Green's function retrieval from reflection data, in absence of a receiver at the virtual source position

Kees Wapenaar; Jan Thorbecke; Joost van der Neut; Filippo Broggini; Evert Slob; Roel Snieder

doi:10.1121/1.4869083

Green's function retrieval from reflection data, in absence of a receiver at the virtual source position

J Acoust Soc Am. 2014 May;135(5):2847-61. doi: 10.1121/1.4869083.

Authors

Kees Wapenaar¹, Jan Thorbecke¹, Joost van der Neut¹, Filippo Broggini², Evert Slob¹, Roel Snieder²

Affiliations

¹ Department of Geoscience and Engineering, Delft University of Technology, 2600 GA Delft, The Netherlands.
² Center for Wave Phenomena, Colorado School of Mines, Golden, Colorado 80401.

PMID: 24815266
DOI: 10.1121/1.4869083

Abstract

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.