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.

scholarly journals A field data example of Marchenko multiple elimination

Geophysics ◽  
2020 ◽  
Vol 85 (2) ◽  
pp. S65-S70 ◽  
Author(s):  
Lele Zhang ◽  
Evert Slob
Keyword(s):  
North Sea ◽  
Seismic Data ◽  
Field Data ◽  
Multiple Reflections ◽  
Coherent Noise ◽  
Data Set ◽  
Model Independent ◽  
Multiple Elimination

Internal multiple reflections have been widely considered as coherent noise in measured seismic data, and many approaches have been developed for their attenuation. The Marchenko multiple elimination (MME) scheme eliminates internal multiple reflections without model information or adaptive subtraction. This scheme was originally derived from coupled Marchenko equations, but it was modified to make it model independent. It filters primary reflections with their two-way traveltimes and physical amplitudes from measured seismic data. The MME scheme is applied to a deepwater field data set from the Norwegian North Sea to evaluate its success in removing internal multiple reflections. The result indicates that most internal multiple reflections are successfully removed and primary reflections masked by overlapping internal multiple reflections are recovered.

Transform-domain noise synthesis and normal moveout-stack deconvolution approach to ground roll attenuation

Geophysics ◽  
2020 ◽  
Vol 86 (1) ◽  
pp. V15-V22
Author(s):  
Felix Oghenekohwo ◽  
Mauricio D. Sacchi
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Field Data ◽  
Transform Domain ◽  
Coherent Noise ◽  
Least Squares Problem ◽  
Fourier Filtering ◽  
Ground Roll ◽  
Seismic Reflections ◽  
Strong Ground

Ground roll is coherent noise in land seismic data that contaminates seismic reflections. Therefore, it is essential to find efficient ways that remove this noise and still preserve reflections. To this end, we have developed a signal and noise separation framework that uses a hyperbolic moveout assumption on reflections, coupled with the synthesis of coherent ground roll. This framework yields a least-squares problem, which we solve using a sparsity-promoting program that gives coefficients capable of modeling the signal and noise. Subtraction of the predicted noise from the observed data produces data with amplitude-preserved reflections. We develop this technique on synthetic and field data contaminated by weak and strong ground roll noise. Compared to conventional Fourier filtering techniques, our method accurately removes the ground roll while preserving the amplitude of the signal.

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.

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.

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.

Noise suppression in 2D and 3D seismic data with data-driven sifting algorithms

Geophysics ◽  
2019 ◽  
Vol 85 (1) ◽  
pp. V1-V10
Author(s):  
Julián L. Gómez ◽  
Danilo R. Velis ◽  
Juan I. Sabbione
Keyword(s):  
Seismic Data ◽  
Noise Suppression ◽  
Department Of Energy ◽  
Time Slice ◽  
3D Seismic ◽  
Coherent Noise ◽  
Data Set ◽  
Amplitude Data ◽  
3D Volume ◽  
2D And 3D

We have developed an empirical-mode decomposition (EMD) algorithm for effective suppression of random and coherent noise in 2D and 3D seismic amplitude data. Unlike other EMD-based methods for seismic data processing, our approach does not involve the time direction in the computation of the signal envelopes needed for the iterative sifting process. Instead, we apply the sifting algorithm spatially in the inline-crossline plane. At each time slice, we calculate the upper and lower signal envelopes by means of a filter whose length is adapted dynamically at each sifting iteration according to the spatial distribution of the extrema. The denoising of a 3D volume is achieved by removing the most oscillating modes of each time slice from the noisy data. We determine the performance of the algorithm by using three public-domain poststack field data sets: one 2D line of the well-known Alaska 2D data set, available from the US Geological Survey; a subset of the Penobscot 3D volume acquired offshore by the Nova Scotia Department of Energy, Canada; and a subset of the Stratton 3D land data from South Texas, available from the Bureau of Economic Geology at the University of Texas at Austin. The results indicate that random and coherent noise, such as footprint signatures, can be mitigated satisfactorily, enhancing the reflectors with negligible signal leakage in most cases. Our method, called empirical-mode filtering (EMF), yields improved results compared to other 2D and 3D techniques, such as [Formula: see text] EMD filter, [Formula: see text] deconvolution, and [Formula: see text]-[Formula: see text]-[Formula: see text] adaptive prediction filtering. EMF exploits the flexibility of EMD on seismic data and is presented as an efficient and easy-to-apply alternative for denoising seismic data with mild to moderate structural complexity.

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.

Predictive removal of scattered noise

Geophysics ◽  
2006 ◽  
Vol 71 (2) ◽  
pp. V41-V49 ◽  
Author(s):  
Gérard C. Herman ◽  
Colin Perkins
Keyword(s):  
Mathematical Model ◽  
Wave Propagation ◽  
Surface Wave ◽  
Seismic Data ◽  
Coherent Noise ◽  
Data Set ◽  
Near Surface ◽  
Unique Data ◽  
Surface Wave Propagation ◽  
Petroleum Development

Land seismic data can be severely contaminated with coherent noise. We discuss a deterministic technique to predict and remove scattered coherent noise from land seismic data based on a mathematical model of near-surface wave propagation. We test the method on a unique data set recorded by Petroleum Development of Oman in the Qarn Alam area (with shots and receivers on the same grid), and we conclude that it effectively reduces scattered noise without smearing reflection energy.

Seismic characterization of a Mississippi Lime resource play in Osage County, Oklahoma, USA

2013 ◽  
Vol 1 (2) ◽  
pp. SB97-SB108 ◽  
Author(s):  
Benjamin L. Dowdell ◽  
J. Tim Kwiatkowski ◽  
Kurt J. Marfurt
Keyword(s):  
Seismic Data ◽  
Seismic Analysis ◽  
High Porosity ◽  
Fracture Density ◽  
Coherent Noise ◽  
High Fracture ◽  
Data Set ◽  
Horizontal Drilling ◽  
Prestack Inversion ◽  
Osage County

With the advent of horizontal drilling and hydraulic fracturing in the Midcontinent, USA, fields once thought to be exhausted are now experiencing renewed exploitation. However, traditional Midcontinent seismic analysis techniques no longer provide satisfactory reservoir characterization for these unconventional plays; new seismic analysis methods are needed to properly characterize these radically innovative play concepts. Time processing and filtering is applied to a raw 3D seismic data set from Osage County, Oklahoma, paying careful attention to velocity analysis, residual statics, and coherent noise filtering. The use of a robust prestack structure-oriented filter and spectral whitening greatly enhances the results. After prestack time migrating the data using a Kirchhoff algorithm, new velocities are picked. A final normal moveout correction is applied using the new velocities, followed by a final prestack structure-oriented filter and spectral whitening. Simultaneous prestack inversion uses the reprocessed and time-migrated seismic data as input, along with a well from within the bounds of the survey. With offsets out to 3048 m and a target depth of approximately 880 m, we can invert for density in addition to P- and S-impedance. Prestack inversion attributes are sensitive to lithology and porosity while surface seismic attributes such as coherence and curvature are sensitive to lateral changes in waveform and structure. We use these attributes in conjunction with interpreted horizontal image logs to identify zones of high porosity and high fracture density.

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.

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