Multiple attenuation in the image space

Geophysics ◽  
2005 ◽  
Vol 70 (1) ◽  
pp. V10-V20 ◽  
Author(s):  
Paul Sava ◽  
Antoine Guitton
Keyword(s):  
Real Data ◽  
Velocity Model ◽  
Image Space ◽  
Radon Transforms ◽  
Data Space ◽  
Multiple Attenuation ◽  
3D Data ◽  
Propagation Effects ◽  
Wavefield Extrapolation ◽  
Multiple Elimination

Multiples can be suppressed in the angle-domain image space after migration. For a given velocity model, primaries and multiples have different angle-domain moveout and, therefore, can be separated using techniques similar to the ones employed in the data space prior to migration. We use Radon transforms in the image space to discriminate between primaries and multiples and employ accurate functions describing angle-domain moveouts. Since every individual angle-domain common-image gather incorporates complex 3D propagation effects, our method has the advantage of working with 3D data and complicated geology. Therefore, our method offers an alternative to the more expensive surface-related multiple-elimination (SRME) approach operating in the data space. Radon transforms are cheap but not necessarily ideal for separating primaries and multiples, particularly at small angles where the moveout discrepancy between the two kinds of events are not large. Better techniques involving signal/noise separation using prediction-error filters can be employed as well, although such approaches fall outside the scope of this paper. We demonstrate, using synthetic and real data examples, the power of our method in discriminating between primaries and multiples after migration by wavefield extrapolation, followed by transformation to the angle domain.

scholarly journals Image-space surface-related multiple prediction

Geophysics ◽  
2007 ◽  
Vol 72 (2) ◽  
pp. S113-S122 ◽  
Author(s):  
Brad Artman ◽  
Gabriel Alvarez ◽  
Ken Matson
Keyword(s):  
Seismic Data ◽  
Velocity Model ◽  
Image Space ◽  
Depth Level ◽  
Image Domain ◽  
Data Space ◽  
The Earth ◽  
Multiple Prediction ◽  
The Cost ◽  
Multiple Elimination

A very important aspect of removing multiples from seismic data is accurate prediction of their kinematics. We cast the multiple prediction problem as an operation in the image space parallel to the conventional surface-related multiple-prediction methodology. Though developed in the image domain, the technique shares the data-driven strengths of data-domain surface-related multiple elimination (SRME) by being independent of the earth (velocity) model. Also, the data are used to predict the multiples exactly so that a Radon transform need not be designed to separate the two types of events. The cost of the prediction is approximately the same as that of data-space methods, though it can be computed during the course of migration. The additional cost is not significant compared to that incurred by shot-profile migration, though split-spread gathers must be used. Image-space multiple predictions are generated by autoconvolving the traces in each shot-gather at every depth level during the course of a shot-profile migration. The prediction in the image domain is equivalent to that produced by migrating the data-space convolutional prediction. Adaptive subtraction of the prediction from the image is required. Subtraction in the image domain, however, provides the advantages of focused energy in a smaller domain since extrapolation removes some of the imperfections of the input data.

scholarly journals Attenuation of specular and diffracted 2D multiples in image space

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. V97-V109 ◽  
Author(s):  
Gabriel Alvarez ◽  
Biondo Biondi ◽  
Antoine Guitton
Keyword(s):  
Radon Transform ◽  
3D Model ◽  
Model Space ◽  
Image Space ◽  
Attractive Alternative ◽  
Seismic Line ◽  
Data Space ◽  
Zero Curvature ◽  
Multiple Elimination ◽  
Water Bottom

In complex areas, the attenuation of specular and diffracted multiples in image space is an attractive alternative to surface-related multiple elimination (SRME) and to data space Radon filtering. We present the equations that map, via wave-equation migration, 2D diffracted and specular water-bottom multiples from data space to image space. We show the equations for both subsurface-offset-domain common-image-gathers (SODCIGs) and angle-domain common-image-gathers (ADCIGs). We demonstrate that when migrated with sediment velocities, the over-migrated multiples map to predictable regions in both SODCIGs and ADCIGs. Specular multiples focus similarly to primaries, whereas diffracted multiples do not. In particular, the apex of the residual moveout curve of diffracted multiples in ADCIGs is not located at the zero aperture angle. We use our equation of the residual moveout of the multiples in ADCIGs to design an apex-shifted Radon transform that maps the 2D ADCIGs into a 3D model space cube whose dimensions are depth, curvature, and apex-shift distance. Well-corrected primaries map to or near the zero-curvature plane and specularly reflected multiples map to or near the zero apex-shift plane. Diffracted multiples map elsewhere in the cube according to their curvature and apex-shift distance. Thus, specularly reflected as well as diffracted multiples can be attenuated simultaneously. We show the application of our apex-shifted Radon transform to a 2D seismic line from the Gulf of Mexico. Diffracted multiples originate at the edges of the salt body and we show that we can successfully attenuate them, along with the specular multiples, in the image Radon domain.

scholarly journals Fast 3D migration-velocity analysis by wavefield extrapolation using the prestack exploding-reflector model

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. WB151-WB167 ◽  
Author(s):  
Claudio Guerra ◽  
Biondo Biondi
Keyword(s):  
Initial Conditions ◽  
Model Space ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Image Space ◽  
Velocity Analysis ◽  
The North ◽  
Migration Velocity Analysis ◽  
Wavefield Extrapolation

In areas of complex geology, migration-velocity estimation should use methods that describe the complexity of wavefield propagation, such as focusing and defocusing, multipathing, and frequency-dependent velocity sensitivity. Migration-velocity analysis by wavefield extrapolation has the ability to address these issues because, in contrast to ray-based methods, it uses wavefields as carriers of information. However, its high cost and lack of flexibility with respect to model parametrization and to target-oriented analysis have prevented its routine industrial use. We overcome those limitations by using new types of wavefields as carriers of information: the image-space generalized wavefields. These wavefields are synthesized from a prestack image computed with wavefield-extrapolation methods, using the prestack exploding-reflector model. Cost of migration-velocity analysis (MVA) by wavefield extrapolation is decreased because only a small number of image-space generalized wavefields are necessary to accurately describe the kinematics of velocity errors and because these wavefields can be easily used in a target-oriented way. Flexibility is naturally incorporated because modeling these wavefields has as the initial conditions selected reflectors, which allow use of a horizon-based parametrization of the model space. In a 3D example of the North Sea, we show that using wavefields synthesized by the prestack exploding-reflector model greatly improves efficiency of MVA by wavefield extrapolation, while yielding a final migration-velocity model that is accurate as evidenced by well focused and structurally reasonable reflectors.

Prestack depth imaging of ocean-bottom node data

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCA57-WCA63 ◽  
Author(s):  
Mathias Alerini ◽  
Bärbel Traub ◽  
Céline Ravaut ◽  
Eric Duveneck
Keyword(s):  
Real Data ◽  
Velocity Model ◽  
Quality Data ◽  
Ocean Bottom ◽  
Model Estimation ◽  
Data Set ◽  
Depth Imaging ◽  
The North ◽  
Multiple Attenuation ◽  
The Common

Ocean-bottom node acquisitions provide high-quality data but usually have large distances between the nodes because of cost. This makes the use of conventional processing difficult and has led to relatively little interest in such data for industrial purposes. We have considered a three-step workflow specifically designed for prestack depth imaging of P-waves recorded by ocean-bottom nodes. It consists of multiple attenuation, velocity model estimation, and prestack depth migration. Whereas multiple attenuation and tomography use data in the common-receiver domain, migration is performed in the common-angle domain. One of the main features is the handling of the sparse receiver geometry during velocity model estimation: the reciprocity of the PP-Green’s functions is used to obtain the required tomographic input using only the common-receiver gathers. The tomographic method also provides an estimate of the geologic dip, which is used to limit the migration operator. This provides migrated images free of migration smiles. The workflow contains no additional assumptions compared to those used to process ocean-bottom cable data. We validate the workflow on a 2D line extracted from a 3D real data set acquired in the North Sea. The results show that it is possible to use ocean-bottom data efficiently for prestack depth imaging.

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.

Migration velocity analysis based on focusing diffractions generated using the CRS wavefront attributes: Application to real land data

Geophysics ◽  
2021 ◽  
pp. 1-50
Author(s):  
German Garabito ◽  
José Silas dos Santos Silva ◽  
Williams Lima
Keyword(s):  
Time Domain ◽  
Real Data ◽  
Normal Incidence ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Velocity Models ◽  
Time Migration ◽  
Migration Velocity Analysis ◽  
The Time Domain

In land seismic data processing, the prestack time migration (PSTM) image remains the standard imaging output, but a reliable migrated image of the subsurface depends on the accuracy of the migration velocity model. We have adopted two new algorithms for time-domain migration velocity analysis based on wavefield attributes of the common-reflection-surface (CRS) stack method. These attributes, extracted from multicoverage data, were successfully applied to build the velocity model in the depth domain through tomographic inversion of the normal-incidence-point (NIP) wave. However, there is no practical and reliable method for determining an accurate and geologically consistent time-migration velocity model from these CRS attributes. We introduce an interactive method to determine the migration velocity model in the time domain based on the application of NIP wave attributes and the CRS stacking operator for diffractions, to generate synthetic diffractions on the reflection events of the zero-offset (ZO) CRS stacked section. In the ZO data with diffractions, the poststack time migration (post-STM) is applied with a set of constant velocities, and the migration velocities are then selected through a focusing analysis of the simulated diffractions. We also introduce an algorithm to automatically calculate the migration velocity model from the CRS attributes picked for the main reflection events in the ZO data. We determine the precision of our diffraction focusing velocity analysis and the automatic velocity calculation algorithms using two synthetic models. We also applied them to real 2D land data with low quality and low fold to estimate the time-domain migration velocity model. The velocity models obtained through our methods were validated by applying them in the Kirchhoff PSTM of real data, in which the velocity model from the diffraction focusing analysis provided significant improvements in the quality of the migrated image compared to the legacy image and to the migrated image obtained using the automatically calculated velocity model.

Marchenko multiple elimination and full wavefield migration in a resonant pinch-out model

Geophysics ◽  
2021 ◽  
pp. 1-59
Author(s):  
Evert Slob ◽  
Lele Zhang ◽  
Eric Verschuur
Keyword(s):  
Constant Velocity ◽  
Local Minimum ◽  
Velocity Model ◽  
Dominant Frequency ◽  
Data Sampling ◽  
Multiple Reflections ◽  
Linear Inversion ◽  
Acoustic Reflection ◽  
Reflection Data ◽  
Multiple Elimination

Marchenko multiple elimination schemes are able to attenuate all internal multiple reflections in acoustic reflection data. These can be implemented with and without compensation for two-way transmission effects in the resulting primary reflection dataset. The methods are fully automated and run without human intervention, but require the data to be properly sampled and pre-processed. Even when several primary reflections are invisible in the data because they are masked by overlapping primaries, such as in the resonant wedge model, all missing primary reflections are restored and recovered with the proper amplitudes. Investigating the amplitudes in the primary reflections after multiple elimination with and without compensation for transmission effects shows that transmission effects are properly accounted for in a constant velocity model. When the layer thickness is one quarter of the wavelength at the dominant frequency of the source wavelet, the methods cease to work properly. Full wavefield migration relies on a velocity model and runs a non-linear inversion to obtain a reflectivity model which results in the migration image. The primary reflections that are masked by interference with multiples in the resonant wedge model, are not recovered. In this case, minimizing the data misfit function leads to the incorrect reflector model even though the data fit is optimal. This method has much lower demands on data sampling than the multiple elimination schemes, but is prone to get stuck in a local minimum even when the correct velocity model is available. A hybrid method that exploits the strengths of each of these methods could be worth investigating.

Velocity inversion by global optimization using finite-offset common-reflection-surface stacking applied to synthetic and Tacutu Basin seismic data

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. R165-R174 ◽  
Author(s):  
Marcelo Jorge Luz Mesquita ◽  
João Carlos Ribeiro Cruz ◽  
German Garabito Callapino
Keyword(s):  
Objective Function ◽  
Real Data ◽  
Velocity Model ◽  
Data Sets ◽  
Layer By Layer ◽  
Velocity Inversion ◽  
Very Fast Simulated Annealing ◽  
Target Layer ◽  
Common Reflection Surface ◽  
The Mean

Estimation of an accurate velocity macromodel is an important step in seismic imaging. We have developed an approach based on coherence measurements and finite-offset (FO) beam stacking. The algorithm is an FO common-reflection-surface tomography, which aims to determine the best layered depth-velocity model by finding the model that maximizes a semblance objective function calculated from the amplitudes in common-midpoint (CMP) gathers stacked over a predetermined aperture. We develop the subsurface velocity model with a stack of layers separated by smooth interfaces. The algorithm is applied layer by layer from the top downward in four steps per layer. First, by automatic or manual picking, we estimate the reflection times of events that describe the interfaces in a time-migrated section. Second, we convert these times to depth using the velocity model via application of Dix’s formula and the image rays to the events. Third, by using ray tracing, we calculate kinematic parameters along the central ray and build a paraxial FO traveltime approximation for the FO common-reflection-surface method. Finally, starting from CMP gathers, we calculate the semblance of the selected events using this paraxial traveltime approximation. After repeating this algorithm for all selected CMP gathers, we use the mean semblance values as an objective function for the target layer. When this coherence measure is maximized, the model is accepted and the process is completed. Otherwise, the process restarts from step two with the updated velocity model. Because the inverse problem we are solving is nonlinear, we use very fast simulated annealing to search the velocity parameters in the target layers. We test the method on synthetic and real data sets to study its use and advantages.

Simultaneous source separation using a robust Radon transform

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. V1-V11 ◽  
Author(s):  
Amr Ibrahim ◽  
Mauricio D. Sacchi
Keyword(s):  
Radon Transform ◽  
Real Data ◽  
Radon Transforms ◽  
Accurate Data ◽  
Quadratic Formula ◽  
Penalty Term ◽  
Source Data ◽  
The Cost ◽  
Simultaneous Source ◽  
Incoherent Noise

We adopted the robust Radon transform to eliminate erratic incoherent noise that arises in common receiver gathers when simultaneous source data are acquired. The proposed robust Radon transform was posed as an inverse problem using an [Formula: see text] misfit that is not sensitive to erratic noise. The latter permitted us to design Radon algorithms that are capable of eliminating incoherent noise in common receiver gathers. We also compared nonrobust and robust Radon transforms that are implemented via a quadratic ([Formula: see text]) or a sparse ([Formula: see text]) penalty term in the cost function. The results demonstrated the importance of incorporating a robust misfit functional in the Radon transform to cope with simultaneous source interferences. Synthetic and real data examples proved that the robust Radon transform produces more accurate data estimates than least-squares and sparse Radon transforms.

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