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.     

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.     

基于解析时间波场外推与波场分解的逆时偏移方法研究

双程波方程逆时深度偏移是复杂介质高精度成像的有效技术,但其结果中通常包含成像方法引起的噪音和假象,一般的滤波方法会破坏成像剖面上的振幅,其中的假象也会给后续地质解释带来困扰.将波场进行方向分解然后实现入射波与反射波的相关成像能够有效地消除这类成像噪音,并提高逆时偏移成像质量.波传播方向的分解通常在频率波数域实现,它会占用大量的存储和计算资源,不便于在沿时间外推的逆时深度偏移中应用.本文提出解析时间波场外推方法,可以在时间外推的每个时间片上实现波传播方向的显式分解,逆时深度偏移中利用分解后的炮检波场进行对应的相关运算,实现成像噪音和成像信号的分离.在模型和实际数据上的测试表明,相比于常规互相关逆时偏移成像结果,本文方法能够有效地消除低频成像噪音和特殊地质构造导致的成像假象.     

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.     

基于时空局域化dreamlet单程波算子的观测系统沉降法偏移

Dreamlet偏移成像目的是探索一类能够对地震波场和单程波传播算子同时分解和压缩的理论和方法,也即实现在压缩域的传播与成像、地震数据在时间和空间的非平稳性质,决定了要实现地震数据的有效稀疏表示,分解方法必须在时间和空间上同时具有局域化性质.Dreamlet由时间和空间局部分解原子的张量积构成,可以看作一种脉冲-小波束形式的波场分解原子.时空局域化的dreamlet单程波传播算子在对波场沿深度方向延拓时,地震数据在时间轴上总是向同一方向流动.随着深度的增加,部分用于成像浅层结构的数据归位至其空间位置后被dreamlet算子丢弃,波场的有效记录时间变短,每一步用于波场延拓的计算量也相应下降.为了充分发挥这一优势,本文介绍dreamlet传播算子与观测系统沉降法偏移相结合的理论与方法.观测系统沉降法偏移每一步都将记录到的所有数据向下延拓,沉降后的波场等效于把源和检波器都放置在目标深度所能接收的反射数据.Dreamlet观测系统沉降过程只保留用于成像观测系统下部地质结构的有效数据,自动丢弃已经用于成像观测系统上部而对下部成像没有贡献的信号.本文通过二维SEG/EAGE叠后和Marmousi叠前数据算例展示了dreamlet传播算子应用于观测系统沉降法偏移的这一特点.数值算例结果显示,在不影响成像质量的前提下,该偏移方法能够有效减少传播数据量,为发展一种快速高效的偏移方法提供了新的思路.     

Reverse time migration of ground-penetrating radar with full wavefield decomposition based on the Hilbert transform

The conventional reverse time migration of ground-penetrating radar data is implemented with the two-way wave equation. The cross-correlation result contains low-frequency noise and false images caused by improper wave paths. To eliminate low-frequency noise and improve the quality of the migration image, we propose to separate the left-up-going, left-down-going, right-up-going and right-down-going wavefield components in the forward- and backward-propagated wavefields based on the Hilbert transform. By applying the reverse time migration of ground-penetrating radar data with full wavefield decomposition based on the Hilbert transform, we obtain the reverse time migration images of different wavefield components and combine correct imaging conditions to generate complete migration images. The proposed method is tested on the synthetic ground-penetrating radar data of a tilt-interface model and a complex model. The migration results show that the imaging condition of different wavefield components can highlight the desired structures. We further discuss the reasons for incomplete images by reverse time migration with partial wavefields. Compared with the conventional reverse time migration methods for ground-penetrating radar data, low-frequency noise can be eliminated in images generated by the reverse time migration method with full wavefield decomposition based on the Hilbert transform.     

Dreamlet source‐receiver survey sinking prestack depth migration

Survey sinking migration downward continues the entire surface observed multi‐shot data to the subsurface step by step recursively. Reflected energy from reflectors at current depth appear at zero time and zero offset in the extrapolated wavefield. The data (seismic records) of t > 0 at this depth are equivalent to the data acquired by a survey system deployed at this depth. This is the reason to name the process ‘survey sinking’. The records of negative time need not to be further propagated since they carry no information to image structures beneath the new survey system. In this paper, we combine survey sinking with dreamlet migration. The dreamlet migration method decomposes the seismic wavefield and one‐way wave propagator by complete time‐space localized bases. The localization on time gives flexibility on time‐varying operations during depth extrapolation. In dreamlet survey sinking migration, it only keeps the data for imaging the structures beneath the sunk survey system and gets rid of the data already used to image structures above it. The deeper the depth is, the shorter is the valid time records of the remaining data and less computation is needed for one depth step continuation. For data decomposition, in addition to time axis, dreamlet survey sinking also decomposes the data for source and receiver gathers, which is a fully localized decomposition of prestack seismic data. A three‐scatter model is first used to demonstrate the computational feature and principle of this method. Tests on the two‐dimensional SEG/EAGE salt model show that with reduced data sets the proposed method can still obtain good imaging quality on complex geology structures and a strong velocity contrast environment.     

基于弹性波全波形反演的主被动源多分量混采地震数据速度建模

在常规地震采集中,被动源地震波场往往被视为噪声而去除,这就造成了部分有用信息的丢失.在目标区进行主动源和被动源弹性波地震数据的多分量混合采集,并对两种数据进行联合应用,使其在照明和频带上优势互补,能显著提高成像和反演的质量.本文针对两种不同类型的主被动源混采地震数据,分别提出了相应的联合全波形反演方法.首先,针对主动源与瞬态被动源弹性波混采地震数据,为充分利用被动源对深部照明的优势,同时有效压制被动震源点附近的成像异常值,提出了基于动态随机组合的弹性波被动源照明补偿反演策略.然后,针对低频缺失主动源与背景噪声型被动源弹性波混采地震数据,为充分利用被动源波场携带的低频信息,并避免对被动源的定位和子波估计,提出了基于地震干涉与不依赖子波算法的弹性波主被动源串联反演策略.最后,分别将两种方法在Marmousi模型上进行反演测试.结果说明,综合利用主动源和被动源弹性波混采地震数据,不仅能增强深部弹性参数反演效果,还能更好地构建弹性参数模型的宏观结构,并有助于缓解常规弹性波全波形反演的跳周问题.     

Receiver function method in reflection seismology

The receiver function method was originally developed to analyse earthquake data recorded by multicomponent (3C) sensors and consists in deconvolving the horizontal component by the vertical component. The deconvolution process removes travel path effects from the source to the base of the target as well as the earthquake source signature. In addition, it provides the possibility of separating the emergent P and PS waves based on adaptive subtraction between recorded components if plane waves of constant ray parameters are considered. The resulting receiver function signal is the local PS wave's impulse response generated at impedance contrasts below the 3C receiver.We propose to adapt this technique to the wide‐angle multi‐component reflection acquisition geometry. We focus on the simplest case of land data reflection acquisition. Our adapted version of the receiver function approach consists in a multi‐step procedure that first removes the P wavefield recorded on the horizontal component and next removes the source signature. The separation step is performed in the τ?p domain while the source designature can be achieved in either the τ?p or the t?x domain. Our technique does not require any a priori knowledge of the subsurface. The resulting receiver function is a pure PS‐wave reflectivity response, which can be used for amplitude versus slowness or offset analysis. Stack of the receiver function leads to a high‐quality S wave image.     

时-空局域化地震波传播方法:Dreamlet叠前深度偏移

提出了一种在时间和空间上完全局域化的波场分解和传播算法─dreamlet偏移方法.Dreamlet是一种脉冲-小波束形式的波场分解原子,它利用多维局部分解变换,把时空域波场映射到局部时间-频率-空间-波数相空间,并用局部相空间的传播算子(dreamlet算子)沿深度延拓.本文利用多维局部余弦变换实现dreamlet算法,分解后的波场系数和传播算子不仅有很好的稀疏性,且均为实数,也即波的传播和成像过程完全在实数域实现.文中推导了局部余弦基dreamlet波场分解和传播算子理论公式并将其应用于叠前深度偏移.在dreamlet相空间波的传播过程为稀疏矩阵相乘,而且延拓后的地表数据波场的有效时间长度随深度的增加不断减小,从而可以减少需要传播的波场系数.二维SEG/EAGE盐丘和SIGSBEE模型算例验证了理论推导的正确性,成像结果显示该方法在横向速度变化剧烈情况下有很好的精度.     

Extending illumination using all multiples: application to 3D acquisition geometry analysis

Recent advances in survey design have led to conventional common‐midpoint‐based analysis being replaced by subsurface‐based seismic acquisition analysis, with emphasis on advanced techniques of illumination analysis. Among them is the so‐called focal beam method, which is a wave‐equation‐based seismic illumination analysis method. The objective of the focal beam method is to provide a quantitative insight into the combined influence of acquisition geometry, overburden structure, and migration operators on the resolution and angle‐dependent amplitude fidelity of the image. The method distinguishes between illumination and sensing capability of a particular acquisition geometry by computing the focal source beam and the focal detector beam, respectively. Sensing is related to the detection properties of a detector configuration, whereas illumination is related to the emission properties of a source configuration. The focal source beam analyses the incident wavefield at a specific subsurface grid point from all available sources, whereas the focal detector beam analyses the sensing wavefield reaching at the detector locations from the same subsurface grid point. In the past, this method could only address illumination by primary reflections. In this paper, we will extend the concept of the focal beam method to incorporate the illumination due to the surface and internal multiples. This in fact complies with the trend of including multiples in the imaging process. Multiple reflections can illuminate a target location from other angles compared with primary reflections, resulting in a higher resolution and an improved illumination. We demonstrate how an acquisition‐related footprint can be corrected using both the surface and the internal multiples.     

基于Hilbert变换的全波场分离逆时偏移成像

逆时偏移方法利用双程波算子模拟波场的正向和反向传播,通常采用互相关成像条件获得偏移剖面,是一种高精度的成像方法.但是传统的互相关成像条件会在偏移结果中产生低频噪声;此外,如果偏移速度中存在剧烈速度变化还可能进一步产生偏移假象.为了提高逆时偏移的成像质量,可在成像过程中先对震源波场和检波点波场分别进行波场分离,然后选择合适的波场成分进行互相关成像.本文基于Hilbert变换,推导了可在偏移过程中进行上下行和左右行波场分离的高效波场分离公式以及相应的成像条件,结合Sigsbee 2B合成数据,给出了不同波场成分的互相关成像结果.数值算例结果表明,采用本文提出的高效波场分离算法以及合理的波场成分互相关成像条件可以获得高信噪比的成像结果.     

弹性波逆时偏移中的稳定激发振幅成像条件

本文针对弹性波逆时偏移,提出稳定的激发振幅成像条件.在震源波场的正向传播过程中,计算每个网格点的能量,并保存最大能量密度的时刻和相应的波场值;在检波器波场的逆时传播过程中,在每个网格点提取最大能量密度时刻的检波器波场值,并利用保存的最大能量震源波场做归一化,获得角度依赖的反射系数成像剖面.相比于归一化互相关成像条件,该成像条件在震源波场的正向传播过程中无需存储波场快照,节省大量磁盘空间和I/O吞吐任务,提高了计算效率;相比于弹性波的激发时间成像条件,该成像条件自动校正了水平分量在震源两侧的极性反转,在多炮叠加时避免振幅损失.数值试验表明,与归一化成像条件相比,稳定激发振幅成像条件具有更小的计算量,偏移剖面的低频假象更弱,水平分量的成像能力更优,具有更高的空间分辨率.     

数据域特征波反射走时反演

地震波的运动学信息(走时、斜率等)通常用于宏观速度建模.针对走时反演方法,一个基本问题是走时拾取或反射时差的估计.对于成像域反演方法,可以通过成像道集的剩余深度差近似计算反射波时差.在数据域中,反射地震观测数据是有限频带信号,如果不能准确地确定子波的起跳时间,难以精确地确定反射波的到达时间.另一方面,如果缺乏关于模型的先验信息,则很难精确测量自地下同一个反射界面的观测数据同相轴和模拟数据同相轴之间的时差.针对走时定义及时差测量问题,首先从叠前地震数据的稀疏表达出发,利用特征波场分解方法,提取反射子波并估计局部平面波的入射和出射射线参数.进一步,为了实现自动和稳定的走时拾取,用震相的包络极值对应的时间定义反射波的到达时,实现了立体数据中间的自动生成.理论上讲,利用包络极值定义的走时大于真实的反射波走时,除非观测信号具有无限带宽(即delta脉冲).然而,走时反演的目的是估计中-大尺度的背景速度结构,因此走时误差导致的速度误差仍然在可以接受的误差范围内.利用局部化传播算子及特征波聚焦成像条件将特征波数据直接投影到地下虚拟反射点,提出了一种新的反射时差估计方法.既避免了周期跳跃现象以及串层等可能性,又消除了振幅因素对时差测量的影响.最后,在上述工作基础之上,提出了一种基于特征波场分解的新型全自动反射走时反演方法(CWRTI).通过对泛函梯度的线性化近似,并用全变差正则化方法提取梯度的低波数部分,实现了背景速度迭代反演.在理论上,无需长偏移距观测数据或低频信息、对初始模型依赖性低且计算效率高,可以为后续的全波形反演提供可靠的初始速度模型.理论和实际资料的测试结果证明了本文方法的有效性.     

基于局部余弦基小波束的观测系统沉降法叠前深度偏移

将局部余弦基小波束波场分解、传播与观测系统沉降法叠前深度偏移相结合,推导了源-检波器观测系统沉降法传播算子.本算法中,先对频率域的共点源和共点检波器道集做局部余弦小波束分解,然后分别沿共小波束源和共小波束检波器在深度方向延拓得到下一层波场.每个深度的波场,都等效于把源和检波器放在该层后所能接收到的地震记录,每点的像值由炮点和检波点重合时的零时刻波场值给出.通过二维SEG/EAGE盐丘模型和Marmousi模型的偏移成像结果验证该方法理论推导的正确性.另外,结果显示该方法继承了小波束域波场延拓在速度扰动较大情况下波传播及成像精度高的优点.     

基于Poynting矢量行波分离的最小二乘逆时偏移

因为在逆时偏移中基于双程波动方程构建震源波场和检波器波场,所以在波场延拓过程中地震波遇到波阻抗界面时,背向发育的反射波会与正常传播的波场互相关产生较强振幅的低频噪声.这一特点使得以逆时偏移为基础的最小二乘偏移方法在梯度计算时同样存在着低频噪声的干扰,从而导致反演收敛的速度减慢.考虑到计算量和存储成本的因素,本文借助Poynting矢量良好的方向指示性实现波场的上下行波分离,并在早期迭代的梯度计算中只保留震源波场和检波器波场沿不同垂直方向传播的组分之间的互相关,有效避免了成像噪声的干扰,提高了算法收敛的速率.数值算例验证了方案的有效性.     

Deghosting by echo‐deblending

A marine source generates both a direct wavefield and a ghost wavefield. This is caused by the strong surface reflectivity, resulting in a blended source array, the blending process being natural. The two unblended response wavefields correspond to the real source at the actual location below the water level and to the ghost source at the mirrored location above the water level. As a consequence, deghosting becomes deblending (‘echo‐deblending’) and can be carried out with a deblending algorithm. In this paper we present source deghosting by an iterative deblending algorithm that properly includes the angle dependence of the ghost: It represents a closed‐loop, non‐causal solution. The proposed echo‐deblending algorithm is also applied to the detector deghosting problem. The detector cable may be slanted, and shot records may be generated by blended source arrays, the blending being created by simultaneous sources. Similar to surface‐related multiple elimination the method is independent of the complexity of the subsurface; only what happens at and near the surface is relevant. This means that the actual sea state may cause the reflection coefficient to become frequency dependent, and the water velocity may not be constant due to temporal and lateral variations in the pressure, temperature, and salinity. As a consequence, we propose that estimation of the actual ghost model should be part of the echo‐deblending algorithm. This is particularly true for source deghosting, where interaction of the source wavefield with the surface may be far from linear. The echo‐deblending theory also shows how multi‐level source acquisition and multi‐level streamer acquisition can be numerically simulated from standard acquisition data. The simulated multi‐level measurements increase the performance of the echo‐deblending process. The output of the echo‐deblending algorithm on the source side consists of two ghost‐free records: one generated by the real source at the actual location below the water level and one generated by the ghost source at the mirrored location above the water level. If we apply our algorithm at the detector side as well, we end up with four ghost‐free shot records. All these records are input to migration. Finally, we demonstrate that the proposed echo‐deblending algorithm is robust for background noise.     

基于可视性分析与能量补偿的金属矿弹性波全波形反演

采用弹性波全波形反演方法精确重建深部金属矿多参数模型,建模过程采用基于地震照明的反演策略.首先给出基于照明理论的观测系统可视性定义,利用可视性分析构建新的目标函数,对反演目标可视性较高的炮检对接收到的地震记录在波场匹配时占有更高的权重,确保了参与反演计算中的地震数据的有效性;其次将给定观测系统对地下介质的弹性波场照明强度作为优化因子,根据地震波在波阻抗界面处的能量分配特点,自适应补偿波场能量分布和优化速度梯度,以提高弹性波全波形反演过程的稳定性和反演结果的精度.理论模型和金属矿模型反演试验结果表明,基于可视性分析和能量补偿的反演策略可以使弹性波全波形反演更快地收敛到目标函数的全局极小值,获得适用于金属矿高分辨率地震偏移成像的多参数模型.     

Generating an Image of Dispersive Energy by Frequency Decomposition and Slant Stacking

We present a new algorithm for calculating an image of dispersive energy in the frequency-velocity (f-v) domain. The frequency decomposition is first applied to a shot gather in the offset-time domain to stretch impulsive data into pseudo-vibroseis data or frequency-swept data. Because there is a deterministic relationship between frequency and time in a sweep used in the frequency decomposition, the first step theoretically completes the transform from time to frequency. The slant stacking is then performed on the frequency-swept data to complete the transform from offset to velocity. This simple two-step algorithm generates an image of dispersive energy in the f-v domain. The straightforward transform only uses offset information of data so that this algorithm can be applied to data acquired with arbitrary geophone-acquisition geometry. Examples of synthetic and real-world data demonstrate that this algorithm generates accurate images of dispersive energy of the fundamental as well as higher modes.     

利用微震数据对震源下方构造直接成像

现有的微震记录直接成像方法是将微震记录既当作入射记录,也当作散射记录,从而实现偏移成像.但此方法并不能突出透射波所携带的来自震源下方的深层散射波信息.本文在假设已知微震位置与子波的前提下,提出了对微震下方构造进行逆时偏移的成像方法.该方法类似于常规的逆时偏移,只是震源位置在地下.这使得在成像时,地下更深部的入射波场相比震源在地表时会更为精确,因此能够获得更加准确的成像结果.该方法会给成像结果带来一种尾波高频干扰：地下的震源发出的上行波与上方介质作用后,所产生的多级散射波会干扰反传波场.对此,在成像过程中,对入射场和散射场都进行左右行波分离,以压制该噪声.而在子波信息未知,无法重构入射场时,使用了激发时间成像条件,也能够实现同等效果的偏移成像,且不会出现尾波高频干扰.利用数值实验验证了本文方法的有效性.