时移地震资料贝叶斯AVO波形反演

针对时移地震差异数据,给出了一种基于贝叶斯理论的AVO波形反演方法.该方法可以利用时移地震差异数据同时反演出纵波阻抗、横波阻抗和密度的变化.利用时移地震资料进行反演,由于采集和处理过程中存在一定的差异,不同年份地震资料在非注采过程影响区域也会存在一定的变化,而该变化会导致反演结果在非注采区域有较大的变化.针对这一问题,本文采用贝叶斯理论框架,将待求的纵横波阻抗、密度变化的先验信息和包含在地震数据中的信息结合起来,对于纵横波阻抗和密度变化,假设其服从Gauss分布,并以时移地震分别反演的结果作为其期望,同时,为了更好地表征储层属性变化,提高分辨率和抑制非注采区域弹性参数的变化,假设弹性参数变化的导数服从改进的Cauchy分布.数值模拟试验和实际资料处理结果皆表明,本文提出的反演方法能够有效地抑制假象,突出储层性质的变化,得到高分辨率的弹性参数变化信息,为研究储层属性的变化和优化开采方案提供更多的有效的信息.     

时移地震资料贝叶斯AVO波形反演

针对时移地震差异数据,给出了一种基于贝叶斯理论的AVO波形反演方法.该方法可以利用时移地震差异数据同时反演出纵波阻抗、横波阻抗和密度的变化.利用时移地震资料进行反演,由于采集和处理过程中存在一定的差异,不同年份地震资料在非注采过程影响区域也会存在一定的变化,而该变化会导致反演结果在非注采区域有较大的变化.针对这一问题,本文采用贝叶斯理论框架,将待求的纵横波阻抗、密度变化的先验信息和包含在地震数据中的信息结合起来,对于纵横波阻抗和密度变化,假设其服从Gauss分布,并以时移地震分别反演的结果作为其期望,同时,为了更好地表征储层属性变化,提高分辨率和抑制非注采区域弹性参数的变化,假设弹性参数变化的导数服从改进的Cauchy分布.数值模拟试验和实际资料处理结果皆表明,本文提出的反演方法能够有效地抑制假象,突出储层性质的变化,得到高分辨率的弹性参数变化信息,为研究储层属性的变化和优化开采方案提供更多的有效的信息.     

TTI介质各向异性参数多波反演与PS波AVO分析

把遗传算法引入到了TTI介质AVO信息反演各向异性参数的过程中,依据TTI介质PP波、PS波反射系数公式,建立Thomsen参数和TTI介质对称轴倾角、方位角的目标函数,分别通过PP波和PS波的反射系数反演出了各向异性参数和对称轴倾角、方位角等信息.文中对反演结果的精确度和稳定性进行了分析,发现PS波的反演结果优于PP波反演结果;对称轴倾角的反演准确性明显优于对称轴方位角.本文通过模型正演合理解释了这一现象的原因.最后,本文通过对PS波AVO梯度的研究,提出了利用PS波振幅定性分析TTI介质对称轴倾角的方法.     

基于逆算子估计的AVO反演方法研究

传统反演算法以优化算法为主,而基于逆算子估计的AVO反演算法则利用了直接求逆的思路.算法的关键在于寻找存在逆函数的子域,进而可以在子域内直接求逆,这种解决反问题的思路不同于一般的优化类算法所采用的直接搜索解的方式,具有更高的效率.AVO反演利用了振幅随着偏移距的变化特征,反演的精度受到地震资料质量的影响,通过加入L1范数约束以及合理的初始模型有助于提高反演的稳定性以及准确度.模型测算和实际应用表明,基于逆算子估计的AVO反演方法具有较高的精确程度和可靠性.     

叠前弹性参数一致性反演方法研究(英文)

常规叠前反演中,纵波速度、横波速度和密度三参数之间,在反演精度上存在明显的差异,"三参数"的一致性反演遂成为重要的研究目标。本文从导致它们精度差异的根源入手,提出了新的叠前反演算法和思路,通过合理的近似,构成参数间的互动和相互约束,使三个参数的反演精度得以同步提高。理论模型试算和实际资料应用表明,三个弹性参数均有较高的反演精度且保持了一致性,与理论模型和实际资料吻合。该方法具有较好的应用前景。     

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.     

频率域全波形反演方法研究进展

全波形反演是一种利用地震波传播的动力学特征来获取地下介质物性参数的反演方法,可为揭示地下精细结构提供重要依据。本文以弹性波方程作为数学模型来模拟地震波传播规律并进行相应的反演方法研究。为提高计算效率与反演结果的准确性,可将近似解析离散化（NAD）算子用于频率域弹性波方程的正演模拟。本文在频率域NAD离散的基础上推导阻抗矩阵的稀疏分块结构与反演目标函数对模型参数的梯度计算公式,由此建立基于NAD算子的频率域弹性波全波形反演方法。为验证该方法的有效性,文中通过数值实验对多种典型介质模型进行反演计算,均得到了理想的反演结果。

     

1D elastic full‐waveform inversion and uncertainty estimation by means of a hybrid genetic algorithm–Gibbs sampler approach

Stochastic optimization methods, such as genetic algorithms, search for the global minimum of the misfit function within a given parameter range and do not require any calculation of the gradients of the misfit surfaces. More importantly, these methods collect a series of models and associated likelihoods that can be used to estimate the posterior probability distribution. However, because genetic algorithms are not a Markov chain Monte Carlo method, the direct use of the genetic‐algorithm‐sampled models and their associated likelihoods produce a biased estimation of the posterior probability distribution. In contrast, Markov chain Monte Carlo methods, such as the Metropolis–Hastings and Gibbs sampler, provide accurate posterior probability distributions but at considerable computational cost. In this paper, we use a hybrid method that combines the speed of a genetic algorithm to find an optimal solution and the accuracy of a Gibbs sampler to obtain a reliable estimation of the posterior probability distributions. First, we test this method on an analytical function and show that the genetic algorithm method cannot recover the true probability distributions and that it tends to underestimate the true uncertainties. Conversely, combining the genetic algorithm optimization with a Gibbs sampler step enables us to recover the true posterior probability distributions. Then, we demonstrate the applicability of this hybrid method by performing one‐dimensional elastic full‐waveform inversions on synthetic and field data. We also discuss how an appropriate genetic algorithm implementation is essential to attenuate the “genetic drift” effect and to maximize the exploration of the model space. In fact, a wide and efficient exploration of the model space is important not only to avoid entrapment in local minima during the genetic algorithm optimization but also to ensure a reliable estimation of the posterior probability distributions in the subsequent Gibbs sampler step.     

Accelerating the T‐matrix approach to seismic full‐waveform inversion by domain decomposition

A seismic variant of the distorted Born iterative inversion method, which is commonly used in electromagnetic and acoustic (medical) imaging, has been recently developed on the basis of the T‐matrix approach of multiple scattering theory. The distorted Born iterative method is consistent with the Gauss–Newton method, but its implementation is different, and there are potentially significant computational advantages of using the T‐matrix approach in this context. It has been shown that the computational cost associated with the updating of the background medium Green functions after each iteration can be reduced via the use of various linearisation or quasi‐linearisation techniques. However, these techniques for reducing the computational cost may not work well in the presence of strong contrasts. To deal with this, we have now developed a domain decomposition method, which allows one to decompose the seismic velocity model into an arbitrary number of heterogeneous domains that can be treated separately and in parallel. The new domain decomposition method is based on the concept of a scattering‐path matrix, which is well known in solid‐state physics. If the seismic model consists of different domains that are well separated (e.g., different reservoirs within a sedimentary basin), then the scattering‐path matrix formulation can be used to derive approximations that are sufficiently accurate but far more speedy and much less memory demanding because they ignore the interaction between different domains. However, we show here that one can also use the scattering‐path matrix formulation to calculate the overall T‐matrix for a large model exactly without any approximations at a computational cost that is significantly smaller than the cost associated with an exact formal matrix inversion solution. This is because we have derived exact analytical results for the special case of two interacting domains and combined them with Strassen's formulas for fast recursive matrix inversion. To illustrate the fact that we have accelerated the T‐matrix approach to full‐waveform inversion by domain decomposition, we perform a series of numerical experiments based on synthetic data associated with a complex salt model and a simpler two‐dimensional model that can be naturally decomposed into separate upper and lower domains. If the domain decomposition method is combined with an additional layer of multi‐scale regularisation (based on spatial smoothing of the sensitivity matrix and the data residual vector along the receiver line) beyond standard sequential frequency inversion, then one apparently can also obtain stable inversion results in the absence of ultra‐low frequencies and reduced computation times.     

基于各向异性全变分约束的多震源弹性波全波形反演

多震源编码技术可以提高全波形反演的计算效率,但同时会引入串扰噪声使反演结果质量降低. 全变分约束可以有效地压制层内噪声并突出模型界面,其与多震源技术的结合,能在大大提高弹性波全波形反演效率的同时提高反演质量. 本文提出了一种高效的动态多震源全波形反演策略,可以在离散串扰噪声的同时保证照明的均匀性. 根据残留串扰噪声的分布特征,构建了与之匹配的基于各向异性全变分约束的弹性波全波形反演方法. 为了减少周期跳跃效应,将基于稀疏约束的低频重构算法应用于弹性波地震记录,给出了利用快速梯度投影算法求解各向异性全变分约束的全波形反演流程. 模型数据测试结果表明本文的方法不仅能有效地抑制多震源方法导致的串扰噪声,同时也能降低观测数据中的噪声对反演结果的影响.

     

基于精确Zoeppritz方程三变量柯西分布先验约束的广义线性AVO反演

常规AVO三参数反演是通过Zoeppritz方程的近似公式来建立AVO正演模拟的过程,然而在P波入射角过临界角和弹性参数在纵向上变化剧烈的情况下,Zoeppritz方程近似公式精度有限.针对这种情况,可以使用精确的Zoeppritz方程来构建反演目标函数,由于精确Zoeppritz方程中P波反射系数和弹性参数之间是一种复杂的非线性关系,通常解决途径是利用非线性的优化算法来进行数值计算,但是非线性优化算法的缺点是计算量过大;另外一种途径是利用广义线性反演的方法,通过泰勒一阶展开式将P波反射振幅展开后,用线性关系近似表达非线性关系,经过几次迭代后,在理论上可以达到很高的精度,但是广义线性反演算法的核心部分——Jacobian矩阵由于矩阵条件数过大,往往会造成反演算法的不稳定,其应用范围得到了限制.贝叶斯反演方法是通过引入模型参数的先验分布结合噪声的似然函数,生成模型参数的后验分布,通过求取模型参数的最大后验概率分布来得到模型参数的反演解,由于引入模型参数的先验分布信息,可以有效的降低反演的不适定问题.本文将两种反演算法的思想相结合,利用广义线性反演算法的思想,构建AVO正演模拟的过程来提高大角度地震数据反演的精度,同时结合贝叶斯理论,通过引入模型参数的先验分布信息构建反演目标函数的正则化项,可以有效降低由于Jacob矩阵条件数过大带来的反演不适定问题,该算法假设模型参数服从三变量柯西分布.     

应用叠前反演弹性参数进行储层预测(英文)

本文是利用叠前弹性参数反演结果进行致密性含气砂岩储层预测的一个实例研究。随着油气勘探开发的发展,叠前地震数据及其反演结果的应用研究已经广泛用于实际生产中。叠前地震数据的特有属性研究,不仅包括简单的AVO特性,还包括其他的弹性属性的变化特性。本文通过对含气砂岩岩芯弹性属性参数响应特征的分析,发现特定弹性属性参数或其组合可以作为流体检测因子。因此,可以利用叠前地震反演得到不同的弹性属性参数结果,进行储层解释和储层描述。该叠前反演方法是基于Zoeppritz方程的Aki—Richard简化公式建立起来的,根据测井数据和地质解释结果建立初始反演模型,反演的地震数据为叠前时间或深度偏移的共反射点道集数据,反演结果可以是不同的弹性属性参数及其组合。通过对一实际的致密性含气砂岩储层进行叠前弹性属性参数反演,并将反演结果与其它预测结果进行对比分析发现弹性属性参数λ和λρ, λ/μ,以及K／μ能够很好地预测含气储层,而且反演结果很好展现出储层中的含气特性。     

基于柯西分布约束和快速近端目标函数优化的三维重力反演方法

优化算法的选取在很大程度上影响着三维重力反演的计算效率,从而制约着三维重力反演的实用性.在复杂地质构造背景下,不同岩性单元之间可能会发生物性突变,产生尖锐边界.为此,本文提出了一种新的基于柯西分布约束和快速近端目标函数（Fast Proximal Objective Function,FPOF）优化的三维重力反演方法.FPOF优化方法的一个突出特点是在每一步迭代过程中逐一计算剖分网格内的未知密度参数,因此,有较低的计算复杂度和较高的计算效率.此外,目标函数中柯西范数（Cauchy norm）的引入会对反演结果施加稀疏性,有助于产生块状效果.理论模型测试表明,本文方法不仅能产生更加聚焦的反演效果,而且反演所需的时间也比传统的共轭梯度优化方法少.最后将本文方法应用于我国西部某地区实际重力数据,反演结果与已知的地质信息有较好的一致性.

     

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.

     

基于常分数阶拉普拉斯算子的黏声方程重建速度与衰减参数的全波形反演方法

地震波在地下介质传播过程中由于非弹性衰减的存在将导致能量损失和相位变化, 精确的速度与衰减参数建模对油气识别、提高强衰减介质中地震波成像的质量都起着至关重要的作用.常分数阶拉普拉斯算子黏声方程由于完全分离的速度频散项与振幅衰减项的优势, 以及在强非均质衰减介质中可以高精度求解的特点, 已被应用于速度与衰减参数的建模中.本文将二阶常分数阶拉普拉斯算子黏声方程拆分为等价的一阶方程组, 并在此一阶方程组的基础上推导出新的梯度公式与伴随方程, 建立了一种新的速度与衰减参数同时重建的全波形反演方法.相较于原二阶常分数阶拉普拉斯算子黏声方程建立的全波形反演流程, 数值实验表明, 新建立的反演流程可以有效避免原梯度数值计算中的噪声, 尤其是可以有效提高衰减参数梯度的反演精度, 从而显著提高反演的收敛速度与反演精度.

     

储层弹性与物性参数地震叠前同步反演的确定性优化方法

储层弹性与物性参数可直接应用于储层岩性预测和流体识别,是储层综合评价和油气藏精细描述的基本要素之一.现有的储层弹性与物性参数地震同步反演方法大都基于Gassmann方程,使用地震叠前数据,通过随机优化方法反演储层弹性与物性参数;或基于Wyllie方程,使用地震叠后数据,通过确定性优化方法反演储层弹性与物性参数.本文提出一种基于Gassmann方程、通过确定性优化方法开展储层弹性和物性参数地震叠前反演的方法,该方法利用Gassmann方程建立储层物性参数与叠前地震观测数据之间的联系,在贝叶斯反演框架下以储层弹性与物性参数的联合后验概率为目标函数,通过将目标函数的梯度用泰勒公式展开得到储层弹性与物性参数联合的方程组,其中储层弹性参数对物性参数的梯度用差分形式表示,最后通过共轭梯度算法迭代求解得到储层弹性与物性参数的最优解.理论试算与实际资料反演结果证明了方法的可行性.     

Analysis of different parameterisations of waveform inversion of compressional body waves in an elastic transverse isotropic Earth with a vertical axis of symmetry

In a multi‐parameter waveform inversion, the choice of the parameterisation influences the results and their interpretations because leakages and the tradeoff between parameters can cause artefacts. We review the parameterisation selection when the inversion focuses on the recovery of the intermediate‐to‐long wavenumbers of the compressional velocities from the compressional body (P) waves. Assuming a transverse isotropic medium with a vertical axis of symmetry and weak anisotropy, analytical formulas for the radiation patterns are developed to quantify the tradeoff between the shear velocity and the anisotropic parameters and the effects of setting to zero the shear velocity in the acoustic approach. Because, in an anisotropic medium, the radiation patterns depend on the angle of the incident wave with respect to the vertical axis, two particular patterns are discussed: a transmission pattern when the ingoing and outgoing slowness vectors are parallel and a reflection pattern when the ingoing and outgoing slowness vectors satisfy Snell's law. When the inversion aims at recovering the long‐to‐intermediate wavenumbers of the compressional velocities from the P‐waves, we propose to base the parameterisation choice on the transmission patterns. Since the P‐wave events in surface seismic data do not constrain the background (smooth) vertical velocity due to the velocity/depth ambiguity, the preferred parameterisation contains a parameter that has a transmission pattern concentrated along the vertical axis. This parameter can be fixed during the inversion which reduces the size of the model space. The review of several parameterisations shows that the vertical velocity, the Thomsen parameter δ, or the Thomsen parameter ε have a transmission pattern along the vertical axis depending on the parameterisation choice. The review of the reflection patterns of those selected parameterisations should be done in the elastic context. Indeed, when reflection data are also inverted, there are potential leakages of the shear parameter at intermediate angles when we carry out acoustic inversion.     

2D acoustic‐elastic coupled waveform inversion in the Laplace domain

Although waveform inversion has been intensively studied in an effort to properly delineate the Earth's structures since the early 1980s, most of the time‐ and frequency‐domain waveform inversion algorithms still have critical limitations in their applications to field data. This may be attributed to the highly non‐linear objective function and the unreliable low‐frequency components. To overcome the weaknesses of conventional waveform inversion algorithms, the acoustic Laplace‐domain waveform inversion has been proposed. The Laplace‐domain waveform inversion has been known to provide a long‐wavelength velocity model even for field data, which may be because it employs the zero‐frequency component of the damped wavefield and a well‐behaved logarithmic objective function. However, its applications have been confined to 2D acoustic media. We extend the Laplace‐domain waveform inversion algorithm to a 2D acoustic‐elastic coupled medium, which is encountered in marine exploration environments. In 2D acoustic‐elastic coupled media, the Laplace‐domain pressures behave differently from those of 2D acoustic media, although the overall features are similar to each other. The main differences are that the pressure wavefields for acoustic‐elastic coupled media show negative values even for simple geological structures unlike in acoustic media, when the Laplace damping constant is small and the water depth is shallow. The negative values may result from more complicated wave propagation in elastic media and at fluid‐solid interfaces. Our Laplace‐domain waveform inversion algorithm is also based on the finite‐element method and logarithmic wavefields. To compute gradient direction, we apply the back‐propagation technique. Under the assumption that density is fixed, P‐ and S‐wave velocity models are inverted from the pressure data. We applied our inversion algorithm to the SEG/EAGE salt model and the numerical results showed that the Laplace‐domain waveform inversion successfully recovers the long‐wavelength structures of the P‐ and S‐wave velocity models from the noise‐free data. The models inverted by the Laplace‐domain waveform inversion were able to be successfully used as initial models in the subsequent frequency‐domain waveform inversion, which is performed to describe the short‐wavelength structures of the true models.     

基于岩石物理分析的叠前弹性反演预测含气砂岩分布(英文)

地震反演是当今最广泛应用于含油气储层预测的技术之一,取得了很多很好的预测效果,但也有失败的例子,达不到区分岩性和识别流体的目的。而本文介绍的建立在岩石物理建模和分析基础上的地震弹性反演,可将含油气储层预测由定性向(半)定量推进一步。根据岩石物理建模和正演扰动分析,可深刻理解岩石物性参数与地震弹性参数之间的内在关系,进而寻找储层岩性、物性和含油气性的敏感地震弹性参数,建立起理论岩石物理解释图版。岩石物理分析结果和所建立的岩石物理解释图版分别用以指导地震反演和反演结果的解释,实现油气储层分布预测和流体检测的目的。文中的含气砂岩分布预测实例研究应用结果表明,这种方法较叠后地震反演储层预测技术具有无可比拟的优越性,效果更佳,效率更高。     

稳定正则化参数估计方法及其在盆地基底重力异常反演中的应用

正则化方法通过带有正则化参数的约束项,将不适定问题转换为一个适定问题.如何选取最优正则化参数一直以来都是正则化研究的难点和热点.本文通过定义解的不稳定性度量来直接估算正则化参数μ的最优值,并将这种正则化参数估计方法应用到二维沉积盆地基底重力反演中.测试该方法在通过对一次野外测量的数据加不同噪声得到的多组数据与多次野外测量中得到的多组数据这两种情况中的反演效果.最后将该方法应用到非洲西海岸的北加蓬次盆进行盆地基底反演,测试该方法的实用性.模型测试的结果显示,在这两种情况下获得的反演解非常接近且能够反演得到较为准确的模型基底深度,故该方法适用于一般情况下只进行一次野外测量的实际重力勘探情况且能得到稳定的最优反演解;实际资料的最优反演结果稳定且符合当地的地质构造背景.在模型测试与实际资料测试中,都能够确定最优正则化参数并得到最优反演结果,证明了该方法在重力反演中的正确性和实用性.