Angle-domain Common-image Gathers Research Articles

Improving input/output performance in 2D and 3D angle-domain common-image gathers from reverse time migration

We have developed a new method of extracting angle-domain common-image gathers (ADCIGs) from prestack reverse time migration (RTM) that has minimal intermediate storage requirements. To include multipathing, we applied an imaging condition for prestack RTM that uses multiple excitation image times. Instead of saving the full-source snapshots at all time steps, we picked and saved only a few of the highest amplitude arrivals, and their corresponding excitation times, of the source wavefield at each grid point, and we crosscorrelated with the receiver wavefield. When extracting the ADCIGs from RTM, we calculated the source propagation direction from the gradient of the excitation times. The result was that the source time snapshots do not have to be saved or reconstructed during RTM or while extracting ADCIGs. We calculated the receiver propagation direction from Poynting vectors during the receiver extrapolation at each time step and the reflector normal direction by the phase-gradient method. With a new strategy that uses three direction vectors (the source and receiver propagation directions as well as the reflector normal direction), we provided more reliable ADCIGs that are free of low-wavenumber artifacts than any two of them do separately, when the migration velocity model was near to the correct velocity model. The 2D and 3D synthetic tests demonstrated the successful application of the new algorithms with acceptable accuracy, improved storage efficiency, and without an input/output bottleneck.

Kirchhoff PSDM angle-gather generation based on the traveltime gradient

Angle-domain common-image gathers (ADCIGs) are the basic data in migration velocity analysis (MVA) and amplitude variation with angle (AVA) analysis. We propose a common-angle gather-generating scheme using Kirchhoff PSDM based on the traveltime gradient field. The scheme includes three major operations: (1) to calculate the traveltime field of the source and the receiver based on the dynamic programming approach; (2) to obtain the reflection angle according to the traveltime gradient field in the image space; and (3) to generate the ADCIGs during the migration process. Because of the computation approach, the method for generating ADCIGs is superior to conventional ray-based methods. We use the proposed ADCIGs generation method in 3D large-scale seismic data. The key points of the method are the following. (1) We use common-shot datasets for migration, (2) we load traveltimes based on the shot aperture, and (3) we use the MPI and OpenMp memory sharing to decrease the amount of input and output (I/O). Numerical examples using synthetic data suggest that the ADCIGs improve the quality of the velocity and the effectiveness of the 3D angle-gather generation scheme.

Reverse time migration of multiples: Eliminating migration artifacts in angle domain common image gathers

Free-surface-related multiples are usually regarded as noise in conventional seismic processing. However, they can provide extra illumination of the subsurface and thus have been used in migration procedures, e.g., in one- and two-way wave-equation migrations. The disadvantage of the migration of multiples is the migration artifacts generated by the crosscorrelation of different seismic events, e.g., primaries and second-order free-surface-related multiples, so the effective elimination of migration artifacts is crucial for migration of multiples. The angle domain common image gather (ADCIG) is a suitable domain for testing the correctness of a migration velocity model. When the migration velocity model is correct, all the events in ADCIGs should be flat, and this provides a criterion for removing the migration artifacts. Our approach first obtains ADCIGs during reverse time migration and then applies a high-resolution parabolic Radon transform to all ADCIGs. By doing so, most migration artifacts will reside in the nonzero curvature regions in the Radon domain, and then a muting procedure can be implemented to remove the data components outside the vicinity of zero curvature. After the application of an adjoint Radon transform, the filtered ADCIGs are obtained and the final denoised migration result is generated by stacking all filtered ADCIGs. A three-flat-layer velocity model and the Marmousi synthetic data set are used for numerical experiments. The numerical results revealed that the proposed approach can eliminate most artifacts generated by migration of multiples when the migration velocity model is correct.

Amplitude-preserving reverse time migration: From reflectivity to velocity and impedance inversion

Conventional methods of prestack depth imaging aim at producing a structural image that delineates the interfaces of the geologic variations or the reflectivity of the earth. However, it is the underlying impedance and velocity changes that generate this reflectivity that are of more interest for characterizing the reservoir. Indeed, the need to generate a better product for geologic interpretation leads to the subsequent application of traditional seismic-inversion techniques to the reflectivity sections that come from typical depth-imaging processes. The drawback here is that these seismic-inversion techniques use additional information, e.g., from well logs or velocity models, to fill the low frequencies missing in traditional seismic data due to the free-surface ghost in marine acquisition. We found that with the help of broadband acquisition and processing techniques, the bandwidth gap between the depth-imaging world and seismic inversion world is reducing. We outlined a theory that shows how angle-domain common-image gathers produced by an amplitude-preserving reverse time migration can estimate impedance and velocity perturbations. The near-angle stacked image provides the impedance perturbation estimate whereas the far-angle image can be used to estimate the velocity perturbation. In the context of marine acquisition and exploration, our method can, together with a ghost compensation technique, be a useful tool for seismic inversion, and it is also adaptable to a full-waveform inversion framework. We developed synthetic and real data examples to test that the method is reliable and provides additional information for interpreting geologic structures and rock properties.

Angle-Domain Gathers Computation Using Poynting Vector of Two-Way Acoustic Wave Equation

Based on two-way acoustic wave equation, we present a method for computing angle-domain common-image gathers for reverse time migration. The method calculates the propagation direction of source wave-fields and receiver wave-fields according to expression of energy flow density vectors (Poynting vectors) of acoustic wave equation in space-time domain to obtain the reflection angle, then apply the normalized cross-correlation imaging condition to achieve the angle-domain common-image gathers. The angle gathers obtained can be used for migration velocity analysis, AVA analysis and so on. Numerical examples and real data examples demonstrate the effectiveness of this method.

Comparison of methods for extracting ADCIGs from RTM

Methods for extracting angle-domain common-image gathers (ADCIGs) during 2D reverse-time migration fall into three main categories; direction-vector-based methods, local-plane-wave decomposition methods, and local-shift imaging condition methods. The direction-vector-based methods, which use either amplitude gradients or phase gradients, cannot handle overlapping events because of an assumption of one propagation direction per imaging point per imaging time; however, the ADCIGs from the direction-vector-based methods have the highest angle resolution. A new direction-vector-based method using instantaneous phase gradients in space and time gives the same propagation directions and ADCIGs as those obtained by the Poynting vector or polarization vector based methods, where amplitudes are large. Angles calculated by the phase gradients have larger uncertainties at smaller amplitudes, but they do not significantly degrade the ADCIGs because they contribute only small amplitudes. The local-plane-wave decomposition and local-shift imaging condition methods, implemented either by a Fourier transform or by a slant stack transform, can handle overlapping events, and produce very similar angle gathers. ADCIGs from both methods depend on the local window size in which the transforms are done. In small local windows, both methods produce ADCIGs with low noise, but also with low angle resolution; in large windows, they have high angle resolution, but contain smeared artifacts.

Polarization-based wave-equation migration velocity analysis in acoustic media

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.

Azimuth–opening angle domain imaging in 3D Gaussian beam depth migration

Common-image gathers indexed by opening angle and azimuth at imaging points in 3D situations are the key inputs for amplitude-variation-with-angle and velocity analysis by tomography. The Gaussian beam depth migration, propagating each ray by a Gaussian beam form and summing the contributions from all the individual beams to produce the wavefield, can overcome the multipath problem, image steep reflectors and, even more important, provide a convenient and efficient strategy to extract azimuth?opening angle domain common-image gathers (ADCIGs) in 3D seismic imaging. We present a method for computing azimuth and opening angle at imaging points to output 3D ADCIGs by computing the source and receiver wavefield direction vectors which are restricted in the effective region of the corresponding Gaussian beams. In this paper, the basic principle of Gaussian beam migration (GBM) is briefly introduced; the technology and strategy to yield ADCIGs by GBM are analyzed. Numerical tests and field data application demonstrate that the azimuth?opening angle domain imaging method in 3D Gaussian beam depth migration is effective.

3D angle gathers with plane-wave reverse-time migration

Angle domain common image gathers (ADCIGs) from reverse-time migration (RTM) provide new tools for imaging complex geologic structures, such as salt flank or subsalt areas, characterized by multiarrivals. Compared with common image gathers from Kirchoff or Beam migration, the ADCIGs from RTM have the advantage of relying on wave propagation, providing a more reliable input for tomography or amplitude analysis. In practice however, most current wide azimuth surveys (e.g., deep-water regions of the Gulf of Mexico) are acquired with coarsely sampled shot and receiver locations on the surface, which leads to severe angular undersampling. This phenomenon is frequently observed on shallow seismic events in high-resolution 3D ADCIGs from common-shot RTM. In addition, because small offsets are frequently not recorded, seismic events are missing at small incidence angles in angle gathers. We have made a detailed study of the angular sampling issue in 3D angle gathers. We then used plane-wave RTM to generate 3D angle gathers. Plane-wave RTM, with its low-cost and automatic angular interpolation, is a promising solution for improving the quality of 3D angle gathers.

Moveout-based wave-equation migration velocity analysis

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.

Subsalt velocity estimation by target-oriented wave-equation migration velocity analysis: A 3D field-data example

We apply target-oriented wave-equation migration velocity analysis to a 3D field data set acquired from the Gulf of Mexico. Instead of using the original surface-recorded data set, we use a new data set synthesized specifically for velocity analysis to update subsalt velocities. The new data set is generated based on an initial unfocused target image and by a novel application of 3D generalized Born wavefield modeling, which correctly preserves velocity kinematics by modeling zero and nonzero subsurface-offset-domain images. The target-oriented inversion strategy drastically reduces the data size and the computation domain for 3D wave-equation migration velocity analysis, greatly improving its efficiency and flexibility. We apply differential semblance optimization (DSO) using the synthesized new data set to optimize subsalt velocities. The updated velocity model significantly improves the continuity of subsalt reflectors and yields flattened angle-domain common-image gathers.

A robust scheme to output angle-domain common image gathers for shot-profile migration

Angle-domain common image gathers (CIGs) play an important role in migration-based velocity updating. One popular criterion of migration velocity analysis (MVA) is the flatness of common-angle imag...

Tomographic velocity inversion for ADCIGs in areas with a rugged surface

Pre-stack depth migration velocity analysis is one of the key techniques influencing image quality. As for areas with a rugged surface and complex subsurface, conventional prestack depth migration velocity analysis corrects the rugged surface to a known datum or designed surface velocity model on which to perform migration and update the velocity. We propose a rugged surface tomographic velocity inversion method based on angle-domain common image gathers by which the velocity field can be updated directly from the rugged surface without static correction for pre-stack data and improve inversion precision and efficiency. First, we introduce a method to acquire angle-domain common image gathers (ADCIGs) in rugged surface areas and then perform rugged surface tomographic velocity inversion. Tests with model and field data prove the method to be correct and effective.

An angle-domain imaging condition for elastic reverse time migration and its application to angle gather extraction

An angle-domain imaging condition is recommended for multicomponent elastic reverse time migration. The local slant stack method is used to separate source and receiver waves into P- and S-waves and simultaneously decompose them into local plane waves along different propagation directions. We calculated the angle-domain partial images by crosscorrelating every possible combination of the incident and scattered plane P- and S-waves and then organized them into P-P and P-S local image matrices. Local image matrix preserves all the angle information related to the seismic events. Thus, by working in the image matrix, it is convenient to perform different angle-domain operations (e.g., filtering artifacts, correcting polarity, or conducting illumination and acquisition aperture compensations). Because local image matrix is localized in space, these operations can be designed to be highly flexible, e.g., target-oriented, dip-angle-dependent or reflection-angle-dependent. After performing angle-domain operations, we can stack the partial images in the local image matrix to generate the depth image, or partially sum them up to produce different angle-domain common image gathers, which can be used for amplitude versus angle and migration velocity analysis. We tested several numerical examples to demonstrate the applications of this angle-domain image condition.

Common-angle image gathers for shot-profile migration: an efficient and stable strategy

Shot-profile-based prestack depth migration is quite attractive for sparse-shot wide-azimuth geometries. Meanwhile, angle-domain common image gathers (ADCIGs) have become an essential tool in seismic processing (e.g. velocity analysis). In this paper, we first revisit the popular schemes of generating ADCIGs by wavefield continuation migration. Then we present an alternative approach to produce common-angle image gathers after shot-profile migration based on a one-way wave equation. The angle information is obtained from a division of two images: the conventional image and the angle-weighted image. The effects of sparse shot sampling on extracting ADCIGs have been investigated. Numerical results demonstrate that the described scheme is efficient and stable and can handle the problem of shot-aliasing well.

Multicomponent joint migration velocity analysis in the angle domain for PP-waves and PS-waves

Employing the vector processing of multicomponent seismic data, elastic Kirchhoff migration is used to conduct a multicomponent joint migration velocity analysis (MVA) of PP- and PS-waves in the angle domain. In vector-wavefield imaging, the elastic imaging condition has been extended to nonzero time and space shifts. We apply the extended imaging condition to elastic Kirchhoff migration to extract angle-domain common-image gathers (ADCIGs) of PP- and PS-waves. This method, which is derived from 3D wave propagation theory, directly operates on the vector wavefields and automatically resolves the problem of PS-wave polarity reversal in the migration sections. Based on the kinematic characteristics of PP- and PS-waves in the incident-angle domain, the velocity updating functions for P- and S-waves are derived. By combining the ADCIGs flatness criterion and the PP- and PS-wave image-depth consistency principle, the accuracy of P- and S-wave velocities can be assessed. The method was tested on a 2D thin-interbed model and the 2D Marmousi2 model. We found that the proposed method extracts the PP- and PS-wave ADCIGs effectively and produces appropriate P- and S-wave velocity fields. This method can be applied to time-delay gathers and to vertical or inline gathers in the 3D case.

Common-image gathers in the incident phase-angle domain from reverse time migration in 2D elastic VTI media

Reverse time migration (RTM) was implemented with a modified crosscorrelation imaging condition for data from 2D elastic vertically transversely isotropy (VTI) media. The computation cost was reduced because scalar qP- and qS-wavefield separations are performed in VTI media, for the source and receiver wavefields only at the RTM imaging time, to calculate the migrated qP and qS images. Angle-domain common-image gathers (CIGs) were extracted from qPqP and qPqS common-source RTM images. The local incident angle was produced as the difference between the qP-wave phase angle, obtained directly from the source wavefield polarization, and the normal to the reflector, calculated as the instantaneous wavenumber direction via a directional Hilbert transform of the stacked image. Angle-domain CIGs were extracted by reordering the prestack-migrated images by local incident phase angle, source by source. Vector decomposition of the source qP-wavefield was required to calculate the qP-wave phase polarization direction for each image point at its imaging time. RTM and angle-domain CIG extraction were successfully implemented and illustrated with a synthetic 2D elastic VTI example.

Direct vector-field method to obtain angle-domain common-image gathers from isotropic acoustic and elastic reverse time migration

We have developed an alternative (new) method to produce common-image gathers in the incident-angle domain by calculating wavenumbers directly from the P-wave polarization rather than using the dominant wavenumber as the normal to the source wavefront. In isotropic acoustic media, the wave propagation direction can be directly calculated as the spatial gradient direction of the acoustic wavefield, which is parallel to the wavenumber direction (the normal to the wavefront). Instantaneous wavenumber, obtained via a novel Hilbert transform approach, is used to calculate the local normal to the reflectors in the migrated image. The local incident angle is produced as the difference between the propagation direction and the normal to the reflector. By reordering the migrated images (over all common-source gathers) with incident angle, common-image gathers are produced in the incident-angle domain. Instantaneous wavenumber takes the place of the normal to the reflector in the migrated image. P- and S-wave separations allow both PP and PS common-image gathers to be calculated in the angle domain. Unlike the space-shift image condition for calculating the common-image gather in angle domain, we use the crosscorrelation image condition, which is substantially more efficient. This is a direct method, and is less dependent on the data quality than the space-shift method. The concepts were successfully implemented and tested with 2D synthetic acoustic and elastic examples, including a complicated (Marmousi2) model that illustrates effects of multipathing in angle-domain common-image gathers.

Target-oriented wavefield tomography using synthesized Born data

We present a new strategy for efficient wave-equation migration-velocity analysis in complex geological settings. The proposed strategy has two main steps: simulating a new data set using an initial unfocused image and performing wavefield-based tomography using this data set. We demonstrated that the new data set can be synthesized by using generalized Born wavefield modeling for a specific target region where velocities are inaccurate. We also showed that the new data set can be much smaller than the original one because of the target-oriented modeling strategy, but it contains necessary velocity information for successful velocity analysis. These interesting features make this new data set suitable for target-oriented, fast and interactive velocity model-building. We demonstrate the performance of our method on both a synthetic data set and a field data set acquired from the Gulf of Mexico, where we update the subsalt velocity in a target-oriented fashion and obtain a subsalt image with improved continuities, signal-to-noise ratio and flattened angle-domain common-image gathers.

Amplitude preserved VSP reverse time migration for angle-domain CIGs extraction

An improved method of generating angle-domain common-image gathers (ADCIGs) by VSP reverse time migration (RTM) is introduced in this paper. The formula which is used to compute the receiver wavefield for VSP RTM is modified by adding an amplitude correction term in order to conveniently output amplitude-preserved ADCIGs. Compared with the surface seismic data, VSP data contains much richer wavefields. However, the direct and downgoing waves can bring about serious imaging artifacts in ADCIGs, especially the direct wave. The feasibility and validity of this method is demonstrated by both numerical and real VSP data from western China. Thus, the ADCIGs from this method can provide reliable basic data for VSP migration velocity analysis, VSP AVO/AVA analysis, and inversion.