多方向正交多项式变换压制多次波

提出一种基于Radon 变换和正交多项式变换的多方向正交多项式变换压制多次波方法.抛物Radon变换对不同曲率方向的同相轴叠加,根据速度差异区分一次波和多次波,但Radon反变换会损伤振幅特性,不利于AVO分析.多方向正交多项式变换在Radon变换(某一曲率方向的零阶特性)的基础上,利用正交多项式变换进一步分析同相轴的高阶多项式分布特性,用正交多项式谱表征同相轴AVO特性;根据一次波和多次波速度差异和同相轴能量分布特征实现多次波压制.该方法的优点是仅用一个曲率参数就可描述同相轴剩余时差参数,提高了一次波和多次波的剩余时差分辨率.实验结果表明,该方法可以有效压制多次波并保留一次波AVO特性.     

线性拉东域预测反褶积在海洋多次波去除中的应用

海洋多次波是海洋地震资料处理中最难去除的噪声,目前时空域预测反褶积、SRME、高精度拉冬切除等方法均能有效衰减部分多次波,但对于强反射界面(如硬海底,海底以下高速层等)产生的多次波,单独采用以上方法仍会产生能量较强的残余多次波,针对该问题,根据多次波与一次波周期性差异在线性拉东域比时空域更为明显且有利于压制长周期多次波的特点,可以将线性拉东域预测反褶积技术作为SRME、高精度拉东切除技术的补充,取长补短,联合应用消除深水海底多次波.本文对线性拉东域预测反褶积的基本原理进行了阐述,讨论了如何选取参数,并对其应用范围进行了分析.将线性拉东域预测反褶积应用于南海某凹陷海洋资料的多次波衰减处理中,有效的消除了残余海底多次波,验证了该方法的实用性.     

共炮检距道集波动方程保幅叠前深度偏移方法

本文提出了一种基于双平方根算子的共炮检距道集波动方程保幅叠前深度偏移方法,将振幅误差补偿作为偏移的一部分与“运动学偏移”一起在偏移过程中实现.其基本内容包括：(1)从保幅的单平方根算子方程出发,推导出由双平方根算子定义的保幅单程波方程;(2)根据地震波摄动理论把速度场分裂为层内常速背景和变速扰动,分别在频率－波数域和频率－空间域求得波场深度延拓的偏移时移量及振幅校正系数,从而得到最终的DSR保幅波场延拓算子;(3)在高频假设条件下,把DSR保幅波场延拓公式中的积分运算进行稳相近似,得到保幅波场延拓的相移公式.理论分析和模型数值试验表明,该方法不但可以使散射能量聚焦、归位,提高成像精度;而且可以输出正确反映地下反射系数的振幅信息,为后续的地震属性分析（如AVO/AVA）提供更真实的地震信息.     

均衡多道1范数匹配多次波衰减的方法与应用研究

反馈迭代法多次波衰减分为预测和相减两个步骤.在匹配相减过程中,当多次波和一次波同相轴不满足正交性,以及去除多次波后的地震记录不满足能量最小的情况下,最小二乘自适应匹配滤波方法不能获得正确的匹配,因此多次波的衰减产生误差.针对这两个问题,本文提出了基于1范数最小的均衡多道自适应匹配滤波法.该方法通过在空间方向上对地震记录进行均衡,避免了多次波和一次波同相轴正交的假设条件.同时利用了1范数对于大异常值保持稳健的特点,因此可以有效地解决去除多次波后的地震记录能量最小的问题.通过对模型数据和野外实际数据的多次波压制结果显示,该方法可以有效、准确地衰减多次波.     

抛物线Radon变换方法在压制地震多次波中的应用

多次波的存在会降低地震资料的信噪比,影响地震资料处理效果和后续的地质解释精度,压制多次波干扰是地震资料处理中的一个重要环节。利用有限差分方法正演模拟几个典型地质模型的地震波场,之后进行动校正,再通过抛物线Radon变换方法把t-x域一次反射波和多次波变换到τ-q域,由于存在速度的差异,Radon域记录中的一次反射波和多次波的能量互相分开,在Radon域对多次波的能量切除,保留反射波的有效信息,达到压制多次波的效果,提高资料的信噪比。通过对实际地震数据进行抛物线Radon变换结果也进一步验证了该方法在压制多次波中的应用效果。      

多波时移地震AVO反演研究

数值模拟了油藏含油饱和度与有效压力变化时移地震AVO的响应,确定利用时移地震AVO区分油藏参数的变化、实现油藏定量解释的可行性.从Aki等 AVO近似方程出发,详细推导了P_P波和P_S转换波时移地震AVO计算公式.结合岩石物理近似关系和本文推导的时移地震AVO计算公式,推导了利用多波时移地震AVO反演油藏含油饱和度和压力变化的方程.数据试验表明,文中推导的多波时移地震AVO方程能较好地反演油藏含油饱和度变化和有效压力变化,实现油藏定量解释.     

基于Russell近似的纵横波联合反演方法研究

PP波和PS波联合反演方法作为有效的地震技术,比单纯纵波反演精度要高,能够提高地震储层识别的精度.以Russell近似理论为基础,推导了新的转换波AVO近似公式,双层模型界面的反射特征数值模拟显示,新公式具有较高的近似精度,且具备直接反演流体因子f、剪切模量μ和密度ρ等参数的优势,有效避免间接反演带来的误差.结合纵横波联合反演理论,提出了基于贝叶斯理论的新型联合反演算法.在实际应用中,对纵波和转换波角道集进行同相轴匹配处理,综合利用纵波和转换波资料携带的信息,实现基于Russell近似的多波联合反演.模型数据和实际资料测试结果表明,反演结果与真实值或测井结果匹配度较高,证实该方法真实有效.     

傅里叶有限差分法保幅叠前深度偏移方法

地震数据中饱含有丰富的走时信息和振幅信息. 为解决传统偏移方法中几何扩散和入射角变化引起的振幅误差问题，本文提出了一种实用的波动方程保幅地震偏移方法. 该方法从全声波方程出发进行单程波保幅分解，得到直观、高效率的直接面对地震波传播波场的压力分量进行延拓的保幅偏移单程波方程，进而推导出一个含有6项的傅里叶有限差分法保幅偏移的算子方程；修改边界条件和成像条件，使修改后的边界条件和成像方程中考虑振幅补偿，从而从三方面补偿几何扩散损失和入射角变化对振幅的影响. 脉冲响应测试、单炮记录的数值试验以及SEG/EAGE盐丘模型的叠前偏移结果表明，该方法不但可以使散射能量聚焦、归位，提高成像精度；而且可以输出正确反映地下反射系数的振幅信息，为后续的地震属性分析(如AVO/AVA)提供更真实的地震信息.     

自适应虚同相轴方法压制地震层间多次波

地震数据中发育的层间多次波是影响速度分析和偏移成像的精度和可靠性的关键.通常情况下,层间多次波的动校正量、叠加速度和频率与一次波并无明显差异,从而对识别、预测和压制多次波带来了极大挑战.传统虚同相轴方法基于物理图像和定性公式,其预测的层间多次波振幅和相位精度难以满足实际需求,造成了其对匹配算法的过度依赖.本文针对传统虚同相轴方法的理论缺陷和计算精度问题,通过理论推导得到了新的自适应虚同相轴方法.相比于传统方法,自适应虚同相轴方法能够显著提高压制多次波能力,同时减少对匹配算法的依赖.本文给出了自适应虚同相轴方法的推导过程,并运用一维和二维模型算例验证了方法相较于传统虚同相轴方法的多次波预测精度优势.通过在PLUTO模型和实际陆地地震数据上的应用实例,证明了本文新研究的自适应虚同相轴方法对去除层间多次波,恢复并突出目标储层同相轴,提高地震成像分辨率的显著作用.     

地震转换波对叠前同时反演的影响研究

叠前同时反演是油气探测的一种有效工具.其理论基础是平面P波Zoeppritz方程计算的反射系数的近似,是入射角的函数.叠前同时反演可以利用三项或两项Fatti方程进行反演分析.本文针对实际油田的测井数据,利用反射率法模拟了仅包含P波一次反射记录,包含P波一次反射和P波层间多次波记录以及全波场地震记录,再利用叠前同时反演对合成地震记录进行反演研究.研究结果表明,在大偏移距处P波主要反射受到其它模式波的污染,从而影响了叠前同时反演结果的精度.对于薄互层介质当转换波影响严重时,使用小角度数据的两项AVO反演比使用大角度数据的三项AVO反演更合理可靠.     

Robust multiple suppression using adaptive beamforming

Minimum variance unbiased (MVU) beamforming is a type of multichannel filtering which extracts coherent signals without distortion, whilst minimizing residual noise power. Adaptive beamforming estimates signal and noise characteristics as part of the extraction process. The adaptive beamformer used here is designed from models of primary and multiple reflection signals having parametrically specified moveout and amplitude variation with offset (MVO and AVO). Phase variation with offset (PVO) can also be included but it is not usually justified in practice. The resulting analysis provides data for input into AVO and PVO schemes for obtaining lithological information. Synthetic data examples illustrate details of implementation of parametric adaptive MVU beamforming and the response characteristics of the resultant design. Real data examples show that data-adaptive beamforming is more flexible and more effective in attenuating multiples in prestack common-midpoint seismic data than Radon transform methods. In common with other prestack multichannel processes, the advantages of beamforming are shown to best effect in data with a good signal-to-noise ratio.     

Antialiasing conditions in the delay‐time Radon transform

The delay‐time Radon transform parametrizes coherent events in a seismic gather by the far‐offset trace delay time, instead of the conventional parabolic curvature or ray parameter. The reformulation may give a different physical insight into the aliasing effect in the Radon transformation and may also lead to a different algorithm. The delay‐time parametrization enables modelling of a seismic gather as the sum of coherent events with any form of moveout curve. For example, a parabolic curve can be used for traces within a moderate offset range and a linear moveout for far‐offset traces. When using this delay‐time Radon transform, it is the number of traces, rather than the spatial sampling, of the input gather that directly controls aliasing in the Radon transform image. A preconditioning operator that implicitly increases the number of input traces by spatial reconstruction (without physically performing the spatial resampling) may minimize aliasing noise in the Radon transform image.     

3D高阶抛物Radon变换地震数据保幅重建

本文结合传统3D抛物Radon变换（PRT）和AVO数据正交多项式拟合,给出了3D高阶抛物Radon变换方法（HOPRT）.该变换增加了描述AVO数据变化的梯度信息和曲率信息,拓展了传统3D抛物Radon变换方法,使其在具有AVO特征的数据重建中具有更高的准确度,从而提高AVO分析的可靠性.文中给出了3D高阶抛物Radon变换进行地震数据保幅重建的流程.理论模型和实际地震资料的重建结果显示了本文方法的优点.     

Multiple attenuation using λ-f domain high-resolution Radon transform

The parabolic Radon transform has been widely used in multiple attenuation. To further improve the accuracy and efficiency of the Radon transform, we developed the 2- fdomain high-resolution Radon transform based on the fast and modified parabolic Radon transform presented by Abbad. The introduction of a new variable 2 makes the transform operator frequency-independent. Thus, we need to calculate the transform operator and its inverse operator only once, which greatly improves the computational efficiency. Besides, because the primaries and multiples are distributed on straight lines with different slopes in the 2-fdomain, we can easily choose the filtering operator to suppress the multiples. At the same time, the proposed method offers the advantage of high-resolution Radon transform, which can greatly improve the precision of attenuating the multiples. Numerical experiments suggest that the multiples are well suppressed and the amplitude versus offset characteristics of the primaries are well maintained. Real data processing results further verify the effectiveness and feasibility of the method.     

Fast hyperbolic deconvolutive Radon transform using generalized Fourier slice theorem

The hyperbolic Radon transform has a long history of applications in seismic data processing because of its ability to focus/sparsify the data in the transform domain. Recently, deconvolutive Radon transform has also been proposed with an improved time resolution which provides improved processing results. The basis functions of the (deconvolutive) Radon transform, however, are time-variant, making the classical Fourier based algorithms ineffective to carry out the required computations. A direct implementation of the associated summations in the time–space domain is also computationally expensive, thus limiting the application of the transform on large data sets. In this paper, we present a new method for fast computation of the hyperbolic (deconvolutive) Radon transform. The method is based on the recently proposed generalized Fourier slice theorem which establishes an analytic expression between the Fourier transforms associated with the data and Radon plane. This allows very fast computations of the forward and inverse transforms simply using fast Fourier transform and interpolation procedures. These canonical transforms are used within an efficient iterative method for sparse solution of (deconvolutive) Radon transform. Numerical examples from synthetic and field seismic data confirm high performance of the proposed fast algorithm for filling in the large gaps in seismic data, separating primaries from multiple reflections, and performing high-quality stretch-free stacking.     

Multiple attenuation: coping with the spatial truncation effect in the Radon transform domain

The limited size of the spatial aperture of a seismic gather causes multiple- and primary-reflection energy to spread out and cross-hatch the image of the parabolic Radon transform. This spatial truncation effect devastatingly impairs the separation of primary and multiple reflections in a Radon demultiple process. It is difficult to suppress the spatial truncation effect completely, but it is at least possible to model or to identify implicitly such an effect and then to design automatically a mute function, i.e. a 2D mask filter in the Radon transform domain. This is referred to as the adaptive surgical mute scheme. By using this scheme, it is possible to extract the multiple-reflection energy cleanly from the Radon transform image, so that the multiple reflections can be more effectively attenuated. It is also possible to preserve the diffused primary-reflection energy after the surgical mute, so that the final multiple-attenuated seismic profile is amplitude-preserved.     

Tracking the amplitude versus offset (AVO) by using orthogonal polynomials1

Inversion for S-wave velocities from the amplitude variation with offset of P-wave data is far from being a standard routine in the seismic processing sequence. However, the need for tracking the amplitude versus offset (AVO) occurs in several situations, for example in order to estimate the zero-offset amplitude, to reveal areas with particular AVO characteristics, or to compress the AVO so that it is more easily obtainable at a later stage of the seismic processing. Furthermore, weak reflections can occasionally, due to the effect of the angle-dependent reflectivity, have a polarity-shift with offset, resulting in a very poor, or even vanishing, stack response. In such cases, the reflection event has to be represented by some other property than its mean amplitude or stack value. We outline how the AVO of seismic data may be extracted and classified by the use of orthogonal polynomials. The main advantage of this method compared to a general polynomial fit is that the AVO may be classified by a unique Spectrum of polynomial coefficients. This is in analogy to Fourier coefficients where the orthogonal basis is harmonic functions. The set of orthogonal polynomials is constructed entirely from the set of offset coordinates, and these polyno-mials are defined only on the offset window considered. Compared to a Fourier transform, this is a major advantage since there is no effect of a limited spatial bandwidth. The AVO of normal-moveout corrected data may be represented by a data gather where the orthogonal polynomial coefficients are given as time traces with each trace revealing a certain AVO characteristic. For instance, the stack is proportional to the zeroth-order coefficient, the mean gradient is given by the firstorder coefficient, while the second-order coefficient indicates whether the AVO increases and then decreases, or vice versa.     

3D targeted multiple attenuation

Short-period multiple reflections pose a particular problem in the North Sea where predictive deconvolution is often only partially successful. The targeted multiple attenuation (TMA) algorithm comprises computation of the covariance matrix of preflattened prestack or post-stack seismic data, the determination of the dominating eigenvectors of the covariance matrix, and subtraction of the related eigenimages followed by reverse flattening. The main assumption made is that the flattened multiple reflections may be represented by the first eigenimage(s) which implies that the spatial amplitude variations of primaries and associated multiples are similar. This assumption usually limits the method to short-period multiple reflections. TMA is applicable post-stack or prestack to common-offset gathers. It is computationally fast, robust towards random noise, irregular geometry and spatial aliasing, and it preserves the amplitudes of primaries provided they are not parallel to the targeted multiples. Application of TMA to 3D wavefields is preferable because this allows a better discrimination between primaries and multiples. Real data examples show that the danger of partially removing primary energy can be reduced by improving the raw multiple model that is based on eigenimages, for example by prediction filtering.     

一阶多次波聚焦变换成像

将多次波转换成反射波并按传统反射波偏移算法成像,是多次波成像的一种方法.聚焦变换能准确的将多次波转换为纵向分辨率更高的新波场记录,其中一阶多次波转换为反射波.本文对聚焦变换提出了两点改进:1)提出局部聚焦变换,以减小存储量和计算量,增强该方法对检波点随炮点移动的采集数据的适应性;2)引入加权矩阵,理论上证明原始记录的炮点比检波点稀疏时,共检波点道集域的局部聚焦变换可以将多次波准确转换成炮点与检波点有相同采样频率的新波场记录.本文在第一个数值实验中对比了对包含反射波与多次波的原始记录做局部聚焦变换和直接对预测的多次波做局部聚焦变换两种方案,验证了第二种方案转换得到的波场记录信噪比更高且避免了第一个方案中切聚焦点这项比较繁杂的工作.第二个数值实验表明:在炮点采样较为稀疏时,该方法能有效的将一阶多次波转换成反射波;转换的反射波能提供更丰富的波场信息,成像结果更均衡、在局部有更高的信噪比,以及较高的纵向分辨率.