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.

Migration images guided high-resolution velocity modeling based on fully convolutional neural network

Current data-driven deep learning(DL)methods typically reconstruct subsurface velocity models directly from pre-stack seismic records.However,these purely data-driven methods are often less robust and produce results that are less physically interpretative.Here,the authors propose a new method that uses migration images as input,combined with convolutional neural networks to construct high-resolution velocity models.Compared to directly using pre-stack seismic records as input,the nonlinearity between migration images and velocity models is significantly reduced.Additionally,the advantage of using migration images lies in its ability to more comprehensively capture the reflective properties of the subsurface medium,including amplitude and phase information,thereby to provide richer physical information in guiding the reconstruction of the velocity model.This approach not only improves the accuracy and resolution of the reconstructed velocity models,but also enhances the physical interpretability and robustness.Numerical experiments on synthetic data show that the proposed method has superior reconstruction performance and strong generalization capability when dealing with complex geological structures,and shows great potential in providing efficient solutions for the task of reconstructing high-wavenumber components.

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.

High-resolution seismicity imaging and early aftershock migration of the 2023 Kahramanmara?(SE Türkiye)M_W7.9&7.8 earthquake doublet

We build a high-resolution early aftershock catalog for the 2023 SE Türkiye seismic sequence with PALM,a seamless workflow that sequentially performs phase picking,association,location,and matched filter for continuous data.The catalog contains 29,519 well-located events in the two mainshocks rupture region during 2023-02-01–2023-02-28,which significantly improves the detection completeness and relocation precision compared to the public routine catalog.Employing the new PALM catalog,we analyze the structure of the seismogenic fault system.We find that the Eastern Anatolian Fault(EAF)that generated the first M_(W)7.9 mainshock is overall near-vertical,whereas complexities are revealed in a small-scale,such as subparallel subfaults,unmapped branches,and stepovers.The seismicity on EAF is shallow(<15 km)and concentrated in depth distribution,indicating a clear lock-creep transition.In contrast,the SürgüFault(SF)that is responsible for the second M_(W)7.8 mainshock is shovel-shaped for the nucleation segment and has overall low dip angles(~40°–80°).Aftershocks on the SF distribute in a broad range of depth,extending down to~35 km.We also analyze the temporal behavior of seismicity,discovering no immediate foreshocks within~5 days preceding the first mainshock,and no seismic activity on the SF before the second mainshock.

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.

Reverse-Time Migration from Rugged Topography to Image Ground-Penetrating Radar Data in Complex Environments

In ground-penetrating radar （GPR） imaging, it is common for the depth of investigation to be on the same order as the variability in surface topography, In such cases, migration fails when it is carried out from a datum after the application of elevation statics, We introduce a reverse-time migration （RTM） algorithm based on the second-order decoupled form of Maxwell＇s equations, which requires computation of only the electric field, The wavefield extrapolation is computed directly from the acquisition surface without the need for datuming, In a synthetic case study, the algorithm significantly improves image accuracy over a processing sequence in which migration is performed after elevation statics, In addition, we acquired a field dataset at the Coral Pink Sand Dunes （CPSD） in Utah, USA, The data were acquired over rugged topography and have the complex internal stratigraphy of multiply eroded, modern, and ancient eolian deposits, The RTM algorithm significantly improves radar depth images in this challenging environment,

Post-stack reverse-time migration using a finite difference method based on triangular grids

Compared with other migration methods, reverse-time migration is based on a precise wave equation, not an approximation, and performs extrapolation in the depth domain rather than the time domain. It is highly accurate and not affected by strong subsurface structure complexity and horizontal velocity variations. The difference method based on triangular grids maintains the simplicity of the difference method and the precision of the finite element method. It can be used directly for forward modeling on models with complex top surfaces and migration without statics preprocessing. We apply a finite difference method based on triangular grids for post-stack reverse-time migration for the first time. Tests on model data verify that the combination of the two methods can achieve near-perfect results in application.

Poststack reverse-time migration using a non-reflecting recursive algorithm on surface relief

Presently the research based on the accurate seismic imaging methods for surface relief, complex structure, and complicated velocity distributions is of great significance. Reverse-time migration is considered to be one of highly accurate methods. In this paper, we propose a new non-reflecting recursive algorithm for reverse-time migration by introducing the wave impedance function into the acoustic wave equation and the algorithm for the surface relief case is derived from the coordinate transformation principle. Using the exploding reflector principle and the zero-time imaging condition of poststack reverse- time migration, poststack numerical simulation and reverse-time migration with complex conditions can be realized. The results of synthetic and real data calculations show that the method effectively suppresses unwanted internal reflections and also deals with the seismic imaging problems resulting from surface relief. So, we prove that this method has strong adaptability and practicality.

A study of perfectly matched layers for joint multicomponent reverse-time migration

Reverse-time migration in finite space requires effective boundary processing technology to eliminate the artificial truncation boundary effect in the migration result.On the basis of the elastic velocity-stress equations in vertical transversely isotropic media and the idea of the conventional split perfectly matched layer（PML）,the PML wave equations in reverse-time migration are derived in this paper and then the high order staggered grid discrete schemes are subsequently given.Aiming at the＂reflections＂from the boundary to the computational domain,as well as the effect of seismic event＇s abrupt changes at the two ends of the seismic array,the PML arrangement in reverse-time migration is given.The synthetic and real elastic,prestack,multi-component,reverse-time depth migration results demonstrate that this method has much better absorbing effects than other methods and the joint migration produces good imaging results.

Prestack reverse-time depth migration of arbitrarily wide-angle wave equations

Based on arbitrarily wide-angle wave equations,a reverse-time propagation scheme is developed by substituting the partial derivatives of depth and time with central differences. The partial derivative of horizontal direction is replaced with high order difference. The imaging condition is computed by solving the eikonal equations. On the basis of above techniques,a prestack reverse-time depth migration algorithm is developed. The processing exam-ples of synthetic data show that the method can remove unwanted internal reflections and decrease the migration noise. The method also has the advantage of fidelity and is applicable of dip angle reflector imaging.

Migration scheme for imaging offset VSP data within local phase space

The imaging of offset VSP data in local phase space can improve the image of the subsurface structure near the well.In this paper,we present a migration scheme for imaging VSP data in a local phase space,which uses the Gabor-Daubechies tight framebased extrapolator（G-D extrapolator） and its high-frequency asymptotic expansion to extrapolate wavefields and also delineates an improved correlation imaging condition in the local angle domain.The results for migrating synthetic and real VSP data demonstrate that the application of the high-frequency G-D extrapolator asymptotic expansion can effectively decrease computational complexity.The local angle domain correlation imaging condition can be used to weaken migration artifacts without increasing computation.

Comparison of Microwave Imaging Algorithms for Short-Range Scenarios

Three dimensional(3-D)imaging algorithms with irregular planar multiple-input-multiple-output(MIMO)arrays are discussed and compared with each other.Based on the same MIMO array,a modified back projection algorithm(MBPA)is accordingly proposed and four imaging algorithms are used for comparison,back-projection method(BP),back-projection one in time domain(BP-TD),modified back-projection one and fast Fourier transform(FFT)-based MIMO range migration algorithm(FFT-based MIMO RMA).All of the algorithms have been implemented in practical application scenarios by use of the proposed imaging system.Back to the practical applications,MIMO array-based imaging system with wide-bandwidth properties provides an efficient tool to detect objects hidden behind a wall.An MIMO imaging radar system,composed of a vector network analyzer(VNA),a set of switches,and an array of Vivaldi antennas,have been designed,fabricated,and tested.Then,these algorithms have been applied to measured data collected in different scenarios constituted by five metallic spheres in the absence and in the presence of a wall between the antennas and the targets in simulation and pliers in free space for experimental test.Finally,the focusing properties and time consumption of the above algorithms are compared.

Elastic reverse-time migration based on amplitude-preserving P- and S-wave separation

Imaging the PP- and PS-wave for the elastic vector wave reverse-time migration requires separating the P- and S-waves during the wave field extrapolation. The amplitude and phase of the P- and S-waves are distorted when divergence and curl operators are used to separate the P- and S-waves. We present a P- and S-wave amplitude-preserving separation algorithm for the elastic wavefield extrapolation. First, we add the P-wave pressure and P-wave vibration velocity equation to the conventional elastic wave equation to decompose the P- and S-wave vectors. Then, we synthesize the scalar P- and S-wave from the vector P- and S-wave to obtain the scalar P- and S-wave. The amplitude-preserved separated P- and S-waves are imaged based on the vector wave reverse-time migration （RTM）. This method ensures that the amplitude and phase of the separated P- and S-wave remain unchanged compared with the divergence and curl operators. In addition, after decomposition, the P-wave pressure and vibration velocity can be used to suppress the interlayer reflection noise and to correct the S-wave polarity. This improves the image quality of P- and S-wave in multicomponent seismic data and the true-amplitude elastic reverse time migration used in prestack inversion.

Reverse-time migration using multidirectional wavefield decomposition method

Reverse-time migration has attracted more and more attention owing to the advantages of high imaging accuracy, no dip restriction, and adaptation to complex velocity models. Cross-correlation imaging method is typically used in conventional reverse-time migration that produces images with strong low-frequency noise. Wavefield decomposition imaging can suppress such noise; however, some residual noise persists in the imaging results. We propose a 2D multidirectional wavefield decomposition method based on the traditional wavefield decomposition method. First, source wavefields and receiver wavefields are separated into eight subwavefields, respectively. Second, cross-correlation imaging is applied to selected subwavefields to produce subimages. Finally, the subimages are stacked to generate the final image. Numerical examples suggest that the proposed method can eliminate the low-frequency noise effectively and produce high-quality imaging profiles.

Least squares reverse-time migration in the pseudodepth domain and reservoir exploration

Least squares reverse-time migration （LSRTM） is an inversion method that removes artificial images and preserves the amplitude of reflectivity sections. LSRTM has been used in reservoir exploration and processing of 4D seismic data. LSRTM is, however, a computationally costly and memory-intensive method. In this study, LSRTM in the pseudodepth domain was combined with the conjugate gradient method to reduce the computational cost while maintaining precision. The velocity field in the depth domain was transformed to the velocity field in the pseudodepth domain; thus, the total number of vertical sampling points was reduced and oversampling was avoided. Synthetic and field data were used to validate the proposed method. LSRTM in the pseudodepth domain in conjunction with the conjugate gradient method shows potential in treating field data.

Extraction of amplitude-preserving angle gathers based on vector wavefield reverse-time migration

Angle-domain common-image gathers （ADCIGs） transformed from the shot- domain common-offset gathers are input to migration velocity analysis （MVA） and prestack inversion. ADCIGs are non-illusion prestack inversion gathers, and thus, accurate. We studied the extraction of elastic-wave ADCIGs based on amplitude-preserving elastic-wave reverse- time migration for calculating the incidence angle of P- and S-waves at each image point and for different source locations. The P- and S-waves share the same incident angle, namely the incident angle of the source P-waves. The angle of incidence of the source P-wavefield was the difference between the source P-wave propagation angle and the reflector dips. The propagation angle of the source P-waves was obtained from the polarization vector of the decomposed P-waves. The reflectors＇ normal direction angle was obtained using the complex wavenumber of the stacked reverse-time migration （RTM） images. The ADCIGs of P- and S-waves were obtained by rearranging the common-shot migration gathers based on the incident angle. We used a horizontally layered model, the graben medium model, and part of the Marmousi-II elastic model and field data to test the proposed algorithm. The results suggested that the proposed method can efficiently extract the P- and S-wave ADCIGs of the elastic-wave reverse-time migration, the P- and S-wave incident angle, and the angle-gather amplitude fidelity, and improve the MVA and prestack inversion.

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.

Application of GPR reverse time migration in tunnel lining cavity imaging

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

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.

An Efficient Algorithm Based on Spectrum Migration for High Frame Rate Ultrasound Imaging

The high frame rate(HFR)imaging technique requires only one emission event for imaging.Therefore,it can achieve ultrafast imaging with frame rates up to the kHz regime,which satisfies the frame rate requirements for imaging moving tissues in scientific research and clinics.Lu’s Fourier migration method is based on a non-diffraction beam to obtain HFR images and can improve computational speed and efficiency.However,in order to obtain high-quality images,Fourier migration needs to make full use of the spectrum of echo signals for imaging,which requires a large number of Fast Fourier Transform(FFT)points and increases the complexity of the hardware when the echo frequency is high.Here,an efficient algorithm using the spectrum migration technique based on the spectrum’s distribution characteristics is proposed to improve the imaging efficiency in HFR imaging.Since the actual echo signal spectrum is of limited bandwidth,low-frequency and high-frequency parts with low-energy have little contribution to the imaging spectrum.We transform the effective part that provides the main energy in the signal spectrum to the imaging spectrum while the ineffective spectrum components are not utilized for imaging.This can significantly reduce the number of Fourier transform points,improve Fourier imaging efficiency,and ensure the imaging quality.The proposed method is evaluated on simulated and experimental datasets.Results demonstrated that the proposed method could achieve equivalent image quality with a reduced point number for FFT compared to the complete spectrum migration.In this paper,it only requires a quarter of the FFT points used in the complete spectrum migration,which can improve the computational efficiency;thus,it is more suitable for real-time data processing.The proposed spectrum migration method has a specific significance for the study and clinical application of HFR imaging.