Print Email Facebook Twitter On seismic interferometry, the generalized optical theorem, and the scattering matrix of a point scatterer Title On seismic interferometry, the generalized optical theorem, and the scattering matrix of a point scatterer Author Wapenaar, C.P.A. Slob, E.C. Snieder, R. Faculty Civil Engineering and Geosciences Department Geoscience & Engineering Date 2010-04-27 Abstract We have analyzed the far-field approximation of the Green's function representation for seismic interferometry. By writing each of the Green's functions involved in the correlation process as a superposition of a direct wave and a scattered wave, the Green's function representation is rewritten as a superposition of four terms. When the scattered waves are modeled with the Born approximation, it appears that a three-term approximation of the Green's function representation (omitting the term containing the crosscorrelation of the scattered waves) yields a nearly exact retrieval, whereas the full four-term expression leads to a significant nonphysical event. This is because the Born approximation does not conserve energy and therefore is an insufficient model to explain all aspects of seismic interferometry. We use the full four-term expression of the Green's function representation to derive the generalized optical theorem. Unlike other recent derivations, which use stationary phase analysis, our derivation uses reciprocity theory. From the generalized optical theorem, we derive the nonlinear scattering matrix of a point scatterer. This nonlinear model accounts for primary and multiple scattering at the point scatterer and conforms with well-established scattering theory of classical waves. The model is essential to explain fully the results of seismic interferometry, even when it is applied to the response of a single point scatterer. The nonlinear scattering matrix also has implications for modeling, inversion, and migration. Subject geophysical techniquesGreen's function methodsinterferometryseismic wavesseismology To reference this document use: http://resolver.tudelft.nl/uuid:9bf7fc0a-55ba-4cd0-91dd-b51b2064b638 DOI https://doi.org/10.1190/1.3374359 Publisher Society of Exploration Geophysicists ISSN 0016-8033 Source Geophysics, 75 (3), 2010 Part of collection Institutional Repository Document type journal article Rights (c) 2010 Society of Exploration Geophysicists Files PDF Wapenaar3_2010.pdf 670.94 KB Close viewer /islandora/object/uuid:9bf7fc0a-55ba-4cd0-91dd-b51b2064b638/datastream/OBJ/view