An improved reverse time migration for subsurface imaging over complex geological structures:A numerical study

In seismic exploration,it is a critical task to image and interpret different seismic signatures over complex geology due to strong lateral velocity contrast,steep reflectors,overburden strata and dipping flanks.To understand the behavior of these seismic signatures,nowadays Reverse Time Migration(RTM)technique is used extensively by the oil&gas industries.During the extrapolation phase of RTM,the source wavefield needs to be saved,which needs high storage memory and large computing time.These two are the main obstacles of RTM for production use.In order to overcome these disadvantages,in this study,a second-generation improved RTM technique is proposed.In this improved form,a shift operator is introduced at the time of imaging condition of RTM algorithm which is performed automatically both in space and time domain.This effort is made to produce a better-quality image by minimizing the computational time as well as numerical artefacts.The proposed method is applied over various benchmark models and validated by implementing over one field data set from the Jaisalmer Basin,India.From the analysis,it is observed that the method consumes a minimum of 45%less storage space and reduce the execution time by 20%,as compared to conventional RTM.The proposed RTM is found to work efficiently in comparison to the conventional RTM both in terms of imaging quality and minimization of numerical artefacts for all the benchmark models as well as field data.

Stable attenuation-compensated reverse time migration and its application to land seismic data

Intrinsic attenuation of the earth causes energy loss and phase distortion in seismic wave propagation.To obtain high-resolution imaging results,these negative effects must be considered during reverse time migration(RTM).We can easily implement attenuation-compensated RTM using the constant Q viscoacoustic wave equation with decoupled amplitude attenuation and phase dispersion terms.However,the nonphysical amplitude-compensation process will inevitably amplify the high-frequency noise in the wavefield in an exponential form,causing the numerical simulation to become unstable.This is due to the fact that the amplitude of the compensation grows exponentially with frequency.In order to achieve stable attenuation-compensated RTM,we modify the analytic expression of the attenuation compensation extrapolation operator and make it only compensate for amplitude loss within the effective frequency band.Based on this modified analytic formula,we then derive an explicit time-space domain attenuation compensation extrapolation operator.Finally,the implementation procedure of stable attenuation-compensated RTM is presented.In addition to being simple to implement,the newly proposed attenuation-compensated extrapolation operator is superior to the conventional low-pass filter in suppressing random noise,which will further improve the imaging resolution.We use two synthetic and one land seismic datasets to verify the stability and effectiveness of the proposed attenuationcompensated RTM in improving imaging resolution in viscous media.

Proper orthogonal decomposition based seismic source wavefield reconstruction for finite element reverse time migration

The large storage requirement is a critical issue in cross-correlation imaging-condition based reverse time migration(RTM),because it requires the operation of the source and receiver wavefields at the same time.The boundary value method(BVM),based on the finite difference method(FDM),can be used to reconstruct the source wavefield in the reverse time propagation in the same way as the receiver wavefield,which can reduce the storage burden of the RTM data.Considering that the FDM cannot well handle models with discontinuous material properties and rough interfaces,we develop a source wavefield reconstruction strategy based on the finite element method(FEM),using proper orthogonal decomposition(POD)to enhance computational efficiency.In this method,we divide the whole time period into several segments,and construct the POD basis functions to get a reduced order model(ROM)for the source wavefield reconstruction in each segment.We show the corresponding quantitative analysis of the storage requirement of the POD-FEM.Numerical tests on the homogeneous model show the effectiveness of the proposed method,while the layered model and part of the Marmousi model tests indicate that the POD-FEM can keep an excellent balance between computational efficiency and memory usage compared with the full-stored method(FSM)and the BVM,and can be effectively applied in imaging.

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.

Viscoacoustic prestack reverse time migration based onthe optimal time-space domain high-order finite-difference method

Prestack reverse time migration （RTM） is an accurate imaging method ofsubsurface media. The viscoacoustic prestack RTM is of practical significance because itconsiders the viscosity of the subsurface media. One of the steps of RTM is solving thewave equation and extrapolating the wave field forward and backward; therefore, solvingaccurately and efficiently the wave equation affects the imaging results and the efficiencyof RTM. In this study, we use the optimal time-space domain dispersion high-order finite-difference （FD） method to solve the viscoacoustic wave equation. Dispersion analysis andnumerical simulations show that the optimal time-space domain FD method is more accurateand suppresses the numerical dispersion. We use hybrid absorbing boundary conditions tohandle the boundary reflection. We also use source-normalized cross-correlation imagingconditions for migration and apply Laplace filtering to remove the low-frequency noise.Numerical modeling suggests that the viscoacoustic wave equation RTM has higher imagingresolution than the acoustic wave equation RTM when the viscosity of the subsurface isconsidered. In addition, for the wave field extrapolation, we use the adaptive variable-lengthFD operator to calculate the spatial derivatives and improve the computational efficiencywithout compromising the accuracy of the numerical solution.

Amplitude preserved VSP reverse time migration for angle-domain CIGs extraction

An improved method of generating angle-domain common-image gathers（ADCIGs） by VSP reverse time migration（RTM） is introduced in this paper.The formula which is used to compute the receiver wavefield for VSP RTM is modified by adding an amplitude correction term in order to conveniently output amplitude-preserved ADCIGs.Compared with the surface seismic data,VSP data contains much richer wavefields.However,the direct and downgoing waves can bring about serious imaging artifacts in ADCIGs,especially the direct wave.The feasibility and validity of this method is demonstrated by both numerical and real VSP data from western China.Thus,the ADCIGs from this method can provide reliable basic data for VSP migration velocity analysis,VSP AVO/AVA analysis,and inversion.

Conjugate gradient and cross-correlation based least-square reverse time migration and its application

Although conventional reverse time migration can be perfectly applied to structural imaging it lacks the capability of enabling detailed delineation of a lithological reservoir due to irregular illumination. To obtain reliable reflectivity of the subsurface it is necessary to solve the imaging problem using inversion. The least-square reverse time migration （LSRTM） （also known as linearized refleetivity inversion） aims to obtain relatively high-resolution amplitude preserving imaging by including the inverse of the Hessian matrix. In practice, the conjugate gradient algorithm is proven to be an efficient iterative method for enabling use of LSRTM. The velocity gradient can be derived from a cross-correlation between observed data and simulated data, making LSRTM independent of wavelet signature and thus more robust in practice. Tests on synthetic and marine data show that LSRTM has good potential for use in reservoir description and four-dimensional （4D） seismic images compared to traditional RTM and Fourier finite difference （FFD） migration. This paper investigates the first order approximation of LSRTM, which is also known as the linear Born approximation. However, for more complex geological structures a higher order approximation should be considered to improve imaging quality.

Variable-grid reverse-time migration of different seismic survey data

With an increasing demand for high-resolution imaging of complex subsurface structures, thin layers and hidden reservoirs, borehole and cross-well seismic migration methods have become important. However, large differences are observed in the frequency bandwidth between the surface, borehole, and cross-well surveys. Thus, variable-grid- based algorithms have been adapted to reverse-time migration. Further, we introduce Lanczos filtering to ensure the stability of wavefield calculations as well as to decrease the artificial reflections that are caused due to the variable grid size. Finally, we observe that the application of this method to surface survey, borehole, and cross-well seismic data suggests improvements in the delineation of minor fractures and steeply dipping faults.

Passive multiple reverse time migration imaging based on wave decomposition and normalized imaging conditions

With the development of seismic exploration,passive-source seismic data has attracted increasing attention.Ambient noise passive seismic sources exists widely in nature and industrial production.Passive seismic data is important in logging while drilling(LWD),large-scale structural exploration,etc.In this paper,we proposed a passive multiple reverse time migration imaging(PMRTMI)method based on wavefield decomposition and normalized imaging conditions method.This method differs from seismic interferometry in that it can use raw passive seismic data directly in RTM imaging without reconstruction of virtual active gather,and we use the wavefield decomposition method to eliminate the low frequency noise in RTM.Further,the energy normalized imaging condition is used in full wavefield decomposition,which can not only enhance the image quality of both edge and deep information but also overcome the wrong energy problem caused by uneven distribution of passive sources;furthermore,this method exhibits high efficiency.Finally,numerical examples with the Marmousi model show the effectiveness of the method.

Multiparameter least-squares reverse time migration for acoustic–elastic coupling media based on ocean bottom cable data

In marine seismic exploration,ocean bottom cable technology can record multicomponent seismic data for multiparameter inversion and imaging.This study proposes an elastic multiparameter lease-squares reverse time migration based on the ocean bottom cable technology.Herein,the wavefield continuation operators are mixed equations:the acoustic wave equations are used to calculate seismic wave propagation in the seawater medium,whereas in the solid media below the seabed,the wavefields are obtained by P-and S-wave separated vector elastic wave equations.At the seabed interface,acoustic–elastic coupling control equations are used to combine the two types of equations.P-and S-wave separated elastic migration operators,demigration operators,and gradient equations are derived to realize the elastic least-squares reverse time migration based on the P-and S-wave mode separation.The model tests verify that the proposed method can obtain high-quality images in both the P-and S-velocity components.In comparison with the traditional elastic least-squares reverse time migration method,the proposed method can readily suppress imaging crosstalk noise from multiparameter coupling.

Pre-stack elastic reverse time migration in tunnels based on cylindrical coordinates

Seismic forward-prospecting in tunnels is an important step to ensure excavation safety. Nowadays, most advanced imaging techniques in seismic exploration involve calculating the solution of elastic wave equation in a certain coordinate system. However, considering the cylindrical geometry of common tunnel body, Cartesian coordinate system seemingly has limited applicability in tunnel seismic forwardprospecting. To accurately simulate the seismic signal received in tunnels, previous imaging method using decoupled non-conversion elastic wave equation is extended from Cartesian coordinates to cylindrical coordinates. The proposed method preserves the general finite-difference time-domain(FDTD)scheme in Cartesian coordinates, except for a novel wavefield calculation strategy addressing the singularity issue inherited at the cylindrical axis. Moreover, the procedure of cylindrical elastic reverse time migration(CERTM) in tunnels is introduced based on the decoupled non-conversion elastic wavefield. Its imaging effect is further validated via numerical experiments on typical tunnel models. As indicated in the synthetic examples, both the PP-and SS-images could clearly show the geological structure in front of the tunnel face without obvious crosstalk artifacts. Migration imaging using PP-waves can present satisfactory results with higher resolution information supplemented by the SS-images. The potential of applying the proposed method in real-world cases is demonstrated in a water diversion tunnel. In the end, we share our insights regarding the singularity treatment and further improvement of the proposed method.

Reverse time migration based on normalized wavefield decomposition imaging condition

With the increasing complexity of prospecting objectives,reverse time migration( RTM) has attracted more and more attention due to its outstanding imaging quality. RTM is based on two-way wave equation,so it can avoid the limits of angle in traditional one-way wave equation migration,image reverse branch,prism waves and multi-reflected wave precisely and obtain accurate dynamic information. However,the huge demands for storage and computation as well as low frequency noises restrict its wide application. The normalized cross-correlation imaging conditions based on wave field decomposition are derived from traditional cross-correlation imaging condition,and it can eliminate the low-frequency noises effectively and improve the imaging resolution. The practical procedure includes separating source and receiver wave field into one-way components respectively,and conducting cross-correlation imaging condition to the post-separated wave field. In this way,the resolution and precision of the imaging result will be promoted greatly.

Least-squares reverse time migration method using the factorization of the Hessian matrix

Least-squares reverse time migration(LSRTM)can eliminate imaging artifacts in an iterative way based on the concept of inversion,and it can restore imaging amplitude step by step.LSRTM can provide a high-resolution migration section and can be applied to irregular and poor-quality seismic data and achieve good results.Steeply dipping refl ectors and complex faults are imaged by using wavefi eld extrapolation based on a two-way wave equation.However,the high computational cost limits the method’s application in practice.A fast approach to realize LSRTM in the imaging domain is provided in this paper to reduce the computational cost signifi cantly and enhance its computational effi ciency.The method uses the Kronecker decomposition algorithm to estimate the Hessian matrix.A low-rank matrix can be used to calculate the Kronecker factor,which involves the calculation of Green’s function at the source and receiver point.The approach also avoids the direct construction of the whole Hessian matrix.Factorization-based LSRTM calculates the production of low-rank matrices instead of repeatedly calculating migration and demigration.Unlike traditional LSRTM,factorization-based LSRTM can reduce calculation costs considerably while maintaining comparable imaging quality.While having the same imaging eff ect,factorization-based LSRTM consumes half the running time of conventional LSRTM.In this regard,the application of factorization-based LSRTM has a promising advantage in reducing the computational cost.Ambient noise caused by this method can be removed by applying a commonly used fi ltering method without signifi cantly degrading the imaging quality.

Steeply dipping structural target-oriented viscoacoustic least-squares reverse time migration and its application

Steeply dipping structural imaging is a significant challenge because surface geophones cannot obtain seismic primary reflection wave information from steeply dipping structures.Prismatic waves with a significant amount of steeply dipping information can be used to improve the imaging eff ect on steeply dipping structures.Subsurface attenuation leads to amplitude loss and phase distortion of seismic waves,and ignoring this attenuation during imaging can cause blurring of migration amplitudes.In this study,we proposed a steeply dipping structural target-oriented viscoacoustic least-squares reverse time migration(LSRTM)method with prismatic and primary waves as an objective function based on the viscous wave equation,while deriving Q-compensated wavefield propagation and joint operators of prismatic and primary waves and the Q-compensated demigration operator.Numerical examples on synthetic and field data verified the advantages of the proposed viscoacoustic LSRTM method of joint primary and prismatic waves over conventional viscoacoustic LSRTM and non-compensated LSRTM when using attenuating observed data.

Attenuation-compensated reverse time migration of GPR data constrained by resistivity

The high-frequency electromagnetic waves of ground-penetrating radar(GPR)attenuate severely when propagated in an underground attenuating medium owing to the influence of resistivity,which remarkably decreases the resolution of reverse time migration(RTM).As an effective high-resolution imaging method,attenuation-compensated RTM(ACRTM)can eff ectively compensate for the energy loss caused by the attenuation related to media absorption under the influence of resistivity.Therefore,constructing an accurate resistivity-media model to compensate for the attenuation of electromagnetic wave energy is crucial for realizing the ACRTM imaging of GPR data.This study proposes a resistivity-constrained ACRTM imaging method for the imaging of GPR data by adding high-density resistivity detection along the GPR survey line and combining it with its resistivity inversion profile.The proposed method uses the inversion result of apparent resistivity data as the GPR RTM-resistivity model for imposing resistivity constraints.Moreover,the hybrid method involving image minimum entropy and RTM is used to estimate the medium velocity at the diff raction position,and combined with the distribution characteristics of the reflection in the GPR profile,a highly accurate velocity model is built to improve the imaging resolution of the ACRTM.The accuracy and eff ectiveness of the proposed method are verified using the ACRTM test of the GPR simulated data of a typical attenuating media model.On this basis,the GPR and apparent resistivity data were observed on a field survey line,and use the GPR resistivity-constrained ACRTM method to image the observed data.A comparison of the proposed method with the conventional ACRTM method shows that the proposed method has better imaging depth,stronger energy,and higher resolution,and the obtained results are more conducive for subsequent data analysis and interpretation.

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

The reverse time migration(RTM)of ground penetrating radar(GPR)is usually implemented in its two-dimensional(2D)form,due to huge computational cost.However,2D RTM algorithm is difficult to focus the scattering signal and produce a high precision subsurface image when the object is buried in a complicated subsurface environment.To better handle the multi-off set GPR data,we propose a three-dimensional(3D)prestack RTM algorithm.The high-order fi nite diff erence time domian(FDTD)method,with the accuracy of eighth-order in space and second-order in time,is applied to simulate the forward and backward extrapolation electromagnetic fi elds.In addition,we use the normalized correlation imaging condition to obtain pre-stack RTM result and the Laplace fi lter to suppress the low frequency noise generated during the correlation process.The numerical test of 3D simulated GPR data demonstrated that 3D RTM image shows excellent coincidence with the true model.Compared with 2D RTM image,the 3D RTM image can more clearly and accurately refl ect the 3D spatial distribution of the target,and the resolution of the imaging results is far better.Furthermore,the application of observed GPR data further validates the eff ectiveness of the proposed 3D GPR RTM algorithm,and its fi nal image can more reliably guide the subsequent interpretation.

An imaging condition for reverse time migration based on wavefield decomposition

Reverse Time Migration(RTM) is a high precision imaging method of seismic wavefield at present,but low-frequency noises severely affect its imaging results.Thus one of most important aspect of RTM is to select the proper noise suppression method.The wavefield characteristics of the Poynting vector are analyzed and the upgoing,downgoing,leftgoing and rightgoing waves are decomposed using the Poynting vector of the acoustic wave equation.The normalized wavefield decomposition cross-correlation imaging condition is used to suppress low-frequency noises in RTM and improve the imaging precision.Numerical experiments using the Mamousi velocity model are performed and the results demonstrate that the upgoing,downgoing,leftgoing and rightgoing waves are well decomposed using the Poynting vector.Compared with the normalized cross-correlation imaging and Laplacian filtering method,the results indicate that the low-frequency noises are well suppressed by using the normalized wavefield decomposition cross-correlation imaging condition.

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.

Combined migration velocity model-building and its application in tunnel seismic prediction

We propose a combined migration velocity analysis and imaging method based on Kirchhoff integral migration and reverse time migration,using the residual curvature analysis and layer stripping strategy to build the velocity model.This method improves the image resolution of Kirchhoff integral migration and reduces the computations of the reverse time migration.It combines the advantages of efficiency and accuracy of the two migration methods.Its application in tunnel seismic prediction shows good results.Numerical experiments show that the imaging results of reverse time migration are better than the imaging results of Kirchhoff integral migration in many aspects of tunnel prediction.Field data show that this method has efficient computations and can establish a reasonable velocity model and a high quality imaging section.Combination with geological information can make an accurate prediction of the front of the tunnel geological structure.

三维各向异性TI介质中的P/S波快速解耦技术及在弹性波逆时偏移中的应用

随着多分量采集技术的发展,弹性波逆时偏移技术在三维各向异性介质复杂地质构造成像中得到了广泛的应用.然而耦合的P波场和S波场,会在传播过程中产生串扰噪声,降低弹性波逆时偏移的成像精度.为了解决这一问题,本研究针对具有倾斜各向异性对称轴的三维横向各向同性(Transverse Isotropy,TI)介质,提出了一种矢量弹性波场快速解耦方法,可以有效提高偏移剖面的成像质量.该方法首先通过坐标转换,将观测系统坐标系的垂直轴旋转到TI介质的对称轴方向,在新坐标系下,根据具有垂直对称轴的三维横向各向同性(Vertical Transverse Isotropy,VTI)介质中的分解算子,推导出三维TI介质解耦算子表达式.接着引入一种在空间域快速计算分解波场的方法,来实现空间域矢量P波场和S波场分离,极大地提高了计算效率.最后,通过点积成像条件,将提出的P/S波分解方法引入到三维TI介质弹性波逆时偏移中,得到高精度的PP和PS成像.与以往的波场分解方法相比,本文方法具有数值稳定和计算效率高的特点.数值算例表明,应用上述三维TI分解算子得到的偏移剖面有效压制了噪声,提高了成像质量.