Abstract
The authors present a framework for Marchenko-type integrals in three-dimensional full wavefield inverse scattering by introducing the homogeneous Green's function of the second kind.
Highlights
Imaging the interior of an object that is only accessible at its boundary is a key problem in many fields, such as seismology [1,2], helioseismology [3], quantum mechanics [4], medical imaging [5,6,7,8,9,10], and nondestructive testing [11,12]
It will be a topic of future research to see what other ways there are for the Marchenko approach to add value to related inverse scattering and imaging schemes and, in this regard, for it to be applied in geophysical and in, e.g., medical applications and nondestructive testing
We introduce the homogeneous Green’s function of the second kind, delivering a framework for focusing functions that is substantially more general than in previous Marchenkorelated applications
Summary
Imaging the interior of an object that is only accessible at its boundary is a key problem in many fields, such as seismology [1,2], helioseismology [3], quantum mechanics [4], medical imaging [5,6,7,8,9,10], and nondestructive testing [11,12]. Recognizing the potential of Marchenko-based Green’s function retrieval and its role in inverse scattering, Wapenaar et al [25,26,27] expanded the Marchenko theory to two and three dimensions Their derivation builds on up and down decomposition of the involved wave fields, both at the acquisition surface and at the depth level of the virtual source of the Green’s function. They use convolution- and correlationtype reciprocity theorems for these decomposed wave fields and describe two different wave states in the true and the truncated medium, i.e., a version of the true medium which is reflection-free everywhere underneath the virtual source location This approach delivers a set of coupled Marchenko equations.
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