On the retrieval of forward-scattered waveforms from acoustic reflection and transmission data with the Marchenko equation

On the retrieval of forward-scattered waveforms from acoustic reflection and transmission data with the Marchenko equation

van der Neut, J.R. (TU Delft Applied Geophysics and Petrophysics)
Brackenhoff, J.A. (TU Delft Applied Geophysics and Petrophysics; ETH Zürich)
Meles, G.A. (TU Delft Applied Geophysics and Petrophysics; University of Lausanne)
Zhang, L. (TU Delft Applied Geophysics and Petrophysics; China University of Geosciences, Wuhan)
Slob, E.C. (TU Delft Applied Geophysics and Petrophysics)
Wapenaar, C.P.A. (TU Delft Applied Geophysics and Petrophysics)

2022

A Green's function in an acoustic medium can be retrieved from reflection data by solving a multidimensional Marchenko equation. This procedure requires a priori knowledge of the initial focusing function, which can be interpreted as the inverse of a transmitted wavefield as it would propagate through the medium, excluding (multiply) reflected waveforms. In practice, the initial focusing function is often replaced by a time-reversed direct wave, which is computed with help of a macro velocity model. Green's functions that are retrieved under this (direct-wave) approximation typically lack forward-scattered waveforms and their associated multiple reflections. We examine whether this problem can be mitigated by incorporating transmission data. Based on these transmission data, we derive an auxiliary equation for the forward-scattered components of the initial focusing function. We demonstrate that this equation can be solved in an acoustic medium with mass density contrast and constant propagation velocity. By solving the auxiliary and Marchenko equation successively, we can include forward-scattered waveforms in our Green's function estimates, as we demonstrate with a numerical example.

acoustic propagation
acoustic signal processing
Acoustic waves
Acoustics
Computational modeling
Focusing
Frequency control
Green's function methods
Mathematical models
Windows

http://resolver.tudelft.nl/uuid:d5eb7259-8f15-43dd-a8d1-1ba11bf4c558

https://doi.org/10.1109/TUFFC.2022.3163906

2022-11-28

0885-3010

IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 69 (5), 1775-1786

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

journal article

© 2022 J.R. van der Neut, J.A. Brackenhoff, G.A. Meles, L. Zhang, E.C. Slob, C.P.A. Wapenaar