Reverse Time Migration Results Research Articles

Deep crustal structures with reverse time migration applied to offshore wide-angle seismic data: Equatorial and North-West Brazilian margins

We image the Moho discontinuity and deep crustal layers by applying the Reverse Time Migration (RTM) method to wide-angle seismic (WAS) data that were acquired along two different profiles in NW and SE offshore Brazil, where the spacing between OBS is 12.5 km and 150 m between shots. The application of this method is quite uncommon to ocean bottom seismometers (OBS) data due to the OBS wide spacing deployment and low folds. We analyze the effectiveness of the RTM method when applied to the reflectivity of the WAS data. We imaged the structures by cross-correlating the forward and backward wavefields given by the acoustic seismic equation. This allowed us to use each interface crossed by a ray as both a source and a receiver. The velocity models used to perform RTM were previously obtained by applying a procedure of two-dimensional forward ray-tracing followed by a damped least-squares travel time inversion. The results obtained have an unexpected large contribution from the wavefield traveling as refractions within the Earth and, because of that, we can talk about recovering refractors from the RTM results. We obtained strong and continuous refractors for depths of 7–15 km that correspond to the basement and the Moho discontinuity. As we move landwards, the refractors that correspond to the Moho discontinuity disappear due to the deepening of the surface. Finally, we investigate how the slight change on the velocity model influences the result of the RTM method. The obtained results are promising for a wide range of applications at a crustal scale seismic exploration, with wide-angle seismic data.

Convolutional Neural-Network-Based Reverse-Time Migration with Multiple Reflections.

Reverse-time migration (RTM) has the advantage that it can handle steep dipping structures and offer high-resolution images of the complex subsurface. Nevertheless, there are some limitations to the chosen initial model, aperture illumination and computation efficiency. RTM has a strong dependency on the initial velocity model. The RTM result image will perform poorly if the input background velocity model is inaccurate. One solution is to apply least-squares reverse-time migration (LSRTM), which updates the reflectivity and suppresses artifacts through iterations. However, the output resolution still depends heavily on the input and accuracy of the velocity model, even more than for standard RTM. For the aperture limitation, RTM with multiple reflections (RTMM) is instrumental in improving the illumination but will generate crosstalks because of the interference between different orders of multiples. We proposed a method based on a convolutional neural network (CNN) that behaves like a filter applying the inverse of the Hessian. This approach can learn patterns representing the relation between the reflectivity obtained through RTMM and the true reflectivity obtained from velocity models through a residual U-Net with an identity mapping. Once trained, this neural network can be used to enhance the quality of RTMM images. Numerical experiments show that RTMM-CNN can recover major structures and thin layers with higher resolution and improved accuracy compared with the RTM-CNN method. Additionally, the proposed method demonstrates a significant degree of generalizability across diverse geology models, encompassing complex thin layers, salt bodies, folds, and faults. Moreover, The computational efficiency of the method is demonstrated by its lower computational cost compared with LSRTM.

Enhancing one-way wave equation-based migration with deep learning

One advantage of one-way wave equation-based migration is its low computational cost. However, due to the limited wavefield propagation angle, it is difficult to use one-way wave equation-based migration for high-precision imaging of structures with large inclinations due to issues such as inaccurate amplitudes and migration image artifacts. In addition, when the model has large horizontal velocity differences, it is difficult for the one-way wave propagator to calculate an accurate wavefield phase. Reverse time migration (RTM) based on the two-way wave propagator has a high resolution and avoids the issues associated with one-way wave propagators; however, it has a high computational cost in practical applications. We develop a convolutional neural network (CNN) application mode that improves one migration method by learning from another one and design a CNN with a structure similar to U-net that combines the advantages of both migration methods. The CNN label is the RTM result, and the corresponding input is the result of one-way wave migration with a generalized screen propagator (GSP). The trained CNN model improves the amplitude in the one-way wave migration image and removes the errors caused by large lateral velocity perturbations. Moreover, by maintaining the high migration calculation efficiency, our CNN model allows for a high resolution, few artifacts, and accurate images of steep structures in the one-way wave migration result. With our method, the accuracy of the one-way wave migration result is close to that of the RTM result. The use of GSP-based migration in our CNN model rather than conventional RTM to generate prospecting images can considerably reduce the calculation costs.

Application of Elastic Reverse Time Migration to Ultrasonic Echo Data in Civil Engineering

The ultrasonic echo technique is widely used in non-destructive testing for investigation and damage analysis of concrete constructions. To improve the ultrasonic imaging of complicated structures in concrete, we transferred a seismic migration technique, the Reverse Time Migration (RTM), to non-destructive testing. In a preliminary study, we tested a 2D acoustic RTM algorithm on measured ultrasonic echo data acquired at a concrete foundation slab. Compared to the conventional used synthetic aperture focusing technique (SAFT) algorithms for ultrasonic data reconstruction, our acoustic RTM results showed a significant improvement in imaging the interior structure of the concrete slab. In contrast to SAFT, RTM is a wavefield-continuation method in time and uses the full wave equation. RTM is, thus, able to include multiple reflections and to handle multi-pathing as well as many other complex situations. As a drawback RTM requires extensive computing power and memory capacity. An RTM algorithm that uses the full elastic wave equation instead of the full acoustic one (as applied in our preliminary work) has the potential to optimize the imaging results even further. This is due to the fact, that our ultrasonic data are generated by exciting elastic waves. In a first step, we tested two 2D elastic RTM algorithms on synthetic ultrasonic echo data generated with a concrete model. Our synthetic elastic RTM results showed an enhancement in imaging the features inside the test model compared to acoustic RTM and SAFT. In a second step, we acquired ultrasonic measurement data at a concrete specimen consisting of three steps and four air-filled tendon ducts. Processing the real ultrasonic data with our elastic RTM codes was successful and improved the reconstruction of the geometries of the steps and tendon ducts. With our study we have shown that elastic RTM is a step forward for ultrasonic testing in civil engineering.

A fast least-squares reverse time migration method using cycle-consistent generative adversarial network

With high imaging accuracy, high signal-to-noise ratio, and good amplitude balance, least-squares reverse time migration (LSRTM) is an imaging algorithm suitable for deep high-precision oil and gas exploration. However, the computational costs limit its large-scale industrial application. The difference between traditional reverse time migration (RTM) and LSRTM is whether to eliminate the effect of the Hessian operator or not while solving Hessian matrix explicitly or eliminating the effect of the Hessian matrix implicitly has a very high requirement on computation or storage capacity. We simulate the inverse Hessian by training a cycle-consistent generative adversarial network (cycleGAN) to construct a mapping relationship between the RTM results and the true reflectivity models. The trained network is directly applied to the RTM imaging results, which improves the imaging quality while significantly reducing the calculation time. We select three velocity models and two velocity models respectively to generate the training and validation data sets, where the validation data is not involved in the training process. The prediction results on the validation data sets show that the trained network significantly improves the imaging quality with almost no additional in computational effort. Finally, we apply the network trained with only synthetics to the field data. The predicted results confirm the effectiveness and good generalization of the proposed method.

An application of the Marchenko internal multiple elimination scheme formulated as a least-squares problem

Images produced by migration of seismic data related to complex geology are often contaminated by artifacts due to the presence of internal multiple reflections. These reflections are created when the seismic wave is reflected more than once in a source-receiver path and can be interpreted as the main coherent noise in seismic data. Several schemes have been developed to predict and subtract internal multiple reflections from measured data, such as the Marchenko multiple elimination (MME) scheme that eliminates the referred events without requiring a subsurface model or an adaptive subtraction approach. The MME scheme is data-driven, can remove or attenuate most of these internal multiples, and was originally based on the Neumann series solution of Marchenko’s projected equations. However, the Neumann series approximate solution is conditioned to a convergence criterion. We reformulate the MME as a least-squares problem (LSMME) in such a way that it can provide an alternative that avoids a convergence condition as required in the Neumann series approach. To demonstrate the LSMME scheme performance, we apply it to 2D numerical examples and compare the results with those obtained by the conventional MME scheme. In addition, we evaluate the successful application of our method through the generation of in-depth seismic images, by applying reverse time migration (RTM) to the original data set and to those obtained through MME and LSMME schemes. From the RTM results, we found that the application of both schemes on seismic data allows the construction of seismic images free of artifacts related to internal multiple events.

Three dimensional reverse time migration on common offset GPR data for void imaging

Three dimensional (3D) Reverse time migration (RTM), as an indispensable imaging technique, has been widely applied to the observed seismic data imaging. However, the RTM of Ground Penetrating radar (GPR) is usually implemented in its two-dimensional (2D) from. This paper proposes a 3D RTM algorithm on common offset GPR data for void imaging. In this algorithm, the 3D finite difference time domain (FDTD) method is applied to calculate the backward extrapolation of electromagnetic fields. And the time zero imaging condition is applied to obtain the final RTM results. Comparisons of the imaging results of 3D and 2D RTM demonstrated that the 3D RTM imaging results were superior to those of 2D RTM. And 3D spatial distribution of Void can be imaged by the proposed 3D RTM algorithm with high accuracy, which can help the subsequent interpretation of GPR profile.

An efficient super-virtual shot encoding scheme for multisource reverse time migration

Reverse time migration (RTM) is a powerful seismic imaging tool that suffers from high computational complexity when dealing with massive data. The simultaneous-shot method can effectively reduce the amount of migration by assembling several sources, although it adds crosstalk noise, which seriously affects the quality of the RTM results. To avoid this problem, we have adopted a time-domain scheme that combines time-delay encoding and amplitude encoding to reduce crosstalk artifacts in simultaneous-source imaging results. This scheme modulates the wavefields of multiple sources to fit the wavefield of a suspended super-virtual shot (SVS), which can eliminate crosstalk artifacts because they are absent in single SVS migration. Numerical examples on a steeply dipping model and the 2D SEG/EAGE salt model show the feasibility of the proposed method. SVS encoding can generate a qualified imaging result and takes less time than plane-wave encoding in the migration process.

A weighted Runge-Kutta discontinuous Galerkin method for reverse time migration

Reverse time migration (RTM) is widely used in the industry because of its ability to handle complex geologic models including steeply dipping interfaces. The quality of images produced by RTM is significantly influenced by the performance of the numerical methods used to simulate the wavefields. Recently, a weighted Runge-Kutta discontinuous Galerkin (WRKDG) method has been developed to solve the wave equation, which is stable, explicit, and efficient in parallelization and suppressing numerical dispersion. By incorporating two different weights for the time discretization, we have obtained a more stable method with a larger time sampling. We apply this numerical method to RTM to handle complex topography and improve imaging quality. By comparing it to the high-order Lax-Wendroff correction method, we determine that WRKDG is efficient in RTM. From the results of the Sigsbee2B data, we can find that our method is efficient in suppressing artifacts and can produce images of good quality when coarse meshes are used. The RTM results of the Canadian Foothills model also demonstrate its ability in handling complex geometry and rugged topography.

Application of GPR reverse time migration in tunnel lining cavity imaging

Correctly locating the tunnel lining cavity is extremely important tunnel quality inspection. High-accuracy imaging results are hard to obtain because conventional one-way wave migration is greatly affected by lateral velocity change and inclination limitation and because the diffracted wave cannot be accurately returned to the real spatial position of the lining cavity. This paper presents a tunnel lining cavity imaging method based on the ground-penetrating radar (GPR) reverse-time migration (RTM) algorithm. The principle of GPR RTM is described in detail using the electromagnetic wave equation. The finite-difference timedomain method is employed to calculate the backward extrapolation electromagnetic fields, and the zero-time imaging condition based on the exploding-reflector concept is used to obtain the RTM results. On this basis, the GPR RTM program is compiled and applied to the simulated and observed GPR data of a typical tunnel lining cavity GPR model and a physical lining cavity model. Comparison of RTM and Kirchhoff migration results reveals that the RTM can better converge the diffracted waves of steel bar and cavity to their true position and have higher resolution and better suppress the effect of multiple interference and clutter scattering waves. In addition, comparison of RTM results of different degrees of noise shows that RTM has strong anti-interference ability and can be used for the accurate interpretation of radar profile in a strong interference environment.

GPR Detection of Tunnel Lining Cavities and Reverse-time Migration Imaging

Tunnel lining cavity is one of the diseases that threaten the safe operation of tunnel, so it has been the attention of test personnel. As a nondestructive testing method, Ground Penetrating Radar (GPR) has been widely used in tunnel lining disease inspection. In order to improve the detection accuracy and success rate of tunnel lining cavities, this paper applies the reverse-time migration (RTM) algorithm to image tunnel lining cavities with high accuracy. Firstly, the principle of GPR pre-stack RTM is described in detail, in which the finite difference time domain (FDTD) method is used to calculate the forward and backward electromagnetic fields, and the normalized cross-correlation imaging condition is used to obtain the RTM results. On this basis, the GPR RTM program is compiled and applied to the simulated dataset of a typical lining cavity GPR model. The comparison of RTM and Kirchhoff migration result showed that the diffracted wave in the steel bar and cavities has good convergence, and the profile’s resolution is improved effectively; In contrast to the Kirchhoff migration result, the RTM result can better focus the radar diffraction wave energy of the steel bars and cavities on the real space location generated by them, weaken the shielding effect of the steel mesh, and suppress multiple interference and clutter scattering waves. Finally, a physical model of lining cavities was detected by GPR, and the RTM algorithm was applied to data processing and interpretation. The RTM delimits the positions of steel mesh and cavities effectively, and the interpretation accuracy of GPR profile has been improved, which provide a scientific and effective way for accurately delimit the scope of tunnel lining cavities.

Q-Compensated Pre-stack Reverse Time Migration in Viscoelastic Media with an Irregular Free Surface

Pre-stack reverse time migration (RTM) is a powerful tool that provides better imaging of complex geological structures than traditional migration methods. An irregular free surface has significant impacts on the characteristics of seismic wave propagation and seismic imaging in mountain or basin areas. In addition, viscoelastic media produce a better representation of the earth than acoustic or elastic media. A main feature of RTM in viscoelastic media is that it can consider compensation for P- and S-wave attenuation effects. In this study, we develop an approach for Q-compensated pre-stack RTM in 2D viscoelastic isotropic media with an irregular free surface. Based on the boundary-conforming method, the viscoelastic model can be discretized to better match the irregular surface and interfaces. The 2D second-order viscoelastic equations and free surface boundary conditions are converted from the Cartesian coordinate system to the curvilinear coordinate system. The finite-difference operators are applied to approximate the viscoelastic wave equations and the irregular free surface in the curvilinear coordinate system. In addition, the convolutional perfectly matched layer (CPML) absorbing boundary condition is selected to effectively suppress artificial reflections from the model boundaries. In the numerical examples, the snapshots, shot gathers and Q-compensated pre-stack RTM results show that our algorithm can obtain an accurate structure image in viscoelastic media in the presence of surface topography.

Reverse Time Migration of Seismic Forward-Prospecting Data in Tunnels Based on Beamforming Methods

For tunneling in complex geological conditions, effective and accurate advanced prospecting techniques are required to detect unexpected geological heterogeneities in front of the tunnel face. Reverse time migration (RTM) method is a promising method to image the geological changes based on seismic forward-prospecting data acquired in tunnels. However, conventional tunnel-based RTM images suffer interference of “trailing” artifacts. Beamforming method can obtain a focused wave front through the stack of wavefield, resulting in improved data quality and RTM results. In this study, we incorporate the beamforming method in RTM imaging procedure, and propose a “sweep and stack” mode RTM method as well as its calculation scheme. Three tunnel-based models with different kinds of geological interfaces are designed to generate synthetic seismic records. Wavefield extrapolation is achieved by an acoustic staggered-grid finite-difference algorithm and zero-lag cross-correlation imaging condition is applied to present RTM results. Analysis and comparison of conventional RTM results and “sweep and stack” mode record-side beamforming RTM results illustrate that, both methods can successfully identify the geological interface ahead of the tunnel face, while record-side beamforming RTM images present more concentrated energy arcs with higher amplitude, which is preferred for geology interpretations. Moreover, the synthetic test in a noisy environment demonstrates that record-side beamforming RTM has better anti-noise capability than the conventional RTM approach. A field test in a highway tunnel construction site is performed to show the good application effects of “sweep and stack” mode RTM in practical seismic detections.

Frequency-domain reverse-time migration with accelerated wave simulation via generalized multiscale finite element

Reverse time migration (RTM) is widely used due to its ability to recover complex geological structures that might not be imaged correctly with methods based on ray theory. However, RTM incurs a considerable computational cost. For this reason, we applied a model reduction technique that solves local spectral problems on a fine grid to simulate wave propagation rapidly on a coarser grid. We can also greatly reduce the computational cost by applying a frequency-domain implementation that requires only one matrix inversion for wave simulation. The multiscale model reduction, a fundamental aspect of the generalized multiscale finite element method, is obtained by utilizing a set of basis functions determined from a local spectral problem. We can tune the accuracy and computational speed by varying the number of basis functions. Applying RTM with fewer basis functions provides results more rapidly, though the usable results are restricted to lower frequencies. However, we can still clearly interpret large-scale structures from the multiscale RTM result. Tuning accuracy and speed of the imaging algorithm is especially useful when the velocity model needs to be actively updated, as it allows faster generation of trial images. In addition, multiscale RTM with a larger number of basis functions can provide faster imaging than the reference case, which uses the continuous-Galerkin finite element approach, without sacrificing accuracy.

Adaptive stabilization forQ-compensated reverse time migration

Reverse time migration (RTM) for attenuating media should take amplitude compensation and phase correction into consideration. However, attenuation compensation during seismic propagation suffers from numerical instability because of the boosted high-frequency ambient noise. We have developed a novel adaptive stabilization method for [Formula: see text]-compensated RTM ([Formula: see text]-RTM), which exhibits superior properties of time variance and [Formula: see text] dependence over conventional low-pass filtering-based method. We derive the stabilization operator by first analytically deriving [Formula: see text]-space Green’s functions for a constant-[Formula: see text] wave equation with decoupled fractional Laplacians and its compensated equation. The time propagator of Green’s function for the viscoacoustic wave equation decreases exponentially, whereas that of the compensated equation is exponentially divergent at a high wavenumber, and it is not stable after the wave is extrapolated for a long time. Therefore, the Green’s functions theoretically explain how the numerical instability existing in [Formula: see text]-RTM arises and shed light on how to overcome this problem pertinently. The stabilization factor required in the proposed method can be explicitly identified by the specified gain limit according to an empirical formula. The [Formula: see text]-RTM results for noise-free data using low-pass filtering and adaptive stabilization are compared over a simple five-layer model and the BP gas chimney model to verify the superiority of the proposed approach in terms of fidelity and stability. The [Formula: see text]-RTM result for noisy data from the BP gas chimney model further demonstrates that our method enjoys a better antinoise performance and helps significantly to enhance the resolution of seismic images.

Comparison of two viscoacoustic propagators for Q-compensated reverse time migration

Without considering intrinsic attenuation, reverse time migration (RTM) of data from lossy media produces smeared migration images because of the [Formula: see text] effects (amplitude loss and velocity dispersion). To mitigate the [Formula: see text] effects during RTM, amplitudes need to be compensated and the propagation velocity of the compensated wavefield needs to be the same as in the attenuating wavefield. We have compared the decoupled constant [Formula: see text] (DCQ) viscoacoustic equation with the viscoacoustic equation based on the generalized standard linear solids (GSLS), for modeling and for [Formula: see text] compensation. The DCQ propagator separates amplitude loss and velocity dispersion operators; for the GSLS propagator, memory variables are used to introduce the [Formula: see text] effects. Amplitude loss and velocity dispersion are decoupled in the DCQ equation, whereas they are coupled in the GSLS equation. Viscoacoustic modeling by the two viscoacoustic propagators produces visually identical seismograms. To compensate for the [Formula: see text] effects, for the DCQ equation, we reverse the sign of the amplitude loss operator and keep the sign of the velocity dispersion operator unchanged. For the GSLS equation, the sign of the memory variables is reversed. Both approaches can compensate for the amplitude loss. Propagation velocities in the attenuating and [Formula: see text]-compensated wavefields are the same for the DCQ equation and are different for the GSLS equation. The [Formula: see text]-compensated wavefield propagates faster than the attenuating wavefield for the GSLS equation. Viscoacoustic RTM is implemented with the source normalized crosscorrelation imaging condition; the source wavefield is attenuated, and [Formula: see text] compensation is applied during receiver wavefield extrapolation. Results of [Formula: see text]-compensated migration on a three-layer model, a salt model, and the BP 2004 model using the DCQ equation are more consistent with the acoustic (nonviscous) RTM results, but they have a wider wavelet and a different [Formula: see text]-dependent amplitude behavior; there is a phase shift in the migration results when using the GSLS equation.

The Application of Reverse-Time Migration in the Z Area of PRM Basin

Reverse time migration (RTM) is an accurate migration method, which is based on two-way wave equation, eliminates angle limitation, and can be capable for imaging of reverse branch and multiple. In the development of an oilfield in Pearl River Mouth (PRM) Basin, RTM has been applied to solve the problems of fault shadow and structure in distinction and the drilling has proven that the RTM result is reliable. This paper introduces the theory of RTM and emphatically discusses parameter selection. The results of RTM showed that it had advantages in resolving fault shadow and the imaging of steep dip structure, and could be utilized in the oilfield.

An efficient symplectic reverse time migration method using a local nearly analytic discrete operator in acoustic transversely isotropic media with a vertical symmetry axis

Reverse time migration (RTM) has become an extremely important imaging method due to its ability of handling complicated velocity models. In recent years, there has been an increasing need to perform RTM with anisotropic velocity models such as transversely isotropic media with a vertical symmetry axis (VTI). Finite difference (FD) is one of the most widely used numerical methods in RTM. However, it often suffers from serious numerical dispersion, resulting in significant loss of imaging resolution. Over the years, a nearly analytic discrete operator has been developed to approximate the high-order spatial partial differential operators, which is effective in suppressing numerical dispersion. Using this operator, we developed a nearly analytic symplectic (NAS) method to numerically solve acoustic VTI wave equations, which preserves the symplectic structure. We have investigated its properties including the stability condition, numerical dispersion relation, and computational efficiency. Also, we applied the NAS method to solve wave equations in RTM in acoustic VTI media. This new method not only reduced numerical dispersion and improved computational efficiency, compared to the conventional numerical methods such as the Lax-Wendroff correction (LWC) method, but it also was symplectic. Our forward-modeling results showed that the computational efficiency of NAS is about four times and its overall memory requirement is about 75% of those of LWC. The RTM results of the 2D prestack Hess acoustic VTI model showed that RTM by using NAS obtained better image quality than that by using LWC when coarse grids were used, which demonstrated that the NAS method can be promising in large-scale anisotropic RTM.

Application of pre-stack reverse time migration based on FWI velocity estimation to ground penetrating radar data

Abstract Reverse-time migration (RTM) is used for subsurface imaging to handle complex velocity models including steeply dipping interfaces and dramatic lateral variations and promises better imaging results compared to traditional migration method such as Kirchhoff migration algorithm. RTM has been increasingly used in seismic surveys for hydrocarbon resource explorations. Based on the similarity of kinematics and dynamics between electromagnetic wave and elastic wave, we develop pre-stack RTM method and apply it to process ground penetrating radar (GPR) data. Finite-difference time domain (FDTD) numerical method is used to simulate the electromagnetic wave propagation including forward and backward extrapolations, the cross-correlation imaging condition is used to obtain the final image. In order to provide a velocity model with relatively higher accuracy as the initial velocity model for RTM, we apply a full waveform inversion (FWI) in time domain to estimate the subsurface velocity structure based on reflection radar data. For testing the effectiveness of the algorithm, we have constructed a complex geological model, common-offset radar data and common-shot profile (CSP) radar reflection data are synthesized. All data are migrated with traditional Kirchhoff migration method and pre-stack RTM method separately, the migration results from pre-stack RTM show better coincidence with the true model. Furthermore, we have performed a physical experiment in a sandbox where a polyvinyl chloride (PVC) box is buried in the sand, the obtained common-offset radar data and common-shot radar data are migrated by using Kirchhoff migration method and pre-stack RTM algorithm separately, the pre-stack RTM result shows that RTM algorithm could get better imaging results.

Multi-Component Seismic Wave Field Prestack Reverse-Time Depth Migration

Based on the elastic wave equation, high-order finite-difference schemes for reverse-time extrapolation in the space of staggered grid and the perfectly matched layer (PML) absorbing boundary condition for the equation are derived. Prestack reverse-time depth migration (RTM) of elastic wave equation using the excitation time imaging condition and normalized cross-correlation imaging condition is carried out. Numerical experiments show that reverse-time migration is not limited for the angle of incidence and dramatic changes in lateral velocity. The reverse-time migration results of normalized cross-correlation imaging condition give the better effect than that of excitation time imaging condition.