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Electromagnetic Green's functions retrieval by cross‐correlation and cross‐convolution in media with losses
Author(s) -
Slob Evert,
Wapenaar Kees
Publication year - 2007
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/2006gl029097
Subject(s) - convolution (computer science) , cross correlation , boundary (topology) , lossless compression , physics , function (biology) , mathematical analysis , computer science , mathematics , algorithm , artificial intelligence , data compression , artificial neural network , evolutionary biology , biology
It is shown that the electromagnetic Green's functions of any linear medium with arbitrary heterogeneity can be obtained from the cross‐correlation, or the cross‐convolution, of two recordings at different receiver locations in an open system. Existing representations are known for cross‐correlations where time‐reversal invariance is exploited and hence they are considered in lossless media. We show here that the cross‐correlation type representations are exact in a configuration with sources on a closed boundary and the medium has non‐zero loss terms only outside this boundary. Furthermore, we show that for cross‐convolution representations the loss mechanisms may exist anywhere in space. Many sources of electromagnetic signals exist in the atmosphere and in populated areas, and these can be used in a large variety of practical passive applications exploiting eddy current or electromagnetic wave techniques.