Seismic imaging of complex structures with the CO-CDS stack method

Various seismic imaging methods are introduced to resolve some of the possible ambiguities of seismic interpretation in complex structures. Reducing dependency of imaging techniques on velocity or using diffraction energy for imaging more structural details are the main topics of the imaging research. In this study, we try to improve the seismic image quality in semi-complex structures by combining the common reflection surface (CRS) method with a diffraction based scheme in the common-offset domain. Previously introduced partial CRS and common offset CRS methods exhibited reliable performance in imaging complex media. Here, we were looking for stable and efficient solutions, preserving advantages of the previous methods. Herewith, the proposed operator fits better to diffractions than to reflections. Therefore, we call it the commonoffset common diffraction surface stack (CO CDS). In a previous study, improvement of the quality of seismic image by the CRS method was achieved by combination of the CDS method with the partial CRS. This resulted in the introduction of the partial CDS. Initially, in this study, the common-offset CRS traveltime equation was modified to the common-offset CDS. The hypothetical shot reflector experiment in the CRS method was changed to shot diffraction point experiment. In the introduced operator, two wavefront curvatures, observed at receivers positions, are set equal in order to satisfy the diffraction condition. In the proposed method, we search for accurate attribute sets for each considered offset individually, and then form a new operator by four coherent attributes. Application of the common- offset CDS method on synthetic and field data shows more details of the geological structures with higher quality, while preserving continuity of reflection events. The proposed method is, however, more expensive than the partial and common offset CRS for large dataset.     

Towards large-scale stochastic refraction tomography: a comparison of three evolutionary algorithms

The main goal of this study is to assess the potential of evolutionary algorithms to solve highly non-linear and multi-modal tomography problems (such as first arrival traveltime tomography) and their abilities to estimate reliable uncertainties. Classical tomography methods apply derivative-based optimization algorithms that require the user to determine the value of several parameters (such as regularization level and initial model) prior to the inversion as they strongly affect the final inverted model. In addition, derivative-based methods only perform a local search dependent on the chosen starting model. Global optimization methods based on Markov chain Monte Carlo that thoroughly sample the model parameter space are theoretically insensitive to the initial model but turn out to be computationally expensive. Evolutionary algorithms are population-based global optimization methods and are thus intrinsically parallel, allowing these algorithms to fully handle available computer resources. We apply three evolutionary algorithms to solve a refraction traveltime tomography problem, namely the differential evolution, the competitive particle swarm optimization and the covariance matrix adaptation–evolution strategy. We apply these methodologies on a smoothed version of the Marmousi velocity model and compare their performances in terms of optimization and estimates of uncertainty. By performing scalability and statistical analysis over the results obtained with several runs, we assess the benefits and shortcomings of each algorithm.     

Separation of PP- and PS-wave reflected seismic data using two-dimensional finite offset common-reflection-surface traveltime approximation

Recently, the interest in PS-converted waves has increased for several applications, such as sub-basalt layer imaging, impedance estimates and amplitude-versus-offset analysis. In this study, we consider the problem of separation of PP- and PS-waves from pre-stacked multicomponent seismic data in two-dimensional isotropic medium. We aim to demonstrate that the finite-offset common-reflection-surface traveltime approximation is a good alternative for separating PP- and PS-converted waves in common-offset and common shot configurations by considering a two-dimensional isotropic medium. The five parameters of the finite-offset common-reflection-surface are firstly estimated through the inversion methodology called very fast simulated annealing, which estimates all parameters simultaneously. Next, the emergence angle, one of the inverted parameters, is used to build an analytical separation function of PP and PS reflection separation based on the wave polarization equations. Once the PP- and PS-converted waves were separated, the sections are stacked to increase the signal-to-noise ratio using the special curves derived from finite-offset common-reflection-surface approximation. We applied this methodology to a synthetic dataset from simple-layered to complex-structured media. The numerical results showed that the inverted parameters of the finite offset common-reflection-surface and the separation function yield good results for separating PP- and PS-converted waves in noisy common-offset and common shot gathers.     

Non‐uniqueness with refraction inversion – a syncline model study

Non‐uniqueness occurs with the 1D parametrization of refraction traveltime graphs in the vertical dimension and with the 2D lateral resolution of individual layers in the horizontal dimension. The most common source of non‐uniqueness is the inversion algorithm used to generate the starting model. This study applies 1D, 1.5D and 2D inversion algorithms to traveltime data for a syncline (2D) model, in order to generate starting models for wave path eikonal traveltime tomography. The 1D tau‐p algorithm produced a tomogram with an anticline rather than a syncline and an artefact with a high seismic velocity. The 2D generalized reciprocal method generated tomograms that accurately reproduced the syncline, together with narrow regions at the thalweg with seismic velocities that are less than and greater than the true seismic velocities as well as the true values. It is concluded that 2D inversion algorithms, which explicitly identify forward and reverse traveltime data, are required to generate useful starting models in the near‐surface where irregular refractors are common. The most likely tomogram can be selected as either the simplest model or with a priori information, such as head wave amplitudes. The determination of vertical velocity functions within individual layers is also subject to non‐uniqueness. Depths computed with vertical velocity gradients, which are the default with many tomography programs, are generally 50% greater than those computed with constant velocities for the same traveltime data. The average vertical velocity provides a more accurate measure of depth estimates, where it can be derived. Non‐uniqueness is a fundamental reality with the inversion of all near‐surface seismic refraction data. Unless specific measures are taken to explicitly address non‐uniqueness, then the production of a single refraction tomogram, which fits the traveltime data to sufficient accuracy, does not necessarily demonstrate that the result is either ‘correct’ or the most probable.     

Common-Reflection-Surface Stack for Converted Waves

The finite-offset (FO) common-reflection-surface (CRS) stack has been shown to be able to handle not only P-P or S-S but also arbitrarily converted reflections. It can provide different stack sections such as common-offset (CO), common-midpoint (CMP) and common-shot (CS) sections with significantly increased signal-to-noise ratio from the multi-coverage pre-stack seismic data in a data-driven way. It is our purpose in this paper to demonstrate the performance of the FO CRS stack on data involving converted waves in inhomogeneous layered media. In order to do this we apply the FO CRS stack for common-offset to a synthetic seismic data set involving P-P as well as P-S converted primary reflections. We show that the FO CRS stack yields convincing improvement of the image quality in the presence of noisy data and successfully extracts kinematic wavefield attributes useful for further analyses. The extracted emergence angle information is used to achieve a complete separation of the wavefield into its P-P and P-S wave components, given the FO CRS stacked horizontal and vertical component sections.     

共偏移距道集平面波叠前时间偏移与反偏移

在Dubrulle提出的共偏移距道集频率波数域叠前时间偏移的基础上,提出了共偏移距道集频率波数域叠前时间偏移与反偏移一对共轭算子.讨论了该对算子的变孔径实现过程.并把该对共轭算子串连起来实现了叠前地震数据的规则化处理.指出最小二乘意义下的叠前地震数据规则化会得到更好的效果.v(z)介质模型和Marmousi模型的数值试验结果表明,方法理论正确、有效.     

适于大规模数据的三维Kirchhoff 积分法体偏移实现方案

为适应实际生产中对大规模三维工区数据处理的效果及效率的要求,提出了按三维成像体输出成像结果的3D Kirchhoff积分法偏移实现方案.将地震数据按共偏移距道集形式排放,每个共偏移距数据的偏移类似于一个3D叠后Kirchhoff积分偏移,极大地降低了对计算机内存和局部盘及I/O通讯率的要求.每个地震道的成像(输出等时面)在由炮检点连线定义的旋转坐标系中进行,更好地考虑了偏移孔径计算及反假频处理.同时兼顾了超大规模地震数据PSTM成像处理中内存需求量、I/O通讯问题、并行处理方案及效率优化的细节问题.并行计算用偏移距号和每个共偏移距数据体中的线号作为一级和二级索引进行任务分解,更适应当前计算机集群中计算节点比较多的情况.最后考虑了在基本不影响效率的前提下的断点保护处理方案.理论及实际数据测试结果说明了该方案的可行性,与商业软件的对比验证了该方案的优越性.在此较完善的实现方案基础上,可以容易地把更优越的积分类偏移方法迅速推向实用化.     

First‐arrival traveltime tomography with modified total‐variation regularization

First‐arrival traveltime tomography is a robust tool for near‐surface velocity estimation. A common approach to stabilizing the ill‐posed inverse problem is to apply Tikhonov regularization to the inversion. However, the Tikhonov regularization method recovers smooth local structures while blurring the sharp features in the model solution. We present a first‐arrival traveltime tomography method with modified total‐variation regularization to preserve sharp velocity contrasts and improve the accuracy of velocity inversion. To solve the minimization problem of the new traveltime tomography method, we decouple the original optimization problem into the two following subproblems: a standard traveltime tomography problem with the traditional Tikhonov regularization and a L₂ total‐variation problem. We apply the conjugate gradient method and split‐Bregman iterative method to solve these two subproblems, respectively. Our synthetic examples show that the new method produces higher resolution models than the conventional traveltime tomography with Tikhonov regularization, and creates less artefacts than the total variation regularization method for the models with sharp interfaces. For the field data, pre‐stack time migration sections show that the modified total‐variation traveltime tomography produces a near‐surface velocity model, which makes statics corrections more accurate.     

Depth migration anisotropy analysis in the time domain

In areas of complex geology such as the Canadian Foothills, the effects of anisotropy are apparent in seismic data and estimation of anisotropic parameters for use in seismic imaging is not a trivial task. Here we explore the applicability of common‐focus point (CFP)‐based velocity analysis to estimate anisotropic parameters for the variably tilted shale thrust sheet in the Canadian Foothills model. To avoid the inherent velocity‐depth ambiguity, we assume that the elastic properties of thrust‐sheet with respect to transverse isotropy symmetry axis are homogeneous, the reflector below the thrust‐sheet is flat, and that the anisotropy is weak. In our CFP approach to velocity analysis, for a poorly imaged reflection point, a traveltime residual is obtained as the time difference between the focusing operator for an assumed subsurface velocity model and the corresponding CFP response obtained from the reflection data. We assume that this residual is due to unknown values for anisotropy, and we perform an iterative linear inversion to obtain new model parameters that minimize the residuals. Migration of the data using parameters obtained from our inversion results in a correctly positioned and better focused reflector below the thrust sheet. For traveltime computation we use a brute force mapping scheme that takes into account weakly tilted transverse isotropy media. For inversion, the problem is set up as a generalized Newton's equation where traveltime error (differential time shift) is linearly dependent on the parameter updates. The iterative updates of parameters are obtained by a least‐squares solution of Newton's equations. The significance of this work lies in its applicability to areas where transverse isotropy layers are heterogeneous laterally, and where transverse isotropy layers are overlain by complex structures that preclude a moveout curve fitting.     

射线追踪的微变网格方法

本文给出一种适用于叠前数据速度分析和叠前深度偏移的快速射线追踪方法──微变网格法；该方法不仅精度高，而且计算速度极快，可适用于当前计算条件下的地球介质速度反演和叠前深度偏移成像的要求．     

2D共炮时间域高斯波束偏移

针对传统射线方法在奇异区成像精度不高,而2D频率域高斯波束叠前深度偏移需要计算成像点处每个频率的格林函数,影响计算效率的问题,本文通过使用复走时代替实走时,改变频率域下成像公式的积分顺序,给出了在时间域下进行高斯波束偏移的方法和计算公式.本文使用复杂数值模型验证了2D时间域高斯波束叠前偏移方法的正确性,并同传统射线偏移成像结果做了对比.对比结果表明时间域高斯波束偏移在成像精度上优于传统射线偏移.     

基于一种反余切紧凑约束的电磁波走时层析研究

电磁波走时层析可用于空洞和孤石等离散块体异常的探测中.在传统电磁波走时层析中,通常采用一个低阶差分泛函来稳定反演过程,而这类泛函都具有光滑约束的性质,在成像结果中难以对此类离散块体异常进行准确的解释.本文基于Tikhonov正则化思想,提出了一种反余切泛函,该泛函具有紧凑约束的性质且无需选择一个聚焦因子.结合弯曲胖射线层析理论和重加权正则化共轭梯度反演算法,对两个理论模型进行了成像效果研究.与低阶差分泛函和最小支撑泛函的成像结果相比,该方法能够更好地突出异常的边界,成像结果中的虚假异常也要更少.同时,还分析讨论了激发电磁波的中心频率以及数据噪音对成像结果的影响.此外,针对一个地下连续墙墙体内部缺陷的现场模型,利用该方法取得了理想的成像结果,良好地揭示了缺陷的形态和位置.     

Efficient traveltime compression for 3D prestack Kirchhoff migration

Kirchhoff 3D prestack migration, as part of its execution, usually requires repeated access to a large traveltime table data base. Access to this data base implies either a memory intensive or I/O bounded solution to the storage problem. Proper compression of the traveltime table allows efficient 3D prestack migration without relying on the usually slow access to the computer hard drive. Such compression also allows for faster access to desirable parts of the traveltime table. Compression is applied to the traveltime field for each source location on the surface on a regular grid using 3D Chebyshev polynomial or cosine transforms of the traveltime field represented in the spherical coordinates or the Celerity domain. We obtain practical compression levels up to and exceeding 20 to 1. In fact, because of the smaller size traveltime table, we obtain exceptional traveltime extraction speed during migration that exceeds conventional methods. Additional features of the compression include better interpolation of traveltime tables and more stable estimates of amplitudes from traveltime curvatures. Further compression is achieved using bit encoding, by representing compression parameters values with fewer bits.     

Solving the complex near‐surface problem using 3D data‐driven near‐surface layer replacement

In many land seismic situations, the complex seismic wave propagation effects in the near‐surface area, due to its unconsolidated character, deteriorate the image quality. Although several methods have been proposed to address this problem, the negative impact of 3D complex near‐surface structures is still unsolved to a large extent. This paper presents a complete 3D data‐driven solution for the near‐surface problem based on 3D one‐way traveltime operators, which extends our previous attempts that were limited to a 2D situation. Our solution is composed of four steps: 1) seismic wave propagation from the surface to a suitable datum reflector is described by parametrized one‐way propagation operators, with all the parameters estimated by a new genetic algorithm, the self‐adjustable input genetic algorithm, in an automatic and purely data‐driven way; 2) surface‐consistent residual static corrections are estimated to accommodate the fast variations in the near‐surface area; 3) a replacement velocity model based on the traveltime operators in the good data area (without the near‐surface problem) is estimated; 4) data interpolation and surface layer replacement based on the estimated traveltime operators and the replacement velocity model are carried out in an interweaved manner in order to both remove the near‐surface imprints in the original data and keep the valuable geological information above the datum. Our method is demonstrated on a subset of a 3D field data set from the Middle East yielding encouraging results.     

Modelling and migration with orthogonal isochron rays

For increasing time values, isochrons can be regarded as expanding wavefronts and their perpendicular lines as the associated orthogonal isochron rays. The speed of the isochron movement depends on the medium velocity and the source-receiver position. We introduce the term equivalent-velocity to refer to the speed of isochron movement. In the particular case of zero-offset data, the equivalent velocity is half of the medium velocity. We use the concepts of orthogonal isochron-rays and equivalent velocity to extend the application of the exploding reflector model to non-zero offset imaging problems. In particular, we employ these concepts to extend the use of zero-offset wave-equation algorithms for modelling and imaging common-offset sections. In our imaging approach, the common-offset migration is implemented as a trace-by-trace algorithm in three steps: equivalent velocity computation, data conditioning for zero-offset migration and zero-offset wave-equation migration. We apply this methodology for modelling and imaging synthetic common-offset sections using two kinds of algorithms: finite-difference and split-step wavefield extrapolation. We also illustrate the isochron-ray imaging methodology with a field-data example and compare the results with conventional common-offset Kirchhoff migration. This methodology is attractive because it permits depth migration of common-offset sections or just pieces of that by using wave-equation algorithms, it extends the use of robust zero-offset algorithms, it presents favourable features for parallel processing, it permits the creation of hybrid migration algorithms and it is appropriate for migration velocity analysis.     

3-D simultaneous inversion for velocity and reflector geometry using multiple classes of arrivals in a spherical coordinate frame

The two key requirements in conducting 3-D simultaneous traveltime tomography on real data at the regional and global scale with multiple classes of arrival time information are (1) it needs an efficient and accurate arrival tracking algorithm for multiply transmitted, reflected (or refracted) and converted waves in a 3-D variable velocity model with embedded velocity discontinuities (or subsurface interfaces), and (2) a subdimensional inversion solver is required which can easily search for different types of model parameters to balance the trade-off between the different types of model parameter updated in the simultaneous inversion process. For these purposes, we first extend a popular grid/cell-based wavefront expanding ray tracing algorithm (the multistage irregular shortest-path ray tracing method), which previously worked only in Cartesian coordinate at the local scale, to spherical coordinates appropriate to the regional or global scale. We then incorporated a fashionable inversion solver (the subspace method) to formulate a simultaneous inversion algorithm, in which the multiple classes of arrivals (including direct and reflected arrivals from different velocity discontinuities) can be used to simultaneously update both the velocity fields and the reflector geometries. Numerical tests indicate that the new inversion method is both applicable and flexible in terms of computational efficiency and solution accuracy, and is not sensitive to a modest level of noise in the traveltime data. It offers several potential benefits over existing schemes for real data seismic imaging.     

Automatic stacking‐velocity estimation using similarity‐weighted clustering

Local seismic event slopes contain subsurface velocity information and can be used to estimate seismic stacking velocity. In this paper, we propose a novel approach to estimate the stacking velocity automatically from seismic reflection data using similarity‐weighted k‐means clustering, in which the weights are local similarity between each trace in common midpoint gather and a reference trace. Local similarity reflects the local signal‐to‐noise ratio in common midpoint gather. We select the data points with high signal‐to‐noise ratio to be used in the velocity estimation with large weights in mapped traveltime and velocity domain by similarity‐weighted k‐means clustering with thresholding. By using weighted k‐means clustering, we make clustering centroids closer to those data points with large weights, which are more reliable and have higher signal‐to‐noise ratio. The interpolation is used to obtain the whole velocity volume after we have got velocity points calculated by weighted k‐means clustering. Using the proposed method, one obtains a more accurate estimate of the stacking velocity because the similarity‐based weighting in clustering takes into account the signal‐to‐noise ratio and reliability of different data points in mapped traveltime and velocity domain. In order to demonstrate that, we apply the proposed method to synthetic and field data examples, and the resulting images are of higher quality when compared with the ones obtained using existing methods.     

三维复杂山地多级次群推进迎风混合法多波型走时计算

三维复杂山地条件下的各种地震波型的走时计算技术,可以直接用于复杂山地区域地震波运动学特性的分析、地震数据采集观测系统的设计以及直接基于三维复杂地表的地震数据处理技术的研发.为了在三维复杂地表条件下准确、灵活且稳定地计算各种地震波型的走时,提出一种多级次群推进迎风混合法.该算法利用不等距迎风差分法简洁稳定地处理三维复杂地表及附近的局部走时计算问题,利用计算精度不错的迎风双线性插值法处理绝大部分均匀正方体网格中的局部走时计算问题,利用群推进法模拟三维复杂地表条件下地震波前的扩展问题,利用多级次算法处理各种类型的地震波的走时计算问题.算法分析和计算实例表明:新方法具有很好的计算精度与效率,且能灵活稳定地处理三维复杂地表复杂介质条件下的多波型走时计算问题.     

Event-oriented velocity estimation based on prestack data in time or depth domain1

A 2D reflection tomographic method is described, for the purpose of estimating an improved macrovelocity field for prestack depth migration. An event-oriented local approach of the ‘layer-stripping’ type has been developed, where each input event is defined by its traveltime and a traveltime derivative, taken with respect to one of four coordinates in the source/receiver and midpoint half-offset systems. Recent work has shown that the results of reflection tomography may be improved by performing event picking in a prestack depth domain. We adopt this approach and allow events to be picked either before or after prestack depth migration. Hence, if events have been picked in a depth domain, such as the common-shot depth domain or the common-offset depth domain, then a depth-time transformation is required before velocity estimation. The event transformation may, for example, be done by conventional kinematic ray tracingr and with respect to the original depth-migration velocity field. By this means, we expect the input events for velocity updating to become less sensitive to migration velocity errors. For the purpose of velocity estimation, events are subdivided into two categories; reference horizon events and individual events. The reference horizon events correspond to a fixed offset in order to provide basic information about reflector geometry, whereas individual events, corresponding to any offset, are supposed to provide the additional information needed for velocity estimation. An iterative updating approach is used, based on calculation of derivatives of event reflection points with respect to velocity. The event reflection points are obtained by ray-theoretical depth conversion, and reflection-point derivatives are calculated accurately and efficiently from information pertaining to single rays. A number of reference horizon events and a single individual event constitute the minimum information required to update the velocity locally, and the iterations proceed until the individual event reflection point is consistent with those of the reference horizon events. Normally, three to four iterations are sufficient to attain convergence. As a by-product of the process, we obtain so-called uncertainty amplification factors, which relate a picking error to the corresponding error in the estimated velocity or depth horizon position. The vector formulation of the updating relationship makes it applicable to smooth horizons having arbitrary dips and by applying velocity updating in combination with a flexible model-builder, very general macro-model structures can be obtained. As a first step in the evaluation of the new method, error-free traveltime events were generated by applying forward ray tracing within given macrovelocity models. When using such ‘perfect’ observations, the velocity estimation algorithm gave consistent reconstructions of macro-models containing interfaces with differential dip and curvature, a low-velocity layer and a layer with a laterally varying velocity function.     

The use of low frequencies in a full‐waveform inversion and impedance inversion land seismic case study

Velocity model building and impedance inversion generally suffer from a lack of intermediate wavenumber content in seismic data. Intermediate wavenumbers may be retrieved directly from seismic data sets if enough low frequencies are recorded. Over the past years, improvements in acquisition have allowed us to obtain seismic data with a broader frequency spectrum. To illustrate the benefits of broadband acquisition, notably the recording of low frequencies, we discuss the inversion of land seismic data acquired in Inner Mongolia, China. This data set contains frequencies from 1.5–80 Hz. We show that the velocity estimate based on an acoustic full‐waveform inversion approach is superior to one obtained from reflection traveltime inversion because after full‐waveform inversion the background velocity conforms to geology. We also illustrate the added value of low frequencies in an impedance estimate.