随机模型在地下水资源计算中的应用：随机水文地质计算理论与方法

详细论述了地下水系统作为随机系统的客观合理性,应用随机模型于地下水资源 计算问题的可行性和必要性,介绍了地下水动态数据的随机处理方法,分类讨论用随机微分方程模拟,预测地下水位;并引入了伊藤随机积分研究地下水运动规律;将反求水文地质参数一维求布依模型推广到导水边界和二维情形。     

Turbidite bed thickness distributions: methods and pitfalls of analysis and modelling

Turbidite bed thickness distributions are often interpreted in terms of power laws, even when there are significant departures from a single straight line on a log–log exceedence probability plot. Alternatively, these distributions have been described by a lognormal mixture model. Statistical methods used to analyse and distinguish the two models (power law and lognormal mixture) are presented here. In addition, the shortcomings of some frequently applied techniques are discussed, using a new data set from the Tarcău Sandstone of the East Carpathians, Romania, and published data from the Marnoso‐Arenacea Formation of Italy. Log–log exceedence plots and least squares fitting by themselves are inappropriate tools for the analysis of bed thickness distributions; they must be accompanied by the assessment of other types of diagrams (cumulative probability, histogram of log‐transformed values, q–q plots) and the use of a measure of goodness‐of‐fit other than R², such as the chi‐square or the Kolmogorov–Smirnov statistics. When interpreting data that do not follow a single straight line on a log–log exceedence plot, it is important to take into account that ‘segmented’ power laws are not simple mixtures of power law populations with arbitrary parameters. Although a simple model of flow confinement does result in segmented plots at the centre of a basin, the segmented shape of the exceedence curve breaks down as the sampling location moves away from the basin centre. The lognormal mixture model is a sedimentologically intuitive alternative to the power law distribution. The expectation–maximization algorithm can be used to estimate the parameters and thus to model lognormal bed thickness mixtures. Taking into account these observations, the bed thickness data from the Tarcău Sandstone are best described by a lognormal mixture model with two components. Compared with the Marnoso‐Arenacea Formation, in which bed thicknesses of thin beds have a larger variability than thicknesses of the thicker beds, the thinner‐bedded population of the Tarcău Sandstone has a lower variability than the thicker‐bedded population. Such differences might reflect contrasting depositional settings, such as the difference between channel levées and basin plains.     

河床冲刷粗化的随机模拟

对冲刷与粗化的相互作用机制进行了分析,并在非均匀沙床面暴露度的随机分布特性、流速分布及起动规律研究的基础上,提出了河床冲刷粗化的随机模型。该模型能同时对河床冲刷深度及粗化稳定级配进行计算。由实验及野外实测资料的验证表明,计算结果与实测值基本相符。     

河流污染带的随机模拟方法

根据随机理论，推导了一个描述污染带变化的概率模型，并采用Ｍｏｎｔｅ－Ｃａｒｌｏ抽样法对其求数值解。该随机模型的解是一个随机物，实例计算表明，它的解能够反映任一计算点的浓度变化趋势及范围，并能够给浓度等值线附加上概率的意义，表现了在不确定因素的影响下，污染带随机变化的情况。     

An extreme value model for expressing grain size and bed thickness as functions of the spatial variation of grain frequency

An extreme value model is developed for the situation where a cloud of sediment particles moves away from the boundary of a defined source area while undergoing constant depletion due to deposition of the larger particles. Taking the particles deposited at distance xfrom the source boundary to represent a distribution of largest extremes derived from a parent distribution of smallest extremes, it is possible to express the mean size of the deposited sediment in terms of the parameters of the original distribution at the source area. Thickness functions can be obtained as the product of expected diameter and particle frequency. If the spatial distribution f(x)of particle frequency along a linear transect can be inferred from a physical process, then this provides sufficient information for the construction of particle size and bed thickness prediction equations. Alternatively, the model places some restrictions on distribution selection if an empirical choice of f(x)is necessary. Some generalizations are obtained for trends in the mean and variance of the deposited particles on the basis of the hazard function of f(x).     

On the frequency distribution of turbidite thickness

The frequency distribution of turbidite thickness records information on flow hydrodynamics, initial sediment volumes and source migration and is an important component of petroleum reservoir models. However, the nature of this thickness distribution is currently uncertain, with log‐normal or negative‐exponential frequency distributions and power‐law cumulative frequency distributions having been proposed by different authors. A detailed analysis of the Miocene Marnoso Arenacea Formation of the Italian Apennines shows that turbidite bed thickness and sand‐interval thickness within each bed have a frequency distribution comprising the sum of a series of log‐normal frequency distributions. These strata were deposited predominantly in a basin‐plain setting, and bed amalgamation is relatively rare. Beds or sand intervals truncated by erosion were excluded from this analysis. Each log‐normal frequency distribution characterizes bed or sand‐interval thickness for a given basal grain‐size or basal Bouma division. Measurements from the Silurian Aberystwyth Grits in Wales, the Cretaceous Great Valley Sequence in California and the Permian Karoo Basin in South Africa show that this conclusion holds for sequences of disparate age and variable location. The median thickness of these log‐normal distributions is positively correlated with basal grain‐size. The power‐law exponent relating the basal grain‐size and median thickness is different for turbidites with a basal A or B division and those with only C, D and E divisions. These two types of turbidite have been termed ‘thin bedded’ and ‘thick bedded’ by previous workers. A change in the power‐law exponent is proposed to be related to: (i) a transition from viscous to inertial settling of sediment grains; and (ii) hindered settling at high sediment concentrations. The bimodal thickness distribution of ‘thin‐bedded’ and ‘thick‐bedded’ turbidites noted by previous workers is explained as the result of a change in the power‐law exponent. This analysis supports the view that A and B divisions were deposited from high‐concentration flow components and that distinct grain‐size modes undergo different depositional processes. Summation of log‐normal frequency distributions for thin‐ and thick‐bedded turbidites produces a cumulative frequency distribution of thickness with a segmented power‐law trend. Thus, the occurrence of both log‐normal and segmented power‐law frequency distributions can be explained in a holistic fashion. Power‐law frequency distributions of turbidite thickness have previously been linked to power‐law distributions of earthquake magnitude or volumes of submarine slope failure. The log‐normal distribution for a given grain‐size class observed in this study suggests an alternative view, that turbidite thickness is determined by the multiplicative addition of several randomly distributed parameters, in addition to the settling velocity of the grain‐sizes present.     

基于微观胶结厚度模型的深海能源土宏观力学特性离散元分析

首先,引入蒋明镜等提出的考虑水合物胶结厚度的深海能源土粒间微观胶结模型,用以反映能源土颗粒之间水合物微观胶结接触力学特性;其次,采用C++语言将模型程序化,并将其引入离散单元法中;然后,对选定的水合物饱和度经过实际二维离散元模拟调算,得出相应的水合物胶结尺寸,以修正水合物临界胶结厚度、最小胶结厚度及胶结宽度,进而确定水合物微观胶结参数;最后,根据所确定的胶结参数,针对不同水合物饱和度试样进行能源土宏观力学特性离散元双轴试验模拟,并从应力-应变、体变、剪胀角等方面与Masui等所进行的能源土室内三轴试验进行对比分析。结果表明：采用考虑粒间胶结厚度的水合物微观胶结模型,能够定性反映深海能源土的宏观力学特性,能源土试样的峰值强度、黏聚力和剪胀角均随水合物饱和度的增加而增加,但水合物饱和度对内摩擦角的影响规律不明朗;能源土试样的峰值强度、残余强度及体积剪缩量随着有效围压的增大而增大;剪胀角随有效围压的增大而减小。     

Stochastic analysis of bed-thickness distribution of sediments

On formation of a bed and distribution of bed thickness, A. N. Kolmogorov presented a mathematical explanation that if repetitive alternations of material accumulation and erosion form a sequence of beds, the resultant bed-thickness distribution curve takes a shape truncated by the ordinate at zero thickness. In this truncated distribution curve, its continuation and extension from positive to negative thickness represents the distribution of beds with negative thickness, that is, the depth of erosion. When a distribution curve, including both positive and negative parts, is expressed by a function f(x),the ratio \(\int_0^\infty {f(x)dx to} \int_{ - \infty }^\infty {f(x)dx} \) ,called Kolmogorov's coefficient and designated as p,is a parameter representing the degree of accumulation in the depositional environment. On the assumption that f(x)is described by the Gaussian distribution function, the coefficient pfor Permian and Pliocene sequences in central Japan was calculated. The coefficients also were obtained from published data for different types of sediments from other areas. It was determined that they are more or less different depending on their depositional environments. The calculated results are summarized as follows: $$\begin{gathered} p = 0.80 - 1.0for{\text{ }}alluvial{\text{ }}or{\text{ }}fluvial{\text{ }}deposits \hfill \\ p = 0.65 - 0.95for{\text{ }}nearshore{\text{ }}sediments \hfill \\ p = 0.55 - 0.95for{\text{ }}geosynclinal{\text{ }}sediments \hfill \\ p = 0.90 - 1.0for{\text{ }}varves \hfill \\ \end{gathered} $$ In addition, a ratio \(q = \int_0^\infty {xf(x)dx/} \int_{ - \infty }^\infty {|x|f(x)dx} \) ,called Kolmogorov's ratio in this paper, is introduced for estimating a degree of total thickness actually observed in the field relative to total thickness once present in a basin. The calculated results of Kolmogorov's ratio are as follows: $$\begin{gathered} q = 0.88 - 1.0for{\text{ }}alluvial{\text{ }}or{\text{ }}fluvial{\text{ }}deposits \hfill \\ q = 0.68 - 0.98for{\text{ }}nearshore{\text{ }}sediments \hfill \\ q = 0.55 - 0.96for{\text{ }}geosynclinal{\text{ }}sediments \hfill \\ q = 0.92 - 1.0for{\text{ }}varves \hfill \\ \end{gathered} $$ The sedimentological significance of these values is discussed.     

土方开挖粘塑性模糊随机损伤机理研究

以基坑工程为例分析了开挖损伤演变的模糊随机性并建立了广义非确定性空间O：Б（s,f）。提出了初始损伤有效张量的概念模型,在“损伤源汇”概念基础上提出了模糊衰减模型,构造了粘塑性模糊随机损伤增量方程并实现了基坑开挖过程的模糊随机损伤模拟。在线性算子基础上提出了模糊随机损伤矢量极限值{Ωu},进而建立了以损伤有效张量为基础的粘塑性模糊随机损伤本构模型及粘塑性非线性模糊随机数值方法。在粘塑性模糊随机损伤有限元基础上建立了粘塑性模糊随机损伤变化率方程,实现了对基坑开挖过程中模糊随机损伤演变发展的全面模拟,完成了模糊随机卸荷损伤模型的构建。     

水库调洪演算的随机数学模型

以介于微分方程和概率论之间的边缘数学分支随机微分方程的数学模型,对水库调洪过程中的随机现象和规律进行数学描述和分析,试图全面正确地综合各种不确定性因素对库水位随机过程的影响.根据水库蓄洪量具有Wiener过程特性的分析,推导了带有随机输入项和随机初始条件的调洪演算Ito方程.在此基础上,运用Fokker-Planck向前方程,求介了调洪过程库水位的概率密度分布.计算成果表明,运用随机微分方程进行水库的调洪演算,有利于正确分析水库调洪的随机过程和进一步开展水库泄洪风险分析.     

考虑河底比降的等流时线划分方法

本文针对等流时线间距离确定问题,考虑干流河段汇流时间、流速、流程和河底比降等因素,推导出新的适用于干流河段的等流时线间距的计算公式.由于支流的河长及其河底比降与干流的河长及其河底比降不相同,因此,本文还推导出适合支流的等流时线划分公式.在实际应用中,采用数字高程模型(DEM)确定河底高程,进而计算河底比降.本文将建议的新的等流时线划分方法应用于南河开峰峪流域汇流计算中,结果表明新的方法具有较好的精度.     

日以下尺度降雨随机模拟研究进展

目前我国作物生长、土壤侵蚀等应用模式发展很快,利用这些模式进行气候变化影响评价的研究逐渐成为热点,但日以下尺度降雨观测资料却严重不足,迫切需要针对我国复杂的气候条件建立日以下尺度降雨模拟模型,为应用模式提供更为精细的降雨资料输入。重点从次降雨事件的划分方法、次降雨事件模型的模拟过程、Bartlett-Lewis和Neyman-Scott点过程模型的模拟过程、参数估计、参数敏感性分析以及模型改进等方面综合概述了日以下尺度降雨随机模拟的进展,同时给出这几种模型的对比研究结果,从而为人们根据不同目的和条件选择不同模型提供借鉴。最后指出,结合点过程和次降雨事件等方法优点的混合模型——基于天气分型的随机模拟模型以及将统计与动力方法相结合的模拟模型,可能是未来降雨模拟的重要发展方向。     

地壳厚度对中国金矿床空间分布规律的制约

圈定成矿远景区并进行矿产勘查,是新一轮找矿突破的重要内容。在当前大数据和深部地球的背景下,文章根据金矿床空间分布对所在的地壳厚度和地表高程进行了空间连接和相关统计分析,并初步圈定了金矿床的成矿远景区。研究结果表明,地壳厚度为35 km和高程为200 m左右的区域,是金矿床产出的有利区域,并且金矿床的地壳厚度极值和频率呈现分形关系,为金矿床靶区的预测,提供了基本的非线性深部矿产资源预测数学模型;根据金矿床和地壳厚度、高程等的关系,对金矿床的优势成矿远景区进行了预测。预测结果显示,松嫩盆地周边,济南-郑州-武汉-长沙-南宁沿线及周边,是金矿床产出的有利远景区域。     

地震非线性随机反演技术在煤层气储层厚度预测中的应用

对煤层气储层进行识别和预测是煤层气勘查工作的一个重要问题。常规的反演方法对储层厚度预测精度不高,不能很好满足实际需要。利用非线性随机反演方法,在充分利用地震资料的基础上,以钻井、测井等已知信息作为约束条件,同时,考虑地下介质的随机性,通过拾取目的层地震反射波振幅、频率、相位等信息,提高了储层预测的精度。该方法在沁水煤田榆社-武乡煤层气区块得到了良好的应用,与实际地质资料对比发现,预测精度与钻井揭露成果吻合率较高,预测的煤层气储层厚度的分布与地质规律吻合。     

运用Fisher模型法评价山西煤层气资源

运用Fisher模型识别法,根据研究区控制煤层气资源的地质因素,选择8种参数,评价了煤层气资源,圈定了远景区和靶区,为开发山西煤层提供了理论依据。     

多维连续参数的随机试验蚁群算法优化反演分析

针对一般蚁群算法难以求解优化反演中的多维连续参数优化问题,借鉴进化思想,提出随机试验蚁群算法求解多维连续参数全局优化问题的方法。该方法主要运用随机试验求出每个参数的任一水平对目标函数的影响度,以此影响度为蚂蚁选择下一个参数水平的能见度,从而确定参数水平被选中的概率。同时考虑到当参数被划分的水平很多时目标函数收敛较慢的缺点,提出用方差分析法来确定参数的水平对目标函数的影响是否显著,将对目标函数影响不显著的参数水平其信息素设置为很小的值,从而加速目标函数的收敛。通过对一个岩土工程优化实例,表明了该算法的有效性。     

小波多尺度分析在煤厚探测中的应用

根据声波反射法探测顶煤厚度中存在的问题,提出了将小波多尺度分析应用到实际煤厚探测信号分析中的信号处理方法。结果表明:小波多尺度分析大大改善了煤层顶板弱反射波的识别能力,提高了煤厚探测的精度。     

Stochastic analysis of beams on reinforced earth beds

The present study comprises Monte-Carlo simulation assisted analysis of foundations resting on reinforced earth beds using the concept of beams on an elastic foundation, treating the modulus of subgrade reaction (MSR) as a stationary stochastic field characterised by mean, variance, autocorrelation function (ACF) and the autocorrelation distance (ACD). Realisations of the MSR, generated by solving a stochastic differential equation, are fed to a deterministic distributed parameter model to generate realisations of two dependent stochastic fields, namely deflection and bending moment in the foundation beam, and two random variables, namely the location of occurrence of maximum deflection and the bending moment. Subsequently these realisations are analysed to evolve probability distribution functions, variance and ACF of the dependent stochastic fields and the random variables. It is revealed that the ACF of these fields is independent of the ACF of the MSR. Further, variance of deflection is found to increase as the ACD of the MSR increases, implying requirement of a larger factor of safety when random soils display low frequency (macro level) variations. On the other hand, variance of the bending moment is larger at smaller ACDs of the MSR, indicating that for bending moments a larger factor of safety is required when the random soils display high frequency (micro level) variations.     

岩溶区桩基冲切破坏模式及安全厚度研究

针对岩溶区桩基冲切破坏模式研究的不足,结合混凝土平板受力特性,运用极限分析原理确立了符合工程实际的岩溶区桩端溶洞顶板冲切破坏机制。引进格里菲斯非线性岩石强度准则,基于功能原理导出了桩端岩层抗冲切破坏的极限荷载,然后通过变分原理求得了冲切破坏体的母线方程,最后通过微分获得了岩层抗冲切安全厚度计算公式。参数分析表明：冲切破坏模式主要取决岩石抗压与抗拉强度之比 , 值越小,冲切破坏体底部直径 越小;反之,冲切破坏体底部直径 越大。一般情况下, 的值在2.0～4.0之间。岩石抗压与抗拉强度的比 也是抗冲切安全厚度确定的主要影响因素,随 值的提高,安全厚度应适当增大。对于石灰岩地区,安全厚度一般取2～3倍桩径较为合理。工程算例对比分析表明,理论计算与实测结果吻合较好,其结果对岩溶区桩基设计有一定参考价值。     

基于随机理论的Nash汇流模型初探

在Nash模型中引入随机微分方程理论,分别假定模型具有随机输入和随机参数的情况,对汇流过程的随机性进行了分析和探讨,并将随机汇流模型应用到沿渡河流域,取得了满意的效果.在Nash模型中引入随机理论,不仅可以给出汇流系统输出的数学期望,而且可以同时给出输出的均方差.这样就能够正确地反映出随机性因素对汇流过程的影响.