Print Email Facebook Twitter On Green’s function retrieval by iterative substitution of the coupled Marchenko equations Title On Green’s function retrieval by iterative substitution of the coupled Marchenko equations Author Van der Neut, J.R. Vasconcelos, I. Wapenaar, C.P.A. Faculty Civil Engineering and Geosciences Department Geoscience & Engineering Date 2015-01-06 Abstract Iterative substitution of the coupled Marchenko equations is a novel methodology to retrieve the Green's functions from a source or receiver array at an acquisition surface to an arbitrary location in an acoustic medium. The methodology requires as input the single-sided reflection response at the acquisition surface and an initial focusing function, being the time-reversed direct wavefield from the acquisition surface to a specified location in the subsurface. We express the iterative scheme that is applied by this methodology explicitly as the successive actions of various linear operators, acting on an initial focusing function. These operators involve multidimensional crosscorrelations with the reflection data and truncations in time. We offer physical interpretations of the multidimensional crosscorrelations by subtracting traveltimes along common ray paths at the stationary points of the underlying integrals. This provides a clear understanding of how individual events are retrieved by the scheme. Our interpretation also exposes some of the scheme's limitations in terms of what can be retrieved in case of a finite recording aperture. Green's function retrieval is only successful if the relevant stationary points are sampled. As a consequence, internal multiples can only be retrieved at a subsurface location with a particular ray parameter if this location is illuminated by the direct wavefield with this specific ray parameter. Several assumptions are required to solve the Marchenko equations. We show that these assumptions are not always satisfied in arbitrary heterogeneous media, which can result in incomplete Green's function retrieval and the emergence of artefacts. Despite these limitations, accurate Green's functions can often be retrieved by the iterative scheme, which is highly relevant for seismic imaging and inversion of internal multiple reflections. Subject controlled source seismologywave scattering and diffraction To reference this document use: http://resolver.tudelft.nl/uuid:c27b50de-0d8a-4a8c-923d-a64633ec9568 Publisher Oxford University Press ISSN 0956-540X Source https://doi.org/10.1093/gji/ggv330 Source Geophysical Journal International, 203 (2), 2015 Part of collection Institutional Repository Document type journal article Rights © 2015 The Authors Files PDF 323650.pdf 7.03 MB Close viewer /islandora/object/uuid:c27b50de-0d8a-4a8c-923d-a64633ec9568/datastream/OBJ/view