模糊划分矩阵在岩土参数概率分布中的应用

讨论如何在小样本条件下用已有的过程经验与试验资料确定岩土参数概率分布,用模糊划分矩阵与BAYES方法相结合,给出由小样本试验数据确定岩土参数的概率分布。     

疏散星团NGC6530天区的恒星自行和成员概率

利用上海天文台的照相底片资料,确定了疏散星团NGC6530天区364颗恒星的自行和成员概率,并对有关自行测定的方法、结果和精度等问题作了较为详细的介绍和讨论。使用的底片历元差为87年,全部恒星自行中误差的均方根值为1．09mas/a。     

P-III分布参数的概率权重矩法S函数计算

概率权重矩法是一种估计统计分布参数的方法.本文根据不完全Γ函数在无限区间积分,推导了P-Ⅲ分布参数的S函数的计算公式.通过现有计算公式比较,其计算结果具有较高的计算精度,避免了的大量的数值积分计算.文中公式只要借助于计算编程进行求解,给定超几何函数项一定的截断误差,其运算具有较高的运行速度.文中计算公式是一种P-Ⅲ分布参数S函数的计算途径.     

Dynamic properties of green water event in the overtopping of extreme waves on a fixed dock

A statistical model is developed to predict wave overtopping volume and rate of extreme waves on a fixed deck. The probability density function for the volume and rate of overtopping water are formulated based on the truncated Weibull distribution with the assumption of local sinusoidal profile for small amplitude waves. Sensitivity to the wave nonlinearity parameter and deck clearance is discussed. The statistical model is compared to laboratory data of the instantaneous free surface elevation measured in front of a fixed deck, and overtopping volume and overtopping rate measured at the leading edge of the deck. The statistical theory compared well with the measured exceedance probability seaward of the deck. The model prediction of the exceedance probability of deck overtopping gave qualitatively good agreement for large overtopping values.     

Probabilistic Models for the Probability of Wave Breaking and Whitecap Coverage Based on Kinematic Breaking Criterion

More and more researches show that neither the critical downward acceleration nor the critical slope of water waves is a universal constant. On the contrary, they vary with particular wave conditions. This fact moders the models either for the probability of wave breaking B or for the whitecap coverage W based on these criteria difficult to apply. In this paper and the one which follows we seek to develop models for the prediction of both B and W based on the kinematical criterion. First, several joint probabihstic distribution functions (PDFs) of wave characteristics are derived, based on which the breaking properties B and W are estimated. The estimation is made on the assumption that a wave breaks ff the horizontal velocity of water particles at its crest exceeds the local wave celerity, and whitecapping occurs in regions of fluid where water particles travel faster than the waves. The consequent B and W depend on wave spectral moments of orders 0 to 4.Then the JONSWAP spectrum is used to represent the fetch-limited sea waves in deep water, so as to relate the probahility of wave breaking and the whitecap coverage with wind parameters. To this end, the time-averaging technique proposed by Glazman (1986) is applied to the estimation of the spectral moments involved, and furthermore, the theoretical models are compared with available observations collected from published literature. From the comparison, the averaging time scale is determined. The final models show that the probability of wave breaking as well as the whitecap coverage depends on the dimensionless fetch. The agreement between these models and the database is reasonable.     

松辽盆地西部张裂缝预测的应力场方法

以松辽盆地地质资料为基础，介绍了应力场和张裂缝预测的计算方法。通过了各种岩性的张破裂概率隶属函数，预测松辽盆地酉部张裂缝区的分布。据此，为今后的油气勘探提出了几点认识和建议。     

Distribution of nonlinear wave crests

The distribution of nonlinear wave crests is examined on the basis of a theoretical probability density previously given elsewhere (J. Eng. Mech. 120 (1994) 1009). Certain errors contained in the original theoretical density are corrected, and the corresponding exceedance distribution is derived. The resulting theoretical forms of the probability density and exceedance distribution are then slightly simplified and compared with nonlinear wave data gathered under hurricane conditions. The results indicate that the proposed theoretical forms describe the observed distributions of large wave crests better than the Rayleigh law. However, the quantitative accuracy of the predictions is somewhat poor, as is typical of approximate theories based on Gram–Charlier-type expansions.     

Multi-Scale Texture Modeling

Patterns of crystallographic preferred orientation are referred to as texture. The specific subject of texture analysis is the experimental determination and interpretation of the statistical distribution of orientations of crystals within a specimen of polycrystalline material, which could be metals or rocks. The objective is to relate an observed pattern of preferred orientation to its generating processes and vice versa. In geosciences, texture of minerals in rocks is used to infer constraints on their tectono-metamorphic history. Since most physical properties of crystals, such as elastic moduli, the coefficients of thermal expansion, or chemical resistance to etching depends on crystal symmetry and orientation, the presence of texture imparts directional properties to the polycrystalline material. A major issue of mathematical texture analysis is the resolution of the inverse problem to determine a reasonable orientation density function on SO(3) from measured pole intensities on , which relates to the inverse of the totally geodesic Radon transform. This communication introduces a wavelet approach into mathematical texture analysis. Wavelets on the two-dimensional sphere and on the rotational group SO(3) are discussed, and an algorithms for a wavelet decomposition on both domains following the ideas of Ta-Hsin Li is given. The relationship of these wavelets on both domains with respect to the totally geodesic Radon transform is investigated. In particular, it is shown that the Radon transform of these wavelets on SO(3) are again wavelets on . A novel algorithm for the inversion of experimental pole intensities to an orientation density function based on this relationship is developed.     

Bayesian estimation of seismic hazard for two sites in Switzerland

Seismic hazard analysis is based on data and models, which both are imprecise and uncertain. Especially the interpretation of historical information into earthquake parameters, e.g. earthquake size and location, yields ambiguous and imprecise data. Models based on probability distributions have been developed in order to quantify and represent these uncertainties. Nevertheless, the majority of the procedures applied in seismic hazard assessment do not take into account these uncertainties, nor do they show the variance of the results. Therefore, a procedure based on Bayesian statistics was developed to estimate return periods for different ground motion intensities (MSK scale).Bayesian techniques provide a mathematical model to estimate the distribution of random variables in presence of uncertainties. The developed method estimates the probability distribution of the number of occurrences in a Poisson process described by the parameter . The input data are the historical occurrences of intensities for a particular site, represented by a discrete probability distribution for each earthquake. The calculation of these historical occurrences requires a careful preparation of all input parameters, i.e. a modelling of their uncertainties. The obtained results show that the variance of the recurrence rate is smaller in regions with higher seismic activity than in less active regions. It can also be demonstrated that long return periods cannot be estimated with confidence, because the time period of observation is too short. This indicates that the long return periods obtained by seismic source methods only reflects the delineated seismic sources and the chosen earthquake size distribution law.     

Probability Density Functions as Botanical-Climatological Transfer Functions for Climate Reconstruction

We present a new procedure, the pdf method (pdf=probability density function), for reconstructing Quaternary climate utilizing botanical data. The procedure includes the advantages of the indicator species method by considering the fossil and modern presence and absence of taxa rather than their frequencies, thus avoiding the need for modern analog plant communities. Overcoming the problematic use of absolute limits to describe climate response ranges is the main progress of the pdf method in comparison to the indicator species method. This advantage results from estimating probability density functions (pdfs) for monthly mean January and July temperature conditional on the present day occurrence of single taxa. Gaussian distributions sufficiently approximate pdfs of many, although not all, studied taxa. On the assumption of statistical independence, the procedure calculates a joint pdf as the product of the pdfs of the individual taxa. This algorithm weights each taxon according to the extent of its climate response range expressed by its covariance structure. We interpret the maximum of the resulting pdf as the most likely climate and its confidence interval as the uncertainty range. To avoid an artificial reduction of uncertainty arising from the use of numerous similar pdfs, a preselection method is proposed based on the Mahalanobis distance between pdfs. The pdf method was applied to the Carpinus phase of a profile from Gröbern, Germany, that spans the last interglaciation (Eemian). The reconstructed most probable January and July temperatures of about 0.0°C and 18.4°C barely differ from the modern values of −0.5°C and 18.3°C.