283 research outputs found
An overview of Marchenko methods
No full textSince the introduction of the Marchenko method in geophysics, many variants have been developed. Using a compact unified notation, we review redatuming by multidimensional deconvolution and by double focusing, virtual seismology, double dereverberation and transmission-compensated Marchenko multiple elimination, and discuss the underlying assumptions, merits and limitations of these methods.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Applied Geophysics and Petrophysic
Plane-Wave Marchenko Imaging Method: Field Data Application
No full textSeismic imaging is often used to interpret subsurface formations. However, images obtained by conventional methods are contaminated with internal multiples. The Marchenko method provides the means to obtain multiple-free subsurface images. Due to the high computational cost of the conventional point-source Marchenko imaging method, the less expensive plane wave Marchenko imaging method can be used to produce subsurface images along planes. This method can be repeated for different incident angles to produce images that account for the variable dip of the subsurface structures. In this abstract, we present the results of applying the plane wave Marchenko imaging method to a 2D marine dataset over the Vøring basin, the North Sea. The results show that, in comparison to the conventional plane-wave image, the plane-wave Marchenko imaging method successfully suppressed internal multiples, resulting in improvements in both the amplitude and continuity of the seismic events.Accepted Author ManuscriptApplied Geophysics and PetrophysicsImPhys/Medical Imagin
Marchenko Inversion
No full textMarchenko inversion is a new way to invert seismic or electromagnetic data recorded during geophysical surveys. The inversion method uses Marchenko theory. This is a recent development which enables the retrieval of Green's functions at any place in the subsurface. A non-recursive Marchenko inversion method has already been introduced but in this thesis a recursive Marchenko inversion method is implemented and analysed. A recursive scheme lies at the center of this new method. In this thesis, the new method is implemented and tested on a 1D subsurface model. The recursive scheme is first validated. This is done by computing a reflection response with it and comparing it with a reflection response resulting from forward modeling. After this, the accuracy of retrieved local reflection coefficients from the recursive inversion method is determined. This is done by comparison with exact reflection coefficients of the subsurface model. After this, several different parameters of the used subsurface model, data computation and the recursive inversion method itself are investigated for their influence on the accuracy of the inversion method. In particular interest is the effect of interval time errors because these result in errors that can build up rapidly through the recursion. However, the method has a big advantage. It is shown that the recursive Marchenko inversion method has a way to retrieve the magnitude of made interval time errors and correct for these when interval times are overestimated. In this way the error build up is stopped. In the end, it is shown that the new method delivers high accuracy results and has an advantage in computational expense compared to the existing recursive Marchenko inversion method. It is concluded that the new method shows promising prospects and that it is worthwhile to investigate the method further.Applied Geophysics | IDEA Leagu
Elastodynamic Marchenko method: advances and remaining challenges
No full textMarchenko methods aim to remove all overburden-related internal multiples. The acoustic and elastodynamic formulations observe identical equations, but different physics. The elastodynamic case highlights that the Marchenko method only handles overburden-generated reflections, i.e. forward-scattered transmitted waves (and so-called fast multiples) remain in the data. Moreover, to constrain an underdetermined problem, the Marchenko method makes two assumptions that are reasonable for acoustic, but not for elastodynamic waves. Firstly, the scheme requires an initial guess that can be realistically estimated for sufficiently-simple acoustic cases, but remains unpredictable for elastic media without detailed overburden knowledge. Secondly, the scheme assumes temporal separability of upgoing focusing and Green’s functions, which holds for many acoustic media but easily fails in presence of elastic effects. The latter limitation is nearly-identical to the monotonicity requirement of the inverse scattering series, indicating that this limitation may be due to the underlying physics and not algorithm dependent. Provided that monotonicity holds, the aforementioned initial estimate can be retrieved by augmenting the Marchenko method with energy conservation and a minimum-phase condition. However, the augmentation relies on the availability of an elastic minimum-phase reconstruction method, which is currently under investigation. Finally, we discuss a geological setting where an acoustic approximation suffices.Accepted Author ManuscriptApplied Geophysics and Petrophysic
Marchenko imaging
No full textTraditionally, the Marchenko equation forms a basis for 1D inverse scattering problems. A 3D extension of the Marchenko equation enables the retrieval of the Green’s response to a virtual source in the subsurface from reflection measurements at the earth’s surface. This constitutes an important step beyond seismic interferometry. Whereas seismic interferometry requires a receiver at the position of the virtual source, for the Marchenko scheme it suffices to have sources and receivers at the surface only. The underlying assumptions are that the medium is lossless and that an estimate of the direct arrivals of the Green’s function is available. The Green’s function retrieved with the 3D Marchenko scheme contains accurate internal multiples of the inhomogeneous subsurface. Using source-receiver reciprocity, the retrieved Green’s function can be interpreted as the response to sources at the surface, observed by a virtual receiver in the subsurface. By decomposing the 3D Marchenko equation, the response at the virtual receiver can be decomposed into a downgoing field and an upgoing field. By deconvolving the retrieved upgoing field with the downgoing field, a reflection response is obtained, with virtual sources and virtual receivers in the subsurface. This redatumed reflection response is free of spurious events related to internal multiples in the overburden. The redatumed reflection response forms the basis for obtaining an image of a target zone. An important feature is that spurious reflections in the target zone are suppressed, without the need to resolve first the reflection properties of the overburden.Geoscience & EngineeringCivil Engineering and Geoscience
Marchenko Focusing Without Up/Down Decomposition
No full textCurrent Marchenko algorithms require up/down separation, and solving the Marchenko equation enables one to retrieve the up/down components of the Green's function. We propose an iterative scheme to relax the need for up/down separation for focusing. By presenting a visual tour, we show how to retrieve the Green's function in the subsurface at a pre-defined location without requiring component decomposition. Our retrieved Green's function contains accurate primary and multiple events of the heterogeneous subsurface and forms the basis for obtaining an image of the subsurface without the need for up/down decomposition.Accepted author manuscriptImPhys/Medical ImagingApplied Geophysics and Petrophysic
Plane-Wave Marchenko Imaging Method
No full textSeismic imaging is often used to interpret subsurface formations. However, images obtained by conventional methods are contaminated with internal multiples. The Marchenko method provides the means to obtain multiple-free subsurface images. Due to the high computational cost of the conventional pointsource Marchenko imaging method, the less expensive plane wave Marchenko imaging method can be used to produce subsurface images along planes. This method can be repeated for different incident angles to produce images that account for the variable dip of the subsurface structures. In this abstract, we present the results of applying the plane wave Marchenko imaging method to a 2D marine dataset over the Vøring basin, the North Sea. The results show that, in comparison to the conventional plane-wave image, the plane-wave Marchenko imaging method successfully suppressed internal multiples, resulting in improvements in both the amplitude and continuity of the seismic events
Representations for the Marchenko Method for imperfectly sampled data
No full textThe Marchenko method is based on two integral representations for focusing functions and Green’s functions. In practice the integrals are replaced by finite summations. This works well for regularly sampled data, but the quality of the results degrades in case of imperfect sampling. We reformulate the integral representations into summation representations which properly account for imperfectly sampled data and we illustrate these representations with numerical examples. We indicate how these representations may be used to modify the Marchenko method to account for imperfect sampling.Accepted Author ManuscriptImPhys/Acoustical Wavefield ImagingApplied Geophysics and Petrophysic
Marchenko without up/down decomposition on the Marmousi model and retrieval of the refracted waves: Are they caused by the Marchenko algorithm?
No full textMarchenko algorithms retrieve the Green’s function for arbitrary subsurface locations, and the retrieved Green’s function includes the primary and multiple reflected waves. The Marchenko algorithms require the estimate of the direct arrivals and the reflected waves; however, most previous Marchenko algorithms also require the up/down components of the Marchenko equation for the Green’s function retrieval. We use the Marmousi model to retrieve the Green’s function without using the up/-down components of the Marchenko equation and show that the retrieved Green’s function matches with the numerically modeled Green’s function. We also show that the refracted waves can be successfully produced independently from the acquisition geometry, i.e., singlesided or two-sided; however, the retrieval of refracted waves that arrive before the first primary waves is inconsistent with the requirement that the Green’s function vanishes before the direct wave. Even though we retrieve such refracted waves, they are caused by the injection of the direct wave into suciently detailed background velocity and density models instead of operations of the Marchenko algorithm on the recorded wavefields.Accepted Author ManuscriptApplied Geophysics and PetrophysicsImPhys/Medical Imagin
Marchenko method for monitoring induced seismicity with virtual receivers
No full textThe Marchenko method can be used to retrieve Green’s functions (including multiple scattering) between virtual sources in the subsurface and physical receivers at the surface or virtual receivers in the subsurface. Here we discuss a variant of the Marchenko method which retrieves the response between physical sources and virtual receivers in the subsurface. We discuss the theory and illustrate it with numerical examples. The main application of the proposed method is monitoring of induced seismicity with virtual receivers in the subsurface.Accepted author manuscriptImPhys/Acoustical Wavefield ImagingApplied Geophysics and Petrophysic
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