Application of the virtual refraction to near‐surface characterization at the Boise Hydrogeophysical Research Site‡

Seismic interferometry is a relatively new technique to estimate the Green's function between receivers. Spurious energy, not part of the true Green's function, is produced because assumptions are commonly violated when applying seismic interferometry to field data. Instead of attempting to suppress all spurious energy, we show how spurious energy associated with refractions contains information about the subsurface in field data collected at the Boise Hydrogeophysical Research Site. By forming a virtual shot record we suppress uncorrelated noise and produce a virtual refraction that intercepts zero offset at zero time. These two features make the virtual refraction easy to pick, providing an estimate of refractor velocity. To obtain the physical parameters of the layer above the refractor we analyse the cross‐correlation of wavefields recorded at two receivers for all sources. A stationary‐phase point associated with the correlation between the reflected wave and refracted wave from the interface identifies the critical offset. By combining information from the virtual shot record, the correlation gather and the real shot record we determine the seismic velocities of the unsaturated and saturated sands, as well as the variable relative depth to the water‐table. Finally, we discuss how this method can be extended to more complex geologic models.     

Seismic interferometry by tangent‐phase correction

We present a modified interferometry method based on local tangent‐phase analysis, which corrects the cross‐correlated data before summation. The approach makes it possible to synthesize virtual signals usually vanishing in the conventional seismic interferometry summation. For a given pair of receivers and a set of different source positions, a plurality of virtual traces is obtained at new stationary projected points located along the signal wavefronts passing through the real reference receiver. The position of the projected points is estimated by minimizing travel times using wavefront constraint and correlation‐signal tangent information. The method uses mixed processing, which is partially based on velocity‐model knowledge and on data‐based blind interferometry. The approach can be used for selected events, including reflections with different stationary conditions and projected points with respect to those of the direct arrivals, to extend the interferometry representation in seismic exploration data where conventional illumination coverage is not sufficient to obtain the stationary‐phase condition. We discuss possible applications in crosswell geometry with a velocity anomaly and a time lapse.     

3D seismic residual statics solutions derived from refraction interferometry

We apply interferometric theory to solve a three‐dimensional seismic residual statics problem to improve reflection imaging. The approach calculates the static solutions without picking the first arrivals from the shot or receiver gathers. The static correction accuracy can be significantly improved by utilising stacked virtual refraction gathers in the calculations. Shots and receivers may be placed at any position in a three‐dimensional seismic land survey. Therefore, it is difficult to determine stationary shots and receivers to form the virtual refraction traces that have identical arrival times, as in a two‐dimensional scenario. To overcome this problem, we use a three‐dimensional super‐virtual interferometry method for residual static calculations. The virtual refraction for a stationary shot/receiver pair is obtained via an integral along the receiver/shot lines, which does not require knowledge of the stationary locations. We pick the maximum energy times on the interferometric stacks and solve a set of linear equations to derive reliable residual static solutions. We further apply the approach to both synthetic and real data.     

地球背景噪声干涉应用研究的新进展

对地震台记录到的长时间的地球背景噪声进行互相关处理,得到的互相关函数可以近似地表征这两个台站之间的格林函数,这种数据处理方法被称为背景噪声干涉.近年来,背景噪声干涉研究在理论和实践上都有了长足进展,并被广泛用于地下波速结构及其演化规律的研究.本文首先简单介绍了背景噪声干涉研究的概念和理论依据,进而重点介绍了针对噪声源性质、互相关函数的波形到时和振幅特性的应用研究.通过对这三个方面研究的回顾,分析总结了该研究领域的新进展及需要解决的问题,并对背景噪声干涉研究的新特点进行了分析和展望.     

Virtual signals combination – phase analysis for 2D and 3D data representation (acoustic medium)

We formulate the Kirchhoff‐Helmholtz representation theory for the combination of seismic interferometry signals synthesized by cross‐correlation and by cross‐convolution in acoustic media. The approach estimates the phase of the virtual reflections from the boundary encompassing a volume of interest and subtracts these virtual reflections from the total seismic‐interferometry wavefield. The reliability of the combination result, relevant for seismic exploration, depends on the stationary‐phase and local completeness in partial coverage regions. The analysis shows the differences in the phase of the corresponding seismic interferometry (by cross‐correlation) and virtual reflector (by cross‐convolution) signals obtained by 2D and 3D formulations, with synthetic examples performed to remove water layer multiples in ocean bottom seismic (OBS) acoustic data.     

Drill‐bit seismic interferometry with and without pilot signals*

We use different interferometry approaches to process the seismic signals generated by a drill‐bit source in one well and recorded by seismic receivers located both in a second borehole and at the surface near the source well. We compare the standard interferometry results, obtained by using the raw drill‐bit data without a pilot signal, with the new interferometry results obtained by using the drill‐bit seismograms correlated with a reference pilot signal. The analysis of the stationary phase shows that the final results have different S/N levels and are affected by the coherent noise in the form of rig arrivals. The interferometry methods are compared by using different deconvolution approaches. The analysis shows that the results agree with the conventional drill‐bit seismograms and that using the reference pilot signal improves the quality of the drill‐bit wavefields redatumed by the interferometry method.     

Retrieval of super‐virtual refraction by cross‐correlation

Topography and severe variations of near‐surface layers lead to travel‐time perturbations for the events in seismic exploration. Usually, these perturbations could be estimated and eliminated by refraction technology. The virtual refraction method is a relatively new technique for retrieval of refraction information from seismic records contaminated by noise. Based on the virtual refraction, this paper proposes super‐virtual refraction interferometry by cross‐correlation to retrieve refraction wavefields by summing the cross‐correlation of raw refraction wavefields and virtual refraction wavefields over all receivers located outside the retrieved source and receiver pair. This method can enhance refraction signal gradually as the source–receiver offset decreases. For further enhancement of refracted waves, a scheme of hybrid virtual refraction wavefields is applied by stacking of correlation‐type and convolution‐type super‐virtual refractions. Our new method does not need any information about the near‐surface velocity model, which can solve the problem of directly unmeasured virtual refraction energy from the virtual source at the surface, and extend the acquisition aperture to its maximum extent in raw seismic records. It can also reduce random noise influence in raw seismic records effectively and improve refracted waves’ signal‐to‐noise ratio by a factor proportional to the square root of the number of receivers positioned at stationary‐phase points, based on the improvement of virtual refraction's signal‐to‐noise ratio. Using results from synthetic and field data, we show that our new method is effective to retrieve refraction information from raw seismic records and improve the accuracy of first‐arrival picks.     

Stationary phase approximation in the ambient noise method revisited

The method of extracting Green's function between stations from cross correlation has proven to be effective theoretically and experimentally.It has been widely applied to surface wave tomography of the crust and upmost mantle.However,there are still controversies about why this method works.Snieder employed stationary phase approximation in evaluating contribution to cross correlation function from scatterers in the whole space,and concluded that it is the constructive interference of waves emitted by the scatterers near the receiver line that leads to the emergence of Green's function.His derivation demonstrates that cross correlation function is just the convolution of noise power spectrum and the Green's function.However,his derivation ignores influence from the two stationary points at infinities,therefore it may fail when attenuation is absent.In order to obtain accurate noise-correlation function due to scatters over the whole space,we compute the total contribution with numerical integration in polar coordinates.Our numerical computation of cross correlation function indicates that the incomplete stationary phase approximation introduces remarkable errors to the cross correlation function,in both amplitude and phase,when the frequency is low with reasonable quality factor Q.Our results argue that the distance between stations has to be beyond several wavelengths in order to reduce the influence of this inaccuracy on the applications of ambient noise method,and only the station pairs whose distances are above several (5) wavelengths can be used.     

Synthesis of a seismic virtual reflector*

We describe a method to process the seismic data generated by a plurality of sources and registered by an appropriate distribution of receivers, which provides new seismic signals as if in the position of the receivers (or sources) there was an ideal reflector, even if this reflector is not present there. The data provided by this method represent the signals of a virtual reflector. The proposed algorithm performs the convolution and the subsequent sum of the real traces without needing subsurface model information. The approach can be used in combination with seismic interferometry to separate wavefields and process the reflection events. The application is described with synthetic examples, including stationary phase analysis and with real data in which the virtual reflector signal can be appreciated.     

基于低频信息补偿的数据驱动Marchenko成像

基于常规地震干涉法和地震超越干涉法,提出了SI和BSI的结合方法SIBSI,即在SI被动源低频信息提取的基础上,重构主动源BSI地震数据,并利用BSI进行格林函数重构和面向目标的Marchenko成像.研究了基于频率优势的主动源低频重构方法,在完整保留了主动源信号高频信息的基础上,有效重构了低频信息,拓宽了地震数据的频带范围.讨论了含有自由表面多次波的地震数据在Marchenko成像中应用的方法.设计了一个含有高阻抗地层的模型,在该模型上使用SI低频信息重构BSI主动源地震数据,最后与纯主动源地震数据的格林函数重构和Marchenko成像进行了对比,证明了本文所提出方法的有效性、抗噪性以及在提高成像效果中的优势.     

二维弹性多波时空域高斯束偏移方法

随着我国勘探开发难度逐步增大,勘探目标开始向裂缝油气藏、岩性油气藏等复杂探区转移,研究高精度、适应性强的多波多分量深度偏移算法在后续的地震解释、属性分析及储层预测中具有重要意义.针对多波多分量地震数据,本文提出了一种二维弹性波时空域高斯束偏移方法.时空域高斯束沿中心射线传播时能够面向成像目标描述局部波场,且对振幅和频率可调制的Gabor基函数有天然的适应性,因而将基于Gabor分解的子波重构方法应用于震源波场构建,从而得到任意点源函数产生的时空域高斯束波场.该方法由于直接在时间域进行计算,可以避开频率域中出现的假频和边缘截断效应等问题.基于各向同性弹性波动方程的Kirchhoff-Helmholtz积分解,利用矢量时空域高斯束传播算子构建格林函数和格林位移张量,并结合上行射线追踪策略,实现了检波点波场的反向延拓.针对矢量波成像问题,本文借鉴弹性波逆时偏移方法从矢量延拓波场中分离出纯纵波分量和纯横波分量,进而采用修改后的内积成像条件产生具有明确物理意义的PP、PS成像结果,避免了转换波成像的极性反转问题.最后利用简单两层模型和不含盐体构造的部分Sigsbee2a模型的成像结果,并将其与应用近似纵横波成像条件、标量和矢量势成像条件的偏移剖面进行对比,验证了本文方法的正确性和有效性.     

Retrieving virtual reflection responses at drill‐bit positions using seismic interferometry with drill‐bit noise

In the field of seismic interferometry, researchers have retrieved surface waves and body waves by cross‐correlating recordings of uncorrelated noise sources to extract useful subsurface information. The retrieved wavefields in most applications are between receivers. When the positions of the noise sources are known, inter‐source interferometry can be applied to retrieve the wavefields between sources, thus turning sources into virtual receivers. Previous applications of this form of interferometry assume impulsive point sources or transient sources with similar signatures. We investigate the requirements of applying inter‐source seismic interferometry using non‐transient noise sources with known positions to retrieve reflection responses at those positions and show the results using synthetic drilling noise as source. We show that, if pilot signals (estimates of the drill‐bit signals) are not available, it is required that the drill‐bit signals are the same and that the phases of the virtual reflections at drill‐bit positions can be retrieved by deconvolution interferometry or by cross‐coherence interferometry. Further, for this case, classic interferometry by cross‐correlation can be used if the source power spectrum can be estimated. If pilot signals are available, virtual reflection responses can be obtained by first using standard seismic‐while‐drilling processing techniques such as pilot cross‐correlation and pilot deconvolution to remove the drill‐bit signatures in the data and then applying cross‐correlation interferometry. Therefore, provided that pilot signals are reliable, drill‐bit data can be redatumed from surface to borehole depths using this inter‐source interferometry approach without any velocity information of the medium, and we show that a well‐positioned image below the borehole can be obtained using interferometrically redatumed reflection responses with just a simple velocity model. We discuss some of the practical hurdles that restrict the application of the proposed method offshore.     

The Relation between Gaussian Beams and Maslov Asymptotic Theory

The application of Maslov asymptotic theory in a general 3-D mixed subspace of 6-D complex phase space is proposed to obtain the integral superpositions of Gaussian packets and beams. The ray method and the superposition of plane waves (Maslov method of Chapman and Drumond [7]) are special limiting cases of the above mentioned approach. The same high-frequency asymptotic expansion formulae for seismic body waves were derived previously in [8] using the Gaussian beam method.     

干涉走时微地震震源定位方法

本文基于地震波场干涉原理,建立了干涉走时微地震震源定位方法.该方法将两个接收点相对于一个微地震事件的走时差(称为干涉走时)的扰动作为残差函数,通过迭代求解最小残差函数,最终获得震源的空间位置.干涉走时震源定位方法利用两个接收点的到时差消除发震时刻未知和速度模型误差的影响,简化了震源定位算法.数值计算表明,本文提出的干涉走时定位方法在速度模型有误差的情况下仍然可以获得准确的微地震震源定位.     

基于平面波模型重访地震背景噪声互相关及空间自相关(SPAC)

自Aki(1957)提出微震的空间自相关(SPatial AutoCorelation,SPAC)技术以来,SPAC技术一直独立发展,并在工程地震领域获得了广泛应用.近20年来,地震干涉(Seisimic Interferometry,SI)在多个领域引起人们的关注,该技术的核心思想是连续地震背景噪声的互相关函数(Noise Crosscorrelation Function,NCF)可以重建系统的格林函数(Green's Function,GF),对该技术的回溯性研究建立了SPAC和NCF的关系:它们是对同一物理现象的不同描述,SPAC在频率域中描述随机平稳噪声的空间相干,NCF在时间域中描述扩散场的互相关.理论上SAPC和NCF技术要求背景噪声源均匀分布,这样的噪声场可以用平面波叠加来模拟.本文基于平面波模型重访地震背景噪声的互相关和空间自相关技术,从单色平面波的互相关表示出发,对地震背景噪声互相关及空间自相关技术进行评述,试图使这些概念更易于理解.与之前众多研究地震干涉技术的理论相比,本文尤其关注以下几点:(1)基于简单的平面波模型,给出不同维度下,源或台站对方位均匀分布时,平面波互相关对入射波的方位平均和台阵对的方位平均结果,并对格林函数GF和时域互相关函数NCF的关系进行总结.(2)给出声源和(或)交叉台站方位分布不均匀时的互相关表示,指出这种非均匀性对方位的依赖关系,与弱各向异性介质中面波速度的方位依赖关系类似,因此,非均匀源的影响在反演时可能会映射到面波方位各向异性结果中.(3)互相关运算中,哪一个台站是虚拟源.NCF包含因果性和非因果性两部分,NCF的非对称性通常用于研究噪声源的方位分布,但由于源和接收的互易关系,及对互相关运算的不同定义和不同的傅里叶变换习惯,哪一个台站是虚拟源在目前的文献中并不明确.(4)方位平均和时间平均的关系.在SPAC处理中,需要对不同方位分布的台站对进行方位平均,本文从理论上说明,单个平面波入射时,交叉台站互相关系数对台站对的方位平均,等价于单个台站对互相关系数对入射波的时间平均.(5)几种特定分布非均匀噪声源的SPAC表示.包括单独的因果性噪声源和非因果性噪声源给出的互相关函数表示,及由此带来的相移问题.(6)利用SPAC、NCF和面波GF之间的关系,给出交叉分量的空间自相关系数表示.(7)衰减介质的空间相干表示.虽然利用地震干涉技术研究介质衰减在理论上仍然存在一些争议,但人们正试图研究从连续背景噪声记录中提取介质衰减的可能性.本文基于平面波模型,给出了不同坐标选择下,衰减介质的空间相干表示,这种表达的不同,指示了由地震干涉技术提取介质衰减的困难.与众多研究地震干涉的理论相比,比如稳相近似理论、互易定理、时间反转声学等,本文主要考虑均匀介质,不涉及非均匀介质的散射,从最简单的平面波模型,理解背景噪声重建系统格林函数这一地震干涉的核心思想和相应的基本概念.     

震源因素对尾波干涉提取经验格林函数的影响

尾波干涉提取经验格林函数作为现今地震学一项重要的研究,其受震源因素的影响值得细致地探讨.本文通过模拟和实际数据的尾波干涉,系统性讨论了震源倾角、方位角和走向以及震中分布对于提取经验格林函数（主要是PKIKP²和PKⅡKP²震相）的影响.我们发现PKIKP²震相的平均信噪比随倾角的增大呈现先增大后减小的变化趋势,并在倾角约为45°时达到最大.基于稳相点分析,本文认为这种变化趋势是因为提取的PKIKP²震相主要贡献来源于近乎径向方向,而倾角为45°的倾滑型断层事件辐射出的P波能量在径向上最大.此外,断层走向对尾波干涉提取Rayleigh面波并无明显影响,而方位角的影响非常显著.当事件近似在台站对的大圆弧上时,尾波干涉才能提取清晰的Rayleigh面波,这与面波稳相区的空间分布一致.对于PKIKP²和PKⅡKP²震相,只有当事件分布与台站对大圆弧近垂直并且事件断层走向与线状台阵近平行时,才能提取清晰的波形.通过计算不同事件和台站分布的震源辐射能量,上述方位角和走向最有利于地核震相的提取.最后,震中分布对尾波干涉提取PKIKP²震相也有一定的影响：当震中与地心连线和PKIKP²震相射线路径之间的锐角夹角越小,并且震中距越小时,提取的地核震相的信噪比越高.     

A tale of two beams: an elementary overview of Gaussian beams and Bessel beams

An overview of two types of beam solutions is presented, Gaussian beams and Bessel beams. Gaussian beams are examples of non-localized or diffracting beam solutions, and Bessel beams are example of localized, non-diffracting beam solutions. Gaussian beams stay bounded over a certain propagation range after which they diverge. Bessel beams are among a class of solutions to the wave equation that are ideally diffraction-free and do not diverge when they propagate. They can be described by plane waves with normal vectors along a cone with a fixed angle from the beam propagation direction. X-waves are an example of pulsed beams that propagate in an undistorted fashion. For realizable localized beam solutions, Bessel beams must ultimately be windowed by an aperture, and for a Gaussian tapered window function this results in Bessel-Gauss beams. Bessel-Gauss beams can also be realized by a combination of Gaussian beams propagating along a cone with a fixed opening angle. Depending on the beam parameters, Bessel-Gauss beams can be used to describe a range of beams solutions with Gaussian beams and Bessel beams as end-members. Both Gaussian beams, as well as limited diffraction beams, can be used as building blocks for the modeling and synthesis of other types of wave fields. In seismology and geophysics, limited diffraction beams have the potential of providing improved controllability of the beam solutions and a large depth of focus in the subsurface for seismic imaging.     

True amplitude elastic Gaussian beam imaging of multicomponent walkaway vertical seismic profiling data

We develop the true‐amplitude prestack migration of multicomponent data based on the use of elastic Gaussian beams for walkaway vertical seismic profile (VSP) acquisition systems. It consists in a weighted summation of multishot data with specific weights, computed by tracing elastic Gaussian beams from each imaging point of the target area towards the sources and receivers. Each pair of beams may be connected with either a pair of P‐rays (PP‐image) or the P‐ray towards sources and the S‐ray to receivers (PS‐image) and is uniquely determined by dip (the angle of the bisector between the rays and the vertical direction) and opening (the angle between the rays) angles. Shooting from the bottom towards the acquisition system helps to avoid well‐known troubles, in particular multipathing for the imaging conditions in complex velocity models. The ability to fix the dip angle and implement summation over opening angles leads to the so‐called selective images that contain mostly interfaces with desired slopes. On the other hand, a set of images computed for a range of opening angles by summation over all available dip angles is used as input of an AVO‐like inversion procedure for the recovery of elastic parameters. The feasibility of this imaging procedure is verified by synthetic data for 2D realistic elastic models.     

Global-scale seismic interferometry: theory and numerical examples

Progress in the imaging of the mantle and core is partially limited by the sparse distribution of natural sources; the earthquake hypocenters are mainly along the active lithospheric plate boundaries. This problem can be approached with seismic interferometry. In recent years, there has been considerable progress in the development of seismic interferometric techniques. The term seismic interferometry refers to the principle of generating new seismic responses by cross‐correlating seismic observations at different receiver locations. The application of interferometric techniques on a global scale could create sources at locations where no earthquakes occur. In this way, yet unknown responses would become available for the application of travel‐time tomography and surface‐wave dispersion studies. The retrieval of a dense‐enough sampling of source gathers would largely benefit the application of reflection imaging. We derive new elastodynamic representation integrals for global‐scale seismic interferometry. The relations are different from other seismic interferometry relations for transient sources, in the sense that they are suited for a rotating closed system like the Earth. We use a correlation of an observed response with a response to which free‐surface multiple elimination has been applied to account for the closed system. Despite the fact that the rotation of the Earth breaks source‐receiver reciprocity, the seismic interferometry relations are shown to be valid. The Coriolis force is included without the need to evaluate an extra term. We synthesize global‐scale earthquake responses and use them to illustrate the acoustic versions of the new interferometric relations. When the sampling of real source locations is dense enough, then both the responses with and without free‐surface multiples are retrieved. When we do not take into account the responses from the sources in the direct neighborhood of the seismic interferometry‐constructed source location, the response with free‐surface multiples can still be retrieved. Even when only responses from sources at a certain range of epicentral distances are available, some events in the Green's function between two receiver locations can still be retrieved. The retrieved responses are not perfect, but the artefacts can largely be ascribed to numerical errors. The reconstruction of internal events – the response as if there was a source and a receiver on (major) contrasts within the model – could possibly be of use for imaging. With modelling it is possible to discover in which region of the correlation panel stationary phases occur that contribute to the retrieval of events. This knowledge opens up a new way of filtering out undesired events and of discovering whether specific events could be retrieved with a given source‐receiver configuration.     

压制空间非平稳地震勘探随机噪声的ROAD径向时频峰值滤波算法

径向时频峰值滤波算法是一种有效保持低信噪比地震勘探记录中反射同相轴的随机噪声压制方法,但该算法对空间非平稳地震勘探随机噪声压制效果不理想.本文研究空间非平稳地震勘探随机噪声,即各道噪声功率不同的地震勘探随机噪声,其在径向滤波轨线上表征近似脉冲噪声,在径向时频峰值滤波过程中干扰相邻道滤波结果.为了减小空间非平稳随机噪声的影响,本文提出一种基于绝对级差统计量(ROAD)的径向时频峰值滤波随机噪声压制方法.该方法首先根据径向轨线上信号的绝对级差统计量检测空间非平稳地震勘探随机噪声,然后结合局部时频峰值滤波和径向时频峰值滤波压制地震勘探记录中的随机噪声.将ROAD径向时频峰值滤波方法应用于合成记录和实际共炮点地震记录,结果表明ROAD径向时频峰值滤波方法可以压制空间非平稳地震勘探随机噪声且不损害有效信号,有效抑制随机噪声空间非平稳对滤波结果的影响.与径向时频峰值滤波相比,ROAD径向时频峰值滤波方法更适用于空间非平稳地震勘探随机噪声压制.