Wave‐equation migration velocity analysis. I. Theory

Prestack depth migration (PSDM) heavily depends on the accuracy of the migration velocity model. Reflection tomography on the base of common-image gathers (CIGs) is an important tool to build such models in depth domain. Unlike the conventional offset domain PSDM, angle domain PSDM can avoid migration artifacts when the velocity models are complex. It is easier to build the back-projection matrix for tomography according to the residual moveout (RMO) on the angle domain common image gathers (ADCIGs). In this abstract, we propose a novel nonlinear post-migration tomography approach to build velocity model using ADCIGs. The picked angle domain RMO is converted to prestack domain as invariants for data-fitting and model updating in the tomography iteration. Synthetic example proves the validity of this approach.

Common-image gathers (CIGs) are extensively used in migration velocity analysis. Any defocused events in the subsurface offset domain or equivalently nonflat events in angle-domain CIGs are accounted for revising the migration velocities. However, CIGs from wave-equation methods such as reverse time migration are often expensive to compute, especially in 3D. Using the excitation amplitude imaging condition that simplifies the forward-propagated source wavefield, we have managed to extract extended images for space and time lags in conjunction with prestack reverse time migration. The extended images tend to be cleaner, and the memory cost/disk storage is extensively reduced because we do not need to store the source wavefield. In addition, by avoiding the crosscorrelation calculation, we reduce the computational cost. These features are demonstrated on a linear [Formula: see text] model, a two-layer velocity model, and the Marmousi model.

In this paper I show that the locally‐constant velocity (straight‐ray approximation) of the residual moveout of the primary reflections in Angle‐Domain Common‐Image Gathers (ADCIGs), is appropriate for specularly‐reflected multiples only at small aperture angles. The approximation is good for the primaries because the difference between the migration velocity and the true velocity is likely to be small. For the multiples, however, this difference may be large, since the migration velocity is chosen for the primaries. Correcting for ray bending at the multiple‐generating interface produces a better approximation that leads to better focusing of the multiples when the ADCIGs are transformed to the Radon domain and better separation between the primaries and the multiple. This in turn allows a more accurate estimate and attenuation of the multiples. I show results with two ADCIGs, one synthetic and one real.

The idea of path-integral imaging is to sum over the migrated images obtained for a set of migration velocity models. Velocities where common-image gathers align horizontally are stationary, thus favoring these images in the overall stack. The overall image forms with no knowledge of the true velocity model. However, the velocity information associated with the final image can be determined in the process. By executing the path-integral imaging twice and weighting one of the stacks with the velocity value, the stationary velocities that produce the final image can then be extracted by a division of the two images. The velocity extraction, interpolation, and smoothing can be done fully automatically, without the need for human interpretation or other intervention. A numerical example demonstrated that quantitative information about the migration velocity model can be determined by double path-integral migration. The so-obtained velocity model can then be used as a starting model for subsequent velocity analysis tools like migration velocity analysis or tomographic methods.

ABSTRACTWave‐equation migration velocity analysis is a technique designed to extract and update velocity information from migrated images. The velocity model is updated through the process of optimizing the coherence of images migrated with the known background velocity model. The capacity for handling multi‐pathing of the technique makes it appropriate in complex subsurface regions characterized by strong velocity variation. Wave‐equation migration velocity analysis operates by establishing a linear relation between a slowness perturbation and a corresponding image perturbation. The linear relationship and the corresponding linearized operator are derived from conventional extrapolation operators and the linearized operator inherits the main properties of frequency‐domain wavefield extrapolation. A key step in the implementation is to design an appropriate procedure for constructing an image perturbation relative to a reference image that represents the difference between the current image and a true, or more correct image of the subsurface geology. The target of the inversion is to minimize such an image perturbation by optimizing the velocity model. Using time‐shift common‐image gathers, one can characterize the imperfections of migrated images by defining the focusing error as the shift of the focus of reflections along the time‐shift axis. The focusing error is then transformed into an image perturbation by focusing analysis under the linear approximation. As the focusing error is caused by the incorrect velocity model, the resulting image perturbation can be considered as a mapping of the velocity model error in the image space. Such an approach for constructing the image perturbation is computationally efficient and simple to implement. The technique also provides a new alternative for using focusing information in wavefield‐based velocity model building. Synthetic examples demonstrate the successful application of our method to a layered model and a subsalt velocity update problem.

Current wave-equation migration velocity analysis schemes suffer from problems such as severe nonlinearity (which causes the issue of cycle skipping) and imprecise objective functions (which can accrue velocity errors by honoring residuals caused by model complexity and incomplete acquisition). To provide an improvement, we developed an alternative method to perform wave-equation migration velocity analysis by maximizing the flatness of the angle-domain common image gathers. We replaced the ray-based tomographic operator with the wave-equation-based one, although keeping the conventional moveout-based tomography work flow. Instead of maximizing the image-stack-power objective function directly with respect to the slowness, we linked the objective function to the slowness indirectly through an intermediate moveout parameter. By focusing on the common image gather kinematics, this approach greatly reduced the risk of cycle skipping in the absence of low-frequency data, and it produced high-quality gradients. In addition, the proposed method did not require explicit picking of the moveout parameters. Our numerical examples demonstrated the great potential of this method: in the first example, in which there is a Gaussian-shaped slowness anomaly, our method produced a well-behaved gradient; in the second example, in which there is a horizontally gradual increase of slowness, the result verified that our method is robust against cycle skipping; in the third example, the result showed that our method works well with reflectors of variable dips. Finally, our test on the Marmousi models concluded that the proposed method converges to a high-quality model that uniformly flattens the angle-domain common-image gathers.

The source extrapolation step in wave-equation prestack reverse-time migration gives wavefield polarization information, which can be used to generate angle-domain common-image gathers (ADCIGs) from seismic reflection data from acoustic media. Concatenation of P-wave polarization segments gives wavefield propagation paths (“wavepaths”), which are similar to the raypaths in ray-based velocity tomography. The ADCIGs provide residual depth moveout (RMO) information, from which a system of linear equations is constructed for tomography to solve for the velocity ratio used for velocity updating. An empirical relation between the RMO data and the velocity ratio updates reduces the amount of computation, and is stabilized by the feedback provided by the iterative loop through prestack migration, to RMO, to velocity update, to prestack migration. Correcting the RMOs to flatten the ADGIGs is the convergence condition. Synthetic data for a layered model with a fault successfully illustrates the method.

Overburden (shallow) anomalies such as channels, sink holes, or karst features pose challenges for seismic time imaging, resulting in an obscured image below the anomalies i.e. pull-ups or push-downs. These anomalies can propagate down to the reservoir masking the image and create structural uncertainties. These relatively small scale (< 1 – 2 km) overburden anomalies cannot be resolved with conventional depth imaging usually, based on migration velocity analysis and residual move out (RMO) minimization only. This paper proposes the application of dip-constrained tomography, in combination with RMO tomography to help resolve these shallow anomalies. Although the method has been widely used elsewhere e.g. in offshore Brazil and North Sea (Chen et al., 2012, Guillaume et al., 2013, Carotti et al., 2015 and Hollingworth et al., 2015), this is the first time it has been applied in a carbonate oilfield in offshore Abu Dhabi. An accurate velocity model is required for seismic depth imaging. The velocity model is optimized using a tomographic technique which is a non-linear optimization process with relevant constraints imposed. The data are migrated using an initial velocity model and common image gathers are obtained. RMO is defined in a cost function and non-linear tomography finds a velocity model minimizing the cost function. An additional structural constraint in the form of an offset-dependent dip constraint is introduced in the cost function for minimizing the misfit between the offset-dependent dip of the events and the expected dip. Dip-constrained tomography was able to obtain a high resolution velocity model in the overburden and provided a robust seismic image essentially free of pull-up and push-down effects in the reservoir. The structural uncertainty in the reservoir was subsequently reduced. Inverting the dip term together with RMO term can potentially correct image distortions e.g. pull-ups and push-downs and focus the image simultaneously. The refined subsurface image can help optimize the reservoir model with less structure uncertainty and can enhance the production profile by providing more flexibility in well design and planning. The methodology was applied on a pilot area which gave quite encouraging results and leads to extend the pre-stack depth imaging to a full-field application.

An important research topic for prospecting seismology is to provide a fast accurate velocity model from pre-stack depth migration. Aiming at such a problem, we propose a quadratic precision generalized nonlinear global optimization migration velocity inversion. First we discard the assumption that there is a linear relationship between residual depth and residual velocity and propose a velocity model correction equation with quadratic precision which enables the velocity model from each iteration to approach the real model as quickly as possible. Second, we use a generalized nonlinear inversion to get the global optimal velocity perturbation model to all traces. This method can expedite the convergence speed and also can decrease the probability of falling into a local minimum during inversion. The synthetic data and Marmousi data examples show that our method has a higher precision and needs only a few iterations and consequently enhances the practicability and accuracy of migration velocity analysis (MVA) in complex areas.

In an ever more challenging context for the acquisition of seismic data in the Mediterranean Sea, reprocessing to improve the quality of legacy data has become increasingly important. This work presents the newly reprocessed, open access dataset SALTFLU acquired in the Algerian basin by the National Institute of Oceanography and Applied Geophysics (OGS) in 2012. We apply a ‘broadband’ reprocessing strategy adapted for short-offset, deep water airgun reflection seismic data and assess if the reprocessed images provide new geological insights on the Mediterranean sub-surface. The workflow relies on an integrated approach combining geophysics and geological interpretation to iteratively build the velocity model. In this way we aim to tackle some of the challenges linked to imaging complex geological structures containing high velocity contrasts with 2-D, short-offset seismic data. We first broaden the bandwidth of the data through multi-domain de-noising, deghosting and a source designature using an operator derived from the seabed reflection. We then perform iterative migration velocity analysis, pre-stack time migration and multiple attenuation in the Radon domain to obtain time-migrated images. The initial velocity model is derived from the resulting time migration velocities, and geologically driven model updates are generated using a combination of travel-time tomography, seismic interpretation of the major salt horizons and velocity gradient flooding. The gradient flooding aims to reproduce the large scale first-order velocity variations, while the travel-time tomography aims to resolve the smaller second-order velocity variations. The results improve our deep geological knowledge of the under-explored Algerian basin down to the base salt and the pre-salt. Fluid indicators are imaged within the Plio-Quaternary of the Algerian basin, which we interpret as thermogenic or biogenic gas sourced from either the Messinian Upper Unit or from the pre-salt, migrating through a hydro-fractured salt. The reprocessed data image lateral and vertical seismic facies variation within the Messinian units that could shed new light on the tectono-stratigraphic processes acting during the Messinian Salinity Crisis. It also reveals numerous previously unresolved volcanic structures within the Formentera basin.

In an ever more challenging context for the acquisition of seismic data in the Mediterranean Sea, reprocessing to improve the quality of legacy data has become increasingly important. This work presents the newly reprocessed, open access dataset SALTFLU acquired in the Algerian basin by the National Institute of Oceanography and Applied Geophysics (OGS) in 2012. We apply a ‘broadband’ reprocessing strategy adapted for short-offset, deep water airgun reflection seismic data and assess if the reprocessed images provide new geological insights on the Mediterranean sub-surface. The workflow relies on an integrated approach combining geophysics and geological interpretation to iteratively build the velocity model. In this way we aim to tackle some of the challenges linked to imaging complex geological structures containing high velocity contrasts with 2-D, short-offset seismic data. We first broaden the bandwidth of the data through multi-domain de-noising, deghosting and a source designature using an operator derived from the seabed reflection. We then perform iterative migration velocity analysis, pre-stack time migration and multiple attenuation in the Radon domain to obtain time-migrated images. The initial velocity model is derived from the resulting time migration velocities, and geologically driven model updates are generated using a combination of travel-time tomography, seismic interpretation of the major salt horizons and velocity gradient flooding. The gradient flooding aims to reproduce the large scale first-order velocity variations, while the travel-time tomography aims to resolve the smaller second-order velocity variations. The results improve our deep geological knowledge of the under-explored Algerian basin down to the base salt and the pre-salt. Fluid indicators are imaged within the Plio-Quaternary of the Algerian basin, which we interpret as thermogenic or biogenic gas sourced from either the Messinian Upper Unit or from the pre-salt, migrating through a hydro-fractured salt. The reprocessed data image lateral and vertical seismic facies variation within the Messinian units that could shed new light on the tectono-stratigraphic processes acting during the Messinian Salinity Crisis. It also reveals numerous previously unresolved volcanic structures within the Formentera basin.

Combining PP-waves with mode-converted PS reflections in migration velocity analysis (MVA) can help build more accurate VTI (transversely isotropic with a vertical symmetry axis) velocity models. To avoid problems caused by the moveout asymmetry of PS-waves and take advantage of efficient MVA algorithms designed for pure modes, here we generate pure SS-reflections from PP and PS data using the PP þ PS ¼ SS method. Then the residual moveout in both PP and SS common-image gathers is minimized during iterative velocity updates. The model is divided into square cells, and the VTI parameters VP0, VS0, e, and δ are defined at each grid point. The objective function also includes the differences between the migrated depths of the same reflectors on the PP and SS sections. Synthetic examples confirm that 2D MVA of PP- and PS-waves may be able to resolve all four relevant parameters of VTI media if reflectors with at least two distinct dips are available. The algorithm is also successfully applied to a 2D line from 3D ocean-bottom seismic data acquired at Volve field in the North Sea. After the anisotropic velocity model has been estimated, accurate depth images can be obtained by migrating the recorded PP and PS data.

In areas of complex geology, migration-velocity analysis (MVA) should use methods that describe the complexity of wavefield propagation, such as focusing and defocusing, multipathing, and frequency-dependent velocity sensitivity. MVA by wavefield extrapolation has the ability to address these issues because it uses wavefields as carriers of information. However, its high cost and lack of flexibility with respect to model parametrization have prevented its routine industrial use. We overcome those limitations by using new wavefields: the image-space generalized wavefields. These wavefields are synthesized from a prestack image computed with wavefield-extrapolation methods, using the pre-stack exploding-reflector model. Cost of 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 have selected reflectors as the initial conditions, allowing the use of a horizon-based parametrization of the model space. In a 3D real data example, we show that using wavefields synthesized by the prestack exploding-reflector model greatly improves efficiency of migration-velocity analysis by wavefield-extrapolation, while yielding a final accurate migration-velocity model evidenced by good quality and reliable depth images.

In the early stage of acoustic full-waveform inversion (AFWI), it is important to exploit the long-wavelength features of the gradient and suppress its short-wavelength features to update the background velocity. However, due to strong near-offset PP reflections and multiples within the pressure data, conventional AFWI sometimes primarily reconstructs the short-wavelength features of a given model and fails to converge on a reliable subsurface P-wave velocity model. Therefore, this study, we propose the usage of pseudo-horizontal particle acceleration (pseudo-ax) data for AFWI, rather than the original pressure data. Because the amplitudes of PP reflections are implicitly weighted according to the reflection angle in pseudo-ax data, the near-offset PP reflections and multiples of the pseudo-ax data are much weaker than those of the pressure data. As a result, AFWI using pseudo-ax data focuses on reconstructing the longer-wavelength features of a given model in the early iterations, and then gradually reconstructs short-wavelength features as the inversion process continues. Using synthetic and real data examples for the Volve oilfield in the North Sea, we examined the effects and feasibility of this strategy. In the synthetic data example, the proposed strategy rapidly reduced far-offset data misfits related to long-wavelength feature updates and achieved smaller model misfits than the conventional strategy. The real data example showed that the velocity model reconstructed using the proposed strategy flattened some of the reflectors at the angle-domain common-image gathers (ADCIGs) better than the velocity model obtained using the conventional strategy. These findings demonstrate that our strategy converges closer to the real P-wave velocity model than the conventional strategy by building a hierarchical velocity model from long- to short-wavelength structures.

SM1.4 SUMMARY In case of severe lateral velocity variations prestack depth migration is not suitable for migration velocity analysis. We therefore propose to substitute prestack depth migration by prestack imaging by coupled linearized inversion (PICLI). Results obtained with the Marmousi model show the improvement offered by this method for migration velocity analysis. PICLI involves a huge amount of computation. Hence we have paid special attention both to the solution of the forward problem and to the optimization algorithm. To simplify the forward problem we make use of paraxial approximations of the wave equation. Efficiency in the optimization algorithm is obtained by an exact calculation of the gradient by means of the adjoint state technique and by an adequate preconditioning. Doing so the above mentioned improvement is obtained at reasonable cost.