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Data‐driven Green's function retrieval and application to imaging with multidimensional deconvolution
Author(s) -
Broggini Filippo,
Wapenaar Kees,
Neut Joost,
Snieder Roel
Publication year - 2014
Publication title -
journal of geophysical research: solid earth
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.983
H-Index - 232
eISSN - 2169-9356
pISSN - 2169-9313
DOI - 10.1002/2013jb010544
Subject(s) - deconvolution , prestack , reflection (computer programming) , multiple , algorithm , computer science , blind deconvolution , iterative method , inverse problem , function (biology) , iterative and incremental development , scattering , inverse scattering problem , inverse , optics , mathematical optimization , geology , mathematics , physics , mathematical analysis , seismology , geometry , arithmetic , software engineering , evolutionary biology , biology , programming language
An iterative method is presented that allows one to retrieve the Green's function originating from a virtual source located inside a medium using reflection data measured only at the acquisition surface. In addition to the reflection response, an estimate of the travel times corresponding to the direct arrivals is required. However, no detailed information about the heterogeneities in the medium is needed. The iterative scheme generalizes the Marchenko equation for inverse scattering to the seismic reflection problem. To give insight in the mechanism of the iterative method, its steps for a simple layered medium are analyzed using physical arguments based on the stationary phase method. The retrieved Green's wavefield is shown to correctly contain the multiples due to the inhomogeneities present in the medium. Additionally, a variant of the iterative scheme enables decomposition of the retrieved wavefield into its downgoing and upgoing components. These wavefields then enable creation of a ghost‐free image of the medium with either cross correlation or multidimensional deconvolution, presenting an advantage over standard prestack migration.