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.     

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.     

基于波场传播方向的波动方程偏移有效去噪方法(英文)

本文研究分析了双程波波动方程偏移成像中广泛存在的三种主要噪声,特别是针对过去研究中没能很好解决的存在于高速盐丘悬垂边界附近的射线状噪声,提出了基于优化成像条件的有效去噪方法。射线状噪声主要来自于震源一侧波场的下行透射波分量和接收阵列一侧波场的上行散射波互相关成像。这一部分能量具有较强的互相关性,但并不携带真实的反射面信息。它广泛存在叠前偏移成像中,与信号在强度上同量级。多数情况下偏移成像中的相关噪声由方向性传播的波场能量产生。利用波场梯度得到的波场传播角度,可以分离出噪声对应的波场能量,并在成像条件中减去。采用这一方法可以有效地去除多种噪声,包括直达波噪声、散射波噪声和射线状噪声。该去噪方法不依赖波场外推算子,在需要时可以方便地运用到几乎所有的波动方程偏移中去。并且该去噪方法针对噪声的物理根源,对信号的损害很小。对去噪后的偏移成像结果额外地进行波数域滤波处理,可以进一步提高叠加图像的质量。这一去噪方法在超广角单程波偏移成像中取得良好效果,我们同时期待其在其他双程波波动方程偏移特别是逆时偏移(RTM)中的成功运用。     

高斯波包反射走时速度反演方法

扰动高斯波包理论指出,在Gabor域描述模型的扰动成分,且入射波场为短时宽带信号时,扰动波场可在时间域通过高斯波包算子描述.在此基础上通过拟合反射波的走时,提出一种速度反演方法.反射波走时残差利用地震道局部波形的互相关函数表示,以走时残差的二范数作为目标函数,优化目标函数实现对速度场的反演.基于一阶Born近似,利用扰动高斯波包理论推导出目标函数对速度场的梯度是本文理论部分的核心内容.梯度包括两部分:正传的背景波场与反传的扰动高斯波包之间的互相关,反传的背景波场和正传的扰动高斯波包之间的互相关.梯度表达式中背景波场和扰动波场均利用高斯波包算子模拟.计算梯度的具体算法中,如何模拟扰动波场,以及如何计算反射波的走时残差是两个要点,文中对此做了详细的讨论.数值实验进一步阐述了反演的实现策略,实验结果表明高斯波包反射走时速度反演方法和实现策略有效可行,并得到了理想的反演结果.     

利用矩阵分解理论的双程波方程叠前深度偏移方法

叠前深度偏移理论及方法一直是地震数据成像中研究的热点问题.业界对单程波叠前深度偏移方法和逆时深度偏移开展了深入的研究,但对双程波方程波场深度延拓理论及成像方法的研究还鲜有报道.本文以地表记录的波场值为基础,利用单程波传播算子估计波场对深度的偏导数,为在深度域求解双程波方程提供充分的边界条件,并提出利用矩阵分解理论实现双程波方程的波场深度外推.通过对强速度变化介质中传播波场的计算,与传统的单程波偏移方法相比,本文提出的偏移方法计算的波场与常规有限差分技术计算的波场相一致,证明了本方法计算的准确性.通过对SEAM模型的成像,在相同的成像参数下,与传统的单程波偏移算法和逆时深度偏移算法方法相比,本文提出的偏移方法能够提供更少的虚假成像和更清晰的成像结果.本文所提偏移算法具有深度偏移和双程波偏移的双重特色,推动和发展了双程波叠前深度偏移的理论和实践.     

VTI介质中准P波方程叠前逆时深度偏移

根据具有垂直对称轴的横向各向同性（VTI）介质中的一阶准P波方程,导出了该方程在交错网格中逆时延拓的高阶有限差分格式,给出了其稳定性条件,采用完全匹配层吸收边界条件解决边界反射问题,分别应用下行波最大能量法和归一化互相关成像条件, 实现了VTI介质中准P波方程的叠前逆时深度偏移．各向异性Marmousi模型的试算结果表明,VTI介质准P波方程叠前逆时深度偏移算法不受地下构造倾角和介质横向速度变化的限制,对复杂模型具有良好的成像能力;应用归一化互相关成像条件能得到更好的成像效果．对比该模型的各向异性和各向同性逆时偏移剖面表明,在各向异性地区采集的纵波数据用各向异性偏移算法理论上能得到更好的成像结果．      

基于Poynting矢量的归一化波场分离互相关逆时偏移成像条件(英文)

叠前逆时偏移是目前精度较高的成像方法,然而严重的低频噪声降低了逆时偏移的构造成像精度,偏移噪声的压制是逆时偏移必需要考虑的问题。分析了低频噪声的产生机理,并根据声波方程Poynting矢量的方向指示地震波场的传播方向的原理,分离出上、下、左、右行波,该方法计算量和存储量都远远小于常用的二维傅里叶变换分离方法,进而提出归一化的波场分离互相关成像条件,以压制逆时偏移低频噪声,提高成像精度。实现了Marmousi模型的试算,表明在波场延拓过程中利用Poynting矢量能够较好的分离上、下、左、右行波,与常规方法、拉普拉斯滤波、二维傅里叶变换波场分离的成像结果对比表明,成像时使用归一化的波场分离互相关成像条件能更好的压制偏移噪声,得到精度更高的逆时偏移成像结果。     

叠前逆时偏移影响因素分析

反射地震勘探中的偏移成像技术是获取地下介质构造形态最有效的手段之一.在叠前深度域偏移方法中,目前工业界采用的方法包括基于射线理论的波动方程积分解法和基于波动理论的微分波动方程单程波解法,这两类方法难以处理地震波横向速度变化剧烈的高陡倾角构造成像问题.近年来勘探地震学研究领域发展起来的叠前逆时偏移采用了双程波求解微分波动方程的算法,这种方法具有相位准确、不受介质横向速度变化和高陡倾角构造的影响、成像精度高、可以利用回转波正确成像等优点,从理论上弥补了当前工业界常规地震偏移所面临的成像缺陷.然而,叠前逆时偏移成像方法从理论走向实用尚需解决如下问题:计算速度和数据存储空间的节省、初始速度模型的建立、震源子波的选择、数值模型边界条件的定义和假像的消除等等.对于计算速度和存储量大的问题,随着计算机硬件的快速发展,将会不断得到改善,同时可以采取一些计算技术和存储策略来加以缓解.本文主要针对初始速度模型的建立、震源子波的选择、数值模型边界条件的定义和假像的消除这些因素,利用简单模型进行了分析.对于反射波造成的传播路径上的假像,给出了一种振幅补偿滤波方法.对勘探地球物理学界给出的SEG/EAGE二维盐丘模型、Marmousi模型和本研究设计的崎岖海底模型进行了叠前逆时偏移成像,均取得了较好的成像效果.     

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.     

2D and 3D amplitude-preserving elastic reverse time migration based on the vector-decomposed P- and S-wave records

The elastic reverse time migration approach based on the vector-wavefield decomposition generally uses the scalar product imaging condition to image the multicomponent seismic data. However, the resulting images contain the crosstalk artefacts and the polarity reversal problems, which are caused by the nonphysical wave modes and the angle-dependent reduction of image amplitudes, respectively. To overcome these two problems, we develop an amplitude-preserving elastic reverse time migration approach based on the vector-decomposed P- and S-wave seismic records. This approach includes two key points. The first is that we employ the vector-decomposed P- and S-wave multicomponent records to independently reconstruct the PP and PS reflection images to mitigate the crosstalk artefacts. The second is that we propose two schemes in addressing the issue of polarity reversal problem in the conventional PP image. One solution is to adopt the angle-dependent equation. Another one is to reconstruct an amplitude-preserving PP image with a separated scalar P-wave particle velocity, which has a clear physical meaning. Numerical examples using two-dimensional and three-dimensional models demonstrate that the proposed elastic reverse time migration approach can provide the images with better amplitude-preserving performance and fewer crosstalk artefacts, compared with the conventional elastic reverse time migration approach based on the scalar product imaging condition.     

基于波场分离的弹性波逆时偏移

尽管叠前逆时偏移成像精度高,但仅针对单一纵波的成像也可能形成地下介质成像盲区,由于基于弹性波方程的逆时偏移成像可形成多波模式的成像数据,因此弹性波逆时偏移成像可提供更为丰富的地下构造信息.本文依据各向同性介质的一阶速度-应力方程组构建震源和检波点矢量波场,再利用Helmholtz分解提取纯纵波和纯横波波场,使用震源归一化的互相关成像条件获得纯波成像,避免了直接使用坐标分量成像而引起的纵横波串扰问题.针对转换波成像的极性反转问题,文中提出一种共炮域极性校正方法.为有效节约存储成本,也提出一种适用于弹性波逆时偏移的震源波场逆时重建方法,在震源波场正传过程中,仅保存PML边界内若干层的速度分量波场,进而逆时重建出所有分量的震源波场.本文分别对地堑模型和Marmousi2模型进行了弹性波逆时偏移成像测试,结果表明:所提出的共炮域极性校正方法正确有效,基于波场分离的弹性波逆时偏移成像的纯波数据能够对复杂地下构造准确成像.     

带正则化校正的TTI介质qP波方程及其逆时偏移方法和应用

各向异性研究对地下介质精确成像有着重要的意义,在当前计算机硬件迅速发展及宽方位地震数据采集日益普遍的情况下,成像必须考虑介质的各向异性.逆时偏移是基于双程波动方程的较为精确的数值解的成像方法,所以相对于其他地震成像方法,它具有很大的优势,譬如不受反射界面的倾角限制、偏移速度结构合适时能够使回转波及多次波正确成像.在各向同性介质中,可使用标量波方程来模拟波场.而在各向异性介质中,P波和SV波是相互耦合的,即不存在单纯的标量波传播,通常利用能代表耦合波场中P波分量运动学特征的拟声波(qP波)进行偏移成像.本文中,我们推导出了TTI介质下qP波控制方程.该方程可采用显式有限差分格式进行求解.通过声学近似,若沿对称轴方向的剪切波速度为零,对于对称轴方向不变且ε≥δ的模型来说,可得到稳定的数值解.但对于TTI介质来说,由于沿对称轴方向各向异性参数是变化的,声学近似会引起波场传播及数值计算的不稳定.因此,我们提出了正则化有限横波的方法,很好地解决了这一问题.最后,给出了Foothill模型的测试结果及某探区实际资料试算结果,展示了采用这个方程进行复杂TTI模型正演和高质量逆时偏移成像结果,证实了该方法的正确性和实际资料应用中的有效性.     

基于逆散射成像条件的最小二乘逆时偏移

最小二乘逆时偏移（LSRTM）相对于常规逆时偏移（RTM）具有分辨率更高、振幅更准确、噪音更少等优势,可以对复杂的地质构造进行有效的成像.这种迭代更新反演成像方法十分依赖目标函数的梯度质量和计算效率.当地质模型中存在强反射界面或者记录中存在折射波时,基于常规互相关成像条件（CCC）的最小二乘逆时偏移梯度会包含很强的低频噪音,从而使反演的收敛速度和成像质量降低.为此,本文在最小二乘逆时偏移的梯度中引进了逆散射成像条件来压制这种低频噪音,并以此提出基于逆散射成像条件（ISC）的最小二乘逆时偏移方法.数值模拟结果表明,两者计算耗时基本一致,但逆散射成像条件能高效压制梯度中的低频噪音,从而使反演过程中收敛加速,成像质量得到显著提高.     

基于波场垂向和水平方向外推的高陡构造偏移

常规的单程波波动方程偏移成像方法对大角度的高陡构造偏移成像存在内在的限制.根据波动方程在各个空间方向的数学特性和高陡构造反射地震波的传播特征,通过把地震波分解为垂向的上下行波、水平方向的前后行波和左右行波,提出基于波场垂向外推和水平方向外推相结合的单程波波动方程高陡构造偏移成像方法,即用波场垂向外推的单程波波动方程偏移成像方法解决中低角度平缓构造的偏移成像,用波场水平方向外推的单程波波动方程偏移成像方法解决中高角度陡倾构造的偏移成像.这种基于波场垂向和水平方向外推相结合的高陡构造偏移成像方法是常规单程波波动方程叠前深度偏移成像方法的补充和改进,它相对基于全波方程的逆时偏移具有计算效率上的优势.     

Topographic elastic least-squares reverse time migration based on vector P- and S-wave equations in the curvilinear coordinates

Elastic least-squares reverse time migration has been applied to multi-component seismic data to obtain high-quality images. However, the final images may suffer from artefacts caused by P- and S-wave crosstalk and severe spurious diffractions caused by complex topographic surface conditions. To suppress these crosstalk artefacts and spurious diffractions, we have developed a topographic separated-wavefield elastic least-squares reverse time migration algorithm. In this method, we apply P- and S-wave separated elastic velocity–stress wave equations in the curvilinear coordinates to derive demigration equations and gradient formulas with respect to P- and S-velocity. For the implementation of topographic separated-wavefield elastic least-squares reverse time migration, the wavefields, gradient directions and step lengths are all calculated in the curvilinear coordinates. Numerical experiments conducted with the two-component data synthetized by a three-topographic-layer with anomalies model and the Canadian Foothills model are considered to verify our method. The results reveal that compared with the conventional method, our method promises imaging results with higher resolution and has a faster residual convergence speed. Finally, we carry out numerical examples on noisy data, imperfect migration velocity and inaccurate surface elevation to analyse its sensitivity to noise, migration velocity and surface elevation error. The results prove that our method is less sensitive to noise compared with the conventional elastic least-squares reverse time migration and needs good migration velocities as other least-squares reverse time migration methods. In addition, when implementing the proposed method, an accurate surface elevation should be obtained by global positioning system to yield high-quality images.     

基于逆虚折射干涉法有效提取近地表弱地震信号

在地震勘探中,地形起伏和近地表速度的剧烈变化会导致地震波旅行时的扰动,通常会通过折射波信息来估算和消除这些扰动.本文在虚折射的基础上提出了逆虚折射干涉法,通过虚折射波场和原始折射波场的互相关,并对所有位于固定相位点上的检波点进行叠加,重构出逆虚折射波场.通过逆虚折射与超级虚折射的叠加,保证了不同偏移距下折射波振幅恢复的一致性,显著提高折射波的信噪比,有效提取弱信号.同时,本文采用反褶积干涉法来压制由于互相关和褶积产生的子波旁瓣的影响,弥补低频和高频能量的损失,改善恢复的折射波场的稳定性和分辨率.该新方法不需要知道近地表复杂速度模型的信息,可以将虚折射的勘探孔径恢复到原始地震记录的最大孔径.合成资料和实际资料的计算结果表明,基于反褶积的逆虚折射干涉法能够从低信噪比的资料中,有效恢复出折射波信息.     

Understanding the reverse time migration backscattering: noise or signal?

Reverse time migration backscattered events are produced by the cross‐correlation between waves reflected from sharp interfaces (e.g., salt bodies). These events, along with head waves and diving waves, produce the so‐called reverse time migration artefacts, which are visible as low wavenumber energy on migrated images. Commonly, these events are seen as a drawback for the reverse time migration method because they obstruct the image of the geologic structure, which is the real objective for the process. In this paper, we perform numeric and theoretical analysis to understand the reverse time migration backscattering energy in conventional and extended images. We show that the reverse time migration backscattering contains a measure of the synchronization and focusing information between the source and receiver wavefields. We show that this synchronization and focusing information is sensitive to velocity errors; this implies that a correct velocity model produces reverse time migration backscattering with maximum energy. Therefore, before filtering the reverse time migration backscattered energy, we should try to obtain a model that maximizes it.     

CGP叠加柱面波偏移成像方法

针对松辽盆地薄砂层油藏的地震勘探问题,提出了一种共检波器接收点(CGP)叠加柱面波偏移成像方法。该方法对小炮点距、小检波器点距、中间放炮观测系统采集地震资料,经CGP道集叠加组合成柱面波剖面;采用下行波射线法向下延拓和上行波波动方程向下延拓的方法,使柱面波剖面偏移成像。通过模型分析和对松辽盆地TK8157测线资料进行处理证明该方法的地震分辨率和保真度较高,在发现小砂体、小断层、地层尖灭等方面有较好的效果。     

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.     

地震多次波成像

地震资料含有各种类型多次波,而传统成像方法仅利用地震一次反射波成像,在地震成像前需将多次波去除.然而,多次波携带了丰富的地下结构信息,多次波偏移能够提供除反射波外的额外地下照明.修改传统逆时偏移方法,用包含一次反射波和多次波的原始记录代替震源子波,将SRME方法预测的表面多次波代替一次反射波作为输入数据,可将表面多次波成像.多次波成像的挑战和困难在于大量串扰噪声的产生,针对表面多次波成像中的成像噪声问题,将最小二乘逆时偏移方法与多次波分阶思想结合起来,发展可控阶数的表面多次波反演成像方法,有望初步实现高精度的表面多次波成像.在消除原始记录中的表面多次波后,通过逆散射级数方法预测得到层间多次波,将层间多次波作为逆时偏移方法的输入数据可将其准确归位到地下反射位置.数值实验表明,多次波成像能够有效地为地下提供额外照明,而可控阶表面多次波最小二乘逆时偏移成像方法几乎完全避免成像噪声.