共查询到20条相似文献，搜索用时 125 毫秒
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多维分形模型不仅采用常规的低阶矩统计, 而且采用高阶矩统计对多维分形分布进行度量, 从而能较细致地刻划正常值以及异常值.地球化学元素的正常值往往服从统计学中的大数定量, 即满足正态分布或对数正态分布, 然而异常值会服从分形分布(Preato).介绍了多维分形领域中的最新发展以及在地球化学研究中特别是研究超常元素空间分布和富集规律中的应用.结果表明, 通常的统计方法只对应于多维分形围绕均值周围的局部特征.为了有效地研究异常值的分布和富集规律, 建议采用高阶矩统计方法和多维分形方法, 并给出了两种分析地球化学元素, 并突出异常值贡献的方法.这些方法不仅可应用于研究微量元素的空间分布和富集规律, 而且可以区分地球化学背景与矿化有关的异常值.还介绍了该方法在对加拿大B.C.省西北部Mitchell-Sulphurets地区金铜矿化蚀变带研究中的应用. 相似文献
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Power and robustness of Aitchison's test for complete subcompositional independence in closed arrays
Alex Woronow 《Mathematical Geology》1986,18(6):563-575
This paper examines some aspects of the power and robustness of the test for complete subcompositional independence proposed by Aitchison (1982). Although the computed test statistics commonly do not approach being 2 distributed throughout their range, the upper tail of their distribution does mimic the 2 distribution sufficiently to yield a quite robust test when variates are drawn from identical distributions with different distribution parameters or even when variates are drawn from different distributions. But the magnitude of correlations among the variables and the proportion of correlated to independent variables that compose the closed data vectors affect the power of the test. 相似文献
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受工程勘察成本及试验场地限制,可获得的试验数据通常有限,基于有限的试验数据难以准确估计岩土参数统计特征和边坡可靠度。贝叶斯方法可以融合有限的场地信息降低对岩土参数不确定性的估计进而提高边坡可靠度水平。但是,目前的贝叶斯更新研究大多假定参数先验概率分布为正态、对数正态和均匀分布,似然函数为多维正态分布,这种做法的合理性有待进一步验证。总结了岩土工程贝叶斯分析常用的参数先验概率分布及似然函数模型,以一个不排水黏土边坡为例,采用自适应贝叶斯更新方法系统探讨了参数先验概率分布和似然函数对空间变异边坡参数后验概率分布推断及可靠度更新的影响。计算结果表明：参数先验概率分布对空间变异边坡参数后验概率分布推断及可靠度更新均有一定的影响,选用对数正态和极值I型分布作为先验概率分布推断的参数后验概率分布离散性较小。选用Beta分布和极值I型分布获得的边坡可靠度计算结果分别偏于保守和危险,选用对数正态分布获得的边坡可靠度计算结果居中。相比之下,似然函数的影响更加显著。与其他类型似然函数相比,由多维联合正态分布构建的似然函数可在降低对岩土参数不确定性估计的同时,获得与场地信息更为吻合的计算结果。另外,构建似然函数时不同位置处测量误差之间的自相关性对边坡后验失效概率也具有一定的影响。 相似文献
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On the basis of the negative binomial distribution of the duration of wet periods calculated per day, an asymptotic model is proposed for distributing the maximum daily rainfall volume during the wet period, having the form of a mixture of Frechet distributions and coinciding with the distribution of the positive degree of a random variable having the Fisher–Snedecor distribution. The method of proving the corresponding result is based on limit theorems for extreme order statistics in samples of a random volume with a mixed Poisson distribution. The adequacy of the models proposed and methods of their statistical analysis is demonstrated by the example of estimating the extreme distribution parameters based on real data. 相似文献
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In this paper, we present three diverse types of applications of extreme value statistics in geology, namely: earthquakes magnitudes, diamond values, and impact crater size distribution on terrestrial planets. Each of these applications has a different perspective toward tail modeling, yet many of these phenomena exhibit heavy or long tails which can be modeled by power laws. It is shown that the estimation of important tail characteristics, such as the extreme value index, is directly linked to the interpretation of the underlying geological process. Only the most extreme data are useful for studying such phenomena, so thresholds must be selected above which the data become power laws. In the case of earthquake magnitudes, we investigate the use of extreme value statistics in predicting large events on the global scale and for shallow intracontinental earthquakes in Asia. Large differences are found between estimates obtained from extreme value statistics and the usually applied standard statistical techniques. In the case of diamond deposits, we investigate the impact of the most precious stones in the global valuation of primary deposits. It is shown that in the case of Pareto-type behavior, the expected value of few extreme stones in the entire deposit has considerable influence on the global valuation. In the case of impact crater distributions, we study the difference between craters distributions on Earth and Mars and distributions occurring on other planets or satellites within the solar system. A striking result is that all planets display the same distributional tail except for Earth and Mars. In a concluding account, we demonstrate the apparent loghyperbolic variation in all of the above-mentioned examples. 相似文献
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褶皱网络中褶皱的空间分布是水力通性分析及渗漏量评估的基础。褶皱的空间分布规律尚待研究。基于一个典型场地的场底褶皱网络,利用K-S检验方法分析了褶皱几何参数服从的概率分布类型,统计得到了褶皱几何参数相应的统计参数。提出了基于褶皱几何参数的统计规律随机生成褶皱网络,并对随机褶皱网络进行渗漏量评估,然后从随机分析得到的渗漏量中选择特征值来表征场地的渗漏量的方法。通过案例分析,研究了该方法的应用。结果表明：对典型场底褶皱网络的统计分析为确定类似场地中褶皱几何参数的概率分布类型和统计参数具有重要的参考价值。由随机生成的褶皱网络得到的渗漏量样本的均值可以作为特征值,用来保守地评估场地内实际的渗漏量。基于案例分析,在对褶皱几何参数统计规律积累了丰富的经验后,可以实现对待建场地的设计不再需要获取整个场地的航拍图像,从而为有褶皱场地渗漏量评估提供了新思路。 相似文献
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Luis Manuel de Vries Jesus Carrera Oriol Falivene Oscar Gratacós Luit Jan Slooten 《Mathematical Geosciences》2009,41(1):29-42
Simulation of flow and solute transport through aquifers or oil reservoirs requires a precise representation of subsurface
heterogeneity that can be achieved by stochastic simulation approaches. Traditional geostatistical methods based on variograms,
such as truncated Gaussian simulation or sequential indicator simulation, may fail to generate the complex, curvilinear, continuous
and interconnected facies distributions that are often encountered in real geological media, due to their reliance on two-point
statistics. Multiple Point Geostatistics (MPG) overcomes this constraint by using more complex point configurations whose
statistics are retrieved from training images. Obtaining representative statistics requires stationary training images, but
geological understanding often suggests a priori facies variability patterns. This research aims at extending MPG to non-stationary
facies distributions. The proposed method subdivides the training images into different areas. The statistics for each area
are stored in separate frequency search trees. Several training images are used to ensure that the obtained statistics are
representative. The facies probability distribution for each cell during simulation is calculated by weighting the probabilities
from the frequency trees. The method is tested on two different object-based training image sets. Results show that non-stationary
training images can be used to generate suitable non-stationary facies distributions. 相似文献
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In order to determine to what extent a spatial random field can be characterized by its low-order distributions, we consider
four models (specifically, random spatial tessellations) with exactly the same univariate and bivariate distributions and
we compare the statistics associated with various multiple-point configurations and the responses to specific transfer functions.
The three- and four-point statistics are found to be the same or experimentally hardly distinguishable because of ergodic
fluctuations, whereas change of support and flow simulation produce very different outcomes. This example indicates that low-order
distributions may not discriminate between contending random field models, that simulation algorithms based on such distributions
may not reproduce the spatial properties of a given model or training image, and that the inference of high-order distribution
may require very large training images. 相似文献
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Observed frequencies of joint orientations are subject to error due to sampling bias. This error should be corrected before statistical inference is made on the distribution of orientation. Corrections (weighting functions) are developed for sampling bias in orientation for finite joints of different sizes and shapes intersecting rectangular exposures. Chi-square goodness-of-fit procedures available for hemispherical normal and bivariate normal distributions are modified to make them applicable for both raw data and data corrected for sampling bias. The aforementioned corrections and procedures were applied to a joint orientation cluster to study the effect of (a) joint orientation, (b) joint size and (c) joint shape, on the statistical distribution of the orientation. The influences of all these aforementioned factors were found to be significant. However, at present, joint sizes and shapes are not measured in field joint surveys. Therefore, it is suggested to make attempts to obtain joint sizes and shapes in field joint mapping surveys. Since the currently available probability distributions are not adequate to represent all joint orientation distributions, it is suggested either to look for new probability distributions or to develop procedures to use empirical distributions in modelling orientation distributions. 相似文献
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基于K-L信息距离的多源信息融合法 总被引：1，自引：0，他引：1
为解决小子样条件下岩土参数概率分布推断的难题,并克服基于专家信息的融合法不可避免地带有主观随意性的弊端,引入信息论中K-L信息距离的概念,基于先验信息可信度,提出一种新的多源信息融合方法。利用K-L信息距离作为参数分布之间距离的度量,定义先验分布差异率,确定融合权重,进而根据Bayes原理得到后验分布,优化岩土参数分布概型。工程实例分析结果表明,该法计算简单,且克服了推断过程中的主观随意性。计算结果显示该法所得融合分布的方差比已有成果所得方差偏小,说明该法可实现统计意义上的参数概型优化,为岩土参数设计值的合理选取提供了参考。 相似文献
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Scott Painter 《Mathematical Geology》1998,30(2):163-179
Stochastic simulations of subsurface heterogeneity require accurate statistical models for spatial fluctuations. Incremental values in subsurface properties were shown previously to be approximated accurately by Levy distributions in the center and in the start of the tails of the distribution. New simulation methods utilizing these observations have been developed. Multivariate Levy distributions are used to model the multipoint joint probability density. Explicit bounds on the simulated variables prevent nonphysical extreme values and introduce a cutoff in the tails of the distribution of increments. Long-range spatial dependence is introduced through off-diagonal terms in the Levy association matrix, which is decomposed to yield a maximum likelihood type estimate at unobserved locations. This procedure reduces to a known interpolation formula developed for Gaussian fractal fields in the situation of two control points. The conditional density is not univariate Levy and is not available in closed form, but can be constructed numerically. Sequential simulation algorithms utilizing the numerically constructed conditional density successfully reproduce the desired statistical properties in simulations. 相似文献
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Recent studies of turbidite bed thickness distributions have demonstrated power-law as well as log-normal statistical distributions. The different distributions may reflect different fan processes and environments and, therefore, could be used as a quantitative method to help identify those environments, including those devoid of sequential patterns. The cumulative distributions of well-known turbidite deposits spanning a range of interpreted fan subenvironments are used to illustrate the potential correlation between cumulative distribution and environments. Assuming that power-law distributions may, for some systems, be the primary input signal, one-dimensional modelling allows semi-quantitative characterization of the effects of different fan processes such as erosion and bed amalgamation. Environments indicative of different fan processes may be characterized based on the degree to which processes have acted as a 'filter' to modify the assumed power-law distribution systematically. This model of the effect of fan processes on the power-law distribution is used to help to account for bed thickness distributions observed in several field sites. 相似文献
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G. J. S. Govett W. D. Goodfellow R. P. Chapman C. Y. Chork 《Mathematical Geosciences》1975,7(5-6):415-446
The exploration geochemist faces a serious problem in reconciling theoretical statistics with the empirical distribution of elements in materials in the earth's crust. The results of computer-simulation experiments being conducted by the Exploration Geochemistry Group at the University of New Brunswick illustrate some of the problems of the relation between frequency distributions and spatial distributions of elements and raise some interesting questions about sampling patterns and physical size of samples. Most importantly, the simulation experiments and empirical examples support the contention that attempts to make an assumption of normality more efficient by performing log transformations on positively skewed data may defeat the purpose of statistical analysis for exploration work. New developments in computer-data presentation and interpretation, including population sorting and classification, illustrate the increasing use of the computer in exploration geochemistry. 相似文献
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Ioannis Kastanas Andreas Georgiou Panagiotis Zavros Evangelos Akylas 《Central European Journal of Geosciences》2014,6(1):79-87
This study presents an integrated method for the estimation and analysis of potential wind-energy resources in Cyprus, which is applied at selected sites on the western side of the island. Firstly, a statistical analysis of wind speed and direction data was conducted at six meteorological stations in western Cyprus, establishing daily, monthly and annual variations of wind speed. Also examined were the Weibull distributions of the wind at each site. These wind statistics serve as the basis for estimating corrected statistical distributions over the extended study areas, which were calculated using the Wind Atlas Analysis and Application Program (WAsP) that modifies wind flow estimates based on local topographic effects. As a result, a geographic and wind-resource database was formulated around each station. Aggregation of this data using statistical weighting methods allows the extrapolation of observed results and the visualization for selected hours of the day over the western part of Cyprus. The results indicate the strong influence of the sea-breeze on the island’s wind potential, and identify a number of areas of higher wind-energy potential suitable for wind-resource exploitation. It is hoped that both the methodology applied and results obtained can be further used by potential investors and wind-energy developers. 相似文献
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基于现场试验的岩体变形模量尺寸效应研究 总被引：6，自引：4，他引：2
岩体力学参数具有随机性和不确定性,合理确定岩体力学参数是岩土工程稳定性分析的基础和关键。以某水电站前期研究的110个钻孔弹模测试数据为研究样本,对其进行了统计特征分析,确定变形模量的概率分布特征更符合Weibull分布。以钻孔弹模仪承压板尺寸为岩体变形模量研究的样本尺度,岩体由该尺度的岩样叠加而成,建立了不同尺寸的立方体岩体数值分析模型,按照Weibull分布随机给出各岩样的变形模量,在此基础上对不同尺寸的岩体分别进行5 000次单轴压缩试验的数值模拟,得到了不同尺度岩体等效变形模量的变化特征,确定了岩体等效变形模量的REV。基于现场实测岩体变形模量与概率统计理论相结合研究岩体变形模量是一个新的尝试,可为该水电站工程岩体力学参数的合理取值提供依据。 相似文献
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Hou Weisheng Cui Chanjie Yang Liang Yang Qiaochu Clarke Keith 《Mathematical Geosciences》2019,51(1):29-51
In each step of geological modeling, errors have an impact on measurements and workflow processes and, so, have consequences that challenge accurate three-dimensional geological modeling. In the context of classical error theory, for now, only spatial positional error is considered, acknowledging that temporal, attribute, and ontological errors—and many others—are part of the complete error budget. Existing methods usually assumed that a single error distribution (Gaussian) exists across all kinds of spatial data. Yet, across, and even within, different kinds of raw data (such as borehole logs, user-defined geological sections, and geological maps), different types of positional error distributions may exist. Most statistical methods make a priori assumptions about error distributions that impact their explanatory power. Consequently, analyzing errors in multi-source and conflated data for geological modeling remains a grand challenge in geological modeling. In this study, a novel approach is presented regarding the analysis of one-dimensional multiple errors in the raw data used for model geological structures. The analysis is based on the relationship between spatial error distributions and different geological attributes. By assuming that the contact points of a geological subsurface are decided by the geological attributes related to both sides of the subsurface, this assumption means that the spatial error of geological contacts can be transferred into specific probabilities of all the related geological attributes at each three-dimensional point, which is termed the “geological attribute probability”. Both a normal distribution and a continuous uniform distribution were transferred into geological attribute probabilities, allowing different kinds of spatial error distributions to be summed directly after the transformation. On cross-points with multiple raw data with errors that follow different kinds of distributions, an entropy-based weight was given to each type of data to calculate the final probabilities. The weighting value at each point in space is decided by the related geological attribute probabilities. In a test application that accounted for the best estimates of geological contacts, the experimental results showed the following: (1) for line segments, the band shape of geological attribute probabilities matched that of existing error models; and (2) the geological attribute probabilities directly show the error distribution and are an effective way of describing multiple error distributions among the input data.
相似文献20.
The reflectance of vitrinite (collotelinite) particles is a widely used parameter as a geothermometer for the estimation of the thermal maturity of organic matter enclosed in rocks. However, several problems have occurred during the last decades, which can be traced back to basically three causes: human mistakes, technical problems, and problems associated with the structural and compositional inhomogeneity of organic matter. Whilst in most cases the first two types of uncertainties can be handled by standardization, the third can cause significant problems during interpretation due to its generally inestimable character. The suppression of vitrinite reflectance and statistical problems originated from small sample size, and outliers belong to this latter type.International standards, such as the ASTM and the ISO, define the vitrinite reflectance parameter as a statistical average of measured data, disregarding the fact that the average is an unresisting and unrobust statistical parameter. In other words, the average is very sensitive to outliers and distribution.The aim of this research was to find and test a better, more resistant, and robust statistical parameter used by traditional parametric and nonparametric statistics, which can be applied in practice instead of the average. Three categories of statistical problems were studied on coal and disperse organic matter (DOM) samples: the distribution of measured values, the effect of data number, and the effect of outliers on statistical parameters. The statistical experiments carried out on numerous original and generated sample sets show that the median (med) and the most frequent value (Mn), a special weighted average, are better parameters to estimate the thermal maturity of organic matter especially above 1% reflectance value. 相似文献