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

Joost Van der Neut, Joeri Brackenhoff, Giovanni Meles, Lele Zhang, Evert Slob, Kees Wapenaar

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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.

Original languageEnglish
Pages (from-to)1775-1786
Number of pages12
JournalIEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
Issue number5
Publication statusPublished - 2022

Bibliographical note

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


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