RTM based wave equation migration velocity analysis

Reverse time migration (RTM) is achieved by a forward and reverse time propagation of source and receiver wavefields respectively, followed by an imaging condition. The quality of the image from any RTM implementation depends directly on the method’s ability to separate the true reflection data from the backscattered correlation noise between the source and receiver wavefields. In this paper we demonstrate the application of an inverse scattering imaging condition that significantly reduces this backscattered correlation noise and results in a much higher quality subsurface image than is achieved by typical RTM imaging conditions.

Summary In this abstract, we discuss some practical issues related to the implementation of reverse time migration (RTM) in a tilted transversely isotropic (TTI) medium. We have proposed a methodology to effectively reduce the cost. Through optimization of the coefficients of high-order difference scheme on the variable grid, larger depth steps at greater depth can be used instead of fixed step size. Synthetic data examples are used to demonstrate the effectiveness of the methodology. Introduction Reverse time migration (RTM) based on solving a two-way wave equation has been one of the most accurate imaging tools available in dealing with large lateral velocity variations and complicated geology such as large dips. RTM for isotropic and vertical transversely isotropic (VTI) medium has been routinely in use in the industry, but the application of RTM in TTI medium is still in the early stage. This lag results from the difficulties in numerical formulations for non-vertical symmetric axes and the subsequent instabilities. The TTI implementation also leads to higher computational costs compared with its isotropic or VTI counterparts. Instead of solving the original anisotropic wave equation, several modified quasi-P wave equations were derived by different authors, that can be used to perform anisotropic RTM for P-waves imaging without cause significant S wave scattering. Alkhalifah (2000) derived a 4th-order partial differential equation (PDE) in time to describe TTI propagation. To avoid solving a high order PDE, Zhou et al. (2006) split Alkhaifah's equation into two coupled 2nd-order PDEs. However it has been observed that their equations cause instability in practice when large dip is at presence. To circumvent this stability issue, Zhang et al. (2009) pursue an equivalent TTI formulation that preserves physical energy with the kinematics retained. Fletcher et al. (2009) proposed adding non-zero shear wave velocity terms to mitigate the instability problem. Unfortunately, their solution adds numerical complexity. In our implementation, to deal with both the stability and accuracy issues in TTI environment, we have to cut the cost dramatically to run it in production environment. To reduce the computational cost of TTI RTM, we use the least-square-root method in the Fourier domain to construct optimized finite difference (FD) schemes of variable grid in depth to approximate the first and second order derivatives. With larger steps in space in deep layers of higher velocity while keeping the same criteria for controlling the numerical dispersion, the total number of grid point is reduced. We analyzed the stability condition for this proposed FD scheme to determine the size of time step, which is related to minimum grid space, maximum velocity as well as the coefficients of FD scheme. With this implementation our RTM has been enhanced greatly in efficiency, and gained success in numerous 3D land imaging projects. Here we will demonstrate the effectiveness of this method using the 2D BP TTI model as a test case.

Reverse time migration: A prospect of seismic imaging methodology

Old abandoned coal working create major hazards in the form of subsidence of the coalfields. To avoid such hazards, there is need to detect these cavities prior to start of deeper seam mining. There are number of geophysical techniques available for detecting subsurface cavity. High-resolution seismic survey is one such technique which provides accurate results as compared to others. Usually, most of the seismic processing and interpretation of these cavity detection was performed based on stacked data only. To understand these signatures more precisely, in our study, an attempt has been made to image these cavities with the help of Reverse Time Migration (RTM) combined with Full Waveform Inversion (FWI). RTM mostly used for hydrocarbon exploration targets with low central frequency as source. Application of this method to shallow subsurface exploration is still in research stage. Like the same way for velocity model updating, FWI gives mostly appropriate optimization results as compare to other techniques, but it also has the limitation to application of low frequency only. In this paper we first develop a 2D realistic Water Filled Cavity (WFC) model with a work flow of RTM combined with FWI in a high-frequency Ricker source wavelet as 100 Hz. In order to provide a velocity model with high accuracy for RTM, we apply FWI to estimate the subsurface velocity by considering an initial smooth velocity model with addition of 30 % Gaussian noise. The conventional RTM fails to image the cavities and yield a large amount of low frequency back scattered noise at shallow depth during the time of cross correlation due to time/space lag. To avoid these situation, we introduced an automatic shift operator at the time of imaging condition that operates automatically both in time or space. It leads to reduce the lag and improve the results by minimizing the noises at shallow subsurface. By comparing both the results it is observed that most of the noises in the migrated section of conventional method were eliminated by the improved form of RTM with the help of FWI velocity model estimation.

After many years of processing seismic streamer data acquired over the Shenzi field in deep-water Gulf of Mexico (GOM) with the best available technology, the workflows have remained highly interpretive, far from robust, often time-consuming, and ultimately proved inadequate for resolving the complexity of the salt and subsalt velocity models. Recent advances in full-waveform inversion (FWI) algorithms combined with a newly acquired, ocean bottom node (OBN) data set have ushered in a fundamental shift in velocity model building and imaging at Shenzi as we move away from mostly interpretation-driven to more data-driven processes. While the velocity model obtained from Time-lag FWI (TLFWI) using the legacy rich-azimuth (RAZ) streamer data provided significant imaging uplift over the best previous processing, an additional step-change improvement in image quality was achieved by running TLFWI with the OBN data. The OBN TLFWI model combined with the long offsets of the OBN data allowed steeply dipping events along the salt feeder to be seen for the first time on the reverse time migration (RTM) image. However, despite these large improvements, the image still suffers in areas of low illumination. Least-squares RTM (LSRTM) showed some good improvement over the RTM but proved less effective where the starting image was too poor. By running TLFWI to a maximum frequency comparable to the RTM, we were able to generate an FWI Image, an estimation of the reflectivity obtained directly from the FWI velocity model, with good S/N, more balanced amplitudes, and improved steep-dip and fault imaging, making it a direct rival to the RTM and LSRTM images.

In the early stage of acoustic full-waveform inversion (AFWI), it is important to exploit the long-wavelength features of the gradient and suppress its short-wavelength features to update the background velocity. However, due to strong near-offset PP reflections and multiples within the pressure data, conventional AFWI sometimes primarily reconstructs the short-wavelength features of a given model and fails to converge on a reliable subsurface P-wave velocity model. Therefore, this study, we propose the usage of pseudo-horizontal particle acceleration (pseudo-ax) data for AFWI, rather than the original pressure data. Because the amplitudes of PP reflections are implicitly weighted according to the reflection angle in pseudo-ax data, the near-offset PP reflections and multiples of the pseudo-ax data are much weaker than those of the pressure data. As a result, AFWI using pseudo-ax data focuses on reconstructing the longer-wavelength features of a given model in the early iterations, and then gradually reconstructs short-wavelength features as the inversion process continues. Using synthetic and real data examples for the Volve oilfield in the North Sea, we examined the effects and feasibility of this strategy. In the synthetic data example, the proposed strategy rapidly reduced far-offset data misfits related to long-wavelength feature updates and achieved smaller model misfits than the conventional strategy. The real data example showed that the velocity model reconstructed using the proposed strategy flattened some of the reflectors at the angle-domain common-image gathers (ADCIGs) better than the velocity model obtained using the conventional strategy. These findings demonstrate that our strategy converges closer to the real P-wave velocity model than the conventional strategy by building a hierarchical velocity model from long- to short-wavelength structures.

The availability of wide-azimuth data and the use of reverse time migration (RTM) have dramatically increased the capabilities of imaging complex subsalt geology. With these improvements, the current obstacle for creating accurate subsalt images now lies in the velocity model. One of the challenges is to generate common image gathers that take full advantage of the additional information provided by wide-azimuth data and the additional accuracy provided by RTM for velocity model updating. A solution is to generate 3D angle domain common image gathers from RTM, which are indexed by subsurface reflection angle and subsurface azimuth angle. We apply these 3D angle gathers to subsalt tomography with the result that there were improvements in velocity updating with a wide-azimuth data set in the Gulf of Mexico.

Reverse-time migration (RTM) using the crosscorrelation imaging condition requires that the forward-propagated source wavefield and the backward-propagated receiver wavefield be accessible within the imaging domain at the same time step. There are two categories of methods to balance the computer memory requirement and the computational complexity of RTM: checkpointing methods and source-wavefield reconstruction methods. We have developed a new source-wavefield reconstruction method to improve the balance between the computer memory requirement and the computational complexity of RTM. During the forward simulation of the source wavefield, we stored boundary wavefields only at one or two layers of spatial grid points and reconstructed the back-propagated source wavefield at the same time step as that of the back-propagated receiver wavefield, using a high-order wave-equation extrapolation scheme. One conventional RTM method uses boundary wavefields stored at multiple layers of spatial grid points and a high-order finite-difference (FD) scheme to reconstruct the back-propagated source wavefield. For an FD scheme with the eighth or sixteenth order of accuracy in space, our new method used only 37.5% of the computer memory required by this conventional method to store the boundary wavefields. This reduction of computer memory usage is significant because storing the boundary wavefields consumes most of the computer memory required for 3D migration using reconstructed source wavefields. Moreover, our method maintained the spatial order of accuracy of the FD scheme for the entire imaging domain, whereas some conventional methods reduce the spatial-order accuracy of the FD scheme near the boundaries to back-propagate the source wavefield to decrease the computer memory requirement. We validated our method using synthetic seismic data. Our method produced 2D and 3D migration images of complex subsurface structures as accurate as those yielded using an RTM method without reducing the spatial order of accuracy near the boundaries.

Using compact representations of Green’s functions we derive a common framework for reverse time migration (RTM) and Kirchhoff migration. These compact Green’s functions (CGFs) are 3D volumes containing traveltimes and amplitudes for the N most representative events in the upcoming/downgoing decomposed 4D wavefields originating from a point source. Within this framework, we implement an RTM algorithm using a multivalued excitation time/amplitude imaging condition. This new approach produces four complementary imaging volumes (different combinations of source and receiver decomposed wavefields) and angle/azimuth gathers with computational effort less than 15% greater than that of plain (one image and no gathers) RTM algorithms. The advantages of separating the image volume into four complementary volumes are well established in the literature (low-frequency noise separation and turning wave imaging); however, its use has been limited by the computational cost. Despite using two source propagations to decompose the source wavefield, we reduce the computations to less than 20% of a single source propagation by performing finite-difference propagation with half the frequency limit used in the receiver wavefield propagation. The combination of CGF and an excitation time/amplitude imaging condition allows receiver wavefield decomposition with only one wavefield propagation. Our RTM algorithm constructs angle/azimuth gathers using a postmigration computation of the source and receiver wavefield’s propagation directions. To compute the propagation directions after migration, we use a new concept: the cumulative wavefield volumes, which are 3D, imaging-condition-guided compressions, of the 4D source and receiver wavefields. We also use CGF to implement a Kirchhoff migration algorithm that produces four complementary image volumes with RTM-like quality. Furthermore, we present synthetic and field data examples to clarify the new concepts and illustrate the results obtained using these methods.

Reverse Time Migration (RTM) 3D angle gathers can be an effective tool for the inversion of dirty salt velocities. Compared to the reflectivity‐based inversion approach (Dirty Salt Velocity Inversion, or DSVI), the differences are twofold. First, DSVI detects dirty salt and performs velocity inversion using only reflectivity. DSVI's reliance on reflectivity yields inaccurate dirty salt velocities when faced with density variations among intra‐salt inclusions. Conversely, tomographic inversion based on 3D angle gathers uses residual curvature analysis of intra‐salt reflectors and the regional base of salt seismic events, making it more reliable. Second, DSVI assumes that sediment inclusions have slower velocities than salt, whereas the angle gather domain tomographic inversion can invert both slow and fast velocities. Using synthetic and real data examples, we showcase this ability and demonstrate that angle gather domain tomographic inversion is a superior tool for velocity update when both slow and fast intra‐salt inclusions are encountered.

Anisotropic models are recognized as a more realistic representation of the subsurface where complex geological environment exists. These models are widely needed by all kinds of migration and interpretation schemes. However, anisotropic model building is still a challenging problem in the industry. In this paper, we propose an approach to building anisotropic models from surface seismic data based on the theory of WaveEquation Migration Velocity Analysis (WEMVA). Because of the ambiguity between depth and δ , we parametrize our model space using only NMO velocity (Vnmo) and the anellipticity parameter η . We present a synthetic data example of anisotropic WEMVA applied to the shallow part of the Hess anisotropic synthetic VTI model. The results show that anisotropic WEMVA is effective in resolving the anisotropic perturbation; however, a unique solution to the inversion requires additional constraining information.

Reverse-time migration (RTM) in 2.5D offers an alternative to improve resolution and amplitude when imaging 2D seismic data. Wave propagation in 2.5D assumes translational invariance of the velocity model. Under this assumption, we implement a finite-difference (FD) modeling algorithm in the mixed time-space/wavenumber domain to simulate the velocity and pressure fields for acoustic wave propagation and apply it in RTM. The 2.5D FD algorithm is truly parallel, allowing an efficient implementation in clusters. Storage and computing time requirements are strongly reduced compared to a full 3D FD simulation of the wave propagation. This feature makes 2.5D RTM much more efficient than 3D RTM, while achieving improved modeling of 3D geometrical spreading and phase properties of the seismic waveform in comparison to 2D RTM. Together with an imaging condition that compensates for uneven illumination and/or the obliquity factor, this allows recover of amplitudes proportional to the earth’s reflectivity. Numerical experiments using synthetic data demonstrate the better resolution and improved amplitude recovery of 2.5D RTM relative to 2D RTM.

Ground-penetrating radar (GPR) profiling is the primary tool to provide detail information of the internal structure and characteristics inside a sand dune in the desert area. However, with the severe elevation change in a short horizontal distance and on the rugged and complex surface topography of the sand dunes, getting clear imaging of the internal structure of sand dunes from the GPR profiling is still a big challenge. The classic imaging technique such as the Kirchhoff migration has been applied to process GPR data on sand dunes, with limited success. The reverse-time migration (RTM) technique is the most advanced imaging technique that can handles GPR data acquired on rugged surface with severe topographic relief to generate subsurface structural images with high fidelity and has been tried to process GPR data on sand dunes. The results are encouraging, and the imaging quality is significantly improved. The finite-difference time-domain (FDTD) method is the major numerical tool for forward and backward continuations of the wave field during the RTM process. There are two aspects for using FDTD in RTM of GPR data on sand dunes still need improvement: the numerical scattering caused by the staircase approximation of the ground surface by using gridding in the Cartesian coordinate, and the negligence of the possible anisotropy of the electromagnetic material properties due to the calcareous cementation bedding inside a sand dune. In this paper, we develop the RTM algorithm based on the staggered grid FDTD that handles the rugged topographic surface by using the curvilinear coordinate, and the possible anisotropic radar wave velocity of the sand dune media. We first demonstrate the equivalency of the nonuniform, isotropic medium and the uniform, anisotropic medium for justifying using the uniform, anisotropic velocity in the RTM by synthetic modeling. Next, we validate our approach of using the synthetic data with the comparison of using the Cartesian coordinate and the curvilinear coordinate in an isotropic medium. The results indicate that the RTM algorithm using the curvilinear coordinate can efficiently eliminate the adverse effect of the staircase approximated boundary of the topography surface. Finally, we processed the real GPR data collected on a sand dune in the Badain Jaran desert by using the curvilinear coordinate and the uniform, anisotropic velocity in FDTD forward and backward wave field continuation. Comparison of the results indicates that the RTM imaging using the boundary-conforming curvilinear coordinate and anisotropic velocity gains more coherent and higher resolution images for the calcareous cementation layers and the water table.

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 L1 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.

To improve the computational efficiency of reverse-time migration (RTM) for vertically transverse isotropic (VTI) media, various acoustic approximations of the elastic wave equations have been presented. Among these, the pseudo-acoustic wave equation, which combines differential and scalar operators, has the advantage that it does not produce shear wave artefacts. In this study, we investigate the feasibility of pseudo-acoustic anisotropic RTM (PA-RTM) for the analysis of synthetic and observed ocean-bottom cable (OBC) datasets of the Volve oil field in the North Sea. To analyse the influence of anisotropic parameters on RTM images and the sensitivity of data components to seismic anisotropy, we perform PA-RTM using synthetic data by incorporating various background models, as well as pressure wavefields and vertical particle acceleration. The synthetic experiments demonstrate that the anisotropic parameter ε plays an important role, whereas δ is negligible in PA-RTM for VTI media, and that vertical particle acceleration is less affected by seismic anisotropy than the pressure wavefields. Our experiments using observed data show that reflectors are better imaged by PA-RTM than by isotropic-RTM, particularly near the reservoir below the strongly anisotropic region, which is supported by angle-domain common image gathers. These results indicate that PA-RTM using only the vertical component is a suitable option for VTI media when insufficient seismic anisotropy data are available.