马尔柯夫链在江汉平原第四纪沉积环境分析中的应用

应用马尔柯夫链基本原理,在系统统计江汉平原监利县周老镇ZL01钻孔揭示的第四系基础上,结合该区的地质特征,进行了极限概率分析、差值矩阵分析、置换分析和熵分析.根据马尔柯夫链的综合分析结果,总结出江汉平原周老镇ZL01钻孔剖面的第四纪沉积主旋回,发现该剖面主要形成于河流沉积环境,并建立了该区第四系的地方性沉积相模式,为研究该地区的沉积作用、判断沉积环境提供定量的解释依据,对研究江汉平原的变迁历史及其保护和开发利用具有重要意义.     

Markov Chain Monte Carlo Implementation of Rock Fracture Modelling

This paper deals with the problem of estimating fracture planes, given only the data at borehole intersections with fractures. We formulate an appropriate model for the problem and give a solution to fitting the planes using a Markov chain Monte Carlo (MCMC) implementation. The basics of MCMC are presented, with particular emphasis given to reversible jump, which is required for changing dimensions. We also give a detailed worked example of the MCMC implementation with reversible jump since our implementation relies heavily on this new methodology. The methods are tested on both simulated and real data. The latter is a unique data set in the form of a granite block, which was sectioned into slices. All joints were located and recorded, and the joint planes obtained by stacking strike lines. This work is important in the risk assessment for the underground storage of hazardous waste. Problems and extensions are discussed.     

Bayesian Mixture Modelling in Geochronology via Markov Chain Monte Carlo

In this paper we develop a generalized statistical methodology for characterizing geochronological data, represented by a distribution of single mineral ages. The main characteristics of such data are the heterogeneity and error associated with its collection. The former property means that mixture models are often appropriate for their analysis, in order to identify discrete age components in the overall distribution. We demonstrate that current methods (e.g., Sambridge and Compston, 1994) for analyzing such problems are not always suitable due to the restriction of the class of component densities that may be fitted to the data. This is of importance, when modelling geochronological data, as it is often the case that skewed and heavy tailed distributions will fit the data well. We concentrate on developing (Bayesian) mixture models with flexibility in the class of component densities, using Markov chain Monte Carlo (MCMC) methods to fit the models. Our method allows us to use any component density to fit the data, as well as returning a probability distribution for the number of components. Furthermore, rather than dealing with the observed ages, as in previous approaches, we make the inferences of components from the “true” ages, i.e., the ages had we been able to observe them without measurement error. We demonstrate our approach on two data sets: uranium-lead (U-Pb) zircon ages from the Khorat basin of northern Thailand and the Carrickalinga Head formation of southern Australia.     

Markov Chain Random Fields for Estimation of?Categorical Variables

Multi-dimensional Markov chain conditional simulation (or interpolation) models have potential for predicting and simulating categorical variables more accurately from sample data because they can incorporate interclass relationships. This paper introduces a Markov chain random field (MCRF) theory for building one to multi-dimensional Markov chain models for conditional simulation (or interpolation). A MCRF is defined as a single spatial Markov chain that moves (or jumps) in a space, with its conditional probability distribution at each location entirely depending on its nearest known neighbors in different directions. A general solution for conditional probability distribution of a random variable in a MCRF is derived explicitly based on the Bayes’ theorem and conditional independence assumption. One to multi-dimensional Markov chain models for prediction and conditional simulation of categorical variables can be drawn from the general solution and MCRF-based multi-dimensional Markov chain models are nonlinear.     

Markov Chain Random Fields for Estimation of Categorical Variables

Multi-dimensional Markov chain conditional simulation (or interpolation) models have potential for predicting and simulating categorical variables more accurately from sample data because they can incorporate interclass relationships. This paper introduces a Markov chain random field (MCRF) theory for building one to multi-dimensional Markov chain models for conditional simulation (or interpolation). A MCRF is defined as a single spatial Markov chain that moves (or jumps) in a space, with its conditional probability distribution at each location entirely depending on its nearest known neighbors in different directions. A general solution for conditional probability distribution of a random variable in a MCRF is derived explicitly based on the Bayes’ theorem and conditional independence assumption. One to multi-dimensional Markov chain models for prediction and conditional simulation of categorical variables can be drawn from the general solution and MCRF-based multi-dimensional Markov chain models are nonlinear.     

Characterising geotechnical model uncertainty by hybrid Markov Chain Monte Carlo simulation

Geotechnical models are usually associated with considerable amounts of model uncertainty. In this study, the model uncertainty of a geotechnical model is characterised through a systematic comparison between model predictions and past performance data. During such a comparison, model input parameters (such as soil properties) may also be uncertain, and the observed performance may be subjected to measurement errors. To consider these uncertainties, the model uncertainty parameters, uncertain model input parameters and actual performance variables are modelled as random variables, and their distributions are updated simultaneously using Bayes’ theorem. When the number of variables to update is large, solving the Bayesian updating problem is computationally challenging. A hybrid Markov Chain Monte Carlo simulation is employed in this paper to decompose the high-dimensional Bayesian updating problem into a series of updating problems in lower dimensions. To increase the efficiency of the Markov chain, the model uncertainty is first characterised with a first order second moment method approximately, and the knowledge learned from the approximate solution is then used to design key parameters in the Markov chain. Two examples are used to illustrate the proposed methodology for model uncertainty characterisation, with insights, discussions, and comparison with previous methods.     

基于权马尔可夫链模型的庐江县降水量预测

由于降水过程的随机性与不确定性,使得降水量预测存在一定的难度。对安徽省庐江县1952~2009年逐年降水资料进行了分析,采用样本-标准差分级法将这58年的逐年降水量序列分为枯水年,偏枯水年,平水年,偏丰水年,丰水年5个状态,采用权马尔可夫链模型预测了2010年的降水量,预测结果与实测结果相吻合。     

A Markov Chain Model for Subsurface Characterization: Theory and Applications

This paper proposes an extension of a single coupled Markov chain model to characterize heterogeneity of geological formations, and to make conditioning on any number of well data possible. The methodology is based on the concept of conditioning a Markov chain on the future states. Because the conditioning is performed in an explicit way, the methodology is efficient in terms of computer time and storage. Applications to synthetic and field data show good results.     

灰色马尔可夫链在深基坑沉降预测中的应用

针对深基坑在开挖后的施工过程中,由于多种因素引起的沉降变形具有随机性的特点,采用灰色马尔可夫链模型对上海市某深基坑的沉降进行了成功预测。结果表明,利用灰色马尔可夫链对深基坑的沉降变形进行预测是可行的。     

A Fixed-Path Markov Chain Algorithm for Conditional Simulation of Discrete Spatial Variables

The Markov chain random field (MCRF) theory provided the theoretical foundation for a nonlinear Markov chain geostatistics. In a MCRF, the single Markov chain is also called a “spatial Markov chain” (SMC). This paper introduces an efficient fixed-path SMC algorithm for conditional simulation of discrete spatial variables (i.e., multinomial classes) on point samples with incorporation of interclass dependencies. The algorithm considers four nearest known neighbors in orthogonal directions. Transiograms are estimated from samples and are model-fitted to provide parameter input to the simulation algorithm. Results from a simulation example show that this efficient method can effectively capture the spatial patterns of the target variable and fairly generate all classes. Because of the incorporation of interclass dependencies in the simulation algorithm, simulated realizations are relatively imitative of each other in patterns. Large-scale patterns are well produced in realizations. Spatial uncertainty is visualized as occurrence probability maps, and transition zones between classes are demonstrated by maximum occurrence probability maps. Transiogram analysis shows that the algorithm can reproduce the spatial structure of multinomial classes described by transiograms with some ergodic fluctuations. A special characteristic of the method is that when simulation is conditioned on a number of sample points, simulated transiograms have the tendency to follow the experimental ones, which implies that conditioning sample data play a crucial role in determining spatial patterns of multinomial classes. The efficient algorithm may provide a powerful tool for large-scale structure simulation and spatial uncertainty analysis of discrete spatial variables.     

基于无偏灰色马尔可夫链的吉林省降水量预测

为了更准确地对吉林省降水量进行预测,分析其时空变化特征,应用无偏灰色马尔可夫链模型对8个具有代表性的雨量站进行降水量预测,并根据预报结果讨论历史数据波动性与预报精度的关系。其中：83%以上预测结果合格,白城、乾安、长春、蛟河、四平、通化6个地区降水量多年呈递减趋势,减幅分别为0.23%、0.09%、0.24%、1.01%、0.51%、0.54%;延吉、靖宇2个地区降水量多年呈递增趋势,增幅分别为2.60%、0.54%。结果表明：无偏灰色马尔可夫链模型预测精度较高,说明该方法适用于吉林省的降水量预测;吉林省中西部地区降水量呈递减趋势,东部地区呈递增趋势,但变幅不大;在波动性与预报精度的关系方面,时间序列的波动性越大预测所产生的误差越大。     

含水层非均质结构的马尔可夫链地质统计方法及应用

针对含水层非均质性对地下水流动和溶质运移模拟的准确性有着重要的影响,但非均质性的刻画十分困难的问题,介绍了马尔可夫转移概率理论方法及其在含水层非均质结构研究中的应用,利用Walther定律建立了三维马尔可夫链,并将该方法用于研究位于山西省介休市龙凤河冲积扇岩相的空间分布规律.结果表明该地区细颗粒具有在垂直方向上向上沉积、水平方向上向外沉积的趋势,细颗粒岩相与粗颗粒岩相之间的关联性强而粗颗粒岩相之间的关联性差.该方法的缺点在于Walther定律的应用可能会增加不确定性.     

一种北江流域年降雨量的权马尔可夫链预测模型

根据北江流域的48个站点的年降雨量资料和泰森多边形计算方法,计算出北江流域的面降雨量。再结合丰、偏丰、平、偏枯、枯水年的频率标准,建立了适用于北江流域年降雨量的分级数值区间,同时,验证了该序列满足马尔可夫链的要求,并考虑该年降雨量序列是相依随机变量的特点,以规范化的各阶自相关系数为权,建立了北江流域年降雨量的权马尔可夫链预测模型,实例验证结果令人满意。     

基于不同邻域系统的马尔可夫链模型的储层岩相随机模拟

针对在油气储层随机模拟中马尔可夫链模型的不同方向的转移概率矩阵求取困难的问题,提出一种二维剖面中不同方向的转移概率矩阵求取方法,这种方法的提出使得不同阶次的各向同性和各向异性的邻域系统的转移概率矩阵的求取变得容易可行。随后,对不同邻域系统的马尔可夫链模型采用蒙特卡罗抽样方法进行了储层岩相随机模拟试验。最后比较了不同邻域系统岩相模拟的结果并探讨了在储层研究中的适用性。     

基于Markov chain理论的科技成果转化的市场预测

科技成果成功转化的主要标志是其产品的市场畅销度。产品的畅销度由于受各种内外部不确定因素影响，具有随机不确定性。基于这种随机不确定性，运用Markov chain对其产品进行市场预测，并通过实证分析说明其有效性，为科技成果的转化提供具体可行的定量依据。     

天津蓟县雾迷山旋回层基本模式及其马尔柯夫链分析

津蓟县的中元古界雾迷山组,是一套碳酸盐岩地层,具近似对称相序组构的环潮坪型碳酸盐米级旋回层序特别以育。其近似对称的相序组构及普遍的1：4叠加形态,表明它们与短偏心率旋回具有成因关联,被命名为雾迷山旋回层来代表真正的碳酸盐沉积旋回。雾迷山旋回层是与高频率产面变化相关的环境加深及环境变浅过程的产物。马尔柯夫链分析的结果表明了雾迷山旋回层的基本相序模式是客观存在的,由于它们以瞬时暴露间断面为界,因而与Vail等（1977）的层序地层概念体系中所定义的“准层序”存在明显的差异。尽管难以断定前寒武纪地球轨道效应旋回的周期安全与显生宙一致,但是,七级韵律层、六级旋回层及五级准层序组之间的垂直叠置形态,以及由它们所指示的周期时限,与显生宙温室效应时期的轨道效应旋回周期是大体一致的。     

A comparative analysis of pre- and post-industrial spatiotemporal drought trends and patterns of Tibet Plateau using Sen slope estimator and steady-state probabilities of Markov Chain

Natural Hazards - The increase of frequency and severity of extreme weather events due to climate change gives evidence of severe challenges faced by infrastructure systems. Among them, the...