Inverse extrapolation of primary seismic waves

Wapenaar, Kees; Peels, G. L.; Budejicky, V.; Berkhout, A. J.

doi:10.1190/1.1442714

Cited by 46 publications

(35 citation statements)

References 12 publications

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“…This approximation properly accounts for travel times and geometrical spreading, but ignores the effect of transmission losses at the interfaces. 42 Using this approximation, the evaluation of Eq. …”

Section: D Marchenko Equationmentioning

confidence: 99%

Green's function retrieval from reflection data, in absence of a receiver at the virtual source position

Wapenaar

Thorbecke

Neut

et al. 2014

The Journal of the Acoustical Society of America

129

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The methodology of Green's function retrieval by cross-correlation has led to many interesting applications for passive and controlled-source acoustic measurements. In all applications, a virtual source is created at the position of a receiver. Here a method is discussed for Green's function retrieval from controlled-source reflection data, which circumvents the requirement of having an actual receiver at the position of the virtual source. The method requires, apart from the reflection data, an estimate of the direct arrival of the Green's function. A single-sided three-dimensional (3D) Marchenko equation underlies the method. This equation relates the reflection response, measured at one side of the medium, to the scattering coda of a so-called focusing function. By iteratively solving the 3D Marchenko equation, this scattering coda is retrieved from the reflection response. Once the scattering coda has been resolved, the Green's function (including all multiple scattering) can be constructed from the reflection response and the focusing function. The proposed methodology has interesting applications in acoustic imaging, properly accounting for internal multiple scattering.

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Section: D Marchenko Equationmentioning

confidence: 99%

Green's function retrieval from reflection data, in absence of a receiver at the virtual source position

Wapenaar

Thorbecke

Neut

et al. 2014

The Journal of the Acoustical Society of America

129

View full text Add to dashboard Cite

show abstract

“…This cylindrical boundary exists between ∂D R and ∂D C and closes the boundary ∂D. The contribution of the integral over ∂D cyl vanishes (but for another reason than Sommerfeld's radiation condition, Wapenaar et al (1989)). …”

Section: A N Au X I L I a Ry F U N C T I O Nmentioning

confidence: 96%

“…Note that we replaced G(x, x A , ω) by a reference Green's functionḠ(x, x A , ω), to be distinguished from the Green's function G(x, x B , ω) in the actual medium. Both Green's functions obey the same wave equation in D (with different source positions), but at and outside ∂D = ∂D R ∪ ∂D C the medium parameters for these Green's functions may be different (Wapenaar et al 1989). For the Green's functionḠ(x, x A , ω) we choose a reference medium which is identical to the actual medium below ∂D R , but homogeneous at and above ∂D R .…”

Section: A N Au X I L I a Ry F U N C T I O Nmentioning

confidence: 99%

A single-sided homogeneous Green's function representation for holographic imaging, inverse scattering, time-reversal acoustics and interferometric Green's function retrieval

Wapenaar¹,

Thorbecke²,

Neut³

2016

Geophysical Journal International

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Green's theorem plays a fundamental role in a diverse range of wavefield imaging applications, such as holographic imaging, inverse scattering, time-reversal acoustics and interferometric Green's function retrieval. In many of those applications, the homogeneous Green's function (i.e. the Green's function of the wave equation without a singularity on the right-hand side) is represented by a closed boundary integral. In practical applications, sources and/or receivers are usually present only on an open surface, which implies that a significant part of the closed boundary integral is by necessity ignored. Here we derive a homogeneous Green's function representation for the common situation that sources and/or receivers are present on an open surface only. We modify the integrand in such a way that it vanishes on the part of the boundary where no sources and receivers are present. As a consequence, the remaining integral along the open surface is an accurate single-sided representation of the homogeneous Green's function. This single-sided representation accounts for all orders of multiple scattering. The new representation significantly improves the aforementioned wavefield imaging applications, particularly in situations where the first-order scattering approximation breaks down.

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“…The time-reversed version of this direct arrival can be used as an approximation for T inv d that takes into account traveltimes and geometric spreading but ignores transmission losses at the interfaces (Wapenaar et al, 1989(Wapenaar et al, , 2014a.…”

Section: Marchenko Iterative Schemementioning

confidence: 99%

Accounting for free-surface multiples in Marchenko imaging

et al. 2017

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Imagine placing a receiver at any location in the earth and recording the response at that location to sources on the surface. In such a world, we could place receivers around our reservoir to better image the reservoir and understand its properties. Realistically, this is not a feasible approach for understanding the subsurface. We have developed an alternative and realizable approach to obtain the response of a buried virtual receiver for sources at the surface. Our method is capable of retrieving the Green's function for a virtual point in the subsurface to the acquisition surface. In our case, a physical receiver is not required at the subsurface point; instead, we require the reflection measurements for sources and receivers at the surface of the earth and a macromodel of the velocity (no small-scale details of the model are necessary). We can interpret the retrieved Green's function as the response to sources at the surface for a virtual receiver in the subsurface. We obtain this Green's function by solving the Marchenko equation, an integral equation pertinent to inverse scattering problems. Our derivation of the Marchenko equation for the Green's function retrieval takes into account the free-surface reflections present in the reflection response (previous work considered a response without free-surface multiples). We decompose the Marchenko equation into up-and downgoing fields and solve for these fields iteratively. The retrieved Green's function not only includes primaries and internal multiples as do previous methods, but it also includes freesurface multiples. We use these up-and downgoing fields to obtain a 2D image of our area of interest, in this case, below a synclinal structure.

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Inverse extrapolation of primary seismic waves

Cited by 46 publications

References 12 publications

Green's function retrieval from reflection data, in absence of a receiver at the virtual source position

Green's function retrieval from reflection data, in absence of a receiver at the virtual source position

A single-sided homogeneous Green's function representation for holographic imaging, inverse scattering, time-reversal acoustics and interferometric Green's function retrieval

Accounting for free-surface multiples in Marchenko imaging

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