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.     

Applying spatial regression to evaluate risk factors for microbiological contamination of urban groundwater sources in Juba,South Sudan

This study developed methodology for statistically assessing groundwater contamination mechanisms. It focused on microbial water pollution in low-income regions. Risk factors for faecal contamination of groundwater-fed drinking-water sources were evaluated in a case study in Juba, South Sudan. The study was based on counts of thermotolerant coliforms in water samples from 129 sources, collected by the humanitarian aid organisation Médecins Sans Frontières in 2010. The factors included hydrogeological settings, land use and socio-economic characteristics. The results showed that the residuals of a conventional probit regression model had a significant positive spatial autocorrelation (Moran’s I?=?3.05, I-stat?=?9.28); therefore, a spatial model was developed that had better goodness-of-fit to the observations. The most significant factor in this model (p-value 0.005) was the distance from a water source to the nearest Tukul area, an area with informal settlements that lack sanitation services. It is thus recommended that future remediation and monitoring efforts in the city be concentrated in such low-income regions. The spatial model differed from the conventional approach: in contrast with the latter case, lowland topography was not significant at the 5% level, as the p-value was 0.074 in the spatial model and 0.040 in the traditional model. This study showed that statistical risk-factor assessments of groundwater contamination need to consider spatial interactions when the water sources are located close to each other. Future studies might further investigate the cut-off distance that reflects spatial autocorrelation. Particularly, these results advise research on urban groundwater quality.     

An Anisotropic Geomechanical Model for Jointed Rock Masses at Taishan Nuclear Power Station, Southern China

An anisotropic geomechanical model for jointed rock mass is presented. Simultaneously with deriving the orthotropic anisotropy elastic parameters along the positive axis, the equivalent compliance matrix for the deflection axis orthotropic anisotropy was derived through a three-dimensional coordinate transformation. In addition, Singh’s analysis of the stress concentration effects of intermittent joints was adopted, based on two groups of intermittent joints and a set of cross-cutting joints in the jointed rock mass. The stress concentration effects caused by intermittent joints and the coupling effect of cross-cutting joints along the deflection-axis are also considered. The proposed anisotropic mechanics parameters method is applied to determine the deformation parameters of jointed granite at the Taishan Nuclear Power Station. Combined with the deterministic mechanical parameters of rock blocks and joints, the deformation parameters and their variability in jointed rock masses are estimated quantitatively. The computed results show that jointed granite at the Taishan Nuclear Power Station exhibits typical anisotropic mechanical characteristics; the elastic moduli in the two horizontal directions were similar, but the elastic modulus in the vertical direction was much greater. Jointed rock elastic moduli in the two horizontal and vertical directions were respectively about 24% and 37% of the core of rock, showing weakly orthotropic anisotropy; the ratio of elastic moduli in the vertical and horizontal directions was 1.53, clearly indicating the transversely isotropic rock mass mechanical characteristics. The method can be popularized to solve other rock mechanics problems in nuclear power engineering.     

Analysis of dry and wet climate characteristics at Uttarakhand (India) using effective drought index

Natural Hazards - Drought is a complex natural disaster that adversely affects human life and the ecosystem. A variety of drought indexes are available for monitoring meteorological drought events....     

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...     

On the occurrences of dry and wet sequences in the Brahmaputra valley

Occurrence of dry and wet days in the Brahmaputra Valley has been studied using a first-order Markov Chain model. The model is fitted to the daily rainfall series recorded at ten stations widely distributed in the valley. The adequacy of the model is tested and found suitable. At all the stations, dry and wet spells having different durations follow geometric distribution. For pre-monsoon and monsoon seasons, the expected dry and wet days, the expected length of a weather cycle and the return period of dry spells having different, durations are calculated, and the results for different stations are compared.     

改进加权马尔科夫链模型在喀什地区承压含水层参数动态识别中的应用研究

承压含水层的估算对于地下水开发利用的合理规划十分重要。而承压含水层参数识别对于含水层水量参数估算至关重要。结合改进加权马尔科夫链模型,以喀什为研究实例,对该地区承压含水层参数进行动态识别,从置信区间分析结果可看出,喀什地区承压含水层参数的变幅为7.93 m^2/min,而承压含水层参数μ的变幅为0.048,从不同置信度下的变幅结果可看出,相比于传统模型,改进加权马尔科夫链模型提高了参数识别收敛效率和计算精度。计算结果的可靠性程度较高。研究成果对于喀什地区含水层水量估算具有重要的参考价值。     

Basic Lithofacies-Succession Model for the Wumishan Cyclothems: Their Markov Chain Analysis and Regularly Vertical Stacking Patterns in the Third-Order Sequences

The Mesoproterozoic Wumishan Formation in the Jixian section of Tianjin is a succession of 3300-m-thick carbonate strata formed in a period of about 100 Ma (1310±20 Ma-1207±10 Ma). In this succession of strata, the carbonate metre-scale cyclic sequences belonging to peritidal type with an approximately symmetrical lithofacies-succession are best developed. The wide development of 1:4 stacking patterns shows that these metre-scale cyclic sequences are genetically related to the short-eccentricity cycles, which are called the Wumishan cyclothems that could truly represent sedimentary cycles. Generally, massive and thick-bedded calcareous dolomites and dolomitic limestones of stromatolite biostromes and thrombolite bioherms constitute the central part of the Wumishan cyclothems. The lower and upper parts consist of tidal flat dolostones, sandy-muddy dolostone and the top part is composed of lagoonal facies dolomitic shales with a paleosol cap. Therefore, an approximately symmetrical lithofacies-successio     

DEM filtration modelling for granular materials: Comparative analysis of dry and wet approaches

A detailed study comparing two – dry and wet – numerical approaches to model filtration processes at stake in actual granular filters is presented using the discrete element method (DEM). In the first approach, the migration of fines is provided by gravitational forces, while in the second, hydrodynamic forces induce their movement. Numerical filtration tests were performed on granular filters involving materials with different gradings and porosities. The study demonstrated that the wet filtration approach generates higher tortuosity due to the possibility for fines to deviate from direct paths towards more open sideways. It leads to a lower coefficient of retention for the filter than if it were characterised using a dry filtration approach. However, the intensity of this feature greatly depends on the grading and the porosity of the granular filter. Finally, an enhanced dry filtration model designated as the “equivalent cyclic wet filtration model” is presented, which better mimics the results obtained through the preferable wet filtration model compared to the original dry filtration model. This new model constitutes a valuable alternative tool for studies of filtration properties in granular materials.     

武汉市大气干湿沉降中溶解态黑碳的季节分布特征

本研究采集了武汉市城区2018年3月至2019年2月的大气总沉降及湿沉降样品,使用苯多羧酸法测定溶解态黑碳含量,并结合气象条件分析溶解态黑碳沉降通量季节变化特征及其影响因素。结果表明,总沉降中溶解态黑碳月浓度范围为0.12～0.83 mg/L,均值为0.40 mg/L,湿沉降溶解态黑碳浓度范围为0.04～0.18 mg/L,均值为0.10 mg/L;溶解态黑碳总沉降和湿沉降年通量分别为269 mg·m^-2·a^-1和65 mg·m^-2·a^-1。溶解态黑碳总沉降通量季节变化为春季>冬季>夏季>秋季,湿沉降通量季节变化为冬季>春季>夏季>秋季。溶解态黑碳湿沉降通量主要受降雨量影响,而总沉降通量除受降雨量影响外还受风速、风向和空气质量等因素的共同影响。     

地形对青藏高原丰枯水年雨季降水量空间分布的影响

采用高分辨率的3"数字高程模型及青藏高原东部102个常规气象观测站5～9月份的降水量资料,根据降水随高度分布将站点分为三类,再采用多元逐步回归的方法,建立了青藏高原40年(1961-2000年)逐年雨季降水量与经度、纬度、海拔、坡度、坡向、开放度等6个地理、地形因子关系模型,并以此为基础,分析了三类区域在丰枯水年里的因子系数的变化规律.结果表明,此法建立的关于高原降水量与诸因子之间方程的相关性显著,相对误差20%,平均相对误差4.4%,估算模型的相关系数均通过0.05的显著性检验;海拔低于1 400 m的第一类区域,主要受地形高度和开放度等局地地形的影响,来改变旱涝年的降水分布特征,海拔高度大于3 600 m的第三类区域,主要受开放度和坡度的影响,其他区域主要受地形的海拔、经度和开放度等局地地形的影响;高原季风是影响第三类区域水汽分布的主要因素,在季风加强时,开放度和经度的影响也随着加强,而坡度和海拔的影响减弱,从而使得水汽的局地性分布特征增强,东西分布差异加大,相应地局地降水分布特征加强,东西差异加大.地理地形因子影响大气的水汽输送和大气的垂直运动,从而导致其对空间降水分配的差异.     

1901~2020年中国西北地区干湿变化的时空特征

西北地区是我国西部大开发的主战场和重要的生态安全屏障,研究西北地区在全球变化背景下的干湿演化规律对我国高质量发展具有重要意义。本研究选取0.5°空间分辨率的逐月标准化降水蒸散指数(SPEI)格点数据集,利用Mann-Kendall趋势检验、EOF经验正交函数分解以及小波分析等方法,探索西北地区1901~2020年月尺度、年尺度、4年尺度的干湿变化时空演化特征。研究结果表明,西北地区SPEI值总体上呈逐渐下降的趋势。空间变化上,西北地区干湿变化情况存在明显的空间分异,研究区西南和西北部分表现为湿润趋势,而在中部和东部则表现为干旱趋势,这种反相变化特征在长时间尺度干旱上表现更加明显。时空模态的分解表明,西北地区月尺度干湿演化具有空间一致性,而在较长时间尺度上,区域干湿演化跷跷板模式占据主导地位,且这种空间差异模式在1990年代末期明显增强。在时间变化上,西北地区干旱具有较显著的2~8年短时间尺度的周期性变化规律,同时具有明显且连续的约11年和约22年长时间尺度的周期性变化特征。基于本分析结果,可以推断西北地区干湿变化时空演化特征可能受太阳活动和厄尔尼诺与南方涛动(ENSO)等因素的影响。研究结果还表明,SPEI指数在中国西北地区干旱分析研究中具有较好的适用性,研究结果可为该地区预防干旱事件和适应气候变化工作提供参考。

     

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.     

A review of Markov Chain Monte Carlo and information theory tools for inverse problems in subsurface flow

Parameter identification is one of the key elements in the construction of models in geosciences. However, inherent difficulties such as the instability of ill-posed problems or the presence of multiple local optima may impede the execution of this task. Regularization methods and Bayesian formulations, such as the maximum a posteriori estimation approach, have been used to overcome those complications. Nevertheless, in some instances, a more in-depth analysis of the inverse problem is advisable before obtaining estimates of the optimal parameters. The Markov Chain Monte Carlo (MCMC) methods used in Bayesian inference have been applied in the last 10 years in several fields of geosciences such as hydrology, geophysics or reservoir engineering. In the present paper, a compilation of basic tools for inference and a case study illustrating the practical application of them are given. Firstly, an introduction to the Bayesian approach to the inverse problem is provided together with the most common sampling algorithms with MCMC chains. Secondly, a series of estimators for quantities of interest, such as the marginal densities or the normalization constant of the posterior distribution of the parameters, are reviewed. Those reduce the computational cost significantly, using only the time needed to obtain a sample of the posterior probability density function. The use of the information theory principles for the experimental design and for the ill-posedness diagnosis is also introduced. Finally, a case study based on a highly instrumented well test found in the literature is presented. The results obtained are compared with the ones computed by the maximum likelihood estimation approach.     

Variability and trends of extreme dry and wet seasonal precipitation in Argentina. A retrospective analysis

The variability in seasonal mean and extreme precipitation is analyzed for several regions of Argentina to the north of 39º S, using long-term monthly time series data which expand from 1860 to 2006. The selected locations can be considered as representative of different climatic regions. This work focuses on the analysis of monthly rainfall distribution, significant seasonal trends, changes in variance and extreme monthly values, in order to establish the magnitude of the seasonal climatic rainfall variability through time for central Argentina. A 40-yr moving window was employed in order to analyze seasonal variability of rainfall extremes. Extremes were computed for different probability levels of a theoretical distribution function over/below the 80th/20th percentile. The gamma distribution was selected among five other theoretical distributions, and the scale and shape parameters were computed using the maximum likelihood estimation (MLE) and the bootstrap method for 1000 resample data sets, as well. Trend analysis was performed for each window on winter and summer means and tested for significance. The use of a moving window allowed detecting the window of maximum absolute values for the trends. Research results show significant temporal shifts in seasonal rainfall distribution and return values (RV) that were computed for different frequencies (once every five, 10 and 20 years). Generally, summer precipitation extremes have become wetter for the whole region. Rainfall amounts for summer wet/dry extremes (W/D) corresponding to the 90th (for W) and 10th (for D) percentiles were subjected to significant increase, but depending on the geographical area this effect spreads slightly differently over records of years. A common-for-all-stations period of such summer increase trend in extreme values spans from the window 1921-1960 to the last window analyzed: 1967-2006. This behavior was not observed for north and west Argentina during winter, except for the region represented by Bahía Blanca, where the 10% D extreme has increased throughout the study period.     

酸性环境干湿循环对泥质砂岩力学特性影响的试验研究

由于库水位升降及降雨等原因,岩体经常处于干湿交替状态,对岩体工程的长期稳定性不利。以三峡库区泥质砂岩为研究对象,进行了酸性环境干湿循环交替作用后的常规单轴与三轴压缩试验研究,获得了泥质砂岩在酸性溶液浸泡干湿循环后的相关力学参数。相对于没有经过干湿循环作用的干燥试件,经过不同次数的干湿循环作用后,泥质砂岩的弹性模量、单轴抗压强度、黏聚力与内摩擦角都有不同程度的降低。各个力学指标的总体变化趋势是在第一次饱水之后有大幅度的降低,此后随着干湿循环次数的增加其降低的幅度逐渐减小。同时,酸性溶液的pH值对力学指标的影响很大,存在对泥质砂岩力学性能影响较大的一个临界pH值,低于此值酸性溶液对泥质砂岩力学性能影响显著增大,高于此值酸性溶液对其力学性能影响较小。