scholarly journals Marchenko redatuming, imaging and multiple elimination, and their mutual relations

Geophysics ◽  
2021 ◽  
pp. 1-103
Author(s):  
Kees Wapenaar ◽  
Joeri Brackenhoff ◽  
Marcin Dukalski ◽  
Giovanni Meles ◽  
Chris Reinicke ◽  
...  
Keyword(s):  
Plane Wave ◽  
Green's Functions ◽  
Green’S Functions ◽  
Mathematical Framework ◽  
Reflection Data ◽  
Efficient Alternative ◽  
Internal Multiples ◽  
Mutual Relations ◽  
Double Focusing ◽  
Multiple Elimination

With the Marchenko method it is possible to retrieve Green's functions between virtual sources in the subsurface and receivers at the surface from reflection data at the surface and focusing functions. A macro model of the subsurface is needed to estimate the first arrival; the internal multiples are retrieved entirely from the reflection data. The retrieved Green's functions form the input for redatuming by multidimensional deconvolution (MDD). The redatumed reflection response is free of internal multiples related to the overburden. Alternatively, the redatumed response can be obtained by applying a second focusing function to the retrieved Green's functions. This process is called Marchenko redatuming by double focusing. It is more stable and better suited for an adaptive implementation than Marchenko redatuming by MDD, but it does not eliminate the multiples between the target and the overburden. An attractive efficient alternative is plane-wave Marchenko redatuming, which retrieves the responses to a limited number of plane-wave sources at the redatuming level. In all cases, an image of the subsurface can be obtained from the redatumed data, free of artefacts caused by internal multiples. Another class of Marchenko methods aims at eliminating the internal multiples from the reflection data, while keeping the sources and receivers at the surface. A specific characteristic of this form of multiple elimination is that it predicts and subtracts all orders of internal multiples with the correct amplitude, without needing a macro subsurface model. Like Marchenko redatuming, Marchenko multiple elimination can be implemented as an MDD process, a double dereverberation process, or an efficient plane-wave oriented process. We systematically discuss the different approaches to Marchenko redatuming, imaging and multiple elimination, using a common mathematical framework.

scholarly journals Internal multiple prediction and removal using Marchenko autofocusing and seismic interferometry

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. A7-A11 ◽  
Author(s):  
Giovanni Angelo Meles ◽  
Katrin Löer ◽  
Matteo Ravasi ◽  
Andrew Curtis ◽  
Carlos Alberto da Costa Filho
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Velocity Model ◽  
Seismic Interferometry ◽  
Reverse Time ◽  
Coherent Noise ◽  
Surface Reflection ◽  
Reflection Data ◽  
Time Migration ◽  
Internal Multiples

Standard seismic processing steps such as velocity analysis and reverse time migration (imaging) usually assume that all reflections are primaries: Multiples represent a source of coherent noise and must be suppressed to avoid imaging artifacts. Many suppression methods are relatively ineffective for internal multiples. We show how to predict and remove internal multiples using Marchenko autofocusing and seismic interferometry. We first show how internal multiples can theoretically be reconstructed in convolutional interferometry by combining purely reflected, up- and downgoing Green’s functions from virtual sources in the subsurface. We then generate the relevant up- and downgoing wavefields at virtual sources along discrete subsurface boundaries using autofocusing. Then, we convolve purely scattered components of up- and downgoing Green’s functions to reconstruct only the internal multiple field, which is adaptively subtracted from the measured data. Crucially, this is all possible without detailed modeled information about the earth’s subsurface. The method only requires surface reflection data and estimates of direct (nonreflected) arrivals between subsurface virtual sources and the acquisition surface. The method is demostrated on a stratified synclinal model and shown to be particularly robust against errors in the reference velocity model used.

Path integral calculation of relativistic Green’s functions for particles in the field of the plane wave

1994 ◽  
Vol 109 (3) ◽  
pp. 219-228 ◽  
Author(s):  
T. Boudjedaa ◽  
L. Chetouani ◽  
L. Guéchi ◽  
T. F. Hammann
Keyword(s):  
Plane Wave ◽  
Path Integral ◽  
Green's Functions ◽  
Green’S Functions

scholarly journals Suppressing nonphysical reflections in Green’s function estimates using source-receiver interferometry

Geophysics ◽  
2012 ◽  
Vol 77 (1) ◽  
pp. Q15-Q25 ◽  
Author(s):  
Simon King ◽  
Andrew Curtis
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Seismic Interferometry ◽  
Elastic Model ◽  
Internal Multiples ◽  
Velocity Spectra ◽  
Interval Velocities ◽  
Streamer Data

Seismic interferometry retrieves the Green’s function propagating between two receiver locations using their recordings from an enclosing boundary of sources. Theory requires that sources completely surround the two receivers, but constraints in exploration seismology restrict sources to locations near the surface of the earth. Seismic interferometry by crosscorrelation then introduces usually undesirable nonphysical reflections (spurious multiples) in the Green’s function estimates. We found that the dominant nonphysical reflections can be converted into physical reflections via convolution using source-receiver interferometry. The resultant Green’s functions display fewer nonphysical reflections and show significantly better agreement with the true Green’s functions than those obtained using crosscorrelational interferometry. Nonphysical reflections can be further suppressed by iterating the convolution step. By comparing the velocity spectra of the Green’s functions retrieved by crosscorrelational and source-receiver interferometry, we can retrospectively identify the dominant nonphysical reflections introduced by crosscorrelational interferometry. We found that the nonphysical reflections are particularly important for constructing the primary reflections and internal multiples in source-receiver interferometry. This is because the primary reflections and internal multiples cannot be created via the convolution of physical reflections. Instead, the primary reflections and internal multiples are retrieved by the appropriate convolution between a nonphysical and physical reflection. We compared crosscorrelational interferometry and source-receiver interferometry using synthetic towed streamer data for a 1D acoustic and 2.5D elastic model, respectively. We also found that the nonphysical reflections obtained using crosscorrelational interferometry allow for the direct estimation of interval velocities and layer thicknesses without the need to use Dix inversion in the 1D example.

scholarly journals On the relation between seismic interferometry and the migration resolution function

Geophysics ◽  
2007 ◽  
Vol 72 (6) ◽  
pp. T61-T66 ◽  
Author(s):  
Jan Thorbecke ◽  
Kees Wapenaar
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Seismic Interferometry ◽  
Resolution Function ◽  
Migration Literature ◽  
Double Focusing ◽  
Wavefield Extrapolation ◽  
Backward Propagation

Seismic interferometry refers to the process of retrieving new seismic responses by crosscorrelating seismic observations at different receiver locations. Seismic migration is the process of forming an image of the subsurface by wavefield extrapolation. Comparing the expressions for backward propagation known from migration literature with the Green’s function representations for seismic interferometry reveals that these seemingly distinct concepts are mathematically equivalent. The frequency-domain representation for the resolution function of migration is identical to that for the Green’s function retrieved by seismic interferometry (or its square, in the case of double focusing). In practice, they differ because the involved Green’s functions in seismic interferometry are all defined in the actual medium, whereas in migration one of the Green’s functions is defined in a background medium.

Fast image-domain target-oriented least-squares reverse time migration

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. A81-A86 ◽  
Author(s):  
Zeyu Zhao ◽  
Mrinal K. Sen
Keyword(s):  
Plane Wave ◽  
Least Squares ◽  
Large Scale ◽  
Green's Functions ◽  
Green’S Functions ◽  
Hessian Matrix ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Image Domain ◽  
Time Migration

We have developed a fast image-domain target-oriented least-squares reverse time migration (LSRTM) method based on applying the inverse or pseudoinverse of a target-oriented Hessian matrix to a migrated image. The image and the target-oriented Hessian matrix are constructed using plane-wave Green’s functions that are computed by solving the two-way wave equation. Because the number of required plane-wave Green’s functions is small, the proposed method is highly efficient. We exploit the sparsity of the Hessian matrix by computing only a couple of off-diagonal terms for the target-oriented Hessian, which further improves the computational efficiency. We examined the proposed LSRTM method using the 2D Marmousi model. We demonstrated that our method correctly recovers the reflectivity model, and the retrieved results have more balanced illumination and higher spatial resolution than traditional images. Because of the low cost of computing the target-oriented Hessian matrix, the proposed method has the potential to be applied to large-scale problems.

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