Conventional Reverse Time Migration Research Articles

Deprimary reverse time migration angle gathers with a stabilized Poynting vector

Deprimary reverse time migration (RTM) mitigates the problem of low-wavenumber noise and false events in conventional RTM, and the generation of high-quality angle-domain common-image gathers or angle gathers during deprimary RTM greatly extends its further applications in velocity model updating and subsurface parameter inversion. Poynting-vector-based methods are the most efficient approach to extract angle gathers from RTM or deprimary RTM. However, the instability problem of Poynting-vector-based methods seriously degrades the quality of the generated angle gathers. The instability problem arises from the oscillatory nature of the Poynting vector. To overcome this issue, we propose a novel approach by harnessing the extra simulated Hilbert transformed wavefield in deprimary RTM. Our approach consists of adding the conventional Poynting vector with an ancillary one derived from the Hilbert transformed wavefield, which allows us to eliminate the oscillatory nature of the conventional Poynting vector and obtain a stable algorithm to extract high-quality angle gathers from RTM or deprimary RTM. By using numerical examples with two synthetic data sets and a field data set from the deepwater Gulf of Mexico, we prove the effectiveness of our method in generating high-quality angle gathers.

Q-compensated viscoelastic reverse time migration in crosswell seismic imaging

Abstract Viscoelastic reverse time migration (RTM) is a practical approach to compensats for attenuation effects in migration, commonly studied in surface seismic research. Compared with conventional surface seismic imaging, the sources and receivers of crosswell seismic imaging are distributed in different wells with higher main frequencies and lower surface noises. The finer structures can be imaged. In this paper, we apply attenuation compensated RTM in crosswell migration to improve the resolution of images in attenuation regions. We solve the viscoelastic equations using the constant Q model because of its advantage of decoupling the amplitude and phase. The fractional-order amplitude and phase Laplacian operators are used. By spectral ration techniques, we observe the relationship between attenuation and frequency in crosswell seismic imaging. We describe the alignment and muting of direct P- and S-waves from full waves in detail. Synthetic examples demonstrate that Q-RTM images the geological structure more clearly than the traditional RTM. We reveal that compensated images describe the three-layer model, tilted fractures and randomly distributed caves more accurately. As the tilted angles increase, only two end points of the tilted fracture can be identified by conventional RTM, the boundary is blurred. We find that caves far from the source well can barely be imaged. By comparison, the compensated RTM approach obtains precise migration results of tilted fractures with arbitrary dip angles and caves. Finally, to approximate the real measurement data, noise is added to the viscoelastic data of the five-layer model. The effective noise immunity in crosswell seismic applications is verified.

Multiparameter vector‐acoustic least‐squares reverse time migration

ABSTRACTThe use of dual‐sensor acquisitions enabled different studies using the so‐called vector‐acoustic equations, which admit particle velocity (displacement or acceleration) information instead of solely the pressure wavefield. With cost far from elastic formulations but comparable with the usually used second‐order acoustic equation, previous works involving the use of vector‐acoustic equations along with multicomponent data have been applied to conventional reverse time migration and full‐waveform inversion, always emphasizing the benefits of using wavefields containing directivity information, which make the receiver ghosts interact constructively with the backpropagated reflected wavefield. Thus, generated results are superior to those of conventional single‐component data imaging techniques, particularly with spatial subsampling of marine seismic data. To assess whether the effects of applying the vector‐acoustic equations persist in a linearized inversion, we developed a multiparameter vector‐acoustic least‐squares reverse time migration, inverting reflectivities associated with velocity and density. To demonstrate the method's performance, we apply it to two‐dimensional numerical examples and compare the results with those obtained by the conventional acoustic least‐squares reverse time migration. The results obtained by the vector‐acoustic least‐squares reverse time migration method are accurate for all inverted parameters and also deliver better convergence when compared with the conventional least‐squares reverse time migration.

Noniterative least-squares reverse time migration based on an efficient asymptotic Hessian/point-spread function estimation

Although reverse time migration (RTM) is a powerful imaging method, it uses only the adjoint of the wave-propagation operator and produces only a blurred image. Through linearized inversion, least-squares RTM (LSRTM) reduces migration artifacts, balances the amplitudes, and improves the resolution of the imaging results. Compared to data-domain LSRTM, image-domain LSRTM (ID-LSRTM) is a more practical choice because it typically requires one round of RTM and subsequently solves the deblurring problem of the conventional RTM image involving the Hessian matrix. The Hessian matrix can be effectively replaced by a set of point-spread functions (PSFs). PSFs are traditionally obtained through one round of demigration-migration; hence, the traditional PSF estimation has a computational cost that is twice that of the RTM. We have deduced an analytic expression of the Hessian/PSF by using an asymptotic Green’s function and derived an efficient estimation strategy for the Hessian/PSF. The proposed method significantly reduces the computational cost and allows more flexible spatial sampling of PSFs without interference. Based on the explicitly calculated PSFs, ID-LSRTM can be achieved by solving an optimization problem with combined total-variation and curvelet-domain [Formula: see text] regularizations. The total computational cost of the proposed LSRTM is approximately the same as that of the conventional RTM. Numerical examples of synthetic and field data find that the proposed LSRTM significantly improves image quality while being highly efficient.

Reverse time migration of GPR data based on accurate velocity estimation and artifacts removal using total variation de-noising

Reverse time migration (RTM) is the important intermediate step for focusing the radar diffracted energy of the targets in ground penetrating radar imaging. The conventional RTM algorithm demands a large number of iterative trial experiments and depends on the experts' decision on the estimation of the velocity or relative permittivity of the subsurface medium. Meanwhile, the RTM profile is vulnerable to artifacts, which are composed of noise interference, multiple interferences, arc-shaped clutter, and crosstalk, so it is difficult to inspect visually. Therefore, we propose a RTM method based on accurate velocity estimation and total variation (TV) de-noising to improve the accuracy of the RTM imaging. Firstly, the appropriate migration velocity is obtained automatically by autofocusing metrics to reduce the number of visual inspection times and corrections in the migration processing. Secondly, the TV de-noising strategy based on split Bregman iterative is applied to the RTM profile with the cross-correlation imaging condition, so that the edge of the target can be obvious and the position can be accurate. Then, we apply the proposed method to the simulation data of the pipeline model and the tunnel lining model. All results show that the selected three different autofocusing metrics have unimodality and unbiasedness, which can focus on a single relative permittivity to obtain appropriate migration velocity. Furthermore, the TV de-noising strategy successfully eliminates artifacts, reconstructs contours, enhances the edge sharpness, and improves the quality and accuracy of the radar profile. Finally, we take the field data of the LiuYang River tunnel to verify the applicability of our method, we choose 2–30 as a wider range of relative permittivity based on prior information. Considering the different lateral velocity of the field data, we adopt lateral segmentation processing to improve the quality of the GPR profile. The tests of simulation data and the field data indicate that the proposed method can provide a scientific and effective way for accurate interpretation of GPR data.

Elastic Correlative Least-Squares Reverse Time Migration Based on Wave Mode Decomposition

The conventional elastic least-squares reverse time migration (LSRTM) generally inverts the parameter perturbation of the model rather than the reflectivity of reflected P- and S-modes, which leads to difficulty in directly interpreting the physical properties of the subsurface media. However, an accurate velocity model that is needed by the separation of seismic records of conventional LSRTM is usually unavailable in real data, which limits its application. In this study, we introduce a new practical correlative LSRTM (CLSRTM) scheme based on wave mode decomposition without amplitude and phase distortion, which frees from separation of seismic records. In this study, we deduced the migration and the de-migration operators using the decoupled P- and S-wave equations in heterogeneous media, which needs no extra wavefield decomposition in simulated data. To accelerate the convergence and improve the efficiency of the inversion, we adopted an analytical step-length formula that can be incidentally computed during the necessary de-migration process and the L-BFGS algorithm. Two numerical examples demonstrate that the proposed method can compensate the energy of deep structures, and generate clear images with balanced amplitudes and enhanced resolution even for the fault structures beneath the salt dome.

Source-Free P-SV Converted-Wave Reverse-Time Migration Using First-Order Velocity-Dilatation-Rotation Equations

The cross-correlation imaging condition between source- and receiver-wavefields is often used in the elastic wave reverse-time migration (RTM) to utilize P- and S-waves. However, it cannot be applied in the absence of source information (e.g., source location, and source wavelet), which is quite common in passive source exploration. We employ a source-free P-SV converted-wave imaging condition, which only requires the back-propagating receiver-wavefield to utilize the P-SV converted waves in imaging the subsurface structures. The imaging condition is independent of source information, which can avoid the extrapolation and reconstruction of the source-wavefield. As a result, the computational cost is decreased to about one-third of conventional RTM that uses source-wavefield reconstruction strategies, e.g., random boundaries. The memory requirement could be also reduced by avoiding the calculation of source-wavefield. Because our imaging condition uses the vector P-wavefield and vector S-wavefield to utilize the P-SV waves, it is necessary to decouple P-wavefield and S-wavefield during the reverse-time extrapolation of receiver-wavefield. We use the first-order velocity-dilatation-rotation elastic wave equations to realize the reverse-time propagation of vector receiver-wavefield, where the vector P-wavefield and vector S-wavefield can be obtained directly. Based on the above methods, a source-free P-SV converted-wave RTM of multi-component seismic data is realized. The model tests show that this method can generate promising subsurface images and can be complementarily used when conventional cross-correlation imaging conditions are not suitable.

Deep Learning for Enhancing Multisource Reverse Time Migration

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.

A Novel FDTD-Based 3-D RTM Imaging Method for GPR Working on Dispersive Medium

Nowadays, benefiting from its strong capability of non-destructive detection, the ground penetrating radar (GPR) has been applied to detect and reconstruct underground targets and has drawn lots of attention both in military and civilian fields. However, in the processing of GPR imaging, due to the dispersion errors caused by random distribution of various particles in soil, conventional imaging methods have disadvantages of low signal-noise ratio (SNR), low resolution and unbalanced amplitude. In this paper, in order to achieve high resolution and high veracity on underground targets 3-D reconstruction, we improved the conventional reverse time migration (RTM) algorithm in perspective of medium constitutive relationship. Besides, we extended the improved RTM method in 3-D environments and reconstructed the 3-D structure of several underground targets. To make RTM algorithm suitable for stepped frequency continuous wave (SFCW) GPR system, we generated three excitation signal models and analyzed the effect of different excitation signals on imaging performance. Finally, through the quantitative analysis of simulation and on-vehicle experimental results, we found that the 3-D images generated by improved RTM method had higher resolution, smaller measurement error, and higher veracity than those of conventional RTM method.

Reduced order model approach for imaging with waves

We introduce a novel, computationally inexpensive approach for imaging with an active array of sensors, which probe an unknown medium with a pulse and measure the resulting waves. The imaging function is based on the principle of time reversal in non-attenuating media and uses a data driven estimate of the ‘internal wave’ originating from the vicinity of the imaging point and propagating to the sensors through the unknown medium. We explain how this estimate can be obtained using a reduced order model (ROM) for the wave propagation. We analyze the imaging function, connect it to the time reversal process and describe how its resolution depends on the aperture of the array, the bandwidth of the probing pulse and the medium through which the waves propagate. We also show how the internal wave can be used for selective focusing of waves at points in the imaging region. This can be implemented experimentally and can be used for pixel scanning imaging. We assess the performance of the imaging methods with numerical simulations and compare them to the conventional reverse-time migration method and the ‘backprojection’ method introduced recently as an application of the same ROM.

Fractured basement imaging using random-space-shift reverse time migration: A vertical seismic profile survey in the Bohai Bay Basin, China

Fractured basements are not only potential reservoirs for hydrocarbon resources, but they also provide significant storage space for carbon dioxide ([Formula: see text]) sequestration and radioactive waste disposal. However, fractured basements are challenging for seismic imaging methods due to the complexities in their fault and fracture networks, strong heterogeneity, highly variable structural dip, and strong impedance contrasts between the basement rocks and the surrounding sediments. We present a field case in which a walkaway vertical seismic profiling (VSP) survey was conducted at a fractured basement play located in the Bohai Bay Basin, China, to improve the resolution compared with a preexisting surface seismic profile. Using the advanced random-space-shift (RSS) reverse time migration (RTM), we obtain a high-resolution image with a clear delineation of the highly faulted dipping basement. From numerical and field examples, we find that the application of the RSS-RTM improves the final image by mitigating unavoidable errors in the migration velocity model, which would otherwise result in an unfocused image using the conventional RTM approach. In addition, we determine the importance of proper wavefield separation using 3C recordings, which is the key to ensuring the quality of the final image. With an optimized VSP imaging workflow, we provide an enhanced image for the fractured basement to support the geologic interpretations and development decisions.

Angle-Weighted Reverse Time Migration With Wavefield Decomposition Based on the Optical Flow Vector

Reverse time migration (RTM) is based on the two-way wave equation, so its imaging results obtained by conventional zero-lag cross-correlation imaging conditions contain a lot of low-wavenumber noises. So far, the wavefield decomposition method based on the Poynting vector has been developed to suppress these noises; however, this method also has some problems, such as unstable calculation of the Poynting vector, low accuracy of wavefield decomposition, and poor effect of large-angle migration artifacts suppression. This article introduces the optical flow vector method to RTM to realize high-precision wavefield decomposition for both the source and receiver wavefields and obtains four directions of wavefields: up-, down-, left-, and right-going. Then, the cross-correlation imaging sections of one-way propagation components of forward- and back-propagated wavefields are optimized and stacked. On this basis, the reflection angle of each imaging point is calculated based on the optical flow vector, and an attenuation factor related to the reflection angle is introduced as the weight to generate the optimal stack images. The tests of theoretical model and field marine seismic data illustrate that compared with the conventional RTM with wavefield decomposition based on the Poynting vector, the angle-weighted RTM with wavefield decomposition based on the optical flow vector proposed in this article can achieve wavefield decomposition for both the source and receiver wavefields and calculate the reflection angle of each imaging point more accurately and stably. Moreover, the proposed method adopts angle weighting processing, which can further eliminate large-angle migration artifacts and effectively improve the imaging accuracy of RTM.

Reverse Time Migration Based on the Pseudo-Space-Domain First-Order Velocity-Stress Acoustic Wave Equation

Reverse time migration (RTM) is an ideal seismic imaging method for complex structures. However, in conventional RTM based on rectangular mesh discretization, the medium interfaces are usually distorted. Besides, reflected waves generated by the two-way wave equation can cause artifacts during imaging. To overcome these problems, a high-order finite-difference (FD) scheme and stability condition for the pseudo-space-domain first-order velocity-stress acoustic wave equation were derived, and based on the staggered-grid FD scheme, the RTM of the pseudo-space-domain acoustic wave equation was implemented. Model experiments showed that the proposed RTM of the pseudo-space-domain acoustic wave equation could systematically avoid the interface distortion problem when the velocity interfaces were considered to compute the pseudo-space-domain intervals. Moreover, this method could effectively suppress the false scattering of dipping interfaces and reflections during wavefield extrapolation, thereby reducing migration artifacts on the profile and significantly improving the quality of migration imaging.

Simulating and imaging wavefield of irregular topography based on spectral element method

For the high-precision seismic imaging of complex structures on irregular topographies, this study proposes a Chebyshev spectral-element reverse time migration (CSE-RTM) method coupled with the implicit Newmark time integral method. The approach is first applied to a numerical example to consider factors affecting numerical accuracy, such as the time step and the pattern of subdivision of the computational domain. The results show that the smaller the time step is, the higher the numerical accuracy is and that numerical accuracy improves when the grid nodes tend to be distributed uniformly in the computational domain. The spectral element method combines the advantages of the stronger boundary-related adaptability of the finite element method with the high accuracy and fast convergence of the spectral method. This method is applied to reverse time migration imaging, and tests of the model show that its accuracy of imaging is higher than that of the conventional finite-difference reverse time migration method in case of complex structures in areas with irregular topography. To improve the efficiency of parallel computing of the CSE-RTM, an iterative algorithm is proposed to solve the hierarchical equilibrium sparse linear equations (HELPs) for it based on the idea of the degrees of cohesion of freedom and local relaxation. This algorithm has the advantage that the efficiency of parallel computation does not decrease with an increasing number of processors while the number of iterations required for convergence is controlled. Owing to the fast convergence of the spectral method on a sparse grid coupled with the parallel computational scheme of HELPs, the efficiency of calculation of the CSE-RTM is significantly improved.

Least-squares reverse-time migration with sparsity constraints

Abstract Least-squares reverse-time migration (RTM) works with an inverse operation, rather than an adjoint operation in a conventional RTM, and thus produces an image with a higher resolution and more balanced amplitude than the conventional RTM image. However, least-squares RTM introduces two side effects: sidelobes around reflectors and high-wavenumber migration artifacts. These side effects are caused mainly by the limited bandwidth of seismic data, the limited coverage of receiver arrays and the inaccuracy of the modeling kernel. To mitigate these side effects and to further boost resolution, we employed two sparsity constraints in the least-squares inversion operation, namely the Cauchy and L1-norm constraints. For solving the Cauchy-constrained least-squares RTM, we used a preconditioned nonlinear conjugate-gradient method. For solving the L1-norm constrained least-squares RTM, we modified the iterative soft thresholding method. While adopting these two solution methods, the Cauchy-constrained least-squares RTM converged faster than the L1-norm constrained least-squares RTM. Application examples with synthetic data and laboratory modeling data demonstrated that the constrained least-squares RTM methods can mitigate the side effects and promote image resolution.

3D reverse time migration using a wavefield domain dynamic approach

3D Reverse-time migration (RTM) is a powerful technique for imaging complex geologic structures. This approach requires a significant computational effort, demanding a high amount of memory for storing the source's wavefields, consequently leading to a high cost to perform the imaging condition. Thus, this work aims to reduce these problems by introducing a dynamic approach (DA) that considers the sparsity of the wavefield in the first periods of propagation. The RTM combined with the DA (RTM-DA) approximates the computational domain to the propagation domain, which is the region delimited by the wavefront. In practical terms, the computational domain expands together with the wavefront, reflecting in a very significant economy of memory and reduction of processing time when compared to the conventional RTM, which we denominate as a static approach (RTM-SA). To reduce the sparsity of the wavefields in the first periods of propagation, we have built an empirical 3D filter that maps each timestep of the wavefield and gives the coordinates to approximate the computational domain to the propagation domain. We compare both approaches using the 3D SEG/EAGE Salt model and demonstrate that the RTM-DA is more efficient than the RTM-SA in terms of memory consumption and computational time, preserving the quality of the seismic image.

Depth-Extrapolation-Based True-Amplitude Full-Wave-Equation Migration from Topography

The lack of an initial condition is one of the major challenges in full-wave-equation depth extrapolation. This initial condition is the vertical partial derivative of the surface wavefield and cannot be provided by the conventional seismic acquisition system. The traditional solution is to use the wavefield value of the surface to calculate the vertical partial derivative by assuming that the surface velocity is constant. However, for seismic exploration on land, the surface velocity is often not uniform. To solve this problem, we propose a new method for calculating the vertical partial derivative from the surface wavefield without making any assumptions about the surface conditions. Based on the calculated derivative, we implemented a depth-extrapolation-based full-wave-equation migration from topography using the direct downward continuation. We tested the imaging performance of our proposed method with several experiments. The results of the Marmousi model experiment show that our proposed method is superior to the conventional reverse time migration (RTM) algorithm in terms of imaging accuracy and amplitude-preserving performance at medium and deep depths. In the Canadian Foothills model experiment, we proved that our method can still accurately image complex structures and maintain amplitude under topographic scenario.

Reproduction wavefield reverse time migration

The reverse time migration (RTM) aims to image subsurface reflectors by incorporating with the two-way wave equation. RTM has advantages that it does not have dip limitations and can generate subsurface images clearly even in the case of complex geological structures in the near surface. We have proposed a reproduction wavefield reverse time migration (RWRTM) algorithm implemented with backward reproduced wavefield instead of the back-propagation of the observed data. Reproduced wavefield can be achieved by using the same modelling algorithm used in the source propagation. In general acquisition systems, e.g. streamer in marine or surface geophone in land, conventional RTM back-propagates data acquired on the top grid points in the numerical domain while RWRTM back-propagates reproduced data located on all grid points in the numerical domain, which lead to the generation of migration images with less migration noises and well-balanced migrated events. To validate RWRTM, numerical tests are conducted. For our examples, RWRTM images have better resolution, improved continuity of structure, reduced migration noises, and balanced amplitude compared to the conventional RTM.

Target-oriented reverse time migration in transverse isotropy media

Reverse time migration (RTM) is a high-precision imaging method for complex structures. However, without considering seismic anisotropy of the subsurface, RTM utilizing the anisotropic seismic data may produce blurred structure images with incorrect positions. Moreover, some exploration targets with insufficient illumination cannot be effectively identified in the migration profile, especially the subsalt structure which is usually the favorable petroleum region for the hydrocarbon reservoir. Therefore, we develop a target-oriented RTM in transverse isotropy media (TO-TIRTM). Instead of classical RTM, the novel method extracts wavefields that carry relatively more information about the exploration target to image structure. In the imaging condition, the constraint with excitation time is introduced to eliminate the interference of multipath on the image. Using synthetic examples, we determined that the kinematic characteristic of wavefield is closely related to anisotropic parameters, and the proposed method has prominent advantages over conventional RTM for imaging insufficient illumination structure.

Reverse-Time Migration by Combining Laplacian Filtering With Wavefield Decomposition for High-Resolution Subsurface Imaging

Reverse-time migration (RTM) is considered to be one of the most accurate migration methods, especially for imaging geologically complex structures. However, the conventional RTM using cross-correlation imaging condition is subject to strong migration artifacts. Recent researches on electromagnetic wavefield decomposition exhibit that the method can greatly suppresses the internal reflection noise, however, it is still subject to residual noise. To further eliminate the low-frequency noise to obtain high-resolution subsurface image, a novel electromagnetic imaging scheme by combining a Laplacian filtering with wavefield decomposition is presented, and the pseudospectral time-domain (PSTD) method is introduced to solve the time-dependent partial differential equations efficiently. In this work, we apply the Laplacian filtering on each wavefield snapshot in space domain to sharpen the field distribution. The filtered wavefields are further decomposed into downgoing and upgoing components for final imaging. Numerical experiments show that the proposed method balances the amplitudes of reflectors, and exhibits higher resolution compared to the conventional RTM.