Common Image Gathers Research Articles

Vector-based elastic reverse time migration

Prestack elastic reverse time migration (RTM) of multicomponent seismic data requires separating PP and PS reflections before, or as part of, applying the image condition, and using image conditions that preserve the angle and amplitude information. Both of these requirements are best achieved when all operations are on vectors. We have created a new 2D migration context for isotropic, elastic RTM, which included decomposition of the elastic source and receiver wavefields into P- and S-wave vectors by decoupled elastodynamic extrapolation, which retained the same stress and particle velocity components as the input data. Then, the propagation directions of the incident and reflected P- and S-waves were calculated directly from the stress and particle velocity definitions of the P- and S-wave Poynting vectors. An excitation-amplitude image condition that scaled the receiver wavelet by the source vector magnitude produced angle-dependent images of PP and PS reflection coefficients with the correct polarities, polarization, and amplitudes. It thus simplified the process of obtaining PP and PS angle-domain common-image gathers (ADCIGs); it was less effort to generate ADCIGs from vector data than from scalar data. We found that the resulting prestack elastic images were nearly identical to the corresponding source-normalized crosscorrelation images and had improved resolution because the wavelet broadening that resulted from the crosscorrelation was not present.

Vertical seismic profile migration velocity analysis via residual moveout in receiver domain common image gathers

The success of imaging vertical seismic profile (VSP) data critically depends upon obtaining and using an accurate subsurface velocity model. First-arrival-time tomography can be used to derive velocities above the receivers. Reflection time tomography can be used to derive velocities below the receivers, but it requires reflection time picking and association with appropriate horizons. We described an alternative, faster way to perform velocity analysis by assessing the residual moveout after migrating walk-away VSP data. We have derived residual moveout equations for migrated common receiver gathers assuming a constant velocity model with a single horizontal reflector. The observed residual moveout in common image gathers in the receiver domain will be aligned and flat if the migration velocity is correct. If the residual moveout is not flat, by digitizing the extreme point on the unstacked, migrated traces in each common receiver gather, we could invert for the velocity of the target layer using our new residual moveout equations. We then extended this method to handle depth and laterally varying layer geometries using an iterative root-mean-square velocity scheme and a layer-stripping strategy. We combined the power of a prestack VSP depth migration using complicated velocity structures with straightforward velocity updating equations. For a range of synthetic cases and geometries, the estimated velocities were within 3% of the actual value.

Vector-acoustic reverse time migration of Volve ocean-bottom cable data set without up/down decomposed wavefields

Methods for wavefield injection are commonly used to extrapolate seismic data in reverse time migration (RTM). Injecting a single component of the acoustic field, for example, pressure, leads to ambiguity in the direction of propagation. Each recorded wavefront is propagated both upward and downward, and spurious (or ghost) reflectors are created alongside real reflectors in the subsurface image. Thus, wavefield separation based on the combination of pressure and particle velocity data is generally performed prior to imaging to extract only the upgoing field from multicomponent seabed or towed marine seismic recordings. By instead combining vector-acoustic (VA) data with monopole- and dipole-type propagators in the extrapolation of shot or receiver gathers, we show that wavefield separation (or deghosting) can instead be performed “on-the-fly” at limited additional cost. This strategy was successfully applied to a line of a North Sea ocean-bottom cable data set, acquired over the Volve field. We then evaluate additional advantages over standard RTM with decomposed fields such as improved handling of the directivity information contained in the acquired VA data for clearer shallow sections and better focused space-lag common image gathers, and imaging of the downgoing component without the need for additional finite-difference modeling via mirror migration. Finally, we prove the robustness of our method with respect to sparse and irregular receiver sampling.

Prestack time-migration velocity analysis using remigration trajectories

We have developed a prestack time-migration tool for local improvement of the seismic migration-velocity model. The method is based on remigration trajectories that describe the position of an image point in the image domain for different source-receiver offsets as a function of the migration velocity. It determines kinematic migration parameters using local-slope information of migrated seismic reflection events. These parameters, in turn, are used to locally correct the velocity model. The main advantage of this technique is that it allows us to carry out a moveout correction not just at a fixed point in a zero-offset (poststack) time-migrated gather, but varying through all offsets of a common-image gather, taking into account the reflection-point displacement in the midpoint direction. In other words, it provides for time-migration velocity analysis from prestack data. We have tested the feasibility of the method on synthetic data from four simple models and the Sigsbee2B data. Our tests determined that the proposed tool increases the velocity-model resolution and provides a plausible time-migrated image. The quality of the initial model is not critical. The procedure is quite efficient. Significant effort was spent on manual event picking.

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.

Removing smearing-effect artifacts in angle-domain common-image gathers from reverse time migration

Local plane-wave decomposition (LPWD) and local shift imaging condition (LSIC) methods for extracting angle-domain common-image gathers (ADCIGs) from prestack reverse time migration are based on the local plane-wave assumption, and both suffer from a trade-off in choosing the local window size. Small windows produce clean ADCIGs, but with low angle resolution, whereas large windows produce noisy ADCIGs, which include smearing-effect artifacts, but with high angle resolution. The cause of the smearing-effect artifacts in LPWD is the crosscorrelation of plane waves obtained by decomposition of the source and receiver wavefronts, at points that do not lie on the source wavefront excitation time trajectory. The cause of the smearing-effect artifacts in LSIC is the decomposition of curved events of offset-domain common-image gathers (ODCIGs) at incorrect depth points at zero offset. These artifacts can occur even if the migration velocity model is correct. Two methods were proposed to remove the artifacts. In the LPWD method, the smearing-effect artifacts were removed by decomposing and crosscorrelating the resulting source and receiver plane waves only at image points and excitation (image) times. In the LSIC method, the artifacts were removed by decomposing curved events in ODCIGs into planar events only at zero-offset target image points. Numerical tests with synthetic data revealed the success of the proposed methods.

Full-azimuth anisotropic prestack time migration in the local-angle domain and its applications on fracture detection

Considering that geologic structures disturb prestack amplitude relationships, anisotropic migration is thus advocated not only for extracting azimuth-preserved common image gathers (CIGs), but also for preserving fracture-induced amplitude responses. However, most conventional anisotropic migration methods are hindered by their inefficiency in either modeling azimuthal traveltime variations at large offsets or characterizing subsurface reflections. Given that prestack time migration is widely applied for most practical purposes, we began with reformulations on a quartic traveltime formula, through which a new set of anisotropic parameters was developed. Then, an anisotropic migration method was established in the local-angle domain (LAD) for more reasonable uses of subsurface wavefield information. We also used a traveltime inversion scheme to estimate those anisotropic parameters required by anisotropic migration. Using this methodology on a physical model with a fracture medium, we derived better focused CIGs by thoroughly correcting the anisotropic effects of overburden. As a result, predicted properties of the fracture medium showed fewer interventions of geologic impacts. In a field example, a comprehensive study was performed on a deep carbonate reservoir to examine influences of different anisotropic migration algorithms on ultimate fracture prediction. Comparisons of the signal-to-noise ratio and agreements with formation microimage information reconfirmed the superiority of LAD anisotropic migration in recovering true properties of subsurface fractures, relative to routine methods (i.e., azimuth-sectored migration and anisotropic migration in the surface-offset domain).

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.

Seismic imaging of subsurface structure using tomographic migration velocity analysis: a case study of South China Sea data

Seismic migration algorithms are often used to reveal subsurface structures and can be roughly divided into stacking methods, pre-stack time migration methods and pre-stack depth migration methods. In theory, pre-stack depth migration methods can provide the most accurate subsurface images. However, these methods are sensitive to the accuracy of the migration velocity model, and thus the creation of a precise migration velocity model is one of the most important steps in seismic processing. We applied the tomographic travel-time inversion and the method of pre-stack Kirchhoff depth migration-based migration velocity analysis (MVA) to certain South China Sea data, in which we iteratively inverted the precise, high-resolution migration velocity model. We selected travel-time differences from the offset-domain common image gathers of the pre-stack Kirchhoff depth migration and inverted the travel-time differences for velocity updating. After several iterations, both the precise migration velocity model and the corresponding pre-stack depth migration image were obtained. The comparisons with Normal Move-out stacking and pre-stack Kirchhoff time migration confirm that the tomographic MVA and corresponding pre-stack Kirchhoff depth migration provide the best image quality and highest-resolution subsurface images from the South China Sea data.

Improving the gradient of the image‐domain objective function using quantitative migration for a more robust migration velocity analysis

ABSTRACTMigration velocity analysis aims at determining the background velocity model. Classical artefacts, such as migration smiles, are observed on subsurface offset common image gathers, due to spatial and frequency data limitations. We analyse their impact on the differential semblance functional and on its gradient with respect to the model. In particular, the differential semblance functional is not necessarily minimum at the expected value. Tapers are classically applied on common image gathers to partly reduce these artefacts. Here, we first observe that the migrated image can be defined as the first gradient of an objective function formulated in the data‐domain. For an automatic and more robust formulation, we introduce a weight in the original data‐domain objective function. The weight is determined such that the Hessian resembles a Dirac function. In that way, we extend quantitative migration to the subsurface‐offset domain. This is an automatic way to compensate for illumination. We analyse the modified scheme on a very simple 2D case and on a more complex velocity model to show how migration velocity analysis becomes more robust.

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.

Image enhancement by multi‐parameter characterization of common image gathers

ABSTRACTWe present an innovative approach for seismic image enhancement using multi‐parameter angle‐domain characterization of common image gathers. A special subsurface angle‐domain imaging system is used to generate the multi‐parameter common image gathers in a summation‐free image space. The imaged data associated with each common image gathers depth point contain direction‐dependent opening‐angle image contributions from all the available incident and scattered wave‐pairs at this point. Each direction‐dependent opening‐angle data can be differently weighted according to its coherency measure. Once the optimal migration velocity is used, it is assumed that in the actual specular direction, the coherency measure (semblance) along reflection events, from all available opening angles and opening azimuths, is larger than that along non‐specular directions. The computed direction‐dependent semblance attribute is designed to operate as an imaging filter which enhances specular migration contributions and suppresses all others in the final migration image. The ability to analyse the structural properties of the image points by the multi‐parameter common image gather allows us to better handle cases of complicated wave propagation and to improve the image quality at poorly illuminated regions or near complex structures. The proposed method and some of its practical benefits are demonstrated through detailed analysis of synthetic and real data examples.

High-fidelity complete wavefield velocity model building and imaging in shallow water environments – A North Sea case study

Accurate sub-surface image reconstruction from prestack depth migration of surface seismic wavefields requires precise knowledge of the local propagation velocities between the recording location and the image location at depth. Such velocity information has traditionally been derived by tomographically inverting residual moveout information of common image gathers, which have been computed using an initial velocity field. This methodology proves to be challenging in shallow water environments, particularly when strong and rapid velocity variations in the very shallow overburden need to be recovered, while moveout information from reflected arrivals is very sparse or not available.

Multiwave velocity analysis based on Gaussian beam prestack depth migration

Prestack depth migration of multicomponent seismic data improves the imaging accuracy of subsurface complex geological structures. An accurate velocity field is critical to accurate imaging. Gaussian beam migration was used to perform multicomponent migration velocity analysis of PP- and PS-waves. First, PP- and PS-wave Gaussian beam prestack depth migration algorithms that operate on common-offset gathers are presented to extract offset-domain common-image gathers of PP- and PS-waves. Second, based on the residual moveout equation, the migration velocity fields of P- and S-waves are updated. Depth matching is used to ensure that the depth of the target layers in the PP- and PS-wave migration profiles are consistent, and high-precision P- and S-wave velocities are obtained. Finally, synthetic and field seismic data suggest that the method can be used effectively in multiwave migration velocity analysis.

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.

Borehole seismic quantitative diagnosis of a seismic velocity model for 3D seismic imaging of subsurface structures

ABSTRACTQuantifying uncertainties of surface seismic velocity models is a difficult task. The use of multifarious vertical seismic profiling data provides quantification of velocity model uncertainties. Two borehole seismic diagnosis methods for velocity model uncertainties are developed. The first method is performed with 3D ray‐traced first arrival times through a surface seismic velocity model and compared with measured first arrival times from downhole receivers. It generates a profile of absolute and relative misfits, indicating the velocity uncertainty as a function of depth. The second approach directly compares the differences between the first arrival incident angles measured from 3‐C borehole seismic data and the calculated first arrival incident angles of seismic rays through the velocity model to quantify the model uncertainties. Five seismic velocity models in the Gulf of Mexico are diagnosed using the diagnosis methods with up to six sets of borehole seismic data recorded in three wells. The uncertainty profiles vary with depths and azimuths, revealing the complexity of velocity model uncertainties and providing some clues for further velocity updating. The diagnosis methods are used as velocity updating QC tools and integrated with the conventional seismic velocity updating flow to complement the criteria of flat common image gathers.

Noise removal by migration of time-shift images

When using seismic data to image complex structures, the reverse time migration (RTM) algorithm generally provides the best results when the velocity model is accurate. With an inexact model, moveouts appear in common image gathers (CIGs), which are either in the surface offset domain or in subsurface angle domain; thus, the stacked image is not well focused. In extended image gathers, the strongest energy of a seismic event may occur at non-zero-lag in time-shift or offset-shift gathers. Based on the operation of RTM images produced by the time-shift imaging condition, the non-zero-lag time-shift images exhibit a spatial shift; we propose an approach to correct them by a second pass of migration similar to zero-offset depth migration; the proposed approach is based on the local poststack depth migration assumption. After the proposed second-pass migration, the time-shift CIGs appear to be flat and can be stacked. The stack enhances the energy of seismic events that are defocused at zero time lag due to the inaccuracy of the model, even though the new focused events stay at the previous positions, which might deviate from the true positions of seismic reflection. With the stack, our proposed approach is also able to attenuate the long-wavelength RTM artifacts. In the case of tilted transverse isotropic migration, we propose a scheme to defocus the coherent noise, such as migration artifacts from residual multiples, by applying the original migration velocity model along the symmetry axis but with different anisotropic parameters in the second pass of migration. We demonstrate that our approach is effective to attenuate the coherent noise at subsalt area with two synthetic data sets and one real data set from the Gulf of Mexico.

Common-reflection-point migration velocity analysis of 2D P-wave data from TTI media

We have developed a common-reflection-point (CRP)-based kinematic migration velocity analysis for 2D P-wave reflection data to estimate the four transversely isotropic (TI) parameters [Formula: see text], [Formula: see text], and [Formula: see text], and the tilt angle [Formula: see text] of the symmetry axis in a TI medium. In each iteration, the tomographic parameter was updated alternately with prestack anisotropic ray-based migration. Iterations initially used layer stripping to reduce the number of degrees of freedom; after convergence was reached, a couple of more iterations over all parameters and all CRPs ensured global interlayer coupling and parameter interaction. The TI symmetry axis orientation was constrained to be locally perpendicular to the reflectors. The [Formula: see text] dominated the inversion, and so it was weighted less than [Formula: see text] and [Formula: see text] in the parameter updates. Estimates of [Formula: see text] and [Formula: see text] were influenced if the error in [Formula: see text] was [Formula: see text]; estimates of [Formula: see text] were also influenced if the error in [Formula: see text] was [Formula: see text]. Examples included data for a simple model with a homogeneous TI layer whose dips allowed recovery of all anisotropy parameters from noise-free data, and a more realistic model (the BP tilted transversely isotropic (TTI) model) for which only [Formula: see text], [Formula: see text], and [Formula: see text] were recoverable. The adequacy of the traveltimes predicted by the inverted anisotropic models was tested by comparing migrated images and common image gathers, with those produced using the known velocity models.