scholarly journals Improving adaptive subtraction in seismic multiple attenuation

Geophysics ◽  
2009 ◽  
Vol 74 (4) ◽  
pp. V59-V67 ◽  
Author(s):  
Shoudong Huo ◽  
Yanghua Wang
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Primary Energy ◽  
Multiple Models ◽  
Multiple Model ◽  
Data Set ◽  
Multiple Attenuation ◽  
Matching Filter ◽  
Theoretical Analyses ◽  
Different Order

In seismic multiple attenuation, once the multiple models have been built, the effectiveness of the processing depends on the subtraction step. Usually the primary energy is partially attenuated during the adaptive subtraction if an [Formula: see text]-norm matching filter is used to solve a least-squares problem. The expanded multichannel matching (EMCM) filter generally is effective, but conservative parameters adopted to preserve the primary could lead to some remaining multiples. We have managed to improve the multiple attenuation result through an iterative application of the EMCM filter to accumulate the effect of subtraction. A Butterworth-type masking filter based on the multiple model can be used to preserve most of the primary energy prior to subtraction, and then subtraction can be performed on the remaining part to better suppress the multiples without affecting the primaries. Meanwhile, subtraction can be performed according to the orders of the multiples, as a single subtraction window usually covers different-order multiples with different amplitudes. Theoretical analyses, and synthetic and real seismic data set demonstrations, proved that a combination of these three strategies is effective in improving the adaptive subtraction during seismic multiple attenuation.

scholarly journals Multiple prediction through inversion: A fully data‐driven concept for surface‐related multiple attenuation

Geophysics ◽  
2004 ◽  
Vol 69 (2) ◽  
pp. 547-553 ◽  
Author(s):  
Yanghua Wang
Keyword(s):  
Seismic Data ◽  
Model Building ◽  
Data Driven ◽  
Multiple Model ◽  
Data Set ◽  
Multiple Attenuation ◽  
Multiple Prediction ◽  
Surface Operator ◽  
Previous Iteration ◽  
Conventional Scheme

This paper introduces a fully data‐driven concept, multiple prediction through inversion (MPI), for surface‐related multiple attenuation (SMA). It builds the multiple model not by spatial convolution, as in a conventional SMA, but by updating the attenuated multiple wavefield in the previous iteration to generate a multiple prediction for the new iteration, as is usually the case in an iterative inverse problem. Because MPI does not use spatial convolution, it is able to minimize the edge effect that appears in conventional SMA multiple prediction and to eliminate the need to synthesize near‐offset traces, required by a conventional scheme, so that it can deal with a seismic data set with missing near‐offset traces. The MPI concept also eliminates the need for an explicit surface operator, which is required by conventional SMA and is comprised of the inverse source signature and other effects. This method accounts implicitly for the spatial variation of the surface operator in multiple‐model building and attempts to predict multiples which are not only accurate kinematically but are also accurate in phase and amplitude.

scholarly journals Efficient 2D multiple attenuation using SRME with curvelet-domain subtraction

2022 ◽  
Vol 43 (1) ◽  
Author(s):  
Szu-Ying Lai ◽  
Yunung Nina Lin ◽  
Ho-Han Hsu
Keyword(s):  
Finite Number ◽  
Least Squares ◽  
Seismic Data ◽  
Parameter Determination ◽  
Prediction Errors ◽  
Geological Condition ◽  
Multiple Model ◽  
Multiple Attenuation ◽  
Time Space ◽  
Multiple Elimination

AbstractSurface Related Multiple Elimination (SRME) usually suffers the issue of either over-attenuation that damages the primaries or under-attenuation that leaves strong residual multiples. This dilemma happens commonly when SRME is combined with least-squares subtraction. Here we introduce a more sophisticated subtraction approach that facilitates better separation of multiples from primaries. Curvelet-domain subtraction transforms both the data and the multiple model into the curvelet domain, where different frequency bands (scales) and event directions (orientations) are represented by a finite number of curvelet coefficients. When combined with adaptive subtraction in the time–space domain, this method can handle model prediction errors to achieve effective subtraction. We demonstrate this method on two 2D surveys from the TAiwan Integrated GEodynamics Research (TAIGER) project. With a careful parameter determination flow, our result shows curvelet-domain subtraction outperforms least-squares subtraction in all geological settings. We also present one failed case where specific geological condition hinders proper multiple subtraction. We further demonstrate that even for data acquired with short cables, curvelet-domain subtraction can still provide better results than least-squares subtraction. We recommend this method as the standard processing flow for multi-channel seismic data.

Regularization and datuming of seismic data by weighted, damped least squares

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. U67-U76 ◽  
Author(s):  
Robert J. Ferguson
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Real Data ◽  
Structural Data ◽  
Irregular Sampling ◽  
Data Set ◽  
Near Surface ◽  
Damped Least Squares ◽  
Wavefield Extrapolation

The possibility of improving regularization/datuming of seismic data is investigated by treating wavefield extrapolation as an inversion problem. Weighted, damped least squares is then used to produce the regularized/datumed wavefield. Regularization/datuming is extremely costly because of computing the Hessian, so an efficient approximation is introduced. Approximation is achieved by computing a limited number of diagonals in the operators involved. Real and synthetic data examples demonstrate the utility of this approach. For synthetic data, regularization/datuming is demonstrated for large extrapolation distances using a highly irregular recording array. Without approximation, regularization/datuming returns a regularized wavefield with reduced operator artifacts when compared to a nonregularizing method such as generalized phase shift plus interpolation (PSPI). Approximate regularization/datuming returns a regularized wavefield for approximately two orders of magnitude less in cost; but it is dip limited, though in a controllable way, compared to the full method. The Foothills structural data set, a freely available data set from the Rocky Mountains of Canada, demonstrates application to real data. The data have highly irregular sampling along the shot coordinate, and they suffer from significant near-surface effects. Approximate regularization/datuming returns common receiver data that are superior in appearance compared to conventional datuming.

Prestack imaging of seismic data using Lp iterative reweighted least-squares wavefield extrapolation filters in the frequency-space domain

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. V243-V252
Author(s):  
Wail A. Mousa
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Least Squares Method ◽  
Filter Design ◽  
Finite Impulse Response ◽  
Weighted Least Squares ◽  
Data Set ◽  
Frequency Space ◽  
Wavefield Extrapolation ◽  
Iterative Reweighted Least Squares

A stable explicit depth wavefield extrapolation is obtained using [Formula: see text] iterative reweighted least-squares (IRLS) frequency-space ([Formula: see text]-[Formula: see text]) finite-impulse response digital filters. The problem of designing such filters to obtain stable images of challenging seismic data is formulated as an [Formula: see text] IRLS minimization. Prestack depth imaging of the challenging Marmousi model data set was then performed using the explicit depth wavefield extrapolation with the proposed [Formula: see text] IRLS-based algorithm. Considering the extrapolation filter design accuracy, the [Formula: see text] IRLS minimization method resulted in an image with higher quality when compared with the weighted least-squares method. The method can, therefore, be used to design high-accuracy extrapolation filters.

Adaptive subtraction using complex-valued curvelet transforms

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. V51-V60 ◽  
Author(s):  
Ramesh (Neelsh) Neelamani ◽  
Anatoly Baumstein ◽  
Warren S. Ross
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Seismic Reflection ◽  
Characteristic Frequency ◽  
Large Scale ◽  
Curvelet Transform ◽  
Real Data ◽  
Text Data ◽  
Data Set ◽  
Complex Valued

We propose a complex-valued curvelet transform-based (CCT-based) algorithm that adaptively subtracts from seismic data those noises for which an approximate template is available. The CCT decomposes a geophysical data set in terms of small reflection pieces, with each piece having a different characteristic frequency, location, and dip. One can precisely change the amplitude and shift the location of each seismic reflection piece in a template by controlling the amplitude and phase of the template's CCT coefficients. Based on these insights, our approach uses the phase and amplitude of the data's and template's CCT coefficients to correct misalignment and amplitude errors in the noise template, thereby matching the adapted template with the actual noise in the seismic data, reflection event-by-event. We also extend our approach to subtract noises that require several templates to be approximated. By itself, the method can only correct small misalignment errors ([Formula: see text] in [Formula: see text] data) in the template; it relies on conventional least-squares (LS) adaptation to correct large-scale misalignment errors, such as wavelet mismatches and bulk shifts. Synthetic and real-data results illustrate that the CCT-based approach improves upon the LS approach and a curvelet-based approach described by Herrmann and Verschuur.

Multiple attenuation with 3D high-order high-resolution parabolic Radon transform using lower frequency constraints

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. V317-V328
Author(s):  
Jitao Ma ◽  
Guoyang Xu ◽  
Xiaohong Chen ◽  
Xiaoliu Wang ◽  
Zhenjiang Hao
Keyword(s):  
High Resolution ◽  
Radon Transform ◽  
Seismic Data ◽  
Computational Cost ◽  
Real Data ◽  
Multiple Model ◽  
Multiple Attenuation ◽  
Common Depth Point ◽  
Frequency Constraint ◽  
Parabolic Radon Transform

The parabolic Radon transform is one of the most commonly used multiple attenuation methods in seismic data processing. The 2D Radon transform cannot consider the azimuth effect on seismic data when processing 3D common-depth point gathers; hence, the result of applying this transform is unreliable. Therefore, the 3D Radon transform should be applied. The theory of the 3D Radon transform is first introduced. To address sparse sampling in the crossline direction, a lower frequency constraint is introduced to reduce spatial aliasing and improve the resolution of the Radon transform. An orthogonal polynomial transform, which can fit the amplitude variations in different parabolic directions, is combined with the dealiased 3D high-resolution Radon transform to account for the amplitude variations with offset of seismic data. A multiple model can be estimated with superior accuracy, and improved results can be achieved. Synthetic and real data examples indicate that even though our method comes at a higher computational cost than existing techniques, the developed approach provides better attenuation of multiples for 3D seismic data with amplitude variations.

scholarly journals Multiple subtraction using an expanded multichannel matching filter

Geophysics ◽  
2003 ◽  
Vol 68 (1) ◽  
pp. 346-354 ◽  
Author(s):  
Yanghua Wang
Keyword(s):  
Hilbert Transform ◽  
Spatial Dimension ◽  
Multiple Model ◽  
Space Domain ◽  
First Derivative ◽  
Multiple Attenuation ◽  
Time Space ◽  
Multichannel Filter ◽  
Matching Filter ◽  
The Hilbert Transform

An expanded multichannel matching (EMCM) filter is proposed for the adaptive subtraction in seismic multiple attenuation. For a normal multichannel matching filter where an original seismic trace is matched by a group of multiple‐model traces, the lateral coherency of adjacent traces is likely to be exploited to discriminate the overlapped multiple and primary reflections. In the proposed EMCM filter, a seismic trace is matched by not only a group of the ordinary multiple‐model traces but also their adjoints generated mathematically. The adjoints of a multiple‐model trace include its first derivative, its Hilbert transform, and the derivative of the Hilbert transform. The convolutional coefficients associated with the normal multichannel filter can be represented as a 2D operator in the time‐space domain. This 2D operator is expanded with an additional spatial dimension in the EMCM filter to improve the robustness of the adaptive subtraction. The multiple‐model traces are generated using moveout equations to afford efficiency in the multiple attenuation application.

Sparseness‐constrained least‐squares inversion: Application to seismic wave reconstruction

Geophysics ◽  
2003 ◽  
Vol 68 (5) ◽  
pp. 1633-1638 ◽  
Author(s):  
Yanghua Wang
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Reconstruction Method ◽  
Sampled Data ◽  
Linear Inversion ◽  
Data Set ◽  
Least Squares Solution ◽  
Working Definition ◽  
The Stability ◽  
Irregularly Sampled Data

The spectrum of a discrete Fourier transform (DFT) is estimated by linear inversion, and used to produce desirable seismic traces with regular spatial sampling from an irregularly sampled data set. The essence of such a wavefield reconstruction method is to solve the DFT inverse problem with a particular constraint which imposes a sparseness criterion on the least‐squares solution. A working definition for the sparseness constraint is presented to improve the stability and efficiency. Then a sparseness measurement is used to measure the relative sparseness of the two DFT spectra obtained from inversion with or without sparseness constraint. It is a pragmatic indicator about the magnitude of sparseness needed for wavefield reconstruction. For seismic trace regularization, an antialiasing condition must be fulfilled for the regularizing trace interval, whereas optimal trace coordinates in the output can be obtained by minimizing the distances between the newly generated traces and the original traces in the input. Application to real seismic data reveals the effectiveness of the technique and the significance of the sparseness constraint in the least‐squares solution.

An application of the Marchenko internal multiple elimination scheme formulated as a least-squares problem

Geophysics ◽  
2021 ◽  
pp. 1-70
Author(s):  
Rodrigo S. Santos ◽  
Daniel E. Revelo ◽  
Reynam C. Pestana ◽  
Victor Koehne ◽  
Diego F. Barrera ◽  
...  
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Neumann Series ◽  
Convergence Criterion ◽  
Coherent Noise ◽  
Data Set ◽  
Least Squares Problem ◽  
Time Migration ◽  
Multiple Elimination ◽  
Seismic Images

Seismic images produced by migration of seismic data related to complex geologies, suchas pre-salt environments, are often contaminated by artifacts due to the presence of multipleinternal reflections. These reflections are created when the seismic wave is reflected morethan once in a source-receiver path and can be interpreted as the main coherent noise inseismic data. Several schemes have been developed to predict and subtract internal multiplereflections from measured data, such as the Marchenko multiple elimination (MME) scheme,which eliminates the referred events without requiring a subsurface model or an adaptivesubtraction approach. The MME scheme is data-driven, can remove or attenuate mostof these internal multiples, and was originally based on the Neumann series solution ofMarchenko’s projected equations. However, the Neumann series approximate solution isconditioned to a convergence criterion. In this work, we propose to formulate the MMEas a least-squares problem (LSMME) in such a way that it can provide an alternative thatavoids a convergence condition as required in the Neumann series approach. To demonstratethe LSMME scheme performance, we apply it to 2D numerical examples and compare theresults with those obtained by the conventional MME scheme. Additionally, we evaluatethe successful application of our method through the generation of in-depth seismic images,by applying the reverse-time migration (RTM) algorithm on the original data set and tothose obtained through MME and LSMME schemes. From the RTM results, we show thatthe application of both schemes on seismic data allows the construction of seismic imageswithout artifacts related to internal multiple events.

Using even terms of the scattering series for deghosting and multiple attenuation of ocean‐bottom cable data

Geophysics ◽  
1999 ◽  
Vol 64 (2) ◽  
pp. 579-592 ◽  
Author(s):  
Luc T. Ikelle
Keyword(s):  
Free Surface ◽  
Seismic Data ◽  
Primary Energy ◽  
Ocean Bottom ◽  
Receiver Side ◽  
Direct Wave ◽  
Sea Floor ◽  
Multiple Attenuation ◽  
Marine Surface ◽  
Streamer Data

Inverse scattering multiple attenuation (ISMA) is a method of removing free‐surface multiple energy while preserving primary energy. The other key feature of ISMA is that no knowledge of the subsurface is required in its application. I have adapted this method to multicomponent ocean‐bottom cable data (i.e., to arrays of sea‐floor geophones and hydrophones) by selecting a subseries made of even terms of the current scattering series used in the free‐surface multiple attenuation of conventional marine surface seismic data (streamer data). This subseries approach allows me to remove receiver ghosts (receiver‐side reverberations) and free‐surface multiples (source‐side reverberations) in multicomponent OBC data. I have processed each component separately. As for the streamer case, my OBC version of ISMA preserves primary energy and does not require any knowledge of the subsurface. Moreover, the preprocessing steps of muting for the direct wave and interpolating for missing near offsets are no longer needed. Knowledge of the source signature is still required. The existing ways of satisfying this requirement for streamer data can be used for OBC data without modification. This method differs from the present dual‐field deghosting method used in OBC data processing in that it does not assume a horizontally flat sea floor; nor does it require the knowledge of the acoustic impedance below the sea floor. Furthermore, it attenuates all free‐surface multiples, including receiver ghosts and source‐side reverberations.

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