scholarly journals Erratum: Dispersion relations for causal Green’s functions: Derivations using the Poincaré–Bertrand theorem and its generalizations [J. Math. Phys. 31, 1356 (1990)]

1991 ◽  
Vol 32 (6) ◽  
pp. 1651-1651 ◽  
Author(s):  
K. T. R. Davies ◽  
R. W. Davies ◽  
G. D. White
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Dispersion Relations ◽  
Math Phys

scholarly journals Asymptotic analysis for dispersion relations and travel times in noise cross-correlations: spherically symmetric case

2018 ◽  
Vol 474 (2218) ◽  
pp. 20180382
Author(s):  
Tianshi Liu ◽  
Haiming Zhang
Keyword(s):  
Asymptotic Analysis ◽  
Surface Waves ◽  
Green's Functions ◽  
Green’S Functions ◽  
Dispersion Relations ◽  
Body Waves ◽  
Spherically Symmetric ◽  
Travel Times ◽  
Cross Correlations ◽  
The Cross

The cross-correlations of ambient noise or earthquake codas are massively used in seismic tomography to measure the dispersion curves of surface waves and the travel times of body waves. Such measurements are based on the assumption that these kinematic parameters in the cross-correlations of noise coincide with those in Green's functions. However, the relation between the cross-correlations of noise and Green's functions deserves to be studied more precisely. In this paper, we use the asymptotic analysis to study the dispersion relations of surface waves and the travel times of body waves, and come to the conclusion that for the spherically symmetric Earth model, when the distribution of noise sources is laterally uniform, the dispersion relations of surface waves and the travel times of SH body-wave phases in noise correlations should be exactly the same as those in Green's functions.

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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