Application of a Neumann‐series method to two problems in acoustic radiation theory that are formulated in terms of Green’s functions

1986 ◽  
Vol 79 (5) ◽  
pp. 1211-1222 ◽  
Author(s):  
Anthony J. Rudgers
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Acoustic Radiation ◽  
Neumann Series ◽  
Series Method ◽  
Radiation Theory

Implementation of the Marchenko method

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. WB29-WB45 ◽  
Author(s):  
Jan Thorbecke ◽  
Evert Slob ◽  
Joeri Brackenhoff ◽  
Joost van der Neut ◽  
Kees Wapenaar
Keyword(s):  
Green's Functions ◽  
Time Window ◽  
Iterative Scheme ◽  
Green’S Functions ◽  
Neumann Series ◽  
Colorado School ◽  
Direct Inversion ◽  
Marchenko Equation ◽  
Conventional Scheme ◽  
Convergence Of The Scheme

The Marchenko method makes it possible to compute subsurface-to-surface Green’s functions from reflection measurements at the surface. Applications of the Marchenko method have already been discussed in many papers, but its implementation aspects have not yet been discussed in detail. Solving the Marchenko equation is an inverse problem. The Marchenko method computes a solution of the Marchenko equation by an (adaptive) iterative scheme or by a direct inversion. We have evaluated the iterative implementation based on a Neumann series, which is considered to be the conventional scheme. At each iteration of this scheme, a convolution in time and an integration in space are performed between a so-called focusing (update) function and the reflection response. In addition, by applying a time window, one obtains an update, which becomes the input for the next iteration. In each iteration, upgoing and downgoing focusing functions are updated with these terms. After convergence of the scheme, the resulting upgoing and downgoing focusing functions are used to compute the upgoing and downgoing Green’s functions with a virtual-source position in the subsurface and receivers at the surface. We have evaluated this algorithm in detail and developed an implementation that reproduces our examples. The software fits into the Seismic Unix software suite of the Colorado School of Mines.

scholarly journals Global estimates for kernels of Neumann series and Green's functions

2014 ◽  
Vol 90 (3) ◽  
pp. 903-918 ◽  
Author(s):  
Michael Frazier ◽  
Fedor Nazarov ◽  
Igor Verbitsky
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Neumann Series ◽  
Global Estimates

Temperature field evaluation of a two-dimensional partial heat flow problem through Green's Functions

2019 ◽  
Author(s):  
Guilherme Ramalho Costa ◽  
José Aguiar santos junior ◽  
José Ricardo Ferreira Oliveira ◽  
Jefferson Gomes do Nascimento ◽  
Gilmar Guimaraes
Keyword(s):  
Temperature Field ◽  
Heat Flow ◽  
Green's Functions ◽  
Flow Problem ◽  
Green’S Functions ◽  
Field Evaluation ◽  
Two Dimensional
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