Strategies for stable attenuation compensation in reverse‐time migration

Attenuation in seismic wave propagation is a common cause for poor illumination of subsurface structures. Attempts to compensate for amplitude loss in seismic images by amplifying the wavefield may boost high‐frequency components, such as noise, and create undesirable imaging artefacts. In this paper, rather than amplifying the wavefield directly, we develop a stable compensation operator using stable division. The operator relies on a constant‐Q wave equation with decoupled fractional Laplacians and compensates for the full attenuation phenomena by performing wave extrapolation twice. This leads to two new imaging conditions to compensate for attenuation in reverse‐time migration. A time‐dependent imaging condition is derived by applying Q‐compensation in the frequency domain, whereas a time‐independent imaging condition is formed in the image space by calculating image normalisation weights. We demonstrate the feasibility and robustness of the proposed methods using three synthetic examples. We found that the proposed methods are capable of properly compensating for attenuation without amplifying high‐frequency noise in the data.     

Poststack diffraction imaging using reverse‐time migration

We propose a method for imaging small‐scale diffraction objects in complex environments in which Kirchhoff‐based approaches may fail. The proposed method is based on a separation between the specular reflection and diffraction components of the total wavefield in the migrated surface angle domain. Reverse‐time migration was utilized to produce the common image gathers. This approach provides stable and robust results in cases of complex velocity models. The separation is based on the fact that, in surface angle common image gathers, reflection events are focused at positions that correspond to the apparent dip angle of the reflectors, whereas diffracted events are distributed over a wide range of angles. The high‐resolution radon‐based procedure is used to efficiently separate the reflection and diffraction wavefields. In this study, we consider poststack diffraction imaging. The advantages of working in the poststack domain are its numerical efficiency and the reduced computational time. The numerical results show that the proposed method is able to image diffraction objects in complex environments. The application of the method to a real seismic dataset illustrates the capability of the approach to extract diffractions.     

Multipathing in three‐parameter common‐image gathers from reverse‐time migration

Reverse‐time migration gives high‐quality, complete images by using full‐wave extrapolations. It is thus not subject to important limitations of other migrations that are based on high‐frequency or one‐way approximations. The cross‐correlation imaging condition in two‐dimensional pre‐stack reverse‐time migration of common‐source data explicitly sums the product of the (forward‐propagating) source and (backward‐propagating) receiver wavefields over all image times. The primary contribution at any image point travels a minimum‐time path that has only one (specular) reflection, and it usually corresponds to a local maximum amplitude. All other contributions at the same image point are various types of multipaths, including prismatic multi‐arrivals, free‐surface and internal multiples, converted waves, and all crosstalk noise, which are imaged at later times, and potentially create migration artefacts. A solution that facilitates inclusion of correctly imaged, non‐primary arrivals and removal of the related artefacts, is to save the depth versus incident angle slice at each image time (rather than automatically summing them). This results in a three‐parameter (incident angle, depth, and image time) common‐image volume that integrates, into a single unified representation, attributes that were previously computed by separate processes. The volume can be post‐processed by selecting any desired combination of primary and/or multipath data before stacking over image time. Separate images (with or without artifacts) and various projections can then be produced without having to remigrate the data, providing an efficient tool for optimization of migration images. A numerical example for a simple model shows how primary and prismatic multipath contributions merge into a single incident angle versus image time trajectory. A second example, using synthetic data from the Sigsbee2 model, shows that the contributions to subsalt images of primary and multipath (in this case, turning wave) reflections are different. The primary reflections contain most of the information in regions away from the salt, but both primary and multipath data contribute in the subsalt region.     

Diffraction imaging by prestack reverse‐time migration in the dip‐angle domain

Prestack image volumes may be decomposed into specular and non‐specular parts by filters defined in the dip‐angle domain. For space‐shift extended image volumes, the dip‐angle decomposition is derived via local Radon transform in depth and midpoint coordinates, followed by an averaging over space‐shifts. We propose to employ prestack space‐shift extended reverse‐time migration and dip‐angle decomposition for imaging small‐scale structural elements, considered as seismic diffractors, in models with arbitrary complexity. A suitable design of a specularity filter in the dip‐angle domain rejects the dominant reflectors and enhances diffractors and other non‐specular image content. The filter exploits a clear discrimination in dip between specular reflections and diffractions. The former are stationary at the specular dip, whereas the latter are non‐stationary without a preferred dip direction. While the filtered image volume features other than the diffractor images (for example, noise and truncation artefacts are also present), synthetic and field data examples suggest that diffractors tend to dominate and are readily recognisable. Averaging over space‐shifts in the filter construction makes the reflectors? rejection robust against migration velocity errors. Another consequence of the space‐shift extension and its angle‐domain transforms is the possibility of exploring the image in a multiple set of common‐image gathers. The filtered diffractions may be analysed simultaneously in space‐shift, scattering‐angle, and dip‐angle image gathers by means of a single migration job. The deliverables of our method obviously enrich the processed material on the interpreter's desk. We expect them to further supplement our understanding of the Earth's interior.     

Increasing resolution of reverse‐time migration using time‐shift gathers

Reverse‐time migration has become an industry standard for imaging in complex geological areas. We present an approach for increasing its imaging resolution by employing time‐shift gathers. The method consists of two steps: (i) migrating seismic data with the extended imaging condition to get time‐shift gathers and (ii) accumulating the information from time‐shift gathers after they are transformed to zero‐lag time‐shift by a post‐stack depth migration on a finer grid. The final image is generated on a grid, which is denser than that of the original image, thus improving the resolution of the migrated images. Our method is based on the observation that non‐zero‐lag time‐shift images recorded on the regular computing grid contain the information of zero‐lag time‐shift image on a denser grid, and such information can be continued to zero‐lag time‐shift and refocused at the correct locations on the denser grid. The extra computational cost of the proposed method amounts to the computational cost of zero‐offset migration and is almost negligible compared with the cost of pre‐stack shot‐record reverse‐time migration. Numerical tests on synthetic models demonstrate that the method can effectively improve reverse‐time migration resolution. It can also be regarded as an approach to improve the efficiency of reverse‐time migration by performing wavefield extrapolation on a coarse grid and by generating the final image on the desired fine grid.     

探地雷达衰减补偿逆时偏移成像方法

探地雷达信号在地下介质中传播时易受到电导率所产生的衰减影响,从而使得传统偏移成像结果在高衰减区域变得模糊.本文提出了衰减补偿的逆时偏移方法来消除电导率的影响.该方法基于麦克斯韦方程组实现电磁波的正演模拟和逆时传播.通过改变衰减项的正负号,保证了逆时传播的时间对称性,从而能够重构出原始波场,实现衰减补偿.数值实验比较了传统逆时偏移方法和衰减补偿逆时偏移方法在存在高导异常区域情况下的成像效果,结果证明了衰减补偿逆时偏移方法能够很好地恢复由电导率造成的信号衰减,从而提高探地雷达剖面的分辨率.     

Least‐squares reverse‐time migration in a matrix‐based formulation

This paper describes least‐squares reverse‐time migration. The method provides the exact adjoint operator pair for solving the linear inverse problem, thereby enhancing the convergence of gradient‐based iterative linear inversion methods. In this formulation, modified source wavelets are used to correct the source signature imprint in the predicted data. Moreover, a roughness constraint is applied to stabilise the inversion and reduce high‐wavenumber artefacts. It is also shown that least‐squares migration implicitly applies a deconvolution imaging condition. Three numerical experiments illustrate that this method is able to produce seismic reflectivity images with higher resolution, more accurate amplitudes, and fewer artefacts than conventional reverse‐time migration. The methodology is currently feasible in 2‐D and can naturally be extended to 3‐D when computational resources become more powerful.     

Visco‐acoustic prestack reverse‐time migration based on the time‐space domain adaptive high‐order finite‐difference method

It is important to include the viscous effect in seismic numerical modelling and seismic migration due to the ubiquitous viscosity in an actual subsurface medium. Prestack reverse‐time migration (RTM) is currently one of the most accurate methods for seismic imaging. One of the key steps of RTM is wavefield forward and backward extrapolation and how to solve the wave equation fast and accurately is the essence of this process. In this paper, we apply the time‐space domain dispersion‐relation‐based finite‐difference (FD) method for visco‐acoustic wave numerical modelling. Dispersion analysis and numerical modelling results demonstrate that the time‐space domain FD method has great accuracy and can effectively suppress numerical dispersion. Also, we use the time‐space domain FD method to solve the visco‐acoustic wave equation in wavefield extrapolation of RTM and apply the source‐normalized cross‐correlation imaging condition in migration. Improved imaging has been obtained in both synthetic and real data tests. The migration result of the visco‐acoustic wave RTM is clearer and more accurate than that of acoustic wave RTM. In addition, in the process of wavefield forward and backward extrapolation, we adopt adaptive variable‐length spatial operators to compute spatial derivatives to significantly decrease computing costs without reducing the accuracy of the numerical solution.     

基于吸收衰减补偿的多分量高斯束逆时偏移

高斯束逆时偏移结合了射线类偏移的高计算效率和波动方程逆时偏移的高精度,能很好地处理焦散点、大倾角成像问题,并且具有面向目标成像的能力.多分量地震资料的偏移技术可以对地下复杂构造进行更准确的成像,由于实际地下介质具有黏滞性,研究黏弹性叠前逆时偏移具有一定的现实意义.本文采用高斯束逆时偏移方法对多分量地震数据进行吸收衰减补偿,首先分别给出纵波和转换波共炮域高斯束叠前逆时偏移方法原理,在此基础上推导补偿吸收衰减的表达式,校正Q引起的振幅衰减和相位畸变,实现基于吸收衰减补偿的多分量高斯束叠前逆时偏移.数值模型的测试结果显示,在考虑地下介质的黏滞性时,本文方法具有更高的成像分辨率.     

Suppressing non‐Gaussian noises with scaled receiver wavefield for reverse‐time migration: comparison of different approaches

Numerical implementation of the gradient of the cost function in a gradient‐based full‐ waveform inversion (FWI) is essentially a migration operator used in wave equation migration. In FWI, minimizing different data residual norms results in different weighting strategies of data residuals at receiver locations prior to back‐propagation into the medium. In this paper, we propose different scaling methods to the receiver wavefield and compare their performances. Using time‐domain reverse‐time migration (RTM), we show that compared to conventional algorithms, this type of scaling is able to significantly suppress non‐Gaussian noise, i.e., outliers. Our tests also show that scaling by its absolute norm produces better results than other approaches.     

Reverse‐time migration from rugged topography using irregular,unstructured mesh

We developed a reverse‐time migration scheme that can image regions with rugged topography without requiring any approximations by adopting an irregular, unstructured‐grid modelling scheme. This grid, which can accurately describe surface topography and interfaces between high‐velocity‐contrast regions, is generated by Delaunay triangulation combined with the centroidal Voronoi tessellation method. The grid sizes vary according to the migration velocities, resulting in significant reduction of the number of discretized nodes compared with the number of nodes in the conventional regular‐grid scheme, particularly in the case wherein high near‐surface velocities exist. Moreover, the time sampling rate can be reduced substantially. The grid method, together with the irregular perfectly matched layer absorbing boundary condition, enables the proposed scheme to image regions of interest using curved artificial boundaries with fewer discretized nodes. We tested the proposed scheme using the 2D SEG Foothill synthetic dataset.     

基于Low rank近似的黏弹性介质衰减补偿微地震逆时定位与裂缝成像

真实地下介质具有黏弹性,地震波在传播过程中会发生耗散与频散.忽视黏弹性介质的吸收衰减效应,逆时延拓过程中地震波将会出现振幅减弱、相位失真等现象,无法准确定位震源真实位置,因此需要对黏弹性介质中传播的波场进行衰减补偿,并通过采用合适的成像算子对微地震震源进行定位与裂缝成像.本文基于耗散与频散解耦的分数阶黏弹性波动方程模拟...     

Generalized diffraction‐stack migration and filtering of coherent noise

We reformulate the equation of reverse‐time migration so that it can be interpreted as summing data along a series of hyperbola‐like curves, each one representing a different type of event such as a reflection or multiple. This is a generalization of the familiar diffraction‐stack migration algorithm where the migration image at a point is computed by the sum of trace amplitudes along an appropriate hyperbola‐like curve. Instead of summing along the curve associated with the primary reflection, the sum is over all scattering events and so this method is named generalized diffraction‐stack migration. This formulation leads to filters that can be applied to the generalized diffraction‐stack migration operator to mitigate coherent migration artefacts due to, e.g., crosstalk and aliasing. Results with both synthetic and field data show that generalized diffraction‐stack migration images have fewer artefacts than those computed by the standard reverse‐time migration algorithm. The main drawback is that generalized diffraction‐stack migration is much more memory intensive and I/O limited than the standard reverse‐time migration method.     

一种黏声波方程逆时偏移成像中的衰减补偿方法

在存在强衰减介质的区域进行逆时偏移成像,需要既能补偿地震波传播过程中的振幅衰减,又能保持其相位不变的高效算法.为此,本文提出了一种利用有限差分模拟进行声波衰减补偿的方法来实现考虑衰减的逆时偏移.这种方法以线性黏弹性体模型为基础,保持其复模量的实部不变,并采用多项式多级优化方法修正复模量的虚部,从而实现在保持相位不变的同时补偿振幅,进而有效提高偏移成像的清晰程度,尤其是对于介质对地震波衰减极为强烈的情形.这一方法在声波方程中只增加了整数阶微分算子进行修正,能够保证利用有限差分法进行数值求解,有利于进行高效的大规模细粒度并行计算和GPU加速计算.数值实验结果验证了这一方法的可行性和有效性,能够很好地提高强衰减介质区域的偏移成像质量.

     

Double plane‐wave reverse‐time migration

We develop a new time‐domain reverse‐time migration method called double plane‐wave reverse‐time migration that uses plane‐wave transformed gathers. Original shot gathers with appropriate data acquisition geometry are double slant stacked into the double plane‐wave domain with minimal slant stacking artefacts. The range of plane‐wave components needed for migration can be determined by estimating the maximum time dips present in shot gathers. This reduces the total number of input traces for migration and increases migration efficiency. Unlike the pre‐stack shot‐profile reverse‐time migration where the number of forward propagations is proportional to the number of shots, the number of forward propagations needed for the proposed method remains constant and is relatively small even for large seismic datasets. Therefore, the proposed method can improve the efficiency of the migration and be suitable for migrating large datasets. Double plane‐wave reverse‐time migration can be performed for selected plane‐wave components to obtain subsurface interfaces with different dips, which makes the migration method target oriented. This feature also makes the method a useful tool for migration velocity analysis. For example, we are able to promptly obtain trial images with nearly horizontal interfaces and adjust velocity models according to common image gathers. Seismic signal coming from steeply dipping interfaces can be included into the migration to build images with more detailed structures and higher spatial resolution as better velocity models become available. Illumination compensation imaging conditions for the proposed method are also introduced to obtain images with balanced amplitudes.     

黏声介质最小平方逆时偏移

介质的黏滞性是普遍存在的.黏滞性介质中的真振幅成像需要校正由介质的黏滞性引起的振幅衰减与速度频散,然而常规的反Q偏移方法存在不稳定问题.本文在反演的框架下求解黏声介质成像问题,在有效避开不稳定的同时实现真振幅成像.首先将波动方程线性化,并依此建立黏声介质最小平方逆时偏移（LSRTM）的目标函数;然后推导波动方程伴随算子,并在此基础上借助伴随状态法推导迭代求解的具体算法;最后通过引入动态相位编码技术将计算量降至与常规逆时偏移相同的数量级.该方法在真振幅成像过程中考虑了介质黏滞性的影响,更接近实际情况,具有更好的振幅保持性.相对于常规逆时偏移,该方法能够自动压制成像噪声,具有更高的成像分辨率及精度.通过模型试算验证了方法的正确性.     

Dual compensation strategy for real‐time hybrid testing

Real‐time hybrid testing is an experimental technique for evaluating the dynamic responses of structural systems under seismic loading. Servo‐hydraulic actuators, by nature, induce inevitable time delay between the command and the achieved displacements. This delay would lead to incorrect test results and even cause instability of the system; therefore, delay compensation is critical for stability and accuracy of hybrid simulations of structural dynamic response. In this paper, a dual delay compensation strategy is proposed by a combination of a phase lead compensator and a restoring force compensator. An outer‐loop feed‐forward phase lead compensator is derived by introducing the inverse model in the z domain. The adaptive law based on the gradient algorithm is used to estimate the system delay in the format of parametric model during the test. It is shown mathematically that the parameter in the delay estimator is guaranteed to converge. The restoring force compensator is adopted to improve the accuracy of experimental results especially when the structure is subjected to high frequency excitations. Finally, analytical simulations of an inelastic SDOF structure are conducted to investigate the feasibility of the proposed strategy. The accuracy of the dual compensation strategy is demonstrated through several shaking table tests. Copyright © 2012 John Wiley & Sons, Ltd.     

Directional‐oriented wavefield imaging: a new wave‐based subsurface illumination imaging condition for reverse time migration

The key objective of an imaging algorithm is to produce accurate and high‐resolution images of the subsurface geology. However, significant wavefield distortions occur due to wave propagation through complex structures and irregular acquisition geometries causing uneven wavefield illumination at the target. Therefore, conventional imaging conditions are unable to correctly compensate for variable illumination effects. We propose a generalised wave‐based imaging condition, which incorporates a weighting function based on energy illumination at each subsurface reflection and azimuth angles. Our proposed imaging kernel, named as the directional‐oriented wavefield imaging, compensates for illumination effects produced by possible surface obstructions during acquisition, sparse geometries employed in the field, and complex velocity models. An integral part of the directional‐oriented wavefield imaging condition is a methodology for applying down‐going/up‐going wavefield decomposition to both source and receiver extrapolated wavefields. This type of wavefield decomposition eliminates low‐frequency artefacts and scattering noise caused by the two‐way wave equation and can facilitate the robust estimation for energy fluxes of wavefields required for the seismic illumination analysis. Then, based on the estimation of the respective wavefield propagation vectors and associated directions, we evaluate the illumination energy for each subsurface location as a function of image depth point and subsurface azimuth and reflection angles. Thus, the final directional‐oriented wavefield imaging kernel is a cross‐correlation of the decomposed source and receiver wavefields weighted by the illuminated energy estimated at each depth location. The application of the directional‐oriented wavefield imaging condition can be employed during the generation of both depth‐stacked images and azimuth–reflection angle‐domain common image gathers. Numerical examples using synthetic and real data demonstrate that the new imaging condition can properly image complex wave paths and produce high‐fidelity depth sections.     

多次波分阶逆时偏移成像

本文深入分析了多次波逆时偏移的成像原理和串扰假象产生机制,并提出了多次波分阶逆时偏移策略,即首先应用自由界面多次波衰减方法对原始炮集记录中的多次波进行剔除得到一次波记录,然后应用一次波记录预测获得各阶多次波记录,最后将各阶多次波记录分别进行逆时偏移成像.模型实验结果表明,多次波分阶逆时偏移其各阶多次波成像剖面均可对真实界面正确成像且其能够有效压制串扰假象,其中一阶多次波逆时偏移剖面的成像精度最高,其深层成像质量明显优于常规多次波逆时偏移.     

Adaptive time series compensator for delay compensation of servo‐hydraulic actuator systems for real‐time hybrid simulation

Hydraulic actuators are typically used in a real‐time hybrid simulation to impose displacements to a test structure (also known as the experimental substructure). It is imperative that good actuator control is achieved in the real‐time hybrid simulation to minimize actuator delay that leads to incorrect simulation results. The inherent nonlinearity of an actuator as well as any nonlinear response of the experimental substructure can result in an amplitude‐dependent behavior of the servo‐hydraulic system, making it challenging to accurately control the actuator. To achieve improved control of a servo‐hydraulic system with nonlinearities, an adaptive actuator compensation scheme called the adaptive time series (ATS) compensator is developed. The ATS compensator continuously updates the coefficients of the system transfer function during a real‐time hybrid simulation using online real‐time linear regression analysis. Unlike most existing adaptive methods, the system identification procedure of the ATS compensator does not involve user‐defined adaptive gains. Through the online updating of the coefficients of the system transfer function, the ATS compensator can effectively account for the nonlinearity of the combined system, resulting in improved accuracy in actuator control. A comparison of the performance of the ATS compensator with existing linearized compensation methods shows superior results for the ATS compensator for cases involving actuator motions with predefined actuator displacement histories as well as real‐time hybrid simulations. Copyright © 2013 John Wiley & Sons, Ltd.