基于新的惩罚因子算法的波场重构反演

全波形反演是一种高精度的反演方法,其目标函数是一个强非线性函数,易受局部极值影响,而且反演过程计算量较大.波场重构反演是近几年提出的一种改进的全波形反演理论.该反演方法通过将波动方程作为惩罚项引入到目标函数中,通过拓宽解的寻找空间减弱了局部极小值的影响,而且反演过程不需要计算伴随波场,提高了计算效率.但该反演方法一直缺少准确的惩罚因子算法,直接影响到该方法的准确度.本文将波场重构反演拓展到时间域并利用梯度法进行波场重构.频率域的惩罚因子用来加强波动方程的约束,而时间域惩罚因子表现为调节模拟波场和实际波场的权重因子.为此,我们根据约束优化理论,在波动方程准确以及重构波场与反演参数解耦的假设下,提出以波动方程为目标函数的新的惩罚因子算法.根据波形反演在应用时普遍存在的噪音干扰、子波错误和低频信息缺失的情况下,应用部分Sigsbee2A模型合成数据对本文提出的算法进行实验.数值实验结果表明：基于新的惩罚因子算法,在其他信息不准确的情况下,波场重构反演可以给出高精度的反演结果.     

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.     

多尺度τ-p谱及其应用

把小波变换与τ-ｐ变换有机地结合起来,本文提出了多尺度τ-ｐ谱的概念,给出了基于多尺度τ-ｐ谱作滤波处理和波场分离的方法．与通常的τ-ｐ变换相比,该方法将x－t域的地震记录变换到（τ,p,a）或（τ,p,f）空间（即多尺度τ-ｐ谱）．多尺度τ-ｐ谱比通常τ-ｐ谱增加了一维,因此用于波场分离或去噪,前者优于后者．若恰当地选择小波函数,该方法抗噪能力强,计算精度高．文中给出了模型及实际地震资料处理实例;证明了此方法的有效性．     

基于改进线性Radon变换的井孔地震上下行波场分离方法

反射波场分离是井孔地震资料处理中极其重要的一个环节,波场分离的质量直接影响成像结果的精度.不管是VSP还是井间地震资料,其反射波时距曲线都近似直线型,根据这一特征,本文提出一种改进的线性Radon变换方法来进行井孔资料的反射波上下行波场分离.该方法基于频率域线性Radon变换,通过引入一个新的变量λ来消除变换算子对频率的依赖性,避免了求取每一频率分量对应的不同变换算子,显著降低了计算成本;文中在求解该方法对应的最小二乘问题时,引入了发展较为成熟的高分辨率Radon变换技术来进一步提高波场分离的精度.采用本文方法进行井孔地震资料的上下行波场分离可以在保证分离精度的前提下有效地提高计算效率.根据上下行波在λ-f域内分布的特殊性,设计简单的滤波算子就可实现上下行波场的分离.最后通过合成数据试算以及实际资料处理（VSP数据和井间地震数据）验证了该方法的可行性和有效性.     

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.     

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.     

基于两步SVD变换的零偏VSP资料上下行波场分离方法

垂直地震剖面(Vertical Seismic Profiling,VSP)资料处理中波场分离是关键问题之一.随着属性提取技术的发展,新的属性参数(例如Q值)提取技术对波场分离的保真性要求越来越高.本文改进了传统奇异值分解(Singular Value Decomposition,SVD)法,给出了一种对波场的动力学特征具有更好的保真性,可以作为Q值提取的预处理步骤的零偏VSP资料上下行波场分离方法.该方法通过两步奇异值分解变换实现:第一步,排齐下行波同相轴,利用SVD变换压制部分下行波能量;第二步,在剩余波场中排齐上行波同相轴,使用SVD变换提取上行波场.在该方法的实现过程中,压制部分下行波能量后的剩余波场中仍然存在较强的下行波干扰,使得上行波同相轴的排齐比较困难.本文给出了一种通过极大化多道数据线性相关程度(Maximize Coherence,MC)排齐同相轴的算法,在一定程度上解决了低信噪比下排齐同相轴的问题.将本文提出的方法用于合成数据和实际资料的处理,并与传统SVD法的处理结果进行对比,结果表明本文提出的波场分离方法具有良好的保真性,得到波场的质量明显优于传统SVD法.通过对本文方法和传统SVD法处理合成数据得到的下行波场提取Q值,然后进行对比可知,本文方法可以有效提高所提取Q值的准确性,适合作为Q值提取的预处理步骤.     

线性同相轴波场分离的高分辨率τ-p变换法

基于最小二乘τ-p变换和τ-p域模型稀疏分布的假设，本文给出高分辨率τ-p变换的推导及其模型空间域的离散采样公式，同时给出了保振幅线性同相轴波场分离的算法流程.在求解本文给出的高分辨率τ-p正变换时，由于待求解的矩阵不具备最小平方法所具有的Toeplitz结构，故采用Cholesky分解法进行计算.本文模拟了井间地震和阵列声波测井中的Stoneley上下行波的分离算法过程，高分辨率正反τ-p变换且滤波所得结果显示本文算法误差小和保振幅的特点.对于在τ-p域距离很近或时间域同相轴近于水平的线性波场，高分辨率算法的聚焦作用使得所分离波场畸变小，体现本文算法精度高的优点.理论模型试算表明本文给出的高分辨率τ-p变换线性波场分离算法具有稳定性、精度高和保振幅的特点.     

Experimental validation of the wavefield transform of electromagnetic fields

The wavefield transform is a mathematical technique for transforming low-frequency electromagnetic (EM) signals to a non-diffusive wave domain. The ray approximation is valid in the transform space and this makes traveltime tomography for 3D mapping of the electrical conductivity distribution in the subsurface possible. The transform, however, imposes stringent frequency bandwidth and signal-to-noise ratio requirements on the data. Here we discuss a laboratory scale experiment designed to collect transform quality EM data, and to demonstrate the practical feasibility of transforming these data to the wavefield domain.
We have used the scalable nature of EM fields to design a time-domain experiment using graphite blocks to simulate realistic field conditions while leaving the time scale undisturbed. The spatial dimensions have been scaled down by a factor of a thousand by scaling conductivity up by a factor of a million. The graphite blocks have two holes drilled into them to carry out cross-well and borehole-to-surface experiments. Steel sheets have been inserted between the blocks to simulate a conductive layer.
Our experiments show that accurate EM data can be recorded on a laboratory scale model even when the scaling of some features, such as drill-hole diameters, is not maintained. More importantly, the time-domain EM data recorded in cross-well and surface-to-borehole modes can be usefully and accurately transformed to the wavefield domain. The observed wavefield propagation delay is proportional to the direct distance between the transmitter and receiver in a homogeneous medium. In a layered medium, data accuracy is reduced and, hence, our results are not so conclusive. On the basis of the experimental results we conclude that the wavefield transform could constitute a valid approach to the interpretation of accurate, undistorted time-domain data if further improvement in the transform can be realized.     

基于Dreamlet变换的地震数据压缩理论与方法

为达到更加有效地表示地震数据的目的,仅仅将地震数据当作普通的图像数据处理是远远不够的,地震数据中蕴含的地震波的运动学特性也应作为重要因素而被考虑到.本文讨论了利用Dreamlet变换方法实现地震数据压缩的方法,并针对地震数据本身所蕴含的频散关系特性进一步提出了多尺度Dreamlet变换压缩方法.Dreamlet变换由2个一维局部谐波变换的张量积构成,它在提供地震波场时间-空间局部化性质的同时可以保留波场的运动学特性.通过对二维SEG/EAGE叠前、叠后数据的算例说明了Dreamlet变换用于地震数据压缩的有效性.利用压缩后的数据进行成像的结果更表明,与Curvelet变换方法相比,Dreamlet与多尺度Dreamlet方法可以提供更高的压缩比;在相同压缩比的条件下,使用Dreamlet与多尺度Dreamlet方法压缩重建后的数据进行成像能更好地保留成像结果中的重要结构.     

Time-domain hyperbolic Radon transform for separation of P-P and P-SV wavefields

A time-domain hyperbolic Radon transform based method for separating multicomponent seismic data into P-P and P-SV wavefields is presented. This wavefield separation method isolates P-P and P-SV wavefields in the Radon panel due to their differences in slowness, and an inverse transform of only part of the data leads to separated wavefields. A problem of hyperbolic Radon transform is that it works in the time domain entailing the inversion of large operators which is prohibitively time-consuming. By applying the conjugate gradient algorithm during the inversion of hyperbolic Radon transform, the computational cost can be kept reasonably low for practical application. Synthetic data examples prove that P-P and P-SV wavefield separation by hyperbolic Radon transform produces more accurate separated wavefields compared with separation by high-resolution parabolic Radon transform, and the feasibility of the proposed separation scheme is also verified by a real field data example.     

Time–Frequency–Wavenumber Analysis of Surface Waves Using the Continuous Wavelet Transform

A modified approach to surface wave dispersion analysis using active sources is proposed. The method is based on continuous recordings, and uses the continuous wavelet transform to analyze the phase velocity dispersion of surface waves. This gives the possibility to accurately localize the phase information in time, and to isolate the most significant contribution of the surface waves. To extract the dispersion information, then, a hybrid technique is applied to the narrowband filtered seismic recordings. The technique combines the flexibility of the slant stack method in identifying waves that propagate in space and time, with the resolution of f–k approaches. This is particularly beneficial for higher mode identification in cases of high noise levels. To process the continuous wavelet transform, a new mother wavelet is presented and compared to the classical and widely used Morlet type. The proposed wavelet is obtained from a raised-cosine envelope function (Hanning type). The proposed approach is particularly suitable when using continuous recordings (e.g., from seismological-like equipment) since it does not require any hardware-based source triggering. This can be subsequently done with the proposed method. Estimation of the surface wave phase delay is performed in the frequency domain by means of a covariance matrix averaging procedure over successive wave field excitations. Thus, no record stacking is necessary in the time domain and a large number of consecutive shots can be used. This leads to a certain simplification of the field procedures. To demonstrate the effectiveness of the method, we tested it on synthetics as well on real field data. For the real case we also combine dispersion curves from ambient vibrations and active measurements.     

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。     

交错网格中基于波数域插值的波场分离方法研究（英文）

应用多分量地震资料进行成像时通常需要先做波场分离,然后再对分离的波型进行成像。其中,波场分离可以在空间域或波数域实现。然而,由于用交错网格有限差分进行弹性波场数值模拟时,用来进行波数域波场分离的质点振动速度分量定义在不同网格节点上,本文提出了利用波数域插值方法来估算同一网格节点所需质点振动速度值;进而给出了先进行波数域插值后进行波场分离的波数域保幅波场分离方案。数值实验结果表明波数域插值方法具有较高的插值精度且保幅波场分离方法具有较好的保幅性,将本文方法进一步应用于弹性波逆时偏移可以获得保幅性较好的成像结果且对存在一定程度速度误差情况具有较好的适应性。     

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.     

时间二阶积分波场的全波形反演

通过对波场的时间二阶积分运算以增强地震数据中的低频成分,提出了一种可有效减小对初始速度模型依赖性的地震数据全波形反演方法—时间二阶积分波场的全波形反演方法.根据散射理论中的散射波场传播方程,推导出时间二阶积分散射波场的传播方程,再利用一阶Born近似对时间二阶积分散射波场传播方程进行线性化.在时间二阶积分散射波场传播方程的基础上,利用散射波场反演地下散射源分布,再利用波场模拟的方法构建地下入射波场,然后根据时间二阶积分散射波场线性传播方程中散射波场与入射波场、速度扰动间的线性关系,应用类似偏移成像的公式得到速度扰动的估计,以此建立时间二阶积分波场的全波形迭代反演方法.最后把时间二阶积分波场的全波形反演结果作为常规全波形反演的初始模型可有效地减小地震波场全波形反演对初始模型的依赖性.应用于Marmousi模型的全频带合成数据和缺失4Hz以下频谱成分的缺低频合成数据验证所提出的全波形反演方法的正确性和有效性,数值试验显示缺失4Hz以下频谱成分数据的反演结果与全频带数据的反演结果没有明显差异.     

高保真VSP波场分离方法研究

三维VSP资料中,各种不同类型的波混杂一起形成复杂的波场.因此,波场分离是三维VSP数据处理关键的第一步.从不同波场的偏振方向和传播方向之差异着手,提出了一种高保真的VSP波场分离方法.首先通过射线追踪和偏振滤波的结合,把复杂波场(分解为简单波场;然后根据简单波场中不同波的传播方向截然相反的特点,进行方向滤波,达到波场分离的目的.实际数据处理表明,与常规波场分离方法相比,本方法大大降低了混波作用以及由此而生的波形畸变.     

射线法模拟分析井间地震观测的波场特征

按照井间地震的观测系统,用改进的突变点加插值射线追踪方法,追踪每炮每道的射线路径,计算几种主要类型的波沿射线路径的波至时间和射线振幅,制作井间地震多炮多道水平分量和垂直分量的合成记录.并将合成记录选排为井间共炮点道集、共接收点道集、共偏移距道集和共中心深度点道集,系统地分析了不同道集内几种主要类型的地震波的传播特征.对野外观测的实际井间地震记录进行了模拟,从复杂的井间地震记录中,识别出井间地震实际观测到的不同类型的波场,为随后的井间地震资料处理和应用提供了依据.     

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Bregman迭代的复杂地震波场稀疏域插值方法

在地震勘探中,野外施工条件等因素使观测系统很难记录到完整的地震波场,因此,资料处理中的地震数据插值是一个重要的问题。尤其在复杂构造条件下,缺失的叠前地震数据给后续高精度处理带来严重的影响。压缩感知理论源于解决图像采集问题,主要包含信号的稀疏表征以及数学组合优化问题的求解,它为地震数据插值问题的求解提供了有效的解决方案。在应用压缩感知求解复杂地震波场的插值问题中,如何最佳化表征复杂地震波场以及快速准确的迭代算法是该理论应用的关键问题。Seislet变换是一个特殊针对地震波场表征的稀疏多尺度变换,该方法能有效地压缩地震波同相轴。同时,Bregman迭代算法在以稀疏表征为核心的压缩感知理论中,是一种有效的求解算法,通过选取适当的阈值参数,能够开发地震波动力学预测理论、图像处理变换方法和压缩感知反演算法相结合的地震数据插值方法。本文将地震数据插值问题纳入约束最优化问题,选取能够有效压缩复杂地震波场的OC-seislet稀疏变换,应用Bregman迭代方法求解压缩感知理论框架下的混合范数反问题,提出了Bregman迭代方法中固定阈值选取的H曲线方法,实现地震波场的快速、准确重建。理论模型和实际数据的处理结果验证了基于H曲线准则的Bregman迭代稀疏域插值方法可以有效地恢复复杂波场的缺失信息。