Prestack Reverse Time Migration Research Articles

Attenuation-compensated reverse time migration based on the stereo-modeling operator

The viscosity in the subsurface is ubiquitous. Prestack reverse time migration (RTM) based on the viscoacoustic wave equation is an accurate imaging method to compensate attenuation. The resolution of an imaging result highly depends on the accuracy of the wave equation solution. We extend the nearly analytic center difference (NACD) method to a viscoacoustic wave equation to compensate seismic attenuation. The NACD method can achieve fourth-order accuracy in the time and space domain. We use the pressure and its gradients to approximate the spatial derivatives based on stereo modeling. Numerical simulations and dispersion analysis demonstrate that our NACD has less numerical dispersion and is more accurate than the Lax-Wendroff correction (LWC) method. Thus, the NACD is less expensive in terms of computational time and storage space. Numerical simulations indicate that the forward modeling of the viscoacoustic wavefield via the NACD is able to obtain more accurate wavefields compared with the conventional LWC method and can accurately simulate the effect of the viscosity on waves in attenuative media. When applied to RTM, the viscous effects of the subsurface can be compensated. Synthetic examples demonstrate that the attenuation-compensated RTM using NACD can obtain an image with higher resolution in attenuative media compared with that using the acoustic RTM. Furthermore, the image determined by the NACD is clearer than that of the LWC method in RTM.

An explicit stable Q-compensated reverse time migration scheme for complex heterogeneous attenuation media

Prestack reverse-time migration (RTM) is a popular imaging technique for complex geological conditions, since the amplitude attenuation and velocity dispersion are common in seismic recordings. To image attenuated seismic recordings accurately, a robust migration algorithm with a stable attenuation compensation approach should be considered. In the context of the Q-compensated RTM approach based on the decoupled fractional Laplacians (DFLs) viscoacoustic wave equation, amplitude compensation can be implemented by flipping the sign of the dissipation term. However, the non-physical magnification of image amplitude could lead to a well-known numerical instability problem. The explicit stabilization operator can rectify the amplitude attenuation and suppress the numerical instability. However, limited by the inconvenient mixed-domain operator, the average Q value rather than the real Q value is often used in the compensation operator, lowering the compensated accuracy of the migration image. To overcome this problem, we propose a novel explicit Q-compensation scheme. The main advantage of the proposed compensation operator is that its order is space-invariant, making it more suitable for handling complex heterogeneous attenuation media. Several two-dimensional (2D) and three-dimensional (3D) synthetic models are used to verify the superiority of the proposed approach in terms of amplitude fidelity and image resolution. Field data further demonstrates that our approach has potential applications and can greatly enhance the resolution of seismic images.

Elastic wave pre-stack reverse-time migration based on the second-order P- and S-wave decoupling equation

Abstract The problems of large computation, large storage and low-frequency noises have been the key factors limiting the development of elastic wave pre-stack reverse-time migration (RTM). Most research has centered on the wave equation of first-order velocity stress and using Helmholtz separation to get pure primary and secondary waves. However, the cost is enormous and the amplitude and phase of wavefields will be changed. So, we use the second-order P- and S-wave decoupling equations to construct seismic wavefields that reduce the number of variables, and the storage space required for boundary wavefields is reduced by ∼78%. Then we bring the boundary-saving approach into our study during the wavefield extrapolation process so that we can reconstruct the source wavefields completely. Finally, for the wave equations of second-order displacement used in this study, the Poynting vector expressed by the traditional method was not applicable. Therefore, we derived the formula of the energy flux density vector represented by displacements and used it in directional traveling wave decomposition to suppress low-frequency noise in the imaging profile. Subsequently, based on the inner product imaging conditions, the RTM of the 2-D salt dome model was calculated. The results illustrate the effectiveness and practicability of the proposed solution.

3D prestack reverse time migration of ground penetrating radar data based on the normalized correlation imaging condition

3D prestack reverse time migration of ground penetrating radar data based on the normalized correlation imaging condition

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.

Efficient Acoustic Reverse Time Migration With an Attenuated and Reversible Random Boundary

Pre-stack reverse time migration (RTM) based on the two-way wave equation has been proved to be the most accurate seismic migration method theoretically. However, it requires reverse-order access to the wavefield calculated in forward time. In recursion computing, such out-of-order access requires that most of the recursion history should be stored on the hard disk. For massive amounts of seismic data, loading the saved wavefield data from the disk during imaging has been the bottleneck of RTM, restricting its wide application. To solve this problem, the wavefield in forward time must be reconstructed in reverse order. Although the random boundary can avoid the disk requirement by creating random velocity around the computational domain when propagate the source function. However, the random wavefield reflected from the boundary can generate unwanted artifacts in the final images. In this paper, we develop an attenuated and reversible random boundary condition which is implemented by mixing the reversible attenuation and random boundary conditions. Similar to the random boundary scheme, the proposed method just needs to save the last one or two wavefield snapshots into the memory in forward process. It then reconstructs the source wavefield in reverse order, while greatly reduces the disk input and output (I/O) requirements. Taking the attenuated property into consideration, the artificial events reflected from the boundary can be eliminated. Thus, our method can improve the imaging quality largely compared with the random boundary scheme. Numerical results demonstrate that the RTM images with our proposed attenuated and reversible random boundary condition can not only eliminate the unwanted artifacts, but also improve the computational efficiency greatly.

Elastic imaging and its benefits — Permian Basin example

Seismic imaging has been continuously advancing since the early days of computer revolution in the 1970s. Practical imaging during this time was carried out only in two dimensions using simplified wave equations on poststack data. Subsequently, in the early 1980s algorithm improvements in wave equation migration after the introduction of one-way phase shift methods and two-way reverse time migration occurred. Concurrently, improvements in ray-based Kirchhoff migration emerged after the introduction of eikonal and wavefront reconstruction solvers for calculation of travel times. In the late 1980s, 3D prestack Kirchhoff migration began to be used. By the early 1990s, 3D wave equation poststack migration began to be used and was followed shortly by implementation of wave equation prestack migration. After the turn of the century, 3D prestack reverse time migration became practical, and a few years later VTI, TTI, and orthorhombic rheology were introduced into the imaging.

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.

A high expansion implicit finite-element prestack reverse time migration method

Building on the concepts of cohesion degree and local relaxation, we propose an integrated hierarchical equilibrium parallel finite-element reverse time migration (HEP-FE-RTM) algorithm, which is a fine-grained central processing unit (CPU) parallel computation method in two-level host-sub-processors mode. A single master process is responsible for data reading and controlling the progress of the calculation, while each subordinate process deals with a part of the depth domain space. This algorithm is able to achieve single source forward-modelling and inversion calculation using more than 2000 CPUs. On the premise of controlling iteration times for convergence, sub-module/processors only communicate with their adjacent counterparts and the host processor, so the level of data exchange is proportional to cohesion degree. This HEP-FE-RTM algorithm has the distinct advantage that parallel efficiency does not decrease as the number of processors increases. In two-level host-sub-processors mode, more than 2000 processors are used and one billion unknowns are solved. By combining the finite-element implicit dynamic Newmark integral scheme, this approach achieves a prestack reverse time migration (RTM) with high expansion. Making full use of the characteristics of high accuracy and strong boundary adaptability of the finite-element method, through the optimisation of finite-element solving, the HEP-FE-RTM algorithm improved the efficiency of parallel computing and achieved RTM implementation using finite element. Model tests show that this method has a significant effect on both imaging efficiency and accuracy.

High-order finite-difference approximations to solve pseudoacoustic equations in 3D VTI media

Pseudoacoustic algorithms are very fast in comparison with full elastic ones for vertical transversely isotropic (VTI) modeling, so they are suitable for many applications, especially reverse time migration. Finite differences using simple grids are commonly used to solve pseudoacoustic equations. We have developed and implemented general high-order 3D pseudoacoustic transversely isotropic formulations. The focus is the development of staggered-grid finite-difference algorithms, known for their superior numerical properties. The staggered-grid schemes based on first-order velocity-stress wave equations are developed in detail as well as schemes based on direct application to second-order stress equations. This last case uses the recently presented equivalent staggered-grid theory, resulting in a staggered-grid scheme that overcomes the problem of large memory requirement. Two examples are presented: a 3D simulation and a prestack reverse time migration application, and we perform a numerical analysis regarding computational cost and precision. The errors of the new schemes are smaller than the existing nonstaggered-grid schemes. In comparison with existing staggered-grid schemes, they require 25% less memory and only have slightly greater computational cost.

Seismic Reverse Time Migration Using A New Wave-Field Extrapolator and a New Imaging Condition

Prestack reverse time migration (RTM), as a two way wave-field extrapolation method, can image steeply dipping structures without any dip limitation at the expense of potential increase in imaging artifacts. In this paper, an efficient symplectic scheme, called Leapfrog-Rapid Expansion Method (L-REM), is first introduced to extrapolate the wavefield and its derivative in the same time step with high accuracy and free numerical dispersion using a Ricker wavelet of a maximum frequency of 25 Hz. Afterwards, in order to suppress the artifacts as a characteristic of RTM, a new imaging condition based on Poynting vector and a type of weighting function is presented. The capability of the proposed new imaging condition is then tested on synthetic data. The obtained results indicate that the proposed imaging condition is able to suppress the RTM artifacts effectively. They also show the ability of the proposed approach for improving the amplitude and compensate for illumination.

Implementation of Elastic Prestack Reverse-Time Migration Using an Efficient Finite-Difference Scheme

Elastic reverse-time migration (RTM) can reflect the underground elastic information more comprehensively than single-component Pwave migration. One of the most important requirements of elastic RTM is to solve wave equations. The imaging accuracy and efficiency of RTM depends heavily on the algorithms used for solving wave equations. In this paper, we propose an efficient staggered-grid finite-difference (SFD) scheme based on a sampling approximation method with adaptive variable difference operator lengths to implement elastic prestack RTM. Numerical dispersion analysis and wavefield extrapolation results show that the sampling approximation SFD scheme has greater accuracy than the conventional Taylor-series expansion SFD scheme. We also test the elastic RTM algorithm on theoretical models and a field data set, respectively. Experiments presented demonstrate that elastic RTM using the proposed SFD scheme can generate better images than that using the Taylor-series expansion SFD scheme, particularly for PS images. FurH. thermore, the application of adaptive variable difference operator lengths can effectively improve the computational efficiency of elastic RTM.

Common-image gathers using the excitation amplitude imaging condition

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.

Polarized wavefield magnitudes with optical flow for elastic angle-domain common-image gathers

We have developed a polarized wavefield magnitude (PWM) approach to determine the polarity of an elastic vector wavefield magnitude, for elastic prestack reverse time migration imaging and common-image gather generation. Explicit decomposition of the coupled elastic wavefield into separate P-waves and converted S-waves is performed by using decoupled elastodynamic wavefield propagation. Stable source and receiver wavefield propagation angles are determined by an optical flow method for elastic media. The sign ambiguity in the propagation directions for incident P- and reflected P- and S-wavefield vector magnitudes is resolved by establishing a relation between the propagation and particle velocity vectors. From the computed propagation angles, PP- and PS-wavefields are imaged using source-normalized crosscorrelation followed by sorting into common-image gathers. Modeling of amplitude variations with angle (AVA) from single-shot migrations and from elastic angle-domain common-image gathers demonstrates that the amplitude fidelity is maintained. Mode-converted PS reflectivities also give an independent set of accurate AVA information. Numerical results for the elastic Marmousi2 model confirm PWM as a physically valid and robust method for elastic wavefield imaging in arbitrarily complicated media.

Reverse Time Migration Using the Pseudospectral Time-Domain Algorithm

We propose a pre-stack reverse time migration (RTM) seismic imaging method using the pseudospectral time-domain (PSTD) algorithm. Traditional pseudospectral method uses the fast Fourier transform (FFT) algorithm to calculate the spatial derivatives, but is limited by the wraparound effect due to the periodicity assumed in the FFT. The PSTD algorithm combines the pseudospectral method with a perfectly matched layer (PML) for acoustic waves. PML is a highly effective absorbing boundary condition that can eliminate the wraparound effect. It enables a wide application of the pseudospectral method to complex models. RTM based on the PSTD algorithm has advantages in the computational efficiency compared to traditional methods such as the second-order and high order finite difference time-domain (FDTD) methods. In this work, we implement the PSTD algorithm for acoustic wave equation based RTM. By applying the PSTD-RTM method to various seismic models and comparing it with RTM based on the eighth-order FDTD method, we find that PSTD-RTM method has better performance and saves more than 50% memory. The method is suitable for parallel computation, and has been accelerated by general purpose graphics processing unit.

Salt-related structure geologic model of Pre-Caspian Basin and analysis on imaging capability

The Pre-Caspian Basin is one of the most prolific petroliferous basins in Kazakhstan. However, the hydrocarbon reservoir is always located in salt dome and pre-salt structures. The salt-related structure is so complex that it is difficult to obtain the satisfied imaging results. In order to improve the imaging precision and provide authentic amplitude information to reservoir prediction, we should analyze the imaging and amplitude preserving capability between different migration methods. According to actual geologic and reservoir characteristics, we design a typical complex salt-related structure model of the basin. Based on the forward modelling seismic record, we compare the one-way wave-equation pre-stack depth migration (WPDM) and pre-stack reverse-time depth migration (RTM). The results show that RTM can greatly improve the imaging quality of salt dome, but its improvement for the pre-salt structures is small compared with WPDM. Both methods are equally capable of preserving seismic reflection characteristics that affected mainly by the lateral variation of overlying strata.

Geometry Determination of a Foundation Slab Using the Ultrasonic Echo Technique and Geophysical Migration Methods

The ultrasonic echo technique is a frequently used method in non destructive testing for geometry determination of concrete building elements. Important tasks are thickness measurements as well as the localization and characterization of built-in components and inhomogeneities. Currently mainly the synthetic aperture focusing family of techniques (SAFT) is used for imaging. These algorithms have difficulties in imaging steeply dipping interfaces and complicated structures such as steps and lower boundaries of voids. As an alternative two geophysical migration methods, pre-stack Kirchhoff depth migration and pre-stack Reverse-time migration (RTM) were tested in this paper at a reinforced concrete foundation slab. The slab consists of various reinforcement contents, different thicknesses and two pile heads. In a first step, both methods were evaluated with synthetic 2D data. In the second step, ultrasonic measurement data recorded with shear wave transducers on a line profile on the foundation slab were processed. The use of an automatic scanner simplified the measurements. A comparison of the geophysical migration results with those of SAFT shows, in particular for RTM, a significant improvement in the imaging of the geometry of the foundation slab. Vertical borders were reconstructed and the location and structure of the lower boundary of the foundation slab were reproduced better. Limitations still exist in imaging the piles below the slab.

A modified excitation amplitude imaging condition for prestack reverse time migration

In wave-equation-based migration, the imaging condition is an important factor that impacts migration accuracy and efficiency. Among the commonly used imaging conditions, the excitation amplitude imaging condition has high resolution, accuracy and low storage and input/output burden when compared with others. However, the excitation amplitude extracted by this imaging condition in its current form will produce a distorted migration image for certain scenarios. In this paper, a modified excitation amplitude imaging condition is proposed that addresses the above problem and produces migrated images free from distortion for complicated geologic models. In this paper, we propose a method to effectively use the modified shortest path method (MSPM) for extracting the maximum amplitude around the first-arrival events. Then, the excitation amplitude imaging condition is applied to obtain a continuous and clear migration image. This process can, to some extent, improve the distorted migration image produced by the traditional excitation amplitude imaging condition. Some numerical tests with synthetic data of Sigsbee2a and Marmousi-II models show that the improvement is feasible and effective in complex-structure media.

Reducing data storage in reverse time migration

Prestack reverse time migration (RTM) requires extensive data storage since it computes wavefields in forward time and accesses wavefields in reverse order. We first review several successful schemes that have been proposed to reduce data storage, but require more computational redundancies. We propose two effective strategies to reduce data storage during RTM. The first strategy is based on the Nyquist sampling theorem, which involves no extra computational cost. The fact is that the time sampling intervals required by numerical algorithms or given by field records is generally several times smaller than that satisfied by the Nyquist sampling theorem. Therefore, we can correlate the source wavefields with the receiver wavefields at the Nyquist time step, which helps decrease storage of time history. The second strategy is based on a lossless compression algorithm, which is widely used in computer science and information theory. The compression approach reduces storage significantly at a little computational cost. Numerical examples show that the two proposed strategies are effective and efficient.

Parallel Scalability of a Fine-Grain Prestack Reverse Time Migration Algorithm

Seismic imaging has evolved significantly due to the high demand from the oil/gas industry for hardware technological advancements, boosting the development of more sophisticated algorithms. In order to deliver the quality and accuracy required, the execution of these algorithms may lead to time infeasible solutions. Aiming at performance improvement, this work conducted the parallelization of the core of a reverse time migration (RTM) algorithm. Furthermore, analysis such as speedup and efficiency was performed in order to assess the scalability of the proposed method. While the many parallelization efforts so far deal with coarse-grain approaches, this letter tackles the intrashot fine-grain parallelization of prestack RTM, which increases the overall concurrency degree of the algorithm. Results using 2-D synthetic data show that the proposed approach is scalable, which means that an increase in hardware resources and/or in problem size will lead to a proportional increase in speed and/or accuracy.