基于支持向量机的非线性AVO反演

本文提出了一种新的AVO非线性反演方法,即利用支持向量机来求解AVO非线性反演问题.文中先对支持向量机的原理进行了阐述,然后建立了适合AVO反演的支持向量机模型.最后利用该方法对模型数据和实际资料进行了反演计算,反演结果表明,该方法在没有牺牲反演效果的情况下较好的解决了传统反演方法所具有的局限性,可以直接从合成记录中提取地层的弹性参数,反演速度快、稳定性好.     

单相介质AVO反演的精度分析

振幅随偏移距变化（AVO）反演是一个非线性的组合最优化过程,理论上可先将该非线性问题线性化,然后求解线性问题;或者直接利用非线性的模拟退火、遗传算法等方法求解.但无论哪种反演思路,实际中影响其精度的因素很多,因此分析AVO反演中的误差来源对提高反演精度和评价反演方法的可靠性非常重要.本文对能造成反演误差的主要因素,噪音、薄层调谐、地震数据处理中的误差、入射角范围等进行了分析,讨论了这些因素可能对反演结果造成的影响,发现在AVO反演过程中可以从优化参数选择和针对性处理方面来减小这些误差,提高反演精度.     

基于改进的贝叶斯推断和最小二乘支持向量机的非线性多波联合AVO反演（英文）

多波地震资料采集和处理技术的发展促进了联合PP波和PS波数据的多波联合AVO反演的应用,常规多波联合反演是线性的,通常基于Zoeppritz方程近似式进行多次迭代,导致其在远炮检距情况下求解得到的纵、横波速度和密度等参数精度不高。多波联合反演存在非线性问题。为此,本文提出了一种基于精确Zoeppritz方程的非线性反演方法。该方法结合改进的贝叶斯推断和最小二乘支持向量机方法来求解非线性反演问题。首先,采用粒子群算法来优化贝叶斯推断的参数初始值。改进的贝叶斯推断是通过最大化超参数的后验概率来获得最小二乘支持向量机的最优参数,提高了最小二乘支持向量机的学习和泛化能力。然后,利用此最优参数建立PP波、PS波反射振幅与弹性参数之间的最优非线性最小二乘支持向量机模型,从而提高了多波联合反演的精度。该方法只需训练一次模型,就可以解决多波联合反演的非线性问题。模型测试表明,利用该方法反演出的弹性参数精度要高于仅用PP波进行贝叶斯线性近似式反演得到的结果。此外加噪模型数据的反演结果表明,该方法具有较好的抗噪性。实际多波资料的应用进一步验证了方法的可行性及其相对于PP波贝叶斯线性近似式反演的优势。     

测井约束地震波形反演的同伦摄动法

测井数据和地震数据是地震勘探中两种最重要的资料. 测井约束地震波形反演是在非线性波形反演的基础上,利用已知测井资料详细的垂直分辨能力和地震资料均匀密集的水平采样特点, 通过迭代反演来求取一个具有较高分辨率的速度参数.本文建立了测井约束反演模型,研究了测井约束下地震波形反演的同伦摄动求解方法.同伦摄动法作为一种新的、求解数学物理中各种非线性问题的有效方法,具有计算速度快、计算精度高的优点.这对于提高反演的精度和效率是十分有益的. 为了表征该方法的有效性和稳定性,分别对水平层状介质模型和逆冲断层带模型进行了数值模拟,并与Landweber迭代法相对比,结果表明该算法具有更好的收敛性,能够取得更为满意的反演效果.     

纵向和横向同时约束AVO反演

为了提高AVO(amplitude versus offset)反演结果的精度和横向连续性,本文提出了一种新的AVO反演约束方法,该方法结合贝叶斯原理和卡尔曼滤波算法实现了对反演参数纵向和横向的同时约束.文章首先结合反演参数的纵向贝叶斯先验概率约束和反演参数的横向连续性假设建立了与卡尔曼滤波算法对应的AVO反演系统的数学模型,然后将该数学模型代入卡尔曼滤波算法框架,利用卡尔曼滤波算法实现了双向约束AVO反演.二维模型测试和实际数据测试结果表明,相对于单纯的纵向贝叶斯先验概率约束,双向约束能更准确地刻画参数的横向变化,得到更准确、横向连续性更好的反演结果.     

相位空间内的解缠绕相位反演

全波形反演方法是一种数据域高精度反演方法,该方法通过匹配观测数据与模拟数据的地震波形,利用梯度法准确反演地下介质参数的分布情况.由于观测数据普遍缺少低频信息,该方法易受周期跳跃现象影响.特别是当地下存在大尺度强反射界面的构造时,地下介质的反演转化为强非线性问题求解.该情形下,即使观测数据包含充足的低频信息,全波形反演也难以给出准确的反演结果.一般可以通过减弱反演对初始模型参数的依赖性来克服上述问题,具体表现为使用新变量(例如瞬时相位、包络等)代替目标函数中的采样后波场,以增强新目标函数的凸性.但是,对该新目标函数进行反演时,伴随状态方程中存在关于新变量和波场的一个链式微分项,该项保留了反演问题的非线性,导致新的反演方法难以处理包含大尺度构造的强非线性反演问题.此外,基于新变量的反演问题依然在波场空间中计算模型梯度,难以充分利用新变量与模型参数之间的弱非线性关系.因此,本文提出用频率域波动方程的相位形式代替传统的波动方程来消除伴随状态方程中的链式微分项,用解缠绕的相位代替目标函数中采样前波场并在相位空间进行反演.该方法可以最大程度地利用地下介质参数和解缠绕相位之间的弱非线性关系,从而削弱反演的非线性性.由于基于频率域波场计算得到相位有严重的缠绕问题,本文采用基于振幅排序的多聚类算法来对相位进行解缠绕.虽然将介质参数到波场的映射替换为介质参数与解缠绕相位的映射,会导致反演结果的分辨率有所下降,但该方法可以在相位空间恢复介质参数的大尺度低波数分量.Marmousi模型测试证明了该方法的有效性和准确性,针对部分BP模型的测试也证明了该方法处理强非线性问题的能力.     

基于贝叶斯理论的AVO三参数波形反演

在实际的AVO反演问题中,叠前数据体中的噪声或其他因素严重影响了AVO反演问题的适定性,而采用先验地质信息作为AVO反演问题的约束条件是解决AVO反演问题不适定的一种可行方法. 文中的似然函数采用了[WTBX]ι[WTBX]p范数的解,并用Cauchy分布表示先验模型参数的分布. 以此为基础,在反演中建立了测井数据的参数协方差矩阵对反演过程进行约束,并采用了共轭梯度算法实现多参数非线性的反演过程. 同时,为了提高反演精度,避免动校正拉伸及依赖于炮检距的调谐效应对参数估计的影响,反演采用动校前地震数据进行参数估计. 从应用效果分析来看,即使叠前道集的信噪比不高,反演的结果也能较好地与实际情况相匹配,为识别储层流体性质提供了新的手段.     

基于地震成像数据稀疏反演的不连续及非均质地质体检测方法

本文针对油气藏储层预测中的不连续及非均质地质信息识别问题,研究基于地震成像数据的稀疏反演方法.由于该类地质体的地震响应特征为弱信号,因此利用平面波破坏滤波器由地震成像数据中去除强反射同相轴.在此基础上,对剩余的地震数据进行非线性加强滤波,并构建L1稀疏反演模型.为有效求解L1模型,采用非光滑泛函L1范数逼近和拟牛顿求解算法.该方法考虑稀疏先验信息,能够提高反演结果信噪比.缝洞模型测试验证该方法在检测断点、微断裂、散射点等小尺度地质体上的有效性,塔北缝洞型碳酸盐岩储层预测的应用效果进一步证实该方法的实用性.     

基于波动方程的叠前地震反演

随着地震勘探和开发的不断深入,面向地质目标的精细储层预测技术变得越来越重要.由于透射损失、层间多次波、波模式转换以及随机噪声等的影响,观测地震数据和待反演的地下介质属性之间呈现出很强的非线性.考虑到这些非线性,本文基于积分波动方程开展叠前地震反演,从观测地震数据中恢复出介质属性和整体波场,其中反演参数是波动方程中的压缩系数、剪切柔度和密度的对比度,相比于常规线性AVO反演的波阻抗弹性参数,它们对流体指示有更强的敏感性.在反演过程中,从平滑的低频背景场出发,交替迭代求解数据方程和目标方程.采用乘性正则化方法于共轭梯度框架下求解反演参数,采用优化的散射级数Neumann序列获得整体波场,这种方法不易陷入局部极值,能收敛到正确解.测井资料和典型山前带模型测试表明,利用上述反演方法能获得高分辨率的深度域地下介质属性,可直接进行储层预测和解释.     

求解地震静校正问题的双尺度反演方法

通过对地震静校正问题的分析,综合线性反演方法的计算速度快和非线性反演方法寻找全局最优解能力强的优点,提出了求解地震静校正问题的双尺度反演方法.在大尺度下采用非线性反演方法为小尺度下的线性反演计算初始模型,利用小尺度下的线性反演方法获得精细模型.对反演参数的选取进行了讨论,使双尺度反演算法具有自适应的特点.理论模型和实际资料的计算表明该方法计算结果精度高、计算速度快.     

Cauchy prior distribution-based AVO elastic parameter estimation via weakly nonlinear waveform inversion

Cauchy priori distribution-based Bayesian AVO reflectivity inversion may lead to sparse estimates that are sensitive to large reflectivities. For the inversion, the computation of the covariance matrix and regularized terms requires prior estimation of model parameters, which makes the iterative inversion weakly nonlinear. At the same time, the relations among the model parameters are assumed linear. Furthermore, the reflectivities, the results of the inversion, or the elastic parameters with cumulative error recovered by integrating reflectivities are not well suited for detecting hydrocarbons and fuids. In contrast, in Bayesian linear AVO inversion, the elastic parameters can be directly extracted from prestack seismic data without linear assumptions for the model parameters. Considering the advantages of the abovementioned methods, the Bayesian AVO reflectivity inversion process is modified and Cauchy distribution is explored as a prior probability distribution and the time-variant covariance is also considered. Finally, we propose a new method for the weakly nonlinear AVO waveform inversion. Furthermore, the linear assumptions are abandoned and elastic parameters, such as P-wave velocity, S-wave velocity, and density, can be directly recovered from seismic data especially for interfaces with large reflectivities. Numerical analysis demonstrates that all the elastic parameters can be estimated from prestack seismic data even when the signal-to-noise ratio of the seismic data is low.     

Joint PP and PS AVO inversion based on Zoeppritz equations

Considering Zoeppritz equations, reflections of PP and PS are only the function of ratios of density and velocity. So the inversion results will be the same if the ratios are the same but values of density, velocities of P-wave and S-wave are different without strict constraint. This paper makes efforts to explore nonlinear simultaneous PP and PS inversion with expectation to reduce the ambiguity of AVO analysis by utilizing the redundancy of multi-component AVO measurements. Accurate estimation of ratio parameters depends on independence of input data. There are only two independent AVO attributes for PP reflectivity (i.e. intercept and gradient) and two for PS reflectivity (i.e. pseudo-intercept and pseudo-gradient or extreme amplitude), respectively. For individual PP and PS inversion, the values of least-squares objective function do not converge around a large neighborhood of chosen true model parameters. Fortunately for joint PP and PS inversion the values of the least-squares objective function show closed contours with single minima. Finally the power function fitting is used to provide a higher precision AVO attributes than traditional polynomial fitting. By using the four independent fitting attributes (two independent attributes for PP and PS respectively), the inversion of four ratio parameters (velocities and densities) would be estimated with less errors than that in traditional method.     

Nonlinear simultaneous inversion of pore structure and physical parameters based on elastic impedance

Carbonate reservoirs have complex pore structures, which not only significantly affect the elastic properties and seismic responses of the reservoirs but also affect the accuracy of the prediction of the physical parameters. The existing rockphysics inversion methods are mainly designed for clastic rocks, and the inversion objects are generally porosity and water saturation. The data used are primarily based on the elastic parameters, and the inversion methods are mainly linear approximations. To date, there has been a lack of a simultaneous pore structure and physical parameter inversion method for carbonate reservoirs. To solve these problems, a new Bayesian nonlinear simultaneous inversion method based on elastic impedance is proposed. This method integrates the differential effective medium model of multiple-porosity rocks, Gassmann equation,Amplitude Versus Offset(AVO) theory, Bayesian theory, and a nonlinear inversion algorithm to achieve the simultaneous quantitative prediction of the pore structure and physical parameters of complex porous reservoirs. The forward modeling indicates that the contribution of the pore structure, i.e., the pore aspect ratio, to the AVO response and elastic impedance is second only to that of porosity and is far greater than that of water saturation. The application to real data shows that the new inversion method for determining the pore structure and physical parameters directly from pre-stack data can accurately predict a reservoir's porosity and water saturation and can evaluate the pore structure of the effective reservoir.     

基于精确Zoeppritz方程的非线性AVO三参数反演

常规AVO三参数反演通常存在密度反演不准确的问题,而密度参数对常规油气藏中的流体识别、流体饱和度计算、孔隙度计算以及非常规油气藏中TOC含量计算、裂缝预测等都至关重要,因此对于研究如何利用大偏移距振幅信息和富含密度信息的PS波地震资料来提高密度反演结果的稳定性和精度显得尤为重要.研究基于贝叶斯反演理论框架,引入三变量Cauchy分布先验约束,利用精确Zoeppritz方程构建了AVO三参数联合反演的目标函数,对目标函数进行Taylor二阶非线性简化,得到模型参数的迭代更新公式,实现了大偏移距地震振幅信息的利用和PP波、PS波联合反演.合成数据和实际地震数据的方法测试结果表明,新方法不仅可以直接反演纵波速度、横波速度和密度,而且还具有很高的精度,尤其是密度反演结果.基于合成数据的PP波、PS波单独反演结果与PP波和PS波联合反演结果对比显示,联合反演稳定性更好,精度更高,抗噪能力更强,验证了该方法的可行性和有效性.与基于Aki-Richards近似公式的反演结果对比表明,该反演方法具有更高的反演精度和更好的抗噪性.     

Joint AVO inversion, wavelet estimation and noise-level estimation using a spatially coupled hierarchical Bayesian model

The main objective of the AVO inversion is to obtain posterior distributions for P-wave velocity, S-wave velocity and density from specified prior distributions, seismic data and well-log data. The inversion problem also involves estimation of a seismic wavelet and the seismic-noise level. The noise model is represented by a zero mean Gaussian distribution specified by a covariance matrix. A method for joint AVO inversion, wavelet estimation and estimation of the noise level is developed in a Bayesian framework. The stochastic model includes uncertainty of both the elastic parameters, the wavelet, and the seismic and well-log data. The posterior distribution is explored by Markov-chain Monte-Carlo simulation using the Gibbs' sampler algorithm. The inversion algorithm has been tested on a seismic line from the Heidrun Field with two wells located on the line. The use of a coloured seismic-noise model resulted in about 10% lower uncertainties for the P-wave velocity, S-wave velocity and density compared with a white-noise model. The uncertainty of the estimated wavelet is low. In the Heidrun example, the effect of including uncertainty of the wavelet and the noise level was marginal with respect to the AVO inversion results.     

PP and PS joint AVO inversion and fluid prediction

The technique of amplitude variation with offset or angle (AVO or AVA) can be used to extract fluid and lithology information from prestack seismic data. Based on three-term AVO equations, three elastic parameters can be inverted for by linear AVO inversion. However, many theoretical and numerical studies have demonstrated that by using offset limited data, a three-term AVO inversion may have problems of instability and inaccuracy while inverting for the density term. We have searched for an elastic parameter that contains density information and inverted this parameter in a more stable manner using offset limited data. First, we test the sensitivity of elastic parameters to hydrocarbon reservoirs and select the optimal fluid factor (ρf) that contains density information and has an excellent performance as an inversion parameter used to detect hydrocarbons. Then, we derive approximate PP and PS reflection coefficient equations in terms of the fluid factor. The derived equations allow us to directly estimate the fluid factor of the reservoir. Finally, we apply these equations to synthetic data by employing a joint AVO inversion technique. The results show that the method is stable and unambiguous.     

P-SV波AVO方法研究进展

为有效地利用AVO(amplitude versus offset)信息来反演岩性参数和预测油气储层，详细介绍了P—SV转换波AVO方法的研究现状和主要进展，并针对几种具有代表性的方法的基本思路、方法特点及参数反演等方面进行了对比和评述。同时，给出了两个不同形式的近似公式，并讨论了利用这两种近似公式进行AVO分析的思路和参数反演的方法，通过对比和讨论可以得出：不同近似的主要目的是为了提高近似精度并体现不同的岩性参数对反射系数的影响、敏感程度及其在参数反演中的意义；根据弹性模量和波速之间的关系，目前所有的PP波和P—SV波反射系数近似公式都可以统一表示成射线参数幂级数的形式，这些结论对于AVO理论研究和参数反演都具有重要意义。