联合多点地质统计学与序贯高斯模拟的随机反演方法

岩相和储层物性参数是油藏表征的重要参数,地震反演是储层表征和油气藏勘探开发的重要手段.随机地震反演通常基于地质统计学理论,能够对不同类型的信息源进行综合,建立具有较高分辨率的储层模型,因而得到广泛关注.其中,概率扰动方法是一种高效的迭代随机反演策略,它能综合考虑多种约束信息,且只需要较少的迭代次数即可获得反演结果.在概率扰动的优化反演策略中,本文有效的联合多点地质统计学与序贯高斯模拟,并结合统计岩石物理理论实现随机反演.首先,通过多点地质统计学随机模拟,获得一系列等可能的岩相模型,扰动更新初始岩相模型后利用相控序贯高斯模拟建立多个储层物性参数模型;然后通过统计岩石物理理论,计算相应的弹性参数;最后,正演得到合成地震记录并与实际地震数据对比,通过概率扰动方法进行迭代,直到获得满足给定误差要求的反演结果.利用多点地质统计学,能够更好地表征储层空间特征.相控序贯高斯模拟的应用,能够有效反映不同岩相中储层物性参数的分布.提出的方法可在较少的迭代次数内同时获得具有较高分辨率的岩相和物性参数反演结果,模型测试和实际数据应用验证了方法的可行性和有效性.     

地震岩相识别概率表征方法

储层岩相分布信息是油藏表征的重要参数,基于地震资料开展储层岩相识别通常具有较强的不确定性.传统方法仅获取唯一确定的岩相分布信息,无法解析反演结果的不确定性,增加了油藏评价的风险.本文引入基于概率统计的多步骤反演方法开展地震岩相识别,通过在其各个环节建立输入与输出参量的统计关系,然后融合各环节概率统计信息构建地震数据与储层岩相的条件概率关系以反演岩相分布概率信息.与传统方法相比,文中方法通过概率统计关系表征了地震岩相识别各个环节中地球物理响应关系的不确定性,并通过融合各环节概率信息实现了不确定性传递的数值模拟,最终反演的岩相概率信息能够客观准确地反映地震岩相识别结果的不确定性,为油藏评价及储层建模提供了重要参考信息.模型数据和实际资料应用验证了方法的有效性.     

工程结构地震破坏概率矩阵分析

本文提出了一种计算工程结构地震坡坏概率矩阵的方法，建立了地震地面运动模型和结构分析模型，对结构进行了随机地震反应分析，并获得了结构随机分应的统计量，进而采用双参数的结构破坏模型，给出了教育处结构地震破坏概率的表达式，利用此方法计算了一座按8度要求设计的钢筋混凝土框架型，给出了计算结构地震坡坏概率的表达式，利用此方法计算了一座按8度要求的钢筋混凝土框架结构的地震破坏概率矩阵，本文提出了方法可以在确定抗震设防标准和进行震害预测时采用。     

岩石物理驱动的相约束叠前地震概率化反演方法

地震岩石物理是连接岩石弹性参数与储层物性参数的桥梁,叠前地震反演是实现地下岩石弹性、物性、岩性及含流体性质定量表征的重要方法.文章构建了碎屑岩地震岩石物理高阶近似模型,推导了利用岩石模量高阶近似(Jacobian、Hessian矩阵)表征的叠前地震AVO反射特征方程,并分析了岩石孔隙度、泥质含量及流体饱和度对AVO反射率的贡献度,探讨了此方程在岩石物性参数直接预测方面的可行性.以此为基础,在待反演模型参数服从混合概率先验模型的前提下,文章提出了基于差分进化-马尔可夫链蒙特卡罗随机模型的相约束叠前地震概率化反演方法,兼具差分进化算法的全局寻优特性和马尔可夫链蒙特卡罗模型的不确定性分析能力;通过多条马尔可夫链的交叉并行,可以同步获得待反演模型参数的多个随机解,进而模拟待反演模型的后验概率密度分布,后验均值作为待反演模型的最优解,方差与置信区间用来评价反演结果的不确定性,实现储层弹性、物性、离散岩相及干岩石骨架等参数的同步预测.通过理论试验和实际资料处理验证了该理论方法的有效性.     

反演模型分辨率的估算方法

反演问题的时空间分辨率或称时空分辨长度是评估模型精细程度的重要参数,决定了该模型应用的范围和价值,但是分辨长度估算却是比反演更复杂和麻烦的数学问题。除了层析成像中广泛利用理论模型恢复试验定性提取空间分辨长度外,通过求解分辨率矩阵可定量获得分辨长度。通过矩阵操作给出的分辨率矩阵包括三类：直接分辨率矩阵、正则化分辨率矩阵和混合分辨率矩阵。这三类矩阵包含了反演本身不同侧面的信息,因此在一个反演应用中,同时提供这三类分辨率矩阵可更全面地评估反演模型分辨率分布。最近An（2012）提出了从大量随机理论模型及其解中统计出分辨率矩阵的方法。这种分辨率矩阵是从模拟真实反演实验的输入和输出模型中通过反演得到的,因此这种分辨率矩阵更能反映整个反演所涉及到的更多因素和过程;同时由于这种分辨率矩阵计算过程无需进行矩阵操作且不依赖于具体正演和反演方法,因此可以被应用于更普遍的反演问题。实际应用证明统计分辨率分析方法适用于对二维和三维层析成像反演模型进行分辨率分析。     

江苏及邻区中强震的灰色马尔柯夫模型

为了探索新的地震灾变预测途径，探讨了集不同手段之长所构筑的一种新模式，其方法是在灰色模型（ＧＭ（１，１））的基础上划分多个与预测值平行的状态区间，考察下一步状态的转移概率，形成灰色马尔柯预测模型，将震级和时间等作为预测要素，通过模型给出了其变化的灰区间和是了大可能值，实例表明，由于灰色预测和马尔柯夫转换概率矩阵两者互补优势，形成的新模型优化了预测结果，作为新方法，灰色马尔柯夫模型值得深入研究。     

用灰色马尔柯夫模型探讨新疆境内Ms≥6.0级地震的年发生概率分布

本文在灰色马尔柯夫模型的基础上,增加了一项二重状态转移概率矩阵,对马氏模型进行了修改,据此,研讨了新疆境内1902—1988年Ms≥6.0级地震在不同状态下的年发生概率分布,其结果是令人满意的。提出的灰色马氏模型可作为中期地震预报手段。     

全国年度地震重点危险区与地震相关性的统计模拟分析

用统计模拟的方法对1990～1997年全国年度重点危险区与地震的相关性进行了分析．由于统计模拟的方法有效地处理了地震和危险区的时空不均匀性,并且得到经运算105 次的统计模拟随机预报概率,将其与实际预报平均概率比较,得到较为客观的结果．结果表明:① 1990～1997年全国年度重点危险区的实际预报平均概率,比完全平均随机划定预报区的统计模拟平均随机概率高0.03719;② 考虑地震活动背景概率时,实际预报平均概率比危险区加权重的统计模拟平均概率高0.02183;③ 将中国大陆依地震分布不均匀性分为新疆西部地区、西南地区和其它地区３个区时,新疆西部地区的实际预报平均概率大大高出统计模拟平均随机概率,其差值为0.20962．      

傅利叶重建法的数值模拟研究

运用ＣＴ技术中的傅利叶重建法，根据任意所给的两个初始速度模型，用几组平行射线束进行扫描，采集走时数据，并利用走时数据反演速度图象．反演结果与初始模型比较两者基本相符合。由此证明，傅利叶重建法在一定条件下可以用来反演地壳速度结构，并可得到较好的结果．这种方法是ＣＴ技术应用于地学研究的一种新的尝试．     

城市供水管网在地震时的连通可靠性分析

考虑地震作用效应和管道抗力的随机特性,建立了埋地管道单元的概率预测模型,评估其在地震时的震害状态。把供水管网系统简化为边权有向网络图,通过Monte Carlo随机模拟过程,近似再现管网中各管段的破坏状态,进而分别结合图论理论方法和模糊关系矩阵法,对管网进行连通可靠性分析。由于Monte Carlo模拟算法是以管网各节点与水源点处于连通状态的近似频率计算来代替精确概率分析,为获得稳定的计算结果,对所用算例进行了5000次模拟。算例分析表明,基于图论方法和模糊关系矩阵法得到的管网连通可靠性结果基本相等。     

A new bivariate Gamma distribution generated from functional scale parameter with application to drought data

Univariate and bivariate Gamma distributions are among the most widely used distributions in hydrological statistical modeling and applications. This article presents the construction of a new bivariate Gamma distribution which is generated from the functional scale parameter. The utilization of the proposed bivariate Gamma distribution for drought modeling is described by deriving the exact distribution of the inter-arrival time and the proportion of drought along with their moments, assuming that both the lengths of drought duration (X) and non-drought duration (Y) follow this bivariate Gamma distribution. The model parameters of this distribution are estimated by maximum likelihood method and an objective Bayesian analysis using Jeffreys prior and Markov Chain Monte Carlo method. These methods are applied to a real drought dataset from the State of Colorado, USA.     

Parameter-independent model reduction of transient groundwater flow models: Application to inverse problems

A new methodology is proposed for the development of parameter-independent reduced models for transient groundwater flow models. The model reduction technique is based on Galerkin projection of a highly discretized model onto a subspace spanned by a small number of optimally chosen basis functions. We propose two greedy algorithms that iteratively select optimal parameter sets and snapshot times between the parameter space and the time domain in order to generate snapshots. The snapshots are used to build the Galerkin projection matrix, which covers the entire parameter space in the full model. We then apply the reduced subspace model to solve two inverse problems: a deterministic inverse problem and a Bayesian inverse problem with a Markov Chain Monte Carlo (MCMC) method. The proposed methodology is validated with a conceptual one-dimensional groundwater flow model. We then apply the methodology to a basin-scale, conceptual aquifer in the Oristano plain of Sardinia, Italy. Using the methodology, the full model governed by 29,197 ordinary differential equations is reduced by two to three orders of magnitude, resulting in a drastic reduction in computational requirements.     

Bayesian flood frequency analysis in the light of model and parameter uncertainties

The specific objective of the paper is to propose a new flood frequency analysis method considering uncertainty of both probability distribution selection (model uncertainty) and uncertainty of parameter estimation (parameter uncertainty). Based on Bayesian theory sampling distribution of quantiles or design floods coupling these two kinds of uncertainties is derived, not only point estimator but also confidence interval of the quantiles can be provided. Markov Chain Monte Carlo is adopted in order to overcome difficulties to compute the integrals in estimating the sampling distribution. As an example, the proposed method is applied for flood frequency analysis at a gauge in Huai River, China. It has been shown that the approach considering only model uncertainty or parameter uncertainty could not fully account for uncertainties in quantile estimations, instead, method coupling these two uncertainties should be employed. Furthermore, the proposed Bayesian-based method provides not only various quantile estimators, but also quantitative assessment on uncertainties of flood frequency analysis.     

Numerical simulation and inversion of MT fields in the 3D electric conductivity model of the Vesuvius volcano

Possibilities for three-dimensional (3D) magnetotelluric (MT) sounding of local objects contained in the Earth’s crust are estimated in a case study of the magma chamber of the Vesuvius volcano. Stochastic inversion of the model MT data by the Markov Chain Monte Carlo (MCMC) method has shown that the most efficient approach is not simultaneous but successive estimation of the geometry and the depth of the anomaly and the assessment of the conductivity distribution within the anomalous region. A zone of equivalence is revealed between the a priori estimate of the depth of the anomalous zone and the a posteriori distribution of electric conductivity within it. Based on the present estimation and previous results, an algorithm for determination of the parameters of local crustal anomaly is proposed.     

基于MCMC的叠前地震反演方法研究

马尔科夫链蒙特卡洛方法(MCMC)是一种启发式的全局寻优算法[1].它在贝叶斯框架下,利用已有资料进行约束,既可使最优解满足参数的统计特性,又通过融入的先验信息,提高解的精度;寻优过程可跳出局部最优,得到全局最优解.利用MCMC方法,可以得到大量来自于后验概率分布的样本,不仅可以得到每个未知参数的估计值,而且可以得到与...     

Effects of uncertainty in rock-physics models on reservoir parameter estimation using seismic amplitude variation with angle and controlled-source electromagnetics data

This paper investigates the effects of uncertainty in rock-physics models on reservoir parameter estimation using seismic amplitude variation with angle and controlled-source electromagnetics data. The reservoir parameters are related to electrical resistivity by the Poupon model and to elastic moduli and density by the Xu-White model. To handle uncertainty in the rock-physics models, we consider their outputs to be random functions with modes or means given by the predictions of those rock-physics models and we consider the parameters of the rock-physics models to be random variables defined by specified probability distributions. Using a Bayesian framework and Markov Chain Monte Carlo sampling methods, we are able to obtain estimates of reservoir parameters and information on the uncertainty in the estimation. The developed method is applied to a synthetic case study based on a layered reservoir model and the results show that uncertainty in both rock-physics models and in their parameters may have significant effects on reservoir parameter estimation. When the biases in rock-physics models and in their associated parameters are unknown, conventional joint inversion approaches, which consider rock-physics models as deterministic functions and the model parameters as fixed values, may produce misleading results. The developed stochastic method in this study provides an integrated approach for quantifying how uncertainty and biases in rock-physics models and in their associated parameters affect the estimates of reservoir parameters and therefore is a more robust method for reservoir parameter estimation.     

随机反演在储层预测中的应用

针对隐蔽油气藏储层预测的需要,开展了地震反演研究,根据目前的实际应用将储层预测中的基于模型的地震反演分为三个实施阶段:即构造反演、声波波阻抗或弹性波阻抗反演以及岩性反演,并对每个阶段的目的、关键技术及其原理进行了详细描述,尤其是详细描述了基于马尔科夫链的蒙特卡罗随机模拟技术.最后给出了一个综合应用测井、地质、地震资料进行反演,从而进行储层预测的实例.     

基于贝叶斯方法的二维大地电磁尖锐边界反演研究

针对常规大地电磁（Magnetotelluric,MT）反演方法对电阻率异常体边界不太敏感的问题,本文尝试基于贝叶斯理论开展二维大地电磁电阻率尖锐边界反演研究.在反演中,模型参数由边界位置及内部电阻率组成,通过贝叶斯理论将模型参数与数据相联系,采用Markov Chain Monte Carlo（MCMC）的Metropolis-Hastings（MH）方法对后验概率密度函数（Posteriori Probability Density,PDD）进行采样.采样过程中无罚值函数约束,完全以数据自身所包含的信息对模型进行约束,同时与有限约束进行比较,并考虑不同起始采样点对结果的影响.以接受率为参考,用模型算例说明MH方法中建议分布函数选择的重要性.当模型参数间相关性较弱时,使用边缘概率分布对采样结果进行分析.该方法能给出模型参数的分布范围,并给出该模型参数范围对应的数据范围.通过与已知模型的对比及数据拟合情况分析检验了该反演方法的有效性.该方法有助于提高大地电磁尖锐边界反演的分辨能力.     

On the performance of a new bivariate pseudo Pareto distribution with application to drought data

A new bivariate pseudo Pareto distribution is proposed, and its distributional characteristics are investigated. The parameters of this distribution are estimated by the moment-, the maximum likelihood- and the Bayesian method. Point estimators of the parameters are presented for different sample sizes. Asymptotic confidence intervals are constructed and the parameter modeling the dependency between two variables is checked. The performance of the different estimation methods is investigated by using the bootstrap method. A Markov Chain Monte Carlo simulation is conducted to estimate the Bayesian posterior distribution for different sample sizes. For illustrative purposes, a real set of drought data is investigated.     

Stratigraphic Columns Modeling and Cyclicity Analysis of the Misoa Formation,Maracaibo Lake,Venezuela, using Markov Chains

A stochastic characterization of a hydrocarbon reservoir, constituted by a sedimentary sequence of sandstones interbbeded with siltstones and shales, has been performed. The stratigraphic unit studied here mainly comprises the C4 sands of the Misoa Formation, located in the Lama Field, Maracaibo Lake (Venezuela). A Markov Chain algorithm, based on the definition of genetic lithofacies relationships along stratigraphic columns, was developed. The application of the Monte Carlo stochastic method using this algorithm, to log data from 11 wells, allowed the generation of pseudo sequences at 20 new locations. This algorithm was able to properly model pseudo stratigraphic sequences and to quantify the relative facies percentage, showing a 82% confidence level related to the proportional content of sediments at a test well. The net sand map obtained integrating the stratigraphic columns, derived from the well information, and the Markov pseudo-columns, suggests the presence of sand bodies with a northeast-southwest orientation that agree with previous geological studies in the area. This map could help in the definition of prospective zones in the field. The existence of stratigraphic memory along the evaluated columns was recognized after applying the algorithm. The embedded Markov method used in the cyclicity analysis of the whole area indicates cyclic transitions just from sandstones to siltstones and from shales to siltstones. Hence for the study area, on average, fining upward and coarsening upward processes can be identified with the Markovian approach, as was expected for the tide-dominated deltaic system associated to the analyzed reservoir.