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This study presents a new Marchenko equation method for wave focusing without wavefield decomposition. This approach successfully retrieves the Green's function from scattered waves, overcoming limitations of previous methods.

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Area of Science:

  • Geophysics
  • Wave physics
  • Inverse problems

Background:

  • The Marchenko equation is crucial for inverse scattering problems.
  • Existing multi-dimensional Marchenko methods rely on wavefield decomposition, which has limitations.
  • Horizontal wave propagation poses challenges for current wavefield decomposition techniques.

Purpose of the Study:

  • To derive a novel Marchenko equation for wave focusing that does not require wavefield decomposition.
  • To overcome limitations of existing methods in multi-dimensional wave focusing.
  • To retrieve the Green's function for arbitrary locations using scattered wave data.

Main Methods:

  • Derivation of a new Marchenko equation.
  • Iterative solution of the Marchenko equation.
  • Utilizing scattered waves recorded on a closed receiver array.
  • Incorporating an estimate of the direct wave.

Main Results:

  • Successfully derived the Marchenko equation for focusing without wavefield decomposition.
  • Retrieved the Green's function for arbitrary locations in the medium.
  • Demonstrated the method's effectiveness in overcoming wavefield decomposition limitations.

Conclusions:

  • The novel Marchenko equation provides a robust method for wave focusing without wavefield decomposition.
  • This technique enhances the retrieval of Green's functions in complex wave propagation scenarios.
  • The findings offer a significant advancement for seismic imaging and geophysical exploration.