Open AccessThe relationship between noise correlation and the Green's function in the presence of degeneracy and the absence of equipartition
Author(s) -
Tsai Victor C.
Publication year - 2010
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.2010.04693.x
Subject(s) - equipartition theorem , degeneracy (biology) , degenerate energy levels , correlation function (quantum field theory) , noise (video) , property (philosophy) , function (biology) , statistical physics , series (stratigraphy) , physics , energy (signal processing) , correlation , mathematics , quantum mechanics , geology , geometry , computer science , philosophy , paleontology , image (mathematics) , biology , bioinformatics , epistemology , artificial intelligence , evolutionary biology , magnetic field , dielectric
SUMMARY Recent derivations have shown that when noise in a physical system has its energy equipartitioned into the modes of the system, there is a convenient relationship between the cross correlation of time‐series recorded at two points and the Green's function of the system. Here, we show that even when energy is not fully equipartitioned and modes are allowed to be degenerate, a similar (though less general) property holds for equations with wave equation structure. This property can be used to understand why certain seismic noise correlation measurements are successful despite known degeneracy and lack of equipartition on the Earth.