Common-image gathers using the excitation amplitude imaging condition

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.

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 Extended Least-squares reverse time migration (ELSRTM) can mitigate sensitivity to accuracy of migration velocity by introducing additional model space such as subsurface offset axis. However, extended model space in ELSRTM can lead to expensive computational costs for assembling migration image volume. To alleviate this computational cost, we propose an efficient ELSRTM strategy based on excitation amplitude (ExA) imaging condition (ELSRTM-ExA). With the aid of computational advantage of ExA imaging condition, computional for assembling the migration image volume in ELSRTM-ExA is performed only once when current propagation time coincides with arrival time of ExA (ExT). Furthermore, required memory for saving forward source wavefield can be dramatically reduced, since the forward source wavefield can be stored as ExA and ExT. In the numerical example, it is demonstrated that ELSRTM-ExA can provide the high-quality migration image for inaccurate migration velocity with computational efficiency.

The earth [Formula: see text] filtering causes poor illumination of the subsurface. Compensating for the attenuated amplitude and distorted phase is crucial during elastic reverse time migration (ERTM) to improve the imaging quality. Conventional [Formula: see text]-compensated ERTM ([Formula: see text]-ERTM) methods tend to boost the attenuated energy to inverse the [Formula: see text] effects. These methods usually suffer from severe numerical instability because of the unlimited amplification of the high-frequency noise. Low-pass filtering is generally used to stabilize the process, however, at the expense of precision. We have developed a stable compensation approach in this paper. Based on the decoupled fractional Laplacians viscoelastic wave equation, two compensation operators are obtained by extrapolating wavefield in the dispersion-only and viscoelastic media. Because no explicit amplification is included, these two operators are absolutely stable for implementation. To improve the division morbidity for calculating the compensation operators, we use the excitation amplitude criterion and embed the operators into a vector-based [Formula: see text]-compensated excitation amplitude imaging condition. With the derived imaging condition, we could compensate for the absorption accurately without needing to concern the stability issue. The [Formula: see text]-ERTM results for noise-free data are carried out over a simple layered model and a more realistic Marmousi model with an attenuating area to verify the feasibility of the proposed approach. The migration results for noisy data from the Marmousi model further prove that the proposed method performs better fidelity, adaptability, and antinoise performance compared with conventional compensation method with low-pass filtering.

International audience

Reverse time migration (RTM) is achieved by a forward and reverse time propagation of source and receiver wavefields respectively, followed by an imaging condition. The quality of the image from any RTM implementation depends directly on the method’s ability to separate the true reflection data from the backscattered correlation noise between the source and receiver wavefields. In this paper we demonstrate the application of an inverse scattering imaging condition that significantly reduces this backscattered correlation noise and results in a much higher quality subsurface image than is achieved by typical RTM imaging conditions.

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.

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.

ABSTRACTWe present a migration velocity analysis (MVA) method based on wavefield extrapolation. Similarly to conventional MVA, our method aims at iteratively improving the quality of the migrated image, as measured by the flatness of angle‐domain common‐image gathers (ADCIGs) over the aperture‐angle axis. However, instead of inverting the depth errors measured in ADCIGs using ray‐based tomography, we invert ‘image perturbations’ using a linearized wave‐equation operator. This operator relates perturbations of the migrated image to perturbations of the migration velocity. We use prestack Stolt residual migration to define the image perturbations that maximize the focusing and flatness of ADCIGs.Our linearized operator relates slowness perturbations to image perturbations, based on a truncation of the Born scattering series to the first‐order term. To avoid divergence of the inversion procedure when the velocity perturbations are too large for Born linearization of the wave equation, we do not invert directly the image perturbations obtained by residual migration, but a linearized version of the image perturbations. The linearized image perturbations are computed by a linearized prestack residual migration operator applied to the background image. We use numerical examples to illustrate how the backprojection of the linearized image perturbations, i.e. the gradient of our objective function, is well behaved, even in cases when backprojection of the original image perturbations would mislead the inversion and take it in the wrong direction.We demonstrate with simple synthetic examples that our method converges even when the initial velocity model is far from correct. In a companion paper, we illustrate the full potential of our method for estimating velocity anomalies under complex salt bodies.

Vector-based excitation amplitude imaging condition for elastic RTM

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.

To improve the computational efficiency of reverse-time migration (RTM) for vertically transverse isotropic (VTI) media, various acoustic approximations of the elastic wave equations have been presented. Among these, the pseudo-acoustic wave equation, which combines differential and scalar operators, has the advantage that it does not produce shear wave artefacts. In this study, we investigate the feasibility of pseudo-acoustic anisotropic RTM (PA-RTM) for the analysis of synthetic and observed ocean-bottom cable (OBC) datasets of the Volve oil field in the North Sea. To analyse the influence of anisotropic parameters on RTM images and the sensitivity of data components to seismic anisotropy, we perform PA-RTM using synthetic data by incorporating various background models, as well as pressure wavefields and vertical particle acceleration. The synthetic experiments demonstrate that the anisotropic parameter ε plays an important role, whereas δ is negligible in PA-RTM for VTI media, and that vertical particle acceleration is less affected by seismic anisotropy than the pressure wavefields. Our experiments using observed data show that reflectors are better imaged by PA-RTM than by isotropic-RTM, particularly near the reservoir below the strongly anisotropic region, which is supported by angle-domain common image gathers. These results indicate that PA-RTM using only the vertical component is a suitable option for VTI media when insufficient seismic anisotropy data are available.

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.

Acoustic VTI modeling and pre-stack reverse-time migration based on the time–space domain staggered-grid finite-difference method

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.