Inverting Angle-Dependent Reflectivity Using Regularized Extended Least-Squares 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.

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.

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.

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.

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.

Reverse time migration (RTM) is a technique used to obtain high-resolution images of underground reflectors; however, this method is computationally intensive when dealing with large amounts of seismic data. Multi-source RTM can significantly reduce the computational cost by processing multiple shots simultaneously. However, multi-source-based methods frequently result in crosstalk artifacts in the migrated images, causing serious interference in the imaging signals. Plane-wave migration, as a mainstream multi-source method, can yield migrated images with plane waves in different angles by implementing phase encoding of the source and receiver wavefields; however, this method frequently requires a trade-off between computational efficiency and imaging quality. We propose a method based on deep learning for removing crosstalk artifacts and enhancing the image quality of plane-wave migration images. We designed a convolutional neural network that accepts an input of seven plane-wave images at different angles and outputs a clear and enhanced image. We built over 500 1024×256 velocity models, and employed each of them using plane-wave migration to produce raw images at 0°, ±10°, ±20°, and ±30° as input of the network. Labels are high-resolution images computed from the corresponding reflectivity models by convolving with a Ricker wavelet. Random sub-images with a size of 512×128 were used for training the network. Numerical examples demonstrated the effectiveness of the trained network in crosstalk removal and imaging enhancement. The proposed method is superior to both the conventional RTM and plane-wave RTM (PWRTM) in imaging resolution. Moreover, the proposed method requires only seven migrations, significantly improving the computational efficiency. In the numerical examples, the processing time required by our method was approximately 1.6% and 10% of that required by RTM and PWRTM, respectively.

Seismic oceanography can provide a two- or three-dimensional view of the water column thermocline structure at a vertical and horizontal resolution from the multi-channel seismic dataset. Several seismic imaging methods and techniques for seismic oceanography have been presented in previous research. In this study, we suggest a new formulation of the frequency-domain reverse-time migration method for seismic oceanography based on the analytic Green's function. For imaging thermocline structures in the water column from the seismic data, our proposed seismic reverse-time migration method uses the analytic Green's function for numerically calculating the forward- and backward-modeled wavefield rather than the wave propagation modeling in the conventional algorithm. The frequency-domain reverse-time migration with analytic Green's function does not require significant computational memory, resources, or a multifrontal direct solver to calculate the migration seismic images as like conventional reverse-time migration. The analytic Green's function in our reverse-time method makes it possible to provide a high-resolution seismic water column image with a meter-scale grid size, consisting of full-band frequency components for a modest cost and in a low-memory environment for computation. Our method was applied to multi-channel seismic data acquired in the Arctic Ocean and successfully constructed water column seismic images containing the oceanographic reflections caused by thermocline structures of the water mass. From the numerical test, we note that the oceanographic reflections of the migrated seismic images reflected the distribution of Arctic waters in a shallow depth and showed good correspondence with the anomalies of measured temperatures and calculated reflection coefficients from each XCDT profile. Our proposed method has been verified for field data application and accuracy of imaging performance.

We developed a seismic imaging method based on reverse time migration (RTM) for exploring deep crustal structures using reflection waves of earthquakes without source information. Instead of wavefield extrapolation from both well-defined sources and receivers in a conventional RTM, only receiver-side wavefield extrapolation is required in the proposed method. Forward- and backward-extrapolated wavefields using the same observation records from all receivers are correlated to illuminate multiple reflections between surface and subsurface boundaries. In this study, we present a two-dimensional numerical simulation to validate the proposed method with a regional crustal structure model and quasi-actual source locations. We also show a case study of an application to actual records of a seismic network observation on land in the Kanto region, Japan. The seismic reflection image along a 190-km pseudo-survey line using hundreds of surrounding local earthquakes shows several continuous reflectors around 20 - 40 km in depth, which are likely part of the Philippine Sea slab. Our results suggest a potential for reflection imaging of deep structures by using the large energy of earthquakes. The proposed method may become a useful technique for imaging crustal structures from huge amounts of seismic data recorded by highdense seismic network observations.

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 conventional marine seismic surveys, due to the time-delayed reflections from the sea surface on both source and receiver sides, ghosts present in recorded seismograms and lead to both phase and spectrum distortions (especially near certain frequency notches). To achieve a high-quality broad-band image/velocity model with conventional reverse time migration (RTM)/full waveform inversion (FWI) that adopts a synthetic zero-phase source wavelet and absorbing surface condition during wavefield modelling, marine seismic data have to be pre-processed to remove ghost effects. However, seismic deghosting is not a trivial task. Instead of employing an external deghosting process, we propose a strategy to compensate for ghost effects during FWI and RTM, which consists of two parts: first, to address phase distortions due to ghost effects by means of obtaining an accurate source wavelet estimation and adopting an appropriate surface boundary condition in both forward and backward wave propagation to appropriately generate ghosts; secondly, to build a compensation operator in the adjoint state computation to mitigate spectrum distortions caused by dominant ghost effects. To demonstrate the success and robustness of the proposed strategy, we present both synthetic experiments and field examples, which suggest that this strategy can lead to successful applications of FWI/RTM directly on marine seismic data without an extra deghosting process.

Summary Intrinsic attenuation in seismic wave propagation leads to amplitude loss and phase dispersion in seismic data. The attenuation effects are a common cause for inaccurate image location and dimmed energy in reverse time migration (RTM). Conventional viscoacoustic RTM (Q-RTM) methods implement attenuation compensation by reversing the sign of the amplitude loss term and keeping the dispersion term unchanged for both forward and backward wavefield extrapolation, which require decoupled viscoacoustic wave equation and give rise to numerical instability issue. To address these problems, we have developed a stable and effective attenuation compensated viscoacousitc RTM method. The proposed method uses an attenuated source and receiver wavefield energy to normalize the crosscorrelation imaging condition to compensate the attenuation effect. Due to the use of attenuated wavefield in the new imaging condition, the instability issue is avoided. Numerical tests prove the validation and effectiveness of the proposed method.

Direct imaging of the steeply dipping structures is challenging for conventional reverse time migration (RTM), especially when there are no strong reflectors in the migration velocity model. To address this issue, we have enhanced the imaging of the steeply dipping structures by incorporating the prismatic waves. We formulate the imaging problem in a nonlinear least-squares optimization framework because the prismatic waves cannot be linearly mapped from the model perturbation. Primary and prismatic waves are jointly imaged to provide a single consistent image that includes structures illuminated by both types of waves, avoiding the complexities in scaling and/or interpreting primary and prismatic images separately. A conjugate gradient algorithm is used to iteratively solve the least-squares normal equation. This inversion procedure can become unstable if directly using the recorded data for migration because it is hindered by the crosstalk caused by imaging primary waves with the prismatic imaging operator. Therefore, we isolate the prismatic waves from the recorded data and image them with the prismatic imaging operator. Our scheme only requires a kinematically accurate and smooth migration velocity model, without the need to explicitly embed the strong reflectors in the migration velocity model. Realistic 2D numerical examples demonstrate that our method can resolve the steeply dipping structures much better than conventional least-squares RTM of primary waves.

We present compact reverse time migration (CRTM), a real-time ultrasound imaging method that can exploit the full waveform information of ultrasonic wave records for imaging breast tissue. Conventional reverse time migration (RTM) computes the gradient of the reflective ultrasound data with respect to the perturbation of the velocity model of the soft tissues and the gradient can indicate the interface between different types of body tissue. In contrast to conventional reflection ultrasound (B-mode), which is based on the high-frequency approximation to the wave equation, the RTM algorithm is based on the complete wave equation, and can thus exploit the full waveform (wide-spectrum) information of the data and provide an image with higher resolution. Unfortunately, the computational burden of RTM is noticeably higher than the ray-based B-mode. This precludes real-time applications, one of the most important features of ultrasound imaging. The proposed CRTM algorithm can significantly reduce the computational costs of RTM, such that it can be applied for real-time imaging. We demonstrate the performance of CRTM through a synthetic experiment of ultrasound breast imaging. CRTM can be potentially adapted to related signal-processing fields, such as seismic imaging, acoustic camera systems, and radar imaging.

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.