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.

Least-squares reverse time migration in visco-acoustic media based on symplectic stereo-modeling method

The authors proposed a symplectic stereo-modeling method(SSM)in the Birkhoffian dynam-ics and apply it to the visco-acoustic least-squares reverse time migration(LSRTM).The SSM adopts ste-reo-modeling operator in space and symplectic Runge-Kutta scheme in time,resulting in great ability in suppressing numerical dispersion and long-time computing.These advantages are further confirmed by numerical dispersion analysis,long-time computation test and computational efficiency comparison.After these theoretical analyses and experiments,acoustic and visco-acoustic LSRTM are tested and compared between SSM method and the conventional symplectic method(CSM)using the fault and marmousi models.Meanwhile,dynamic source encoding and exponential decay moving average gradients method are adopted to reduce the computation cost and improve the convergence rate.The imaging results show that LSRTM based on visco-acoustic wave equations effectively takes into account the influence of viscosity can therefore compensate for the amplitude attenuation.Besides,SSM method not only has high numerical accuracy and computational efficiency,but also performs effectively in LSRTM.

Huber inversion-based reverse-time migration with de-primary imaging condition and curvelet-domain sparse constraint

Least-squares reverse-time migration(LSRTM) formulates reverse-time migration(RTM) in the leastsquares inversion framework to obtain the optimal reflectivity image. It can generate images with more accurate amplitudes, higher resolution, and fewer artifacts than RTM. However, three problems still exist:(1) inversion can be dominated by strong events in the residual;(2) low-wavenumber artifacts in the gradient affect convergence speed and imaging results;(3) high-wavenumber noise is also amplified as iteration increases. To solve these three problems, we have improved LSRTM: firstly, we use Hubernorm as the objective function to emphasize the weak reflectors during the inversion;secondly, we adapt the de-primary imaging condition to remove the low-wavenumber artifacts above strong reflectors as well as the false high-wavenumber reflectors in the gradient;thirdly, we apply the L1-norm sparse constraint in the curvelet-domain as the regularization term to suppress the high-wavenumber migration noise. As the new inversion objective function contains the non-smooth L1-norm, we use a modified iterative soft thresholding(IST) method to update along the Polak-Ribie re conjugate-gradient direction by using a preconditioned non-linear conjugate-gradient(PNCG) method. The numerical examples,especially the Sigsbee2 A model, demonstrate that the Huber inversion-based RTM can generate highquality images by mitigating migration artifacts and improving the contribution of weak reflection events.

Regularized least-squares migration of simultaneous-source seismic data with adaptive singular spectrum analysis

Simultaneous-source acquisition has been recog- nized as an economic and efficient acquisition method, but the direct imaging of the simultaneous-source data produces migration artifacts because of the interference of adjacent sources. To overcome this problem, we propose the regularized least-squares reverse time migration method （RLSRTM） using the singular spectrum analysis technique that imposes sparseness constraints on the inverted model. Additionally, the difference spectrum theory of singular values is presented so that RLSRTM can be implemented adaptively to eliminate the migration artifacts. With numerical tests on a fiat layer model and a Marmousi model, we validate the superior imaging quality, efficiency and convergence of RLSRTM compared with LSRTM when dealing with simultaneoussource data, incomplete data and noisy data.

Stretching correction for amplitude-preserving vector wavefield reverse-time migration

The migration of multi-wave seismic data is aimed at obtaining the P- and S-wave imaging results of the amplitude preserving. But the P- and S-wave stretching effect produced by the reverse time migration of the elastic wave equation will not only reduce the vertical resolution of the migration results and the amplitude preserving of the large reflection angle. In this paper, the reverse time migration technique of amplitude preserving vector wave-field separating is used. Based on the analysis of the stretch mechanism and the influencing factors of stretch magnitude, the paper gave the stretch correcting factors. Then, realize the stretch correction method at the time that after the reverse extrapolation and before the imaging by solving the problem which is how to calculate the P-wave and Ps-wave propagation directions of imaging points at different times. The stretch correction method can improve the vertical resolution and amplitude fidelity of the imaging results and provide high fidelity input data for seismic data interpretation and inversion.

Elastic-Wave Reverse Time Migration Random Boundary-Noise Suppression Based on CycleGAN

In elastic-wave reverse-time migration(ERTM),the reverse-time reconstruction of source wavefield takes advantage of the computing power of GPU,avoids its disadvantages in disk-access efficiency and reading and writing of temporary files,and realizes the synchronous extrapolation of source and receiver wavefields.Among the existing source wavefield reverse-time reconstruction algorithms,the random boundary algorithm has been widely used in three-dimensional(3D)ERTM because it requires the least storage of temporary files and low-frequency disk access during reverse-time migration.However,the existing random boundary algorithm cannot completely destroy the coherence of the artificial boundary reflected wavefield.This random boundary reflected wavefield with a strong coherence would be enhanced in the cross-correlation image processing of reverse-time migration,resulting in noise and fictitious image in the migration results,which will reduce the signal-to-noise ratio and resolution of the migration section near the boundary.To overcome the above issues,we present an ERTM random boundary-noise suppression method based on generative adversarial networks.First,we use the Resnet network to construct the generator of CycleGAN,and the discriminator is constructed by using the PatchGAN network.Then,we use the gradient descent methods to train the network.We fix some parameters,update the other parameters,and iterate,alternate,and continuously optimize the generator and discriminator to achieve the Nash equilibrium state and obtain the best network structure.Finally,we apply this network to the process of reverse-time migration.The snapshot of noisy wavefield is regarded as a 2D matrix data picture,which is used for training,testing,noise suppression,and imaging.This method can identify the reflected signal in the wavefield,suppress the noise generated by the random boundary,and achieve denoising.Numerical examples show that the proposed method can significantly improve the imaging quality of ERTM.

Elastic reverse time migration based on vector wavefield decomposition

Prestack elastic reverse time migration( RTM) requires multicomponent seismic data. But for multicomponent elastic Kirchhoff migration,there is a limitation that ray theory no longer applies if thegeology becomes complicated. In this paper,the authors have created a new 2D migration context for isotropic,elastic RTM,which included decomposition of the elastic source and receiver wavefields into P and S wave vectors by decoupled elastodynamic extrapolation,which retained the same stress and particle velocity components as the input data. Then we appliedsource-normalized crosscorrelation imaging condition in elastic reverse time migration to compensate the energy of deep strata. We found that the resulting images were nearly identical to the velocity model,and the resolution has been improved. Our method is a wavefielddecomposition based on vector,and we can alsoavoid the problem of polarity reversal of converted shear wave imaging. It proved the applicability of the method proposed in our paper.

Reverse-Time Prestack Depth Migration of GPR Data from Topography for Amplitude Reconstruction in Complex Environments

With increased computational power, reverse-time prestack depth migration（RT-PSDM） has become a preferred imaging tool in seismic exploration, yet its use has remained relatively limited in ground-penetrating radar（GPR） applications. Complex topography alters the wavefield kinematics making for a challenging imaging problem. Model simulations show that topographic variation can substantially distort reflection amplitudes due to irregular wavefield spreading, attenuation anomalies due to irregular path lengths, and focusing and defocusing effects at the surface. The effects are magnified when the topographic variations are on the same order as the depth of investigation––a situation that is often encountered in GPR investigations. Here, I use a full wave-equation RT-PSDM algorithm to image GPR data in the presence of large topographic variability relative to the depth of investigation. The source and receiver wavefields are propagated directly from the topographic surface and this approach inherently corrects for irregular kinematics, spreading and attenuation. The results show that when GPR data are acquired in areas of extreme topography, RT-PSDM can accurately reconstruct reflector geometry as well as reflection amplitude.

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 en- coding 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 am- plitude 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 P- LSRTM is more robust than conventional RTM in the presence of migration velocity errors.

Research progress on seismic imaging technology

High-precision seismic imaging is the core task of seismic exploration,guaranteeing the accuracy of geophysical and geological interpretation.With the development of seismic exploration,the targets become more and more complex.Imaging on complex media such as subsalt,small-scale,steeply dipping and surface topography structures brings a great challenge to imaging techniques.Therefore,the seismic imaging methods range from stacking-to migration-to inversion-based imaging,and the imaging accuracy is becoming increasingly high.This review paper includes:summarizing the development of the seismic imaging;overviewing the principles of three typical imaging methods,including common reflection surface(CRS)stack,migration-based Gaussian-beam migration(GBM)and reverse-time migration(RTM),and inversion-based least-squares reverse-time migration(LSRTM);analyzing the imaging capability of GBM,RTM and LSRTM to the special structures on three typical models and a land data set;outlooking the future perspectives of imaging methods.The main challenge of seismic imaging is to produce high-precision images for low-quality data,extremely deep reservoirs,and dual-complex structures.

Local events-based fast RTM surface-offset gathers via dip-guided interpolation

Reverse Time Migration(RTM)Surface Ofset Gathers(SOGs)are demonstrated to deliver more superior residual dip information than ray-based approaches.It appears more powerful in complex geological settings,such as salt areas.Still,the computational cost of constructing RTM SOGs is a big challenge in applying it to 3D feld data.To tackle this challenge,we propose a novel method using dips of local events as a guide for RTM gather interpolation.The residual-dip information of the SOGs is created by connecting local events from depth-domain to time-domain via ray tracing.The proposed method is validated by a synthetic experiment and a feld example.It mitigates the computational cost by an order of magnitude while producing comparable results as fully computed RTM SOGs.

Least-Squares Seismic Inversion with Stochastic Conjugate Gradient Method

With the development of computational power, there has been an increased focus on data-fitting related seismic inversion techniques for high fidelity seismic velocity model and image, such as full-waveform inversion and least squares migration. However, though more advanced than conventional methods, these data fitting methods can be very expensive in terms of computational cost. Recently, various techniques to optimize these data-fitting seismic inversion problems have been implemented to cater for the industrial need for much improved efficiency. In this study, we propose a general stochastic conjugate gradient method for these data-fitting related inverse problems. We first prescribe the basic theory of our method and then give synthetic examples. Our numerical experiments illustrate the potential of this method for large-size seismic inversion application.

Modeling and RTM for arbitrary-order pure acoustic wave equation in VTI media using normalized pseudo-analytical method

The conventional pseudo-acoustic wave equations（PWEs） in vertical transversely isotropic（VTI）media may generate SV-wave artifacts and propagation instabilities when anisotropy parameters cannot satisfy the pseudo-acoustic assumption. One solution to these issues is to use pure acoustic anisotropic wave equations, which can produce stable and pure P-wave responses without any SVwave pollutions. The commonly used pure acoustic wave equations（PAWEs） in VTI media are mainly derived from the decoupled P-SV dispersion relation based on first-order Taylor-series expansion（TE）, thus they will suffer from accuracy loss in strongly anisotropic media. In this paper, we adopt arbitrary-order TE to expand the square root term in Alkhalifah＇s accurate acoustic VTI dispersion relation and solve the corresponding PAWE using the normalized pseudoanalytical method（NPAM） based on optimized pseudodifferential operator. Our analysis of phase velocity errors indicates that the accuracy of our new expression is perfectly acceptable for majority anisotropy parameters. The effectiveness of our proposed scheme also can be demonstrated by several numerical examples and reverse-time migration（RTM） result.