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GoSeveral method exist to invert for a velocity model from seismic data. Most commonly used methods are defined in the image domain. However, some methods that are defined in the data domain also exist. In this paper we review and compare a few methods on synthetic data, using the convolutional model and NMO traveltimes to model the data. Special attention will be given to the behavior of the different methods in the presence of multiples. In traditional MVA methods these usually pose a problem since multiples are not flattened or focused for the correct velocity model. In the data domain multiples do focus for the correct velocity model if they are correctly modeled. This is illustrated with a simple example. Another simple example illustrates how ideas from waveform inversion and data-domain velocity analysis can be combined to obtain the correct velocity model and reflectivity from synthetic data with multiples.

In waveform inversion one tries to infer a set of model parameters, in particular velocity, from seismic data by fitting the data in a leastsquares sense (Tarantola, 1984). While intuitively pleasing, this approach has several drawbacks. First, in order to get reliable results, the modeling used has to be accurate. Second, because of the absence of low frequencies in the data, it is difficult to obtain information about the slowly-varying components of the velocity model. The latter problem is addressed by Migration Velocity Analysis (MVA). However, this approach is usually based on high-frequency and/or one-way approximations of the wave equation. This prevents MVA to yield good results in the presence of strong multiples, which are not accounted for by these approximations. However, there are that try to use the multiples by removing them or transforming them into primaries (Verschuur and Berkhout, 2007).

Velocity analysis can also be performed in the data domain by generating data for the estimated reflectivity and comparing them to the observed data (Chavent et al., 1994; Plessix et al., 1999). Recently a method has been proposed that uses the correlation of observed and predicted data (van Leeuwen and Mulder, 2007a). This correlation will ''focus'' for the correct velocity model. By automatically updating the velocity model to optimize the amount of focusing it is indeed possible to obtain a good NMO velocity model (van Leeuwen and Mulder, 2007b). We will refer to this velocity analysis method as DVA in the rest of the paper.

In principle, it should be possible to obtain a good velocity model with DVA in the presence of multiples, if the multiples are modeled correctly. But to model the multiples correctly, the migrated image, from which the synthetic data are modeled, has to be correct. In general the migrated image will contain spurious events due to multiples in the data. However, by iteratively updating the migrated image, it should be possible to obtain the correct reflectivity if the velocity model is correct. This leads to two extremes: (1) given the correct velocity model, we can obtain the correct reflectivity with least-squares inversion; (2) given the correct reflectivity, we can obtain the correct velocity model with the data-correlation method.

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)

In the physical insight, the data-consistence-based timespace convolution method for multiples'' generation and prediction was discussed. The predicted multiples can be matched to multiples in original data by a linear (leastsquares) inversion process, and then be subtracted from original data. The surface-related multiple-attenuation can be implemented in an iterative adaptive procedure and can be made very efficient. The iterative multiple suppression process are illustrated with a field data example. Comparing with other de-multiple methods, the results show that the process is very effective and stable, attenuating the multiple energy while keeping the primary events not damaged.

attenuation, Berkhout, data, elimination, energy, especially, event, iteration, knowledge management, method, multiple, prediction, procedure, receiver, result, section, shot gather, source, surface, trace

SPE Disciplines:

Model-based surface related multiple modeling (3D SRMM) can be achieved by the use of pre-stack demigration algorithms, thus avoiding the constrains on the shot positions distribution required by the data-based methods. In the following, we show a new method for modeling internal multiples in 3D by using a model-based technique. This method follows a parallel flow with respect to those employed by the data-based multiple modeling techniques, and allows for the construction of internal multiple events produced between upper layers reflecting the energy downward, and lower layers reflecting the energy upward. The method has been applied to Wide Azimuth Towed Streamer data from the Gulf of Mexico.

Artificial Intelligence, data, equation, event, extrapolation, Figure, meeting, method, model-based reasoning, modeling, multiple, reflection, reflectivity, reflectivity model, reflector, result, section, source, structure, surface, Wave

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)

To improve the subsalt exploration success rate and the subsalt image quality and to get greater reservoir illumination, the wide azimuth towed streamer (WATS) acquisition technique has gained popularity in the past few years. To maximize the benefit-to-cost ratio of a WATS project, a detailed feasibility study which considers acquisition, processing and imaging issues is necessary. As processing is concerned, multiple attenuation is an important step whose sensitivity to the acquisition parameters may have a determining role in WATS survey design optimization. This paper shows that while wave equation based 3D SRME is absolutely beneficial in the processing of WATS data, it is robust enough and is insensitive to the acquisition parameters.

acquisition, Acquisition Parameter, attenuation, azimuth, cable, configuration, crossline, data, depth, design, Figure, geometry, multiple, prediction, result, SRME, SRME impact, streamer, vessel

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)

At the EAGE 2008 annual conference (Neelamani et al., 2008), we proposed a complex curvelet transform-based algorithm to adaptively subtract from seismic data, noises that can be approximated by a single template. In this paper, we extend that approach so that we can subtract noises that need several templates to be approximated. The complex curvelet transform decomposes a geophysical dataset in terms of small reflector pieces, with each piece having a different frequency, location, and direction. The properties of complex curvelet transforms enable us to precisely change the amplitude and shift the location of each seismic reflector piece in a noise template by controlling the amplitude and phase of its complex curvelet coefficient. We fold these insights into an iterative, convergent algorithm to simultaneously adapt all noise templates. The basic step during the iteration is to adapt each noise template to the actual noise on an event-by-event basis by using the phase and amplitude of the data''s and template''s complex curvelet coefficients. Results illustrate that the proposed complex curvelet-based approach improves upon the conventional least squares subtraction approach.

approach, coefficient, curvelet, curvelet coefficient, curvelet function, Curvelet transform, dataset, Figure, input, Magnitude, multiple, noise, noise template, Phase, reflector, signal, subtraction, template

Inverting seismic wavefields lies at the heart of seismic data processing and imaging- whether one is applying "a poor man''s inverse" by correlating wavefields during imaging or whether one inverts wavefields as part of a focal transform interferrometric deconvolution or as part of computing the "data inverse". The success of these wavefield inversions depends on the stability of the inverse with respect to data imperfections such as finite aperture, bandwidth limitation, and missing data. In this paper, we show how curvelet domain sparsity promotion can be used as a suitable prior to invert seismic wavefields. Examples include, seismic data regularization with the focused curvelet-based recovery by sparsity-promoting inversion (fCRSI), which involves the inversion of the primarywavefield operator, the prediction of multiples by inverting the adjoint of the primary operator, and finally the inversion of the data itself-the so-called "data inverse". In all cases, curveletdomain sparsity leads to a stable inversion.

In this paper, we demonstrate that the discrete curvelet transform (Candes et al., 2006; Hennenfent and Herrmann, 2006) can be used to invert seismic wavefields stably, even in case where the data volumes are sampled incompletely. The crux of our method lies in the combination of the curvelet transform, which attains a fast decay for the magnitude-sorted curvelet coefficients for arbitrary wavefields (see e.g. Candes et al., 2006; Hennenfent and Herrmann, 2006; Herrmann et al., 2008; Herrmann and Hennenfent, 2008, and the references therein), with a sparsity promoting program. By themselves sparsitypromoting programs are not new to the geosciences (Sacchi et al., 1998). However, sparsity promotion with the curvelet transform is relatively new (see e.g. Herrmann et al., 2008, for an overview). The curvelet transform''s unparalleled ability to detect wavefront-like events that are locally linear and coherent means it is particularly well suited to seismic data problems. In this paper, we show how this transform can be used to regularize the inversion of seismic wavefields. This type of inversion proves difficult in practice because of the problem size, finite aperture, source/receiver signatures and the presence of noise. By using 3-D curvelets in the shot-receiver-time domain, we leverage continuity along multidimensional wavefronts maximally. As opposed to damped least-squares-a popular method for the regularization of geophysical inverse problems at the expense of additional smoothing-curveletdomain sparsity promotion preserves wavefronts. This property explains our recent successes applying this strategy to synthetic and real field data with applications ranging from wavefield reconstruction (Herrmann and Hennenfent, 2008; Hennenfent and Herrmann, 2008), wavefield separation, migration amplitude recovery (Herrmann et al., 2008), and compressed wavefield extrapolation (Lin and Herrmann, 2007). In this paper, we continue to leverage curvelet-domain sparsity promotion towards wavefield inversion with applications including the inversion of primary wavefields part of focusing, the inversion of the adjoint of the primary wavefield part of defocusing for multiple prediction, and finally the stable computation of Berkhout''s data inverse Berkhout (2006); Berkhout and Verschuur (2007). First, we briefly introduce the curvelet transform, followed by a common-problem formulation for curvelet-based wavefield inversion (CWI) by sparsity promotion and its application.

Oilfield Places:

Model based multiple prediction approaches require an adaptive subtraction step that is able to correct for differences between the real and predicted multiples. The commonly used subtraction process derives shaping operators, in the least squares sense, to minimize the energy difference between the predicted multiples and the field record. Although the minimum energy assumption allows a computationally efficient adaptive subtraction, it can lead to attenuation of primary information. This abstract illustrates how a simple amplitude clipping approach can significantly improve the effectiveness of the least squares adaptive subtraction and minimize primary attenuation.

amplitude, application, approach, attenuation, energy, estimate, event, example, Figure, filter, model-based reasoning, multiple, prediction, process, Program Committee, record, result, shot record, subtraction, wavelet, workshop organizer

If singly scattered seismic waves illuminate the entirety of a subsurface structure of interest, standard methods can be applied to image it. In many cases, subsalt imaging for example, a combination of restricted acquisition geometry and imperfect velocity models results in regions of the model that are not illuminated with singly scattered waves. We present an approach to use multiply scattered waves to illuminate such structures, and illustrate the method by creating images of the base of salt with an erroneous velocity model. This method builds upon past work in which methods to predict artifacts in imaging from multiply scattered waves have been developed and shares similarities with current techniques of imaging with surface-related multiples.

In this paper we discuss a method for subsalt imaging using internal multiples. Our approach extends the work of Malcolm and de Hoop (2005) by including illumination in a series representation that models the data as a superposition of different phases. By explicitly including illumination in the series representation we identify those multiples which carry information about regions of the subsurface not illuminated by singly scattered waves.

Imaging with internal multiples in the framework of the one-way wave equation requires a "multi-pass" approach reminiscent of the generalized Bremmer series (de Hoop, 1996). Turning waves are accounted for in such an approach as discussed by Xu and Jin (2006); Zhang et al. (2006); see also Hale et al. (1991). In the multi-pass approach, starting at the surface (or top), waves are first propagated downwards and then stored at each depth; in the second "pass", starting at the bottom, reflection operators derived from the estimated standard image are applied to the stored fields and the results are propagated, accumulatively, back upwards. For turning waves, or doubly scattered waves this up-going field is correlated with the saved down-going field to form an image of steeply-dipping reflectors (for doubly scattered waves this is similar to the work of Jin et al. (2006); Xu and Jin (2007)). For internal multiples the source-side up-going field is correlated with the receiver-side up-going field to form an image of e.g. the base of salt. A related method for imaging with surface-related multiples has been proposed by Berkhout & Verschuur (1994; 2006) in which one leg of the surface multiple generates a new primary wave with the source at the surface reflection point; similar techniques are also discussed in Guitton (2002). Another method for imaging with surface-related multiples with particular emphasis on reducing crosstalk between the two (or more) images is given in Brown and Guitton (2005). For surface-related multiples, this improves the range of scattering angles illuminated for a single data set and allows the imaging of a larger region. Interferometric techniques can be applied to multiples to allow standard migration techniques to be applied to the resulting data; this is discussed in Schuster et al. (2004); Jiang (2006); Jiang et al. (2007); Vasconcelos et al. (2007). Here we use internal multiples, recorded at the surface, to image around complicated structures, such as salt domes, to create an image of the base of salt using waves that have not passed through it.

Matching seismic wavefields lies at the heart of seismic processing whether one is adaptively subtracting multiples predictions or groundroll. In both cases, the predictions are matched to the actual to-be-separated wavefield components in the observed data. The success of these wavefield matching procedures depends on our ability to (

amplitude, Bayesian, curvelet, Curvelet transform, data, equation, estimate, Figure, filter, Herrmann, method, multiple, Program Committee, result, scaling, separation, SRME, vector, workshop organizer

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Technology:

- IT > AI > Representation & Reasoning (0.47)
- IT > AI > Machine Learning (0.35)

Multiples are successfully removed from seismic data to increase the signal-to-noise ratio in a 3D land dataset acquired in Abu Dhabi. The anti-multiple process aims at removing, in user specified spatial-temporal windows, surface and inter-bed multiple energy, which are associated with particular primary events. The anti-multiple is designed in the f-xy domain. In order to emphasize the fact that this process targets a particular multiple events, it is sometimes referred to as pattern recognition. In this particular study, the noise attenuation is performed pre stack, on constant offset time migrated data volumes.

Abu Dhabi, attenuation, Case History, data, domain, event, Figure, knowledge management, land, meeting, multiple, prediction, process, reference, seg las vegas, surface, target area

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Thank you!