Fourier transform

2011 ◽  
Vol 67 (2) ◽  
pp. I_915-I_924
Author(s):  
Takanori Harada ◽  
Ryosuke Matsuda ◽  
Masaki Nakamura ◽  
Yushi Awada
Keyword(s):  
Fourier Transform ◽  
Green's Functions ◽  
Green’S Functions ◽  
Layered Media ◽  
Cartesian Coordinates ◽  
3 Dimensional

Efficient Computation of Green's Functions for Lossy Uniaxial Anisotropic Layered Media

Radio Science ◽  
2019 ◽  
Vol 54 (3) ◽  
pp. 196-214 ◽  
Author(s):  
Dawei Li ◽  
Donald R. Wilton ◽  
David R. Jackson ◽  
Ji Chen ◽  
Hanming Wang
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Layered Media ◽  
Efficient Computation

Exact Green’s functions using leaking modes for axisymmetric boreholes in solid elastic media

Geophysics ◽  
1989 ◽  
Vol 54 (5) ◽  
pp. 609-620 ◽  
Author(s):  
R. A. W. Haddon
Keyword(s):  
Wave Propagation ◽  
Fourier Transform ◽  
Elastic Wave ◽  
Fast Fourier Transform ◽  
Numerical Method ◽  
Green's Functions ◽  
Green’S Functions ◽  
Elastic Media ◽  
Complex Frequency ◽  
Residue Theory

By choosing appropriate paths of integration in both the complex frequency ω and complex wavenumber k planes, exact Green’s functions for elastic wave propagation in axisymmetric fluid‐filled boreholes in solid elastic media are expressed completely as sums of modes. There are no contributions from branch line integrals. The integrations with respect to k are performed exactly using Cauchy residue theory. The remaining integrations with respect to ω are then carried out partly by using the fast Fourier transform (FFT) and partly by using another numerical method. Provided that the number of points in the FFT can be taken sufficiently large, there are no restrictions on distance. The method is fast, accurate, and easy to apply.

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