Elastodynamic Green's function retrieval through single-sided Marchenko inverse scattering

Filho, Carlos Alberto da Costa; Ravasi, Matteo; Curtis, Andrew; Meles, Giovanni Angelo

doi:10.1103/physreve.90.063201

Cited by 78 publications

(61 citation statements)

References 28 publications

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“…In this paper, we restrict ourselves to applications in acoustic media. Extensions of the methodology for elastodynamic wave propagation have been presented by da Costa Filho et al (2014) and .…”

Section: Introductionmentioning

confidence: 99%

On Green's function retrieval by iterative substitution of the coupled Marchenko equations

Neut¹,

Vasconcelos

Wapenaar³

2015

Geophys. J. Int.

117

114

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S U M M A R YIterative substitution of the coupled Marchenko equations is a novel methodology to retrieve the Green's functions from a source or receiver array at an acquisition surface to an arbitrary location in an acoustic medium. The methodology requires as input the single-sided reflection response at the acquisition surface and an initial focusing function, being the time-reversed direct wavefield from the acquisition surface to a specified location in the subsurface. We express the iterative scheme that is applied by this methodology explicitly as the successive actions of various linear operators, acting on an initial focusing function. These operators involve multidimensional crosscorrelations with the reflection data and truncations in time. We offer physical interpretations of the multidimensional crosscorrelations by subtracting traveltimes along common ray paths at the stationary points of the underlying integrals. This provides a clear understanding of how individual events are retrieved by the scheme. Our interpretation also exposes some of the scheme's limitations in terms of what can be retrieved in case of a finite recording aperture. Green's function retrieval is only successful if the relevant stationary points are sampled. As a consequence, internal multiples can only be retrieved at a subsurface location with a particular ray parameter if this location is illuminated by the direct wavefield with this specific ray parameter. Several assumptions are required to solve the Marchenko equations. We show that these assumptions are not always satisfied in arbitrary heterogeneous media, which can result in incomplete Green's function retrieval and the emergence of artefacts. Despite these limitations, accurate Green's functions can often be retrieved by the iterative scheme, which is highly relevant for seismic imaging and inversion of internal multiple reflections.

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Section: Introductionmentioning

confidence: 99%

On Green's function retrieval by iterative substitution of the coupled Marchenko equations

Neut¹,

Vasconcelos

Wapenaar³

2015

Geophys. J. Int.

117

114

View full text Add to dashboard Cite

show abstract

“…Research to extending the Marchenko focusing method for elastodynamic wave fields has only started recently. Da Costa et al [20][21][22] investigate an elastodynamic extension of Ref. [12] and illustrate with numerical experiments the advantages and limitations of their approach.…”

Section: Time-reversal Methodsmentioning

confidence: 99%

“…Da Costa et al [20][21][22] independently derived a similar 3D elastodynamic Marchenko scheme and illustrated it with 2D numerical examples. For a shallow focal point (situated in the second layer) several arrivals in the Green's functions are well recovered.…”

Section: Extension To 3d Inhomogeneous Mediamentioning

confidence: 99%

Single-sided Marchenko focusing of compressional and shear waves

Wapenaar

2014

Phys. Rev. E

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In time-reversal acoustics, waves recorded at the boundary of a strongly scattering medium are sent back into the medium to focus at the original source position. This requires that the medium can be accessed from all sides. We discuss a focusing method for media that can be accessed from one side only. We show how complex focusing functions, emitted from the top surface into the medium, cause independent foci for compressional and shear waves. The focused fields are isotropic and act as independent virtual sources for these wave types inside the medium. We foresee important applications in nondestructive testing of construction materials and seismological monitoring of processes inside the Earth.

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“…The retrieved Green's functions find valuable applications in modern seismic imaging schemes, where not only primary reflections but also internal multiples are correctly migrated Broggini et al, 2014). Extensions of the scheme have been presented for elastic media (da Costa Filho et al, 2014; and it has been shown how free-surface multiples can also be included (Singh et al, 2014). In all these cases, the multidimensional Marchenko equation is solved by iterative substitution.…”

Section: Introductionmentioning

confidence: 99%

Inversion of the Multidimensional Marchenko Equation

et al. 2015

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SUMMARYFocusing functions are defined as wavefields that focus at a specified location in a heterogeneous subsurface. These functions can be directly related to Green's functions and hence they can be used for seismic imaging of complete wavefields, including not only primary reflections but all orders of internal multiples. Recently, it has been shown that focusing functions can be retrieved from single-sided reflection data and an initial operator (which can be computed in a smooth background velocity model of the subsurface) by iterative substitution of the multidimensional Marchenko equation. In this work, we show that the Marchenko equation can also be inverted directly for the focusing functions. Although this approach is computationally more expensive than iterative substitution, additional constraints can easily be imposed. Such a flexibility might be beneficial in specific cases, for instance when the recorded data are incomplete or when additional measurements (e.g. from downhole receivers) are available.

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Elastodynamic Green's function retrieval through single-sided Marchenko inverse scattering

Cited by 78 publications

References 28 publications

On Green's function retrieval by iterative substitution of the coupled Marchenko equations

On Green's function retrieval by iterative substitution of the coupled Marchenko equations

Single-sided Marchenko focusing of compressional and shear waves

Inversion of the Multidimensional Marchenko Equation

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