Generalized optical theorems for the reconstruction of Green's function of an inhomogeneous elastic medium
Abstract
This paper investigates the reconstruction of elastic Green's function from the crosscorrelation of waves excited by random noise in the context of scattering theory. Using a general operator equation, the resolvent formula, Green's function reconstruction is established when the noise sources satisfy an equipartition condition. In an inhomogeneous medium, the operator formalism leads to generalized forms of optical theorem involving the offshell $T$matrix of elastic waves, which describes scattering in the nearfield. The role of temporal absorption in the formulation of the theorem is discussed. Previously established symmetry and reciprocity relations involving the onshell $T$matrix are recovered in the usual farfield and infinitesimal absorption limits. The theory is applied to a point scattering model for elastic waves. The $T$matrix of the point scatterer incorporating all recurrent scattering loops is obtained by a regularization procedure. The physical significance of the point scatterer is discussed. In particular this model satisfies the offshell version of the generalized optical theorem. The link between equipartition and Green's function reconstruction in a scattering medium is discussed.
 Publication:

Acoustical Society of America Journal
 Pub Date:
 2011
 DOI:
 10.1121/1.3652856
 arXiv:
 arXiv:1103.1517
 Bibcode:
 2011ASAJ..130.3674M
 Keywords:

 Physics  Geophysics
 EPrint:
 doi:10.1121/1.3652856