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.

scholarly journals Reconstructing the primary reflections in seismic data by Marchenko redatuming and convolutional interferometry

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. Q15-Q26 ◽  
Author(s):  
Giovanni Angelo Meles ◽  
Kees Wapenaar ◽  
Andrew Curtis
Keyword(s):  
Velocity Model ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Seismic Reflection Data ◽  
Surface Reflection ◽  
Reflection Data ◽  
Reference Velocity ◽  
Time Migration ◽  
Recorded Data

State-of-the-art methods to image the earth’s subsurface using active-source seismic reflection data involve reverse time migration. This and other standard seismic processing methods such as velocity analysis provide best results only when all waves in the data set are primaries (waves reflected only once). A variety of methods are therefore deployed as processing to predict and remove multiples (waves reflected several times); however, accurate removal of those predicted multiples from the recorded data using adaptive subtraction techniques proves challenging, even in cases in which they can be predicted with reasonable accuracy. We present a new, alternative strategy to construct a parallel data set consisting only of primaries, which is calculated directly from recorded data. This obviates the need for multiple prediction and removal methods. Primaries are constructed by using convolutional interferometry to combine the first-arriving events of upgoing and direct-wave downgoing Green’s functions to virtual receivers in the subsurface. The required upgoing wavefields to virtual receivers are constructed by Marchenko redatuming. Crucially, this is possible without detailed models of the earth’s subsurface reflectivity structure: Similar to the most migration techniques, the method only requires surface reflection data and estimates of direct (nonreflected) arrivals between the virtual subsurface sources and the acquisition surface. We evaluate the method on a stratified synclinal model. It is shown to be particularly robust against errors in the reference velocity model used and to improve the migrated images substantially.

Noise removal by migration of time-shift images

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. S105-S111 ◽  
Author(s):  
Sheng Xu ◽  
Feng Chen ◽  
Bing Tang ◽  
Gilles Lambare
Keyword(s):  
Time Lag ◽  
Real Data ◽  
Velocity Model ◽  
Noise Removal ◽  
Time Shift ◽  
Reverse Time ◽  
Coherent Noise ◽  
Data Set ◽  
Depth Migration ◽  
Time Migration

When using seismic data to image complex structures, the reverse time migration (RTM) algorithm generally provides the best results when the velocity model is accurate. With an inexact model, moveouts appear in common image gathers (CIGs), which are either in the surface offset domain or in subsurface angle domain; thus, the stacked image is not well focused. In extended image gathers, the strongest energy of a seismic event may occur at non-zero-lag in time-shift or offset-shift gathers. Based on the operation of RTM images produced by the time-shift imaging condition, the non-zero-lag time-shift images exhibit a spatial shift; we propose an approach to correct them by a second pass of migration similar to zero-offset depth migration; the proposed approach is based on the local poststack depth migration assumption. After the proposed second-pass migration, the time-shift CIGs appear to be flat and can be stacked. The stack enhances the energy of seismic events that are defocused at zero time lag due to the inaccuracy of the model, even though the new focused events stay at the previous positions, which might deviate from the true positions of seismic reflection. With the stack, our proposed approach is also able to attenuate the long-wavelength RTM artifacts. In the case of tilted transverse isotropic migration, we propose a scheme to defocus the coherent noise, such as migration artifacts from residual multiples, by applying the original migration velocity model along the symmetry axis but with different anisotropic parameters in the second pass of migration. We demonstrate that our approach is effective to attenuate the coherent noise at subsalt area with two synthetic data sets and one real data set from the Gulf of Mexico.

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 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.

Adaptive stabilization for Q-compensated reverse time migration

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. S15-S32 ◽  
Author(s):  
Yufeng Wang ◽  
Hui Zhou ◽  
Hanming Chen ◽  
Yangkang Chen
Keyword(s):  
Wave Equation ◽  
Green's Functions ◽  
Green’S Functions ◽  
Numerical Instability ◽  
Adaptive Stabilization ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Gas Chimney ◽  
Low Pass

Reverse time migration (RTM) for attenuating media should take amplitude compensation and phase correction into consideration. However, attenuation compensation during seismic propagation suffers from numerical instability because of the boosted high-frequency ambient noise. We have developed a novel adaptive stabilization method for [Formula: see text]-compensated RTM ([Formula: see text]-RTM), which exhibits superior properties of time variance and [Formula: see text] dependence over conventional low-pass filtering-based method. We derive the stabilization operator by first analytically deriving [Formula: see text]-space Green’s functions for a constant-[Formula: see text] wave equation with decoupled fractional Laplacians and its compensated equation. The time propagator of Green’s function for the viscoacoustic wave equation decreases exponentially, whereas that of the compensated equation is exponentially divergent at a high wavenumber, and it is not stable after the wave is extrapolated for a long time. Therefore, the Green’s functions theoretically explain how the numerical instability existing in [Formula: see text]-RTM arises and shed light on how to overcome this problem pertinently. The stabilization factor required in the proposed method can be explicitly identified by the specified gain limit according to an empirical formula. The [Formula: see text]-RTM results for noise-free data using low-pass filtering and adaptive stabilization are compared over a simple five-layer model and the BP gas chimney model to verify the superiority of the proposed approach in terms of fidelity and stability. The [Formula: see text]-RTM result for noisy data from the BP gas chimney model further demonstrates that our method enjoys a better antinoise performance and helps significantly to enhance the resolution of seismic images.

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.

Strategies for imaging with Marchenko-retrieved Green’s functions

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. Q23-Q37 ◽  
Author(s):  
Satyan Singh ◽  
Roel Snieder
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Imaging Techniques ◽  
Imaging Condition ◽  
Surface Reflection ◽  
Reflection Data ◽  
First Arrival ◽  
The One

Recent papers show that imaging with the retrieved Green’s function constructed by the Marchenko equations, called Marchenko imaging, reduces artifacts from internal and free-surface multiples compared with standard imaging techniques. Even though artifacts are reduced, they can still be present in the image, depending on the imaging condition used. We have found that when imaging with the up- and downgoing Green’s functions, the multidimensional deconvolution (MDD) imaging condition yields better images than correlation and deconvolution. “Better” in this case means improved resolution, fewer artifacts, and a closer match with the true reflection coefficient of the model. We have determined that the MDD imaging condition only uses primaries to construct the image, whereas multiples are implicitly subtracted in the imaging step. Consequently, combining the first arrival of the downgoing Green’s function with the complete upgoing Green’s function produces superior (or at least equivalent) images than using the one-way Green’s functions because the first arrival of the downgoing Green’s function excludes all the downgoing multiply reflected waves. We also find that standard imaging algorithms which use the redatumed reflection response, constructed with the one-way Green’s functions, produce images with reduced artifacts from multiples compared with standard imaging conditions, which use surface reflection data. All imaging methods that rely on the Marchenko equations require the same inputs as standard imaging techniques: the reflection response at the surface and a smooth estimate of the subsurface velocities.

Joint imaging of angle-dependent reflectivity and estimation of the migration velocity model using multiple scattering

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. R859-R868
Author(s):  
Mikhail Davydenko ◽  
D. J. Verschuur
Keyword(s):  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Velocity Analysis ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Image Domain ◽  
Time Migration ◽  
Internal Multiples ◽  
Angle Dependent Reflectivity

Migration velocity analysis is an important method for providing an accurate velocity model for seismic imaging, which is crucial for correct focusing and localization of subsurface information. Conventionally, only primaries are considered as a source of information for both methods. The use of surface multiples in imaging is becoming more common due to the use of inversion-based approaches, which allow us to handle the crosstalk associated with multiples. However, including internal multiples in imaging and velocity estimation is not straightforward using the standard combination of reverse time migration in combination with image-domain velocity tomography. Incorporating internal multiples in imaging and velocity estimation is possible with the joint migration inversion (JMI) methodology, in which internal multiples are explicitly modeled using the estimated reflectivity via a data-domain objective function. However, to correctly match the observed data, the angle-dependent reflectivity and the migration velocity model need to be determined, which provide an over-parameterization of the inversion problem. Therefore, we have extended the JMI methodology to carry out velocity analysis via the extended image domain, in which the angle-dependent reflectivity is updated via data-domain matching. Examples of synthetic and field data with strong internal multiples demonstrate the validity of our method.

Comparison between interferometric migration and reduced-time migration of common-depth-point data

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. SI189-SI196 ◽  
Author(s):  
Min Zhou ◽  
Zhiyong Jiang ◽  
Jianhua Yu ◽  
Gerard T. Schuster
Keyword(s):  
Green's Functions ◽  
Arrival Time ◽  
Green’S Functions ◽  
Velocity Model ◽  
Migration Velocity ◽  
Arrival Times ◽  
Model Based ◽  
Common Depth Point ◽  
Time Migration ◽  
Reduced Time

One of the difficulties in seeing beneath salt is that the migration velocity in the salt and above it is not well known. This can lead to defocusing of migration images beneath the salt. In this paper, we show that reduced-time migration (RTM) and interferometric migration (IM) can partly mitigate this problem. RTM time-shifts the traces with the time difference between the calculated arrival time [Formula: see text] and the natural arrival time [Formula: see text] of a reference reflection, where [Formula: see text] and [Formula: see text] denote the source and receiver locations on the surface, respectively. We use the terms natural and calculated to represent, respectively, the arrival times that are velocity-independent (traveltimes directly extracted from the data without knowledge of the velocity model) and velocity-dependent (traveltimes calculated by ray tracing through a given velocity model). The benefit of RTM is a significant reduction of defocusing errors caused by errors in the migration velocity. IM, on the other hand, requires extrapolation of the surface data below salt using the natural arrival times [Formula: see text] of the subsalt reference reflector, and migration of the extrapolated data below the salt. The benefit with IM is that no salt velocity model is needed, so the model-based defocusing errors are, in theory, eliminated. To reduce computational time, we implement IM with a seminatural Green’s function (combination of model-based calculated and picked natural traveltimes). Because no explicit data extrapolation is needed, IM with seminatural Green’s functions is more cost-efficient than the standard IM. In this paper, we tested both RTM and IM with seminatural Green’s functions on a synthetic and a field common-depth-point (CDP) data set, the latter from the Gulf of Mexico (GOM). Results show that both RTM and IM can remove the significant kinematic distortions caused by the overburden without knowledge of the overburden velocity.

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