Conventional RTM Research Articles

Target-oriented Q-compensated reverse-time migration by using optimized pure-mode wave equation in anisotropic media

Research on seismic anisotropy and attenuation plays a significant role in exploration geophysics. To enhance the imaging quality for complicated structures, we develop several effective improvements for anisotropic attenuation effects in reverse-time migration (Q-RTM) on surface and vertical seismic profiling (VSP) acquisition geometries. First, to suppress pseudo-shear wave artifact and numerical instability of the commonly used anisotropic pseudo-acoustic wave equations, an optimized pure P-wave dispersion relation is derived and the corresponding pure-mode wave equation is solved by combining the finite-difference and Possion methods. Second, a simplified anisotropic pure-mode visco-acoustic wave equation (PVAWE) based on standard linear solid model is established. Third, a time-dispersion correlation strategy is applied to improve the modeling accuracy. Fourth, we extend a target-oriented scheme to anisotropic attenuated modeling and imaging. Instead of the conventional wavefield modeling and RTM, the proposed approach can extract available wavefield information near the target regions and produce high imaging resolution for target structures. Last, both anisotropic surface and VSP Q-RTMs are executed by combining optimized PVAWE, time-dispersion correlation and target-oriented algorithm. Modeling examples demonstrate the advantages of our schemes. Moreover, our modified Q-compensated imaging workflow can be regarded as a supplement to the classical anisotropic RTM.

Improving the memory efficiency of RTM using both Nyquist sampling and DCT based on GPU

Abstract Reverse time migration (RTM) is used to obtain complex structural images of subsurface media. The RTM can be expressed as a zero-lag cross-correlation between the source and receiver wave fields. As imaging conditions can be calculated based on the pre-stored source wavefield and the received wavefield generated during backward modelling, only the source wavefield must be stored in the memory (or disc). Therefore, reducing source-wavefield storage requirements can improve memory efficiency. High-performance computing based on graphic processing units (GPUs) is being developed to reduce the computational time in wave-propagation modelling. Accordingly, GPU-based RTM technology has the potential to improve the computational efficiency of RTM. Storage of the source wavefield wholly in GPU video random-access memory (VRAM) may further improve computational efficiency. In this paper, we present a new algorithm for a three-dimensional (3D) GPU-based RTM that can enable efficient storage of the source wavefield in VRAM using both Nyquist sampling and discrete cosine transform (DCT) compression. A numerical example employing a modified SEG/EAGE 3D overthrust model presented in this study verifies that the proposed algorithm requires only 2% of the memory usage of conventional RTM while producing similar results.

Efficient least-squares reverse time migration using local cross-correlation imaging condition

Abstract The data-domain least-squares reverse time migration (LSRTM), a promising imaging method for obtaining a high-resolution reflectivity image, can be implemented by matching the de-migrated data to the observed one. However, LSRTM requires expensive computational costs in its implementation due to tremendous memory usage (direct storage on disk/memory) for saving source wavefields and repeatable forward/backward wavefield simulations with iterations compared to conventional RTM. Although the source wavefield reconstruction technique can be used to reduce the memory usage, additional computational cost is inevitable because it is implemented during backward wavefield simulation. To alleviate the computational burden, we have developed an efficient LSRTM scheme with local cross-correlation imaging condition (LSRTM-LC), which can use pre-saved source wavefields according to the window size. Because the window size is much shorter than the total recording time for wavefield extrapolation, storing source wavefields into computer memory can be feasible. In addition, the procedure for storing source wavefields is implemented only at the first iteration because the background velocity is fixed during iterations of LSRTM. To validate the feasibility of the LSRTM-LC scheme, we have carried out several numerical tests with synthetic datasets. Numerical tests demonstrated that LSRTM-LC can provide us with equivalent de-migrated data from saved source wavefields and the gradient vector obtained from LSRTM-LC compared to those obtained from the conventional LSRTM. As a result, LSRTM-LC can generate the same quality of reflectivity models as conventional LSRTM, however, it requires less computational costs compared to conventional LSRTM.

Characterization of the CRTM process applicated to a door reinforcement

The automotive industry has benefited to some extent from composites for several decades, especially for non-primary structural applications. Technologies such as GMT, LFT or SMC are used to manufacture interior components, functional parts or body parts, with productivity standards and very competitive prices. But despite these successful applications, their expansion to more structural parts is not possible because of the limited properties of the materials and largely because the current manufacturing processes and facilities are not ready for mass manufacturing. When it is intended to manufacture pieces with high fiber contents and / or large pieces, the increase in fiber content decreases the permeability of the preform, necessitating longer filling times, and generating impregnation problems and high pore contents. In order to solve these drawbacks associated with conventional RTM, different alternatives have been explored: increasing the injection pressure, injecting through multiple entries or reducing the viscosity of the resin among others. One of the most promising is the combination of RTM and compression, called CRTM (Compression RTM). Comparing with conventional RTM, the mold remains partially open in the injection phase, generating a space not occupied by the fibers that exerts a preferred flow path for the resin without having to penetrate the preform. The objective of the project has been to characterize the CRTM process and apply this knowledge in the manufacture of a side door reinforcement.

A GPU implementation of least-squares reverse time migration

Least-squares reverse time migration (LSRTM) is a seismic imaging method that can provide higher-resolution image of the subsurface structures compared to other methods. However, LSRTM is computationally expensive. To reduce the computational time of LSRTM, GPU can be utilized. This leads to the objective of this work which is to develop a GPU implementation of LSRTM. In this work, the two-dimensional first-order acoustic wave equations are solved using the second-order finite difference on a staggered grid and a perfectly matched layer is used as an absorbing boundary condition. The adjoint-state method is used to compute the gradient of the objective function. A linear conjugate gradient method is used to minimize the objective function. Both forward- and backward-propagation of wavefields using the finite-difference method are performed on a single GPU using the NVIDIA CUDA library. For a verification purpose, the GPU program of LSRTM was applied to a synthetic data set generated from the Marmousi model. Numerical results show that LSRTM can provide an image with a higher resolution of subsurface structure compared to a conventional RTM image. For a computational cost issue, the GPU-version of LSRTM is significantly faster than the serial CPU-version of LSRTM.

Energy Flow Domain Reverse-Time Migration for Borehole Radar

A modified 2-D reverse-time migration algorithm in the energy flow domain, called EF-RTM, is proposed for short impulse borehole radar (BHR) imaging. The key of the approach is based on Poynting's theorem, which allows decomposition of the energy flux density (EFD) derived from the source and receiver wave fields in different wave-propagation directions. Then, imaging conditions, for example, zero-lag cross correlation (prestack migration) and zero-time imaging principle (poststack migration), are applied to the decomposed EFD-field components to obtain the migrated sections. The characteristics of the resulting images can be optionally combined or separately used for better BHR data imaging, interpretation, and analysis. In this paper, the EF-RTM algorithm is validated by numerical modeling and real field data and compared with the conventional RTM algorithm. All the results show that this new EF-RTM method is superior to the conventional RTM method: it inherits the high precision of RTM with additional imaging advantages, such as natural wave-field decomposition in different directions, improved migrated cross-range resolution, a better focus of the target's shape, and migration noise reduction.

Diffraction imaging using geometric-mean reverse time migration and common-reflection surface

Diffracted waves contain a great deal of valuable information about small-scale subsurface structure such as faults, pinch-outs, karsts, and fractures, which are closely related to hydrocarbon accumulation and production. Therefore, diffraction separation and imaging with high spatial resolution play an increasingly critical role in seismic exploration. We have applied the geometric-mean reverse time migration (GmRTM) method to diffracted waves for imaging only subsurface diffractors based on the difference of the wave phenomena between diffracted and reflected waves. Numerical tests prove the advantages of this method on diffraction imaging with higher resolution as well as fewer artifacts compared to conventional RTM even when we only have a small number of receivers. Then, we developed a workflow to extract diffraction information using a fully data-driven method, called common-reflection surface (CRS), before we applied GmRTM. Application of this workflow indicates that GmRTM further improves the quality of the image by combining with the diffraction-separation technique CRS in the data domain.

A 3-D High-Order Reverse-Time Migration Method for High-Resolution Subsurface Imaging With a Multistation Ultra-Wideband Radar System

A three-dimensional high-order reverse-time migration (3-D HO-RTM) method is proposed to perform subsurface electromagnetic imaging with an ultra-wideband radar (UWBR) system consisting of a multi-input and multi-output antenna array. By using a UWBR system to collect temporal scattering signals, subsurface targets can be detected, and the image of targets can be obtained by imaging methods such as the back-propagation method, frequency-wavenumber migration technique, time-reversal mirror, and reverse-time migration method. The proposed HO-RTM method is based on the high-order finite-difference time-domain (HO-FDTD) method to significantly reduce the computational cost in the conventional RTM method. The measured data from an experimental lunar exploration system Chang'E-5 have been collected on a 7 m × 2.5 m × 2.5 m laboratory model with volcanic ash and validated by the 3-D HO-RTM method. Results show that all buried objects can be effectively identified by the HO-RTM, and its computer memory and CPU time are only 3.87% and 0.7128% of the conventional RTM method, respectively.

Least-squares reverse time migration with an angle-dependent weighting factor

Least-squares reverse time migration (LSRTM) produces higher quality images than conventional RTM. However, directly using the standard gradient formula, the inverted images suffer from low-wavenumber noise. Using a simple high-pass filter on the gradient can alleviate the effect of the low-wavenumber noise. But, owing to the illumination issue, the amplitudes are not balanced and in the deep part they are often weak. These two issues can be mitigated by the iterative approach, but it needs more iterations. We introduced an angle-dependent weighting factor to weight the gradient of LSRTM to suppress the low-wavenumber noise and also to emphasize the gradient in the deep part. An optimal step length for the L2-norm objective function is also presented to scale the gradient to the right order. Two numerical examples performed with the data synthesized on the Sigsbee2A and Marmousi models indicate that when using this weighted gradient combined with the preconditioned [Formula: see text]-BFGS algorithm with the optimal step length, only a few iterations can achieve satisfying results.

A Nonlinear Method for Imaging with Acoustic Waves Via Reduced Order Model Backprojection

We introduce a novel nonlinear imaging method for the acoustic wave equation based on data-driven model order reduction. The objective is to image the discontinuities of the acoustic velocity, a coefficient of the scalar wave equation from the discretely sampled time domain data measured at an array of transducers that can act as both sources and receivers. We treat the wave equation along with transducer functionals as a dynamical system. A reduced order model (ROM) for the propagator of such system can be computed so that it interpolates exactly the measured time domain data. The resulting ROM is an orthogonal projection of the propagator on the subspace of the snapshots of solutions of the acoustic wave equation. While the wavefield snapshots are unknown, the projection ROM can be computed entirely from the measured data, thus we refer to such ROM as data-driven. The image is obtained by backprojecting the ROM. Since the basis functions for the projection subspace are not known, we replace them with the ones computed for a known smooth kinematic velocity model. A crucial step of ROM construction is an implicit orthogonalization of solution snapshots. It is a nonlinear procedure that differentiates our approach from the conventional linear imaging methods (Kirchhoff migration and reverse time migration - RTM). It resolves all dynamical behavior captured by the data, so the error from the imperfect knowledge of the velocity model is purely kinematic. This allows for almost complete removal of multiple reflection artifacts, while simultaneously improving the resolution in the range direction compared to conventional RTM.

A guide to least-squares reverse time migration for subsalt imaging: Challenges and solutions

Least-squares reverse time migration (LSRTM) overcomes the shortcomings of conventional migration algorithms by iteratively fitting the demigrated synthetic data and the input data to refine the initial depth image toward true reflectivity. It gradually enhances the effective signals and removes the migration artifacts such as swing noise during conventional migration. When imaging the subsalt area with complex structures, many practical issues have to be considered to ensure the convergence of the inversion. We tackle those practical issues such as an unknown source wavelet, inaccurate migration velocity, and slow convergence to make LSRTM applicable to subsalt imaging in geologic complex areas such as the Gulf of Mexico. Dynamic warping is used to realign the modeled and input data to compensate for minor velocity errors in the subsalt sediments. A windowed crosscorrelation-based confidence level is used to control the quality of the residual computation. The confidence level is further used as an inverse weighting to precondition the data residual so that the convergence rates in shallow and deep images are automatically balanced. It also helps suppress the strong artifacts related to the salt boundary. The efficiency of the LSRTM is improved so that interpretable images in the area of interest can be obtained in only a few iterations. After removing the artifacts near the salt body using LSRTM, the image better represents the true geology than the outcome of conventional RTM; thus, it facilitates the interpretation. Synthetic and field data examples examine and demonstrate the effectiveness of the adaptive strategies.

Adaptive least-squares RTM with applications to subsalt imaging

Least-squares reverse time migration (LSRTM) refines the seismic image toward true reflectivity by inversion. Its iterative nature and modeling capability enable the use of synthetic data to guide the preconditioning of input data. When the velocity contains errors, dynamic warping can be used to shift the input data and force the traveltime to be consistent with the imperfect migration velocity. A crosscorrelation-based confidence level is introduced to control the quality of dynamic warping for field data. The confidence level also is used as an inverse weighting to adaptively precondition the data residual. The adaptive preconditioning automatically balances data fitting in the shallow and deep and speeds up convergence in subsalt. Both synthetic and field data experiments based in the Gulf of Mexico show that the adaptive LSRTM can improve the image quality in subsalt effectively and efficiently. Within only a few iterations, the adaptive LSRTM suppresses the salt halo artifacts and increases the signal-to-noise ratio in poorly illuminated areas. It also improves the termination of sediments against salt boundaries and enhances subsalt image coherency. Compared with conventional RTM, the adaptive LSRTM image is more favorable to geologic interpretation.

Viscoacoustic modeling and imaging using low-rank approximation

A constant-[Formula: see text] wave equation involving fractional Laplacians was recently introduced for viscoacoustic modeling and imaging. This fractional wave equation has a convenient mixed-domain space-wavenumber formulation, which involves the fractional-Laplacian operators with a spatially varying power. We have applied the low-rank approximation to the mixed-domain symbol, which enables a space-variable attenuation specified by the variable fractional power of the Laplacians. Using the proposed approximation scheme, we formulated the framework of the [Formula: see text]-compensated reverse time migration ([Formula: see text]-RTM) for attenuation compensation. Numerical examples using synthetic data demonstrated the improved accuracy of using low-rank wave extrapolation with a constant-[Formula: see text] fractional-Laplacian wave equation for seismic modeling and migration in attenuating media. Low-rank [Formula: see text]-RTM applied to viscoacoustic data is capable of producing images comparable in quality with those produced by conventional RTM from acoustic data.

Plane-wave least-squares reverse time migration for rugged topography

We present a method based on least-squares reverse time migration with plane-wave encoding (P-LSRTM) for rugged topography. Instead of modifying the wave field before migration, we modify the plane-wave encoding function and fill constant velocity to the area above rugged topography in the model so that P-LSRTM can be directly performed from rugged surface in the way same to shot domain reverse time migration. In order to improve efficiency and reduce I/O (input/output) cost, the dynamic encoding strategy and hybrid encoding strategy are implemented. Numerical test on SEG rugged topography model show that P-LSRTM can suppress migration artifacts in the migration image, and compensate amplitude in the middle-deep part efficiently. Without data correction, P-LSRTM can produce a satisfying image of near-surface if we could get an accurate near-surface velocity model. Moreover, the pre-stack PLSRTM is more robust than conventional RTM in the presence of migration velocity errors.

Improved seismic image by Q-compensated reverse time migration: Application to crosswell field data, west Texas

To test the effectiveness of the [Formula: see text]-compensated reverse time migration ([Formula: see text]-RTM) method, we applied it to crosswell seismic data from western Texas. This crosswell field survey was aimed at determining the boundaries and even the internal features of the reservoir. In this area, the reservoir geologic body exhibits strong attenuation that reduces high frequencies more rapidly. Thus, conventional acoustic RTM produces a dimmed image (reduced amplitude and low resolution) of the reservoir area and structures underneath. In contrast, [Formula: see text]-RTM is able to compensate for the attenuation effects during imaging. The [Formula: see text] and [Formula: see text] profiles needed for [Formula: see text]-RTM were produced by joint traveltime and frequency shift tomography. Preprocessing of the data was carried out to reduce noise, remove tube waves, and to separate up- and downgoing wavefields. Along with recovered high wavenumbers, the final [Formula: see text]-RTM image provided many details about geologic layers and structures. The lateral and vertical extent and internal structures within the reservoir unit were clearly determined. These geologic features were also correlated to the velocity profile and sonic logs. We concluded that [Formula: see text]-RTM imaging practically improved the image resolution in attenuating geologic media.

Least-squares reverse time migration of marine data with frequency-selection encoding

The phase-encoding technique can sometimes increase the efficiency of the least-squares reverse time migration (LSRTM) by more than one order of magnitude. However, traditional random encoding functions require all the encoded shots to share the same receiver locations, thus limiting the usage to seismic surveys with a fixed spread geometry. We implement a frequency-selection encoding strategy that accommodates data with a marine streamer geometry. The encoding functions are delta functions in the frequency domain, so that all the encoded shots have unique nonoverlapping frequency content, and the receivers can distinguish the wavefield from each shot with a unique frequency band. Because the encoding functions are orthogonal to each other, there will be no crosstalk between different shots during modeling and migration. With the frequency-selection encoding method, the computational efficiency of LSRTM is increased so that its cost is comparable to conventional RTM for the Marmousi2 model and a marine data set recorded in the Gulf of Mexico. With more iterations, the LSRTM image quality is further improved by suppressing migration artifacts, balancing reflector amplitudes, and enhancing the spatial resolution. We conclude that LSRTM with frequency-selection is an efficient migration method that can sometimes produce more focused images than conventional RTM.

Multi‐source least‐squares reverse time migration

ABSTRACTLeast‐squares migration has been shown to improve image quality compared to the conventional migration method, but its computational cost is often too high to be practical. In this paper, we develop two numerical schemes to implement least‐squares migration with the reverse time migration method and the blended source processing technique to increase computation efficiency. By iterative migration of supergathers, which consist in a sum of many phase‐encoded shots, the image quality is enhanced and the crosstalk noise associated with the encoded shots is reduced. Numerical tests on 2D HESS VTI data show that the multisource least‐squares reverse time migration (LSRTM) algorithm suppresses migration artefacts, balances the amplitudes, improves image resolution and reduces crosstalk noise associated with the blended shot gathers. For this example, the multisource LSRTM is about three times faster than the conventional RTM method. For the 3D example of the SEG/EAGE salt model, with a comparable computational cost, multisource LSRTM produces images with more accurate amplitudes, better spatial resolution and fewer migration artefacts compared to conventional RTM. The empirical results suggest that multisource LSRTM can produce more accurate reflectivity images than conventional RTM does with a similar or less computational cost. The caveat is that the LSRTM image is sensitive to large errors in the migration velocity model.