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.

Fast least-squares prestack time migration via accelerating the explicit calculation of Hessian matrix with dip-angle Fresnel zone

Amplitude versus offset analysis is a fundamental tool for determining the physical properties of reservoirs but generally hampered by the blurred common image gathers(CIGs).The blurring can be optimally corrected using the blockwise least-squares prestack time migration(BLS-PSTM),where common-offset migrated sections are divided into a series of blocks related to the explicit offsetdependent Hessian matrix and the following inverse filtering is iteratively applied to invert the corresponding reflectivity.However,calculating the Hessian matrix is slow.We present a fast BLS-PSTM via accelerating Hessian calculation with dip-angle Fresnel zone(DFZ).DFZ is closely related to optimal migration aperture,which significantly attenuates migration swings and reduces the computational cost of PSTM.Specifically,our fast BLS-PSTM is implemented as a two-stage process.First,we limit the aperture for any imaging point with an approximated the projected Fresnel zone before calculating the Hessian matrix.Then,we determine whether a seismic trace contributes to the imaging point via DFZ during calculating the Hessian matrix.Numerical tests on synthetic and field data validate the distinct speedup with higher-quality CIGs compared to BLS-PSTM.

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.

The application of amplitude-preserved processing and migration for carbonate reservoir prediction in the Tarim Basin,China

Conventional seismic exploration method based on post-stack data usually fails to identify the distribution of fractured and caved carbonate reservoirs in the Tarim Basin,so the rich pre-stack information should be applied to the prediction of carbonate reservoirs.Amplitude-preserved seismic data processing is the foundation.In this paper,according to the feature of desert seismic data （including weak reflection,fast attenuation of high frequency components,strong coherent noises,low S/N and resolution）,a set of amplitude-preserved processing techniques is applied and a reasonable processing flow is formed to obtain the high quality data.After implementing a set of pre-stack amplitude-preserved processing,we test and define the kernel parameters of amplitude-preserved Kirchhoff PSTM （pre-stack time migration） and subsequent gathers processing,in order to obtain the amplitude-preserved gathers used to the isotropic pre-stack inversion for the identification of caved reservoirs.The AVO characteristics of obtained gathers fit well with the synthetic gathers from logging data,and it proves that the processing above is amplitudepreserved.The azimuthal processing techniques,including azimuth division and binning enlargement,are implemented for amplitude-preserved azimuthal gathers with the uniform fold.They can be used in the anisotropic inversion to detect effective fractures.The processing techniques and flows are applied to the field seismic data,and are proved available for providing the amplitude-preserved gathers for carbonate reservoir prediction in the Tarim Basin.

Migration routes and strategies of Grey Plovers (Pluvialis squatarola) on the East Atlantic Flyway as revealed by satellite tracking

Background:While the general migration routes of most waders are known,details concerning connectivity between breeding grounds, stopover sites and wintering grounds are often lacking.Such information is critical from the conservation perspective and necessary for understanding the annual cycle.Studies are especially needed to identify key stopover sites in remote regions. Using satellite transmitters, we traced spring and autumn migration routes and connectivity of Grey Plovers on the East Atlantic Flyway.Our findings also revealed the timing,flight speed, and duration of migrations. Methods:We used ARGOS satellite transmitters to track migration routes of 11 Grey Plovers that were captured at the German Wadden Sea where they had stopped during migration.Birds were monitored for up to 3 years,2011-2014.Results:Monitoring signals indicated breeding grounds in the Taimyr and Yamal regions;important staging sites on the coasts of the southern Pechora Sea and the Kara Sea;and wintering areas that ranged from NW-Ireland to Guinea Bissau.The average distance traveled from wintering grounds to breeding grounds was 5534 km. Migration duration varied between 42 and 152 days;during this period birds spent about 95% of the time at staging sites.In spring most plovers crossed inland Eastern Europe, whereas in autumn most followed the coastline.Almost all of the birds departed during favorable wind conditions within just 4 days (27-30 May) on northward migration from the Wadden Sea.In spring birds migrated significantly faster between the Wadden Sea and the Arctic than on return migration in autumn (12 vs.37 days),with shorter stopovers during the northward passage.Conclusions:Our study shows that satellite tags can shed considerable light on migration strategies by revealing the use of different regions during the annual cycle and by providing detailed quantitative data on population connectivity and migration timing.

Reverse Time Migration with Elastodynamic Gaussian Beams

Elastic migration has been widely paid attention by employing the vector processing of mul- ticomponent seismic data. Ray based elastic Kirchhoff migration has such properties as high flexibility and high efficiency. However, it has failed to solve many problems caused by multipath. On the other hand, elastic reverse-time migration （RTM） based on the two-way wave equation is known to be capable of dealing with these problems, but it is extremely expensive when applied in 3D cases and velocity model building. Based on the elastic Kirchhoff-Helmholtz integral, we calculate deeoupled backward-continued wavefields by introducing elastic Green functions for P- and S-waves, which is expressed by a summation of elastodynamic Gaussian beams. The PP and polarity-corrected PS images are obtained by calculating the correlation between downward and deeoupled backward-continued vector wavefields, where polarity correction is performed by analyzing the relation between the polarization direction of converted PS waves and incident angle on the interface. To a large extent, our method combines the high efficiency of ray-based migration with the high accuracy of wave-equation based reverse-time migration. Application of this method to multicomponent synthetic datasets from the fault model and Marmousi 2 model demonstrates the validity, flexibility and accuracy of the new method.

Source wavefield reconstruction based on an implicit staggered-grid finite-difference operator for seismic imaging

Reverse time migration and full waveform inversion involve the crosscorrelation of two wavefields,propagated in the forward-and reverse-time directions,respectively.As a result,the forward-propagated wavefield needs to be stored,and then accessed to compute the correlation with the backward-propagated wavefield.Boundary-value methods reconstruct the source wavefield using saved boundary wavefields and can significantly reduce the storage requirements.However,the existing boundary-value methods are based on the explicit finite-difference(FD)approximations of the spatial derivatives.Implicit FD methods exhibit greater accuracy and thus allow for a smaller operator length.We develop two(an accuracy-preserving and a memory-efficient)wavefield reconstruction schemes based on an implicit staggered-grid FD(SFD)operator.The former uses boundary wavefields at M layers of grid points and the spatial derivatives of wavefields at one layer of grid points to reconstruct the source wavefield for a(2M+2)th-order implicit SFD operator.The latter applies boundary wavefields at N layers of grid points,a linear combination of wavefields at M–N layers of grid points,and the spatial derivatives of wavefields at one layer of grid points to reconstruct the source wavefield(0≤N<M).The required memory of accuracy-preserving and memory-efficient schemes is(M+1)/M and(N+2)/M times,respectively,that of the explicit reconstruction scheme.Numerical results reveal that the accuracy-preserving scheme can achieve accurate reconstruction at the cost of storage.The memory-efficient scheme with N=2 can obtain plausible reconstructed wavefields and images,and the storage amount is 4/(M+1)of the accuracy-preserving scheme.

Phaseless Imaging by Reverse Time Migration: Acoustic Waves

We propose a reliable direct imaging method based on the reverse time migration for finding extended obstacles with phaseless total field data.We prove that the imaging resolution of the method is essentially the same as the imaging results using the scattering data with full phase information when the measurement is far away from the obstacle.The imaginary part of the cross-correlation imaging functional always peaks on the boundary of the obstacle.Numerical experiments are included to illustrate the powerful imaging quality.

A Stable Q Compensated Reverse Time Migration Method Based on Excitation Amplitude Imaging Condition

The stability and efficiency,especially the stability,are generally concerned issues in Q compensated reverse time migration(Q-RTM).The instability occurs because of the exponentially boosted high frequency ambient noise during the forward or backward seismic wavefield propagation.The regularization and low-pass filtering methods are two effective strategies to control the instability of the wave propagation in Q-RTM.However,the regularization parameters are determined experimentally,and the wavefield cannot be recovered accurately.The low-pass filtering method cannot balance the selection of cutoff frequency for varying Q values,and may damage the effective signals,especially when the signal-to-noise ratio(SNR)of the seismic data is low,the Q-RTM will be a highly unstable process.In order to achieve the purpose of stability,the selection of cutoff frequency will be small enough,which can cause great damage to the effective high frequency signals.In this paper,we present a sta-ble Q-RTM algorithm based on the excitation amplitude imaging condition,which can compensate both the amplitude attenuation and phase dispersion.Unlike the existing Q-RTM algorithms enlarging the amplitude,the exponentially attenuated seismic wavefield will be used during both the forward and backward wavefield propagation of Q-RTM.Therefore,the new Q-RTM algorithm is relative stable,even for the low SNR seismic data.In order to show the accuracy and stability of our stable Q-RTM algorithm clearly,an example based on Graben model will be illustrated.Then,a realistic BP gas chimney model further demonstrates that the proposed method enjoys good stability and anti-noise performance compared with the traditional Q-RTM with amplitude amplification.Compare the Q-RTM images of these two models to the reference images obtained by the acoustic RTM with acoustic seismic data,the new Q-RTM results match the reference images quite well.The proposed method is also tested using a field seismic data,the result shows the effectiveness of our proposed method.

Performance Analysis of a High-Order Discontinuous Galerkin Method Application to the Reverse Time Migration

This work pertains to numerical aspects of a finite element method based discontinuous functions.Our study focuses on the Interior Penalty Discontinuous Galerkin method(IPDGM)because of its high-level of flexibility for solving the full wave equation in heterogeneousmedia.We assess the performance of IPDGMthrough a comparison study with a spectral element method(SEM).We show that IPDGM is as accurate as SEM.In addition,we illustrate the efficiency of IPDGM when employed in a seismic imaging process by considering two-dimensional problems involving the Reverse Time Migration.

Effect of organic modifiers on the capacity factor in micellar electrokinetic chromatography

Organic modifiers were effective both to extend the migration time window and to improve the separation of very hydrophobic compounds in MEKC. An iteration method was used to determine the migration time of micelles. The quantitative relationship between the capacity factor k' and the concentration of organic modifiers was derived, which was investigated experimentally. The linear solvation energy relationships (LSER) methodology was applied to MEKC, and good linear relationships between lnk' and solvatochromic parameters of 15 solutes were obtained in the presence of organic modifier in different concentrations, which indicated a new access in MEKC to predict k' from the structural parameters of solutes. The effect of column temperature T on k' was also investigated.

Theoretical analysis of high-speed rail seismic imaging

We do theoretical research on using high-speed rail(HSR)as an active source to perform reverse time migration(RTM)and analyze the influence of the interferometric field on the seismic imaging results.When a train runs on a rail viaduct,the evenly spaced piers of the viaduct generate a nearly spherical interferometric wavefield with radically travelling waves in frequency-determined directions.We find that the directions span stationary areas of the interference phases,of which cross-talks deteriorating HSR seismic imaging can be well suppressed by stacking.Accordingly,we propose a method for performing RTM by employing HSR data.Numerical tests primarily verify the proposed method by use of 2 D and 3 D acoustic wave equations.Subsequently,we execute least square RTM to suppress crosstalk artifacts,further improving the imaging quality.At last,we stack images derived from trains with different velocities,which extends the frequency band,effectively overcoming the limit from the discrete spectrum of the source wavelet.

Seismic Imaging of Complex Structures in the Tarim Basin

Conventional time imaging techniques are not capable of producing accurate seismic imaging of the subsurface in the mountain front of the Tarim Basin, China. Their imaged structures have led to some major drilling failures before, bearing a disrepute that ＂their structural closures have wheels and their structural highs have springs＂. This article first lists the imaging challenges, and explains in a schematic why the time imaging techniques fail in this area. Then through a series of real data examples, it demonstrates that when there exist lateral velocity variations, depth imaging is the only solution to tackle the imaging challenges in this area. Depth imaging accounts for the complexity of the wavefield, therefore produces superior and geological plausible images. The core task in properly performing depth imaging is building the velocity model. This article stresses some the main aspects in this regard.

Demasking Multiple Artifact in Crustal Seismic Images from Marine Reflection Data in the Southern California Borderland

Marine seismic reflection surveys are often masked by strong water-bottom multiples that limit the use of data beyond the first multiple waves. In this study, we have successfully suppressed much of the multiple artifacts in the depth images of two of the marine seismic reflection profiles from the Los Angeles regional seismic experiment （LARSE） by applying reverse time migration （RTM）. In contrast to most seismic reflection methods that use only primary reflections and diffractions, the two-way RTM migrates both primaries and multiple reflections to their places of origination： seabed multiples to the sea bottom and primaries to the reflecting interfaces. Based on the RTM depth sections of LARSE lines 1 and 2, we recognize five stratigraphic units from the sea bottom to a depth of 6 km. These units are Pliocene and younger strata, probably Miocene syntectonic strata, two deeper sequences of unknown age and lithology as well as Miocene volcanic layers on Catalina ridge. Several inferred igneous intrusions in the upper crust comprise a sixth unit. The existence of a thick sedimentary section in the Catalina Basin, which might include Paleogene and Cretaceous fore-arc strata, has important geologic significance. If borne out by further studies, significant revisions of current structural and stratigraphic interpretations of the California borderland would be warranted.

Making True Amplitude Angle Domain Common Image Gathers Using Invertible Radon Transform

Converting subsurface offset domain common image gathers(ODCIGs)to angle domain common image gathers(ADCIGs)through a Radon Transform(RT)in either the spatial or wavenumber domain is efficient and valid except for the distortion of both frequency spectrum and amplitude versus angle(AVA)effect.This paper presents two modifications to the existing method to keep the frequency spectrum of the resultant ADCIGs the same as the input data and to preserve the relative amplitudes.The spectrum invariance is achieved by replacing the conventional RT or slant slack by an invertible RT.Amplitude preservation is obtained by applying an amplitude correction factor in the angle domain.Tests on both synthetic and field datasets validate the accuracy of these modifications.

The Effect of Strong Near Surface Scattering on Seismic Imaging: Investigation Based on Resolution Analysis

In land seismic exploration,strong near-surface heterogeneities can cause serious problems in seismic data acquisition and the quality of depth imaging.By introducing random velocity models to simulate velocity fluctuations in the near-surface layer and using the point spread function to characterize image quality,we examine how the scattering generated in near-surface heterogeneities can affect the subsurface image.In addition to the commonly known scattering noises which lower the signal to noise ratio in seismic data,our results also reveal that intermediate scale hetero-geneities generate forward scattering which forms phase or travel time fluctuations.Due to intermediate-scale uncertainty in the shallow part of the migration velocity model,these phase changes are carried to the target by the extrapolated wavefields,breaking the zero phase image condition at the image point.This is a primary reason for deteriorated image quality in regions with strong near-surface scattering.If this intermediate-scale information can be obtained and built into the migration velocity,the subsurface image quality can be largely improved.These results can be the ba-sis for further numerical investigations and field experiments.The proposed analysis method can also be used to evaluate other potential methods for dealing with near-surface scattering.