Generalized optical theorems for the reconstruction of Green's function of an inhomogeneous elastic medium

Ludovic Margerin (1) , Haruo Sato (2)

1 IRAP - Institut de recherche en astrophysique et planétologie
2 Department of Geophysics

This paper investigates the reconstruction of elastic Green's function from the cross-correlation 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 off-shell $T$-matrix of elastic waves, which describes scattering in the near-field. The role of temporal absorption in the formulation of the theorem is discussed. Previously established symmetry and reciprocity relations involving the on-shell $T$-matrix are recovered in the usual far-field 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 off-shell version of the generalized optical theorem. The link between equipartition and Green's function reconstruction in a scattering medium is discussed.

Mots clés: Green function retrieval; scattering; optical theorem; T-matrix

Domaines: Géophysique [physics.geo-ph]; Géophysique [physics.geo-ph]; Milieux et Changements globaux

Ludovic Margerin, Haruo Sato. Generalized optical theorems for the reconstruction of Green's function of an inhomogeneous elastic medium. 2011. ⟨hal-00574211v2⟩