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Some properties of Green's functions for diffuse field interpretation
Author(s) -
SánchezSesma Francisco J.,
IturraránViveros Ursula,
Perton Mathieu
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3947
Subject(s) - mathematics , field (mathematics) , interpretation (philosophy) , diffusion , green s , mathematical analysis , uncorrelated , green's function , function (biology) , boundary (topology) , displacement (psychology) , spectral density , statistical physics , statistics , pure mathematics , physics , quantum mechanics , computer science , psychology , evolutionary biology , psychotherapist , biology , programming language
Within elastic solids subjected to illumination from uncorrelated sources, as those that arise from multiple scattering, it has been established that the displacement field has intensities that are similar to diffusion‐like field. It is found that in this case, the average correlation of motions in the frequency domain, between two points, is proportional to the imaginary part of Green's function for those two receivers. For a single station, the average auto‐correlation equals the average power spectrum, and this gives the imaginary part of Green's function at the source. To gain insight on the properties of Green's functions, particularly regarding their connection with diffuse fields, we study some of their characteristics for simplified cases. Specifically, we deal with 2D and 3D acoustic layers with various boundary conditions. In practice, we assume these Green's functions are related with a diffuse field, and we explore the analytical consequences. The aim of this study is to gather insight to understand patterns found when studying real data or to have a guide to interpret their trends. Copyright © 2016 John Wiley & Sons, Ltd.