Reda Baina

Nonlinear 3D tomographic least-squares inversion of residual moveout in Kirchhoff prestack-depth-migration common-image gathers

Velocity-model estimation with seismic reflection tomographyisanonlinearinverseproblem.Wepresentanewmethodforsolvingthenonlineartomographicinverseproblemusing 3D prestack-depth-migrated reflections as the input data, i.e., our method requires that prestack depth migration PSDMbeperformedbeforetomography.Themethodisapplicable to any type of seismic data acquisition that permits seismic imaging with Kirchhoff PSDM.Afundamental conceptofthemethodisthatwedissociatethepossiblyincorrect initialmigrationvelocitymodelfromthetomographicvelocity model. We take the initial migration velocity model and the residual moveout in the associated PSDM common-image gathers as the reference data. This allows us to consider themigrateddepthoftheinitialPSDMastheinvariantobservation for the tomographic inverse problem. We can therefore formulate the inverse problem within the general framework of inverse theory as a nonlinear least-squares data fitting between observed and modeled migrated depth. The modeledmigrateddepthiscalculatedbyraytracinginthetomographic model, followed by a finite-offset map migration in the initial migration model.The inverse problem is solved iteratively with a Gauss-Newton algorithm. We applied the method to a North Sea data set to build an anisotropic layer velocitymodel.

3D preserved-amplitude prestack depth migration and amplitude versus angle relevance

Although amplitude versus angle (AVA) analysis is currently performed on unmigrated prestack data, there is increasing evidence that more reliable and better resolved AVA attributes can be obtained by inversion after prestack migration, either in time (Mosher et al., 1996) or in depth (Beydoun et al., 1993)—even when considering flat structures. In principle at least, the use of prestack depth migration before inversion appears a better option because it involves a less approximate description of wave propagation and provides better results in terms of location, resolution, and accuracy of AVA targets. For successful AVA inversion after migration, amplitude preservation naturally is of utmost importance. Two approaches may be used. The classical sequence consists of “preserved amplitude preprocessing” in which trace amplitudes are corrected by estimating the decay due to wave propagation and then so-called “kinematic” processing (DMO, prestack time or depth migration), without amplitude weights. In that case, final amplitude values simply come from the amplitudes of the preprocessed prestack data and this can obviously affect the AVA analysis adversely. As an alternate solution, traces are preprocessed with as little alteration as possible of their original amplitudes and then fed to a “preserved-amplitude” PsDM scheme (PAPsDM), in which migration weights are designed to fully account for dynamic propagation effects and acquisition effects (e.g., geometrical spreading and irregular illumination corrections). The latter solution is being recognized as a valuable and efficient tool to improve quantitative discrimination of reservoirs. In this article, we compare results obtained with these two approaches on calibrated synthetic data in order to underline that reliable amplitudes of subsurface parameters can be computed in heterogeneous media. Because real-sized applications require accurate and efficient tools, a second example is presented that uses real data. This is included to establish that such applications of ray-based quantitative Kirchhoff migration and subsequent …

Poststack diffraction imaging using reverse‐time migration

We propose a method for imaging small-scale diffraction objects in complex environments in which Kirchhoff-based approaches may fail. The proposed method is based on a separation between the specular reflection and diffraction components of the total wavefield in the migrated surface angle domain. Reverse-time migration was utilized to produce the common image gathers. This approach provides stable and robust results in cases of complex velocity models. The separation is based on the fact that, in surface angle common image gathers, reflection events are focused at positions that correspond to the apparent dip angle of the reflectors, whereas diffracted events are distributed over a wide range of angles. The high-resolution radon-based procedure is used to efficiently separate the reflection and diffraction wavefields. In this study, we consider poststack diffraction imaging. The advantages of working in the poststack domain are its numerical efficiency and the reduced computational time. The numerical results show that the proposed method is able to image diffraction objects in complex environments. The application of the method to a real seismic dataset illustrates the capability of the approach to extract diffractions.

Aperture Optimized Two-pass Kirchhoff Migration

The migration aperture is a critical parameter in Kirchhoff PSDM to obtain the best image quality from a given dataset. Reducing the migration aperture generally enhances the signal/noise ratio and reduces computation time but to the detriment of dipping events imaging. Aperture is the result of a compromise. Moreover a constant aperture can never be optimal in complex media. We must use a spatially variable aperture to optimize the image quality in complex media.

Residual stereotomographic inversion

Depth migration requires highly accurate knowledge of the subsurface velocity field. Different traveltime tomographic methods are used for this purpose. Stereotomography is a tomographic method that uses local dip estimates in addition to traveltimes for velocity model estimation. We present a new methodology for velocity model updating. It combines poststack stereotomography and residual moveout velocity inversion. The former is used for initial model construction and the latter for updating the velocity model. Residual inversion is a kind of stereotomographic inversion applied to common reflection point (CRP) gathers after model-based moveout correction. Velocity analysis can be made more efficient by preselecting the traces that contribute to a series of CRP gathers and using only these traces for inversion. The algorithm is defined in a two-step procedure. First, ray tracing from the reflection point for nonzero reflection offsets defines the source and receiver locations of the data traces in the CRS gather. Then these traces are moveout corrected according to the calculated traveltimes and residual moveout is estimated. The interval velocity model is updated by fitting the velocity that minimizes estimated residuals. Application of the proposed technique demonstrates its robustness and reliability for fast and automatic velocity model estimation.

Separation of Diffraction Objects in Post-Stack Reverse Time Depth Migration

This paper proposes a new method for imaging small- scale diffraction objects. Its basis is separation of specular reflection and diffraction components of the total wavefield in the migrated domain. Reverse-time migration has been utilized to produce surface dip-angle common image gathers. One uses continuity of diffractions in the dip-angle CIGs as a criterion for separating reflections from diffractions. Synthetic and data examples illustrate efficient application of the method.

Optimal aperture Kirchhoff migration in dip angle domain

Summary Kirchhoff migration may suffer from migration noise and artifacts due to operator or data aliasing, truncated aperture or non-optimal migrated weights. This noise can be essentially reduced by using an optimal aperture of the migration operator which includes mostly the specular energy and not long “tails” of the diffraction operator. The paper proposes a way to compute optimal aperture migration images. It is achieved by considering migrated common image gathers in the dip angle domain. In this domain reflections appear as concave-shaped events where the specular energy is concentrated in a vicinity of the apex position. Limiting the aperture by the apices vicinity, optimal migration images can be constructed. The method uses a matching pursuit technique to extract these events which are described by operators in the Radon space.