The methodology of Green's function retrieval by cross-correlation has led to many interesting applications for passive and controlled-source acoustic measurements. In all applications, a virtual source is created at the position of a receiver. Here a method is discussed for Green's function retrieval from controlled-source reflection data, which circumvents the requirement of having an actual receiver at the position of the virtual source. The method requires, apart from the reflection data, an estimate of the direct arrival of the Green's function. A single-sided three-dimensional (3D) Marchenko equation underlies the method. This equation relates the reflection response, measured at one side of the medium, to the scattering coda of a so-called focusing function. By iteratively solving the 3D Marchenko equation, this scattering coda is retrieved from the reflection response. Once the scattering coda has been resolved, the Green's function (including all multiple scattering) can be constructed from the reflection response and the focusing function. The proposed methodology has interesting applications in acoustic imaging, properly accounting for internal multiple scattering.
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May 01 2014
Green's function retrieval from reflection data, in absence of a receiver at the virtual source position
Kees Wapenaar;
Department of Geoscience and Engineering, Delft University of Technology
, 2600 GA Delft, The Netherlands
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Jan Thorbecke;
Jan Thorbecke
Department of Geoscience and Engineering, Delft University of Technology
, 2600 GA Delft, The Netherlands
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Joost van der Neut;
Joost van der Neut
Department of Geoscience and Engineering, Delft University of Technology
, 2600 GA Delft, The Netherlands
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Filippo Broggini;
Center for Wave Phenomena, Colorado School of Mines
, Golden, Colorado 80401
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Evert Slob;
Evert Slob
Department of Geoscience and Engineering, Delft University of Technology
, 2600 GA Delft, The Netherlands
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Roel Snieder
Roel Snieder
Center for Wave Phenomena, Colorado School of Mines
, Golden, Colorado 80401
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a)
Author to whom correspondence should be addressed. Electronic mail: C.P.A.Wapenaar@TUDelft.NL
b)
Present address: Exploration and Environmental Geophysics, Institute of Geophysics, ETH Zürich, Zürich, Switzerland.
J. Acoust. Soc. Am. 135, 2847–2861 (2014)
Article history
Received:
June 30 2013
Accepted:
March 06 2014
Citation
Kees Wapenaar, Jan Thorbecke, Joost van der Neut, Filippo Broggini, Evert Slob, Roel Snieder; Green's function retrieval from reflection data, in absence of a receiver at the virtual source position. J. Acoust. Soc. Am. 1 May 2014; 135 (5): 2847–2861. https://doi.org/10.1121/1.4869083
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