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Three-dimensional single-sided Marchenko inverse scattering, data-driven focusing, Green's function retrieval, and
Kees Wapenaar1, Filippo Broggini, Evert Slob
1Department of Geoscience and Engineering, Delft University of Technology, 2600 GA Delft, The Netherlands. c.p.a.wapenaar@tudelft.nl
Physical Review Letters
|March 12, 2013
Summary
Researchers developed a 3D Marchenko equation for inverse scattering problems. This enables imaging of complex 3D media using single-sided reflection data and an iterative focusing method.
Area of Science:
- Geophysics
- Applied Mathematics
- Wave Propagation
Background:
- The one-dimensional Marchenko equation is foundational for inverse scattering problems with single-sided access.
- Imaging inhomogeneous media often requires multi-sided access, limiting applications.
Purpose of the Study:
- To derive a three-dimensional (3D) Marchenko equation for single-sided inverse scattering.
- To develop a method for imaging 3D strongly scattering inhomogeneous media accessible from one side.
Main Methods:
- Derivation of the 3D Marchenko equation relating reflection response to internal fields.
- Application of a 3D iterative data-driven focusing method to solve the equation.
- Generation of the 3D Green's function with a virtual source within the medium.
Main Results:
- Successfully derived the 3D Marchenko equation for single-sided reflection data.
- Demonstrated that the iterative focusing method solves the 3D equation.
- The method yields the 3D Green's function, enabling imaging of complex media.
Conclusions:
- The 3D single-sided Marchenko equation provides a new framework for inverse scattering.
- The iterative solution method is effective for imaging 3D inhomogeneous media with limited access.
- This approach advances the capability to image complex subsurface structures.
