Amplitude‐preserved common image gathers by wave‐equation migration

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.

In this paper we present the improved algorithm for angle domain common imaging gathers (ADCIG) during Kirchhoff pre‐stack time migration (PSTM). The algorithm can calculate relatively true incident angle under three‐dimensional circumstance, while the traditional ray‐parameter method could not handle the incident angle for the dipping events. Compared with straight‐ray Kirchhhoff angle domain gathers method presented in recent years, our method is able to extract wide‐angle information. Increased angular illumination is beneficial for AVA inversion. The results of synthetic model data have verified that: for V(z) (layered) media, the traveltime calculation taking ray‐bending effect into account, is much more accurate than straight ray for large angle. Thus the wide angles of ADCIG are flatter than the straight assumption. Moreover, the range of ADCIG is enlarged. The ADCIG and its AVA inversion of 3‐D field data have also demonstrated the improvement at wide angle.

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.

Summary The angle-domain common image gathers (ADCIGs) describe the reflectivity variation over the reflection angles which are important for seismic exploration. However, because of the limitation of seismic frequency band and acquisition geometry, conventional reverse time migration (RTM) produces the ADCIGs with low fidelity. We propose a reflection angle-domain extended least-squares RTM (AELSRTM) to improve the quality of the ADCIGs in which the Poynting vector is used to efficiently calculate the angles. We first derive a feasible pseudo-extended linearized modeling operator which could map the ADCIGs into the seismic data. The modeling operator, associated with an adjoint operator, are then used to build an extended linearized inversion framework for inverting the angle-dependent reflectivity. Taking advantage of the simplicity and coherency of the ADCIGs, we impose a series of low-rank constraints on the extended angle dimension and a sparse constraint on the whole dimension to ensure the production of high-quality ADCIGs. We conduct numerical examples on the Marmousi model, and the results demonstrate that AELSRTM could produce the ADCIGs and the stacked image with higher fidelity than RTM, which provides a reliable input for anisotropic model building and amplitude versus angle 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.

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.

Wavelength-dependent Fresnel beam propagator and migration in VTI media

True-amplitude wave-equation migration provides a quality migrated image of the earth's interior. In addition, the amplitude of the output provides an estimate of the angular-dependent reflection coefficient, similar to the output of Kirchhoff inversion. Recently, true-amplitude wave-equation migration for common-shot data has been proposed to generate amplitude-reliable, shot-domain, common-image gathers in heterogeneous media. We present a method to directly produce angle-domain common-image gathers from both common-shot and shot-receiver wave-equation migration. Generating true-amplitude, shot-domain, common-image gathers requires a deconvolution-type imaging condition using the ratio of the upgoing and downgoing wavefield, each downward-projected to the image point. Producing true-amplitude, angle-domain, common-image gathers requires, instead, the product of the upgoing wavefield and the complexconjugate of the downgoing wavefield in the imaging condition. Since multiplication is a more stable computational process than division, the new methods proposed provide more stable ways of inverting seismic data. Furthermore, the resulting common-image gathers can be directly used for migrated amplitude-variation-with angle analysis and tomography-based velocity analysis. Shot-receiver wave-equation migration requires new true-amplitude, one-way wave equations with one depth variable and transverse variables for the coordinates corresponding to sources and receivers, hence, two transverse coordinates in 2D and four transverse coordinates in 3D. We propose a modified double-square-root one-way wave equation to produce true amplitude common-image angle gathers. We also demonstrate the new methods with some synthetic examples. Some numerical examples show that the new methods we propose give better amplitude performance on the migrated angle gathers.

Tomograhic model building has commonly been conducted by using offset gathers from the prestack migration. However, in complex media, common offset images may yield an inconsistent image of the subsurface and thus cause problems in the model building process. The angle domain common image gathers (ADCIGs), on the other hand, do not suffer from such inconsistency and open a new opportunity for model building. The same model updating steps in the offset domain can be followed in angle domain with a different picking tool and a slightly different equation set up procedure. The residual picking is done robustly and efficiently using a single parameter curvature analysis. The angle gather ray tracing is more efficient than offset gather ray tracing. The method can be applied to angle gathers from ray-based or wave equation imaging. The field data test shows that this new work flow can provide a model that improves the base of salt and images below the salt.

The ideal approach for continuous reservoir monitoring allows generation of fast and accurate images to cope with the massive data sets acquired for such a task. Conventionally, rigorous depth-oriented velocity-estimation methods are performed to produce sufficiently accurate velocity models. Unlike the traditional way, the target-oriented imaging technology based on the common-focus point (CFP) theory can be an alternative for continuous reservoir monitoring. The solution is based on a robust data-driven iterative operator updating strategy without deriving a detailed velocity model. The same focusing operator is applied on successive 3D seismic data sets for the first time to generate efficient and accurate 4D target-oriented seismic stacked images from time-lapse field seismic data sets acquired in a [Formula: see text] injection project in Saudi Arabia. Using the focusing operator, target-oriented prestack angle domain common-image gathers (ADCIGs) could be derived to perform amplitude-versus-angle analysis. To preserve the amplitude information in the ADCIGs, an amplitude-balancing factor is applied by embedding a synthetic data set using the real acquisition geometry to remove the geometry imprint artifact. Applying the CFP-based target-oriented imaging to time-lapse data sets revealed changes at the reservoir level in the poststack and prestack time-lapse signals, which is consistent with the [Formula: see text] injection history and rock physics.

Angle domain common image gathers (ADCIGs) are the basic data for the MVA and AVA. In this paper, a common angle gather output scheme of Kirchhoff PSDM is introduced. It includes: (1) the traveltime calculation is based on the dynamic programming approach adapted to arbitrary medium, (2) obtaining the reflection angle i according to the gradient of traveltime filed in the image space, (3) ADCIGs are extracted in the migration process. We compare the offset domain common image gathers(ODCIGs) of numerical models with the ADCIGs of numerical models. Numerical examples on synthetic data demonstrate the feasibility of the method.

Similar to primary reflections, multiples also carry the amplitude versus angle (AVA) information. An alternative approach is proposed to estimate the amplitude changes of multiples with respect to incident/reflection angles. The method is referred as multiple amplitude versus angle (mAVA), with which, the multiples are first decomposed into different orders using the surface-related multiple elimination (SRME). Then, the amplitude change with incident angle for a specific-order multiple is measured based on a wavefield angle decomposition method. The dip angle of the reflector is obtained from the image generated by multiples. From these, the multiple reflection angle can be estimated, and the related angle domain common image gathers are obtained. After illumination correction, we can obtain the mAVA for analysis in the cross-plot domain. Numerical examples are provided to demonstrate the AVA analysis using surface multiple data.

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.

Convolution of the recorded data with itself is a convenient way of generating multiple models and is the basis for Surface Related Multiple Prediction (SRMP/SRME). The completeness of the multiple model however relies on recording all the primary paths leading to multiple generation. In practice, with limited offset recordings and in areas of complex subsurface geometries (especially steep dips) we might only record the multiple path and not the primary, leading to incomplete multiple models. In image space, this translates to modeling multiples at fewer opening angles than are actually present. In this article, I show that the Angle Domain Common Image Gathers (ADCIGs) of multiple models provide useful angular information which may be used to infill or extrapolate missing angles and make up for the missing multiples in the model generated using SRMP.

Summary The Kuqa foreland basin is rich in oil and gas resources. However, the images of interest subsalt overthrust structures often have significant distortions due to strong lateral heterogeneity in the shallow and middle-deep velocity. The precise velocity estimation is the key to solve this imaging problem. In this paper, two steps are taken: Firstly, we obtain the accurate shallow velocity with the tomographic inversion based on BP (back propagation) neural network. Secondly, we build the proper middle-deep velocity with the ADCIGs (angle domain common imaging gathers) based tomographic inversion under the constraints of geological knowledge and logging data. The resulting PSDM (prestack depth migration) images are greatly improved and consistent with well data.