Attenuation compensation in multicomponent Gaussian beam prestack depth migration

Gaussian beam prestack depth migration is an accurate imaging method of subsurface media. Prestack depth migration of multicomponent seismic data improves the accuracy of imaging subsurface complex geological structures. Viscoelastic prestack depth migration is of practical significance because it considers the viscosity of the subsurface media. We use Gaussian beam migration to compensate for the attenuation in multicomponent seismic data. First, we use the Gaussian beam method to simulate the wave propagation in a viscoelastic medium and introduce the complex velocity Q-related and exact viscoelastic Zoeppritz equation. Second, we discuss PP- and PS-wave Gaussian beam prestack depth migration algorithms for common-shot gathers to derive expressions for the attenuation and compensation. The algorithms correct the amplitude attenuation and phase distortion caused by Q, and realize multicomponent Gaussian beam prestack depth migration based on the attenuation compensation and account for the effect of inaccurate Q on migration. Numerical modeling suggests that the imaging resolution of viscoelastic Gaussian beam prestack depth migration is high when the viscosity of the subsurface is considered.

High angle prestack depth migration with absorption compensation

The absorption effect of actual subsurface media can weaken wavefield energy, decrease the dominating frequency, and further lead to reduced resolution. In migration, some actions can be taken to compensate for the absorption effect and enhance the resolution. In this paper, we derive a one-way wave equation with an attenuation term based on the time- space domain high angle one-way wave equation. A complicated geological model is then designed and synthetic shot gathers are simulated with acoustic wave equations without and with an absorbing term. The derived one-way wave equation is applied to the migration of the synthetic gathers without and with attenuation compensation for the simulated shot gathers. Three migration profiles are obtained. The first and second profiles are from the shot gathers without and with attenuation using the migration method without compensation, the third one is from the shot gathers with attenuation using the migration method with compensation. The first and third profiles are almost the same, and the second profile is different from the others below the absorptive layers. The amplitudes of the interfaces below the absorptive layers are weak because of their absorption. This method is also applied to field data. It is concluded from the migration examples that the migration method discussed in this paper is feasible.

Anisotropic converted wave amplitude-preserving prestack time migration by the pseudo-offset method

In this paper, we use the method of pseudo-offset migration （POM） to complete converted wave pre-stack time migration with amplitude-preservation in an anisotropic medium. The method maps the original traces into common conversion scatter point （CCSP） gathers directly by POM, which simplifies the conventional processing procedure for converted waves. The POM gather fold and SNR are high, which is favorable for velocity analysis and especially suitable for seismic data with low SNR. We used equivalent anisotropic theory to compute anisotropic parameters. Based on the scattering wave traveltime equation in a VTI medium, the POM pseudo-offset migration in anisotropic media was deduced. By amplitude-preserving POM gather mapping, velocity analysis, stack processing, and so on, the anisotropic migration results were acquired. The forward modeling computation and actual data processing demonstrate the validity of converted wave pre-stack time migration with amplitude-preservation using the anisotropic POM method.

Traveltime tomography and prestack depth migration for vertical seismic profiling of an angle-domain walkaway on a complex surface

Walkaway VSP cannot obtain accurate velocity field,as it asymmetrically reflects ray path and provides uneven coverage to underground target,thereby presenting issues related to imaging quality.In this study,we propose combining traveltime tomography and prestack depth migration for VSP of an angle-domain walkaway,in a bid to establish accurate two-dimensional and three-dimensional(3 D)velocity models.First,residual curvature was defined to update velocity,and an accurate velocity field was established.To establish a high-precision velocity model,we deduced the relationship between the residual depth and traveltime of common imaging gathers(CIGs)in walkaway VSP.Solving renewal velocity using the least squares method,a four-parameter tomographic inversion equation was derived comprising formation dip angle,incidence angle,residual depth,and sensitivity matrix.In the angle domain,the reflected wave was divided into up-and down-transmitted waves and their traveltimes were calculated.The systematic cumulative method was employed in prestack depth migration of a complex surface.Through prestack depth migration,the offset-domain CIGs were obtained,and dip angle was established by defining the stack section horizon.Runge–Kutta ray tracing was employed to calculate the ray path from the reflection point to the detection point,to determine the incident angle,and to subsequently calculate the ray path from the reflection point to the irregular surface.The offset-domain residual depths were mapped to the angle domain,and a new tomographic equation was established and solved.Application in the double complex area of the Tarim Basin showed the four-parameter tomographic inversion equation derived in this paper to be both correct and practical and that the migration algorithm was able to adapt to the complex surface.

Amplitude.preserving plane-wave prestack time migration for AVO analysis

To support amplitude variation with offset （AVO） analysis in complex structure areas, we introduce an amplitude-preserving plane-wave prestack time migration approach based on the double-square-root wave equation in media with little lateral velocity variation. In its implementation, a data mapping algorithm is used to obtain offset-plane-wave data sets from the common-midpoint gathers followed by a non-recursive phase-shift solution with amplitude correction to generate common-image gathers in offset-ray-parameter domain and a structural image. Theoretical model tests and a real data example show that our prestack time migration approach is helpful for AVO analysis in complex geological environments.

Beamlet prestack depth migration and illumination： A test based on the Marmousi model

Beamlet sources have strong local and directional character and can easily accomplish local illumination and migration. Besides, they provide better migration results than conventional migration methods. We introduce the basic principles of beamlet prestack depth migration that includes a windowed Fourier transform and frame theory. We explain the Gabor-Daubechies （G-D） frame based on a Gaussian function. Beamlet decomposition provides information on the local space and direction of wavefield. We synthesize the beamlet source and beamlet records in the wavelet domain using both rectangle and Gaussian windows and then extrapolate the synthesized data with a Fourier finite-difference operator. We test the method using the standard Marmousi model. By comparing and analyzing the migration results of single directional beamlet and beamlets with different windows and directions, we demonstrate the validity of the prestack depth migration with Gaussian beamlets method.

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.

The Offset-Domain Prestack Depth Migration with Optimal Separable Approximation

The offset-domain prestack depth migration with optimal separable approximation, based on the double square root equation, is used to image complex media with large and rapid velocity variations. The method downward continues the source and the receiver wavefields simultaneously. The mixed domain algorithm with forward Fourier and inverse Fourier transform is used to construct the double square root equation wavefield extrapolation operator. This operator separates variables in the wave number domain and variables in the space domain. The phase operation is implemented in the wave number domain, whereas the time delay for lateral velocity variation is corrected in the space domain. The migration algorithm is efficient since the seismic data are not computed shot by shot. The data set test of the Marmousi model indicates that the offset-domain migration provides a satisfied seismic migration section on which complex geologic structures are imaged in media with large and rapid lateral velocity variations.

Prestack Depth Migration by a Parallel 3D PSPI

Prestack depth migration for seismic reflection data is commonly used tool for imaging complex geological structures such as salt domes, faults, thrust belts, and stratigraphic structures. Phase shift plus interpolation (PSPI) algorithm is a useful tool to directly solve a wave equation and the results have natural properties of the wave equation. Amplitude and phase characteristics, in particular, are better preserved. The PSPI algorithm is widely used in hydrocarbon exploration because of its simplicity, efficiency, and reduced efforts for computation. However, meaningful depth image of 3D subsurface requires parallel computing to handle heavy computing time and great amount of input data. We implemented a parallelized version of 3D PSPI for prestack depth migration using Open-Multi-Processing (Open MP) library. We verified its performance through applications to 3D SEG/EAGE salt model with a small scale Linux cluster. Phase-shift was performed in the vertical and horizontal directions, respectively, and then interpolated at each node. This gave a single image gather according to shot gather. After summation of each single image gather, we got a 3D stacked image in the depth domain. The numerical model example shows good agree- ment with the original geological model.

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.

Methods for wave equation prestack depth migration and numerical experiments

In this paper the methods of wave theory based prestack depth migration and their implementation are studied. Using the splitting of wave operator, the wavefield extrapolation equations are deduced and the numerical schemes are presented. The numerical tests for SEG/EAEG model with MPI are performed on the PC-cluster. The numerical results show that the methods of single-shot (common-shot) migration and synthesized-shot migration are of practical values and can be applied to field data processing of 3D prestack depth migration.

Preserved amplitude migration based on the one way wave equation in the angle domain

Traditional pre-stack depth migration can only provide subsurface structural information. However, simple structure information is insufficient for petroleum exploration which also needs amplitude information proportional to reflection coefficients. In recent years, pre-stack depth migration algorithms which preserve amplitudes and based on the one- way wave equation have been developed. Using the method in the shot domain requires a deconvolution imaging condition which produces some instability in areas with complicated structure and dramatic lateral variation in velocity. Depth migration with preserved amplitude based on the angle domain can overcome the instability of the one-way wave migration imaging condition with preserved amplitude. It can also offer provide velocity analysis in the angle domain of common imaging point gathers. In this paper, based on the foundation of the one-way wave continuation operator with preserved amplitude, we realized the preserved amplitude prestack depth migration in the angle domain. Models and real data validate the accuracy of the method.

Internal Multiple Prediction Based on Imaging Profile Prediction and Kirchhoff Demigration

This paper introduces an internal multiple prediction method based on imaging profile prediction and Kirchhoff demigration.First,based on an inputted prestack time migration profile,the method predicts the prestack time migration profile that only includes internal multiples by inverse scattering series method.Second,the method uses velocity-weighted Kirchhoff demigration to create shot gathers that contains only internal multiples.Internal multiple prediction based on the prestack time migration profile effectively reduces the computational cost of multiple predictions,and the internal-multiple shot gathers created by Kirchhoff demigration remarkably reduces the complexity of the practical problem.Internal multiple elimination can be conducted through the combined adaptive multiple subtraction based on event tracing.Synthetic and field data tests show that the method effectively predicts internal multiples and possesses considerable potential in field data processing,particularly in areas where internal multiples develop seriously.

Influences of coarse grid selection on Kirchhoff beam migration

Kirchhoff beam migration is a beam migration method, which focuses on rapid imaging of geological structures. Although this imaging method ignores the amplitude information in the calculation process, it can calculate multi-arrival traveltime. This migration method takes into account both imaging accuracy and computational efficiency. Kirchhoff beam migration employs coarse grid techniques in several key steps such as traveltime calculation, weight function calculation, and imaging calculation. The selection of the coarse mesh size has an important influence on the computational efficiency and imaging accuracy of the migration imaging method. This paper will analyze this influence and illustrate the analysis results by the Marmousi data sets.

Kirchhoff PSDM angle-gather generation based on the traveltime gradient

Angle-domain common-image gathers（ADCIGs） are the basic data in migration velocity analysis（MVA） and amplitude variation with angle（AVA） analysis. We propose a common-angle gather-generating scheme using Kirchhoff PSDM based on the traveltime gradient field. The scheme includes three major operations：（1） to calculate the traveltime field of the source and the receiver based on the dynamic programming approach;（2） to obtain the refl ection angle according to the traveltime gradient field in the image space; and（3） to generate the ADCIGs during the migration process. Because of the computation approach, the method for generating ADCIGs is superior to conventional ray-based methods. We use the proposed ADCIGs generation method in 3D large-scale seismic data. The key points of the method are the following.（1） We use common-shot datasets for migration,（2） we load traveltimes based on the shot aperture, and（3） we use the MPI and Open Mp memory sharing to decrease the amount of input and output（I/O）. Numerical examples using synthetic data suggest that the ADCIGs improve the quality of the velocity and the effectiveness of the 3D angle-gather generation scheme.

Finite-difference calculation of traveltimes based on rectangular grid

To the most of velocity fields, the traveltimes of the first break that seismic waves propagate along rays can be computed on a 2-D or 3-D numerical grid by finite-difference extrapolation. Under ensuring accuracy, to improve calculating efficiency and adaptability, the calculation method of first-arrival traveltime of finite-difference is de- rived based on any rectangular grid and a local plane wavefront approximation. In addition, head waves and scat- tering waves are properly treated and shadow and caustic zones cannot be encountered, which appear in traditional ray-tracing. The testes of two simple models and the complex Marmousi model show that the method has higher accuracy and adaptability to complex structure with strong vertical and lateral velocity variation, and Kirchhoff prestack depth migration based on this method can basically achieve the position imaging effects of wave equation prestack depth migration in major structures and targets. Because of not taking account of the later arrivals energy, the effect of its amplitude preservation is worse than that by wave equation method, but its computing efficiency is higher than that by total Green′s function method and wave equation method.

Finite-difference calculation of traveltimes based on rectangular grid

To the most of velocity fields, the traveltimes of the first break that seismic waves propagate along rays can be computed on a 2-D or 3-D numerical grid by finite-difference extrapolation. Under ensuring accuracy, to improve calculating efficiency and adaptability, the calculation method of first-arrival traveltime of finite-difference is de- rived based on any rectangular grid and a local plane wavefront approximation. In addition, head waves and scat- tering waves are properly treated and shadow and caustic zones cannot be encountered, which appear in traditional ray-tracing. The testes of two simple models and the complex Marmousi model show that the method has higher accuracy and adaptability to complex structure with strong vertical and lateral velocity variation, and Kirchhoff prestack depth migration based on this method can basically achieve the position imaging effects of wave equation prestack depth migration in major structures and targets. Because of not taking account of the later arrivals energy, the effect of its amplitude preservation is worse than that by wave equation method, but its computing efficiency is higher than that by total Green′s function method and wave equation method.

深反射地震成像揭示的班公湖-怒江缝合带中段Moho断阶及其大地构造意义

揭示班公湖-怒江(班怒)缝合带Moho(莫霍面)结构对于认识中特提斯洋壳俯冲和南羌塘坳陷成因具有重要地球动力学意义。基于横跨班怒缝合带的深反射地震数据(88°30′E),本文采用了中长波长静校正、噪声压制、优化叠加和叠前深度偏移(PSDM)等地震处理技术,获得了深度域地震反射偏移剖面、层速度场和高分辨率Moho结构。由深度域剖面显示,班怒缝合带Moho位于地表以下65~80 km,呈不连续北向抬升趋势,指示在拉萨地块与南羌塘地块之间存在岩石圈上地幔断阶,最大阶步可达15 km。综合分析缝合带两侧的Moho形态认为,这些断阶受南侧拉萨地体的岩石圈上地幔以19.5°北倾俯冲与北侧南羌塘地块的上地壳抬升驱动,可能与深部存在局部熔融相关。班怒缝合带下的Moho结构表明,随着晚侏罗世—早白垩世中特提斯洋闭合,南羌塘地体由边缘海沉积向前陆盆地转换,形成南羌塘坳陷。

应用曲率谱和Siamese网络的叠前深度偏移速度建模

速度建模是叠前深度偏移的重要环节,通常需要在层位约束下对观测点的地层速度进行横向外推,然而在速度建模初期缺乏地震解释层位等格架信息。为此,文中提出了一种基于曲率谱横向相似性和改进循环结构Siamese网络的速度模型建立方法。Siamese网络是目前常用的基于深度学习的目标识别和追踪网络,可以快速进行目标图像的相似度对比,而且不需要人工制作标签。曲率谱可以看成反应地层特征和速度信息的二维图像,将速度建模作为横向特征相似性类比问题,通过类比曲率谱可以自动得到地层的格架和速度更新信息。首先,将叠前深度偏移后的道集转换为曲率谱;其次,确定待搜索曲率谱图像及其对应的目标追踪对象,并求取当前追踪对象与目标追踪对象的相似系数;然后,基于相似系数更新参考曲率谱图像和当前追踪对象;最后,在遍历完全部追踪对象时,基于各个追踪对象的层速度及深度建立速度模型。理论模型和实际数据试验结果表明,该方法能在没有解释资料的条件下快速生成符合地质构造和地层特征的速度模型。

复杂山地深度域地震成像处理方法--以龙门山山前带海棠铺复杂构造区为例

山前带复杂构造区蕴藏了丰富的油气资源。地震资料信噪比低和速度建模困难是目前山前带地震数据精确成像面临的主要问题。以龙门山山前带海棠铺地区地震数据为例,开展了叠前深度域地震成像处理方法攻关研究,重点在叠前噪声压制和叠前深度偏移速度建模等两方面开展了研究,具体如下。①加强低频弱信号保护,采用二次信噪分离技术,对噪声记录中有效信号进行二次信噪分离,最大限度保护低频弱信号不受损伤。②优化叠前深度偏移速度建模流程:首先优化传统深度域速度场更新输入道集与偏移输入道集共用一个道集的方式,对驱动速度场更新的输入道集进行五维数据规则化处理以提高其信噪比;然后以地质导向为基础,精细刻画强反射速度缺失界面,联合层析反演并融合深度域近地表速度模型,建立具有地质模型约束的深度域速度场;得到了精确的速度模型后,再修改偏移成像输入道集及偏移方法,将五维数据规则化前的地震道集作为输入道集,将全方位角度域叠前深度偏移作为最终偏移成像方法。将该方法应用于川西北海棠铺地区的地震数据处理,结果表明所提方法大幅提高了研究区的地震成像精度,最终得到的叠前深度偏移成像结果信噪比高,偏移归位合理,为进一步推动该区的深入勘探开发,提供了可供借鉴的深度域地震成像处理经验。