关于线性矩法与概率权矩法同解关系的分析研究

对线性矩法与概率权矩法进行了分析，认为线性矩法与概率权矩法对统计参数估计的结果是一致的，它们之间具有同解关系，其计算结果略存在的差异乃是由于采用不同近似公式的计算误差所致。     

线性矩法的特点评析和应用问题

介绍了线性矩法的无偏估计与直接计算的关系，讨论了在概率权重矩计算过程中各系列之间的高度相关性及其对结果的影响，建立了直接计算线性矩法的Cv和Cs近似公式，叙述了适线问题和相应的经验频率公式。文中认为，水文频率计算时，由于资料的随机性和处理方法上的概化性，故用任何计算方法得到的结果，具有不同程度的不确定性，只能作为估计的初值，需通过时空上综合平衡，再经合理性分析和调整后，才能取用。     

论不连序系列样本概率权重矩不偏计算公式

人们普遍认为要从理论上通过数学分析的方法来论证不连序系列样本概率权重矩的偏倚性是很困难的。本文根据次序统计量理论，分析推证了不连序系列样本概率权重矩的不偏计算公式，论证结果具有较重要的理论和实用意义。     

基于高阶概率权重矩的广义极值分布参数估计

研究基于高阶概率权重矩的广义极值分布参数估计。根据高阶概率权重矩法原理,建立了广义极值分布高阶概率权重矩估算参数模型。以陕北地区4个水文测站的年最大洪峰流量序列为例,结果表明:高阶概率权重矩法能赋予大洪水值更多的权重。蒙特卡洛试验表明:适当提高阶数可以减小误差,但阶数过高反而会增大误差。     

考虑历史洪水资料的期望概率权重矩法参数估计统计试验研究

为有效利用历史洪水资料,提高洪水资料系列参数的估计精度,研究期望概率权重矩法在广义极值分布参数估计中的应用。采用蒙特卡洛试验研究期望概率权重矩法的统计特性,并与部分概率权重矩法做比较。结果表明:期望概率权重矩法具有良好的稳定统计特性,并且是具有历史洪水资料系列进行参数估计的一种简单、稳定和有效的参数估计方法,具有推广意义。     

线性矩法与常规矩法对太湖流域降雨频率分析的比较研究

介绍了线性矩法的基本理论,并与常规矩法进行了初步的比较与分析,说明了其理论上的优越性;以太湖流域的雨量资料为例,选取4个站点分别应用线性矩法和常规矩法估计其不同重现期下年极值降雨频率设计值;最后,利用Monte Carlo方法对太湖流域内96个站点数据进行模拟,比较线性矩法和常规矩法所估计的统计参数。结果表明:线性矩法估计的参数在精确性、不偏性及稳健性方面较常规矩法更优。     

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.     

概率权重矩法估计P—Ⅲ型分布参数用表的近似表达式

以概率权重矩法估计Ｐ－Ⅲ型分布参数需用专门数表，实用上十分不便。本文对该数表建立了近似表达式，从而大大简化了查表和内插运算。验算表明，近似表达式能满足工程运算的精度要求。     

可考虑历史洪水信息的广义极值分布线性矩法的研究

在水文及其他行业中广义极值分布(GEV)是一种较为常用的分布线型,包括极值Ⅰ型、极值Ⅱ型和极值Ⅲ型分布.在介绍了该分布线性矩与其参数关系后,给出了有效的可以考虑历史洪水信息的线性矩公式,并对由线性矩推求分布密度函数中k值作了改进.通过统计试验计算分析了线性矩在该分布中的统计性能及历史洪水公式的适用性,并与绝对值准则和平方和准则两种不同优化适线法、矩法作了比较.统计试验表明,改进k值计算后的线性矩法略优于传统线性矩法.从总体上讲,改进k值计算后的线性矩法优于平方和准则适线法及矩法,其参数及设计值的不偏性很好,与绝对值准则适线法总体上相当.     

概率权重矩法估计P－Ⅲ型分布参数用表的近似表达式

以概率权重矩法估计Ｐ－Ⅲ型分布参数需用专门数表，实用上十分不便。本文对该数表建立了近似表达式，从而大大简化了查表和内插运算。验算表明，近似表达式能满足工程运算的精度要求。     

P-III型分布混合权函数估计法的研究

为克服传统的马秀峰权函数法所存在的缺陷,提出了一种可考虑线性矩法优点的新的权函数估计法即混合权函数法,经过统计试验论证,该法对传统的马秀峰权函数法有较大改进,是一种统计性能较优秀的参数估计方法。     

Moment tensors and micromechanical models

A numerical modelling approach that simulates cracking and failure in rock and the associated seismicity is presented and a technique is described for quantifying the seismic source mechanisms of the modelled events. The modelling approach represents rock as an assemblage of circular particles bonded together at points of contact. The connecting bonds can break under applied stress forming cracks and fractures in the modelled rock. If numerical damping is set to reproduce realistic levels of attenuation, then energy is released when the bonds break and seismic source information can be obtained as damage occurs. A technique is described by which moment tensors and moment magnitudes can be calculated for these simulated seismic events. The technique basically involves integrating around the source and summing the components of force change at the surrounding particle contacts to obtain the elements of the moment tensor matrix. The moment magnitude is then calculated from the eigenvalues of the moment tensor. The modelling approach is tested by simulating a well-controlled experiment in which a tunnel is excavated in highly stressed granite while microseismicity is recorded. The seismicity produced by the model is compared to the actual recorded seismicity underground. The model reproduces the spatial and temporal distribution of seismicity observed around the tunnel and also the magnitudes of the events. A direct comparison between the actual and simulated moment tensors is not performed due to the two-dimensional nature of the model, however, qualitative comparisons are presented and it is shown that the model produces intuitively realistic source mechanisms. The ability to obtain seismic source information from the models provides a unique means for model validation through comparison with actual recorded seismicity. Once it is established that the model is performing in a realistic manner, it can then be used to examine the micromechanics of cracking, failure and the associated seismicity and to help resolve the non-uniqueness of the geophysical interpretation. This is demonstrated by examining in detail the mechanics of one of the modelled seismic events by observation of the time dependence of the moment tensor and by direct examination of the particle motions at the simulated source.     

Regional flood frequency modeling for a large basin in India

The computation of flood magnitude and its likely occurrence to design different hydraulic structures are major challenges to the research community. The present study has been carried out to identify the homogeneous regions in the Mahanadi basin in Chhattisgarh part (data from 26 gauge/discharge sites) of India using conventional and clustering-based homogeneity tests and then computation and identification of probability-weighted moment and L-moment-based best regional distributions for different regions. Different simple to complex distributions like Extreme Value-I, Generalized Extreme Value, Logistic, Generalized Logistic, Generalized Pareto, Normal and Log-normal, Wakeby-4, and Wakeby-5 was used in the analysis through standardizing procedure to compute regional distributions. The best-fit distribution selected by simulating several series and compute L-kurtosis along with the L-moment ratio diagram. The homogeneity analysis confirmed that this basin can broadly be divided into two different homogeneous regions with 15 and 11 stations in the first (Region-1) and second (Region-2) regions, respectively. The GEV distribution was found best suited for Region-1 while the Generalized Pareto worked well for Region-2. To make results more convenient for field application, catchment area-based equations were converted in the form of Dicken’s or Ryve’s formulae for these regions to estimate flood quantiles of any return period.

     

花岗岩巴西劈裂试验的矩张量反演研究

为了研究岩石张拉破坏的过程和机制,首先通过模拟计算,验证了加权反演法在进行巴西劈裂试验矩张量求解方面的优越性;其次基于花岗岩的巴西劈裂试验,进行声发射监测、事件定位及矩张量反演,并分析标准反演法和加权反演法对应矩张量结果的差别;使用聚类分析K均值算法对矩张量结果进行分簇研究。研究结果表明：模拟计算中加权反演法可以降低巴西劈裂试验矩张量反演误差;室内花岗岩巴西劈裂试验中,加权反演法较大程度地优化了声发射事件的剪切成分以及压/拉应力轴的分布,使得反演结果更加合理。针对加权反演结果,所有事件可分成3簇,同簇内事件的破裂类型、应力状态、破裂机制、辐射模式等均相近;不同簇中的事件在时空上交叉分布,试验后期在圆盘东?西方向上具有较为明显张拉特性的事件骤增,于圆盘中心附近聚集并占据主导,最终导致试样的宏观破裂。研究结果解释了花岗岩巴西劈裂试验的破裂过程和破裂机制,为岩石力学行为研究提供进一步指导。     

A Relative Moment Tensor Inversion Technique Applied to Seismicity Induced by Mining

Summary. Studies of source mechanisms of mining-induced seismic events play an important role in understanding the various modes of failure observed around underground excavations and enable the geometry of likely planes of failure to be determined. These planes can be mapped using conventional techniques, for example, geological fracture mapping. However, such an approach is often problematical due to limited access to the site and/or poor exposures (if any) of the failure plane. An added difficulty is that planes of failure often do not follow faults of geological origin, but are related to the geometry of the advancing stope face. For example, the development of face-parallel shear zones ahead of deep-level stope faces. In such cases, the stresses induced by mining dominate over the geological structure in the critical region close to the stope face. Seismic methods therefore have the potential of being a practical method of studying the development of seismic shear zones underground.Slip on such a failure plane generates a three dimensional elastic wave that propagates through the rockmass, carrying a wealth of information regarding the source rupture process. The ground motions caused by the passage of the wave can be recorded by arrays of sensitive instruments called seismometers. These sets of recordings (seismograms) provide the basic data that seismologists use to study these elastic waves as they propagate through the Earth. Conventional seismic analyses provide scalar measurements of the rupture size and intensity. However, through a process known as moment tensor inversion (MTI), the seismograms recorded from a seismic event can be used to calculate a moment tensor that describes the three dimensional nature of the source mechanism. Interpretation of the moment tensor gives insight into whether the rockmass failed in tension, compression or shear and indicates the direction of movement and the failure plane.Moment tensor solutions computed using conventional MTI methods are sensitive to noise and may be biased due to systematic errors in the measurements. The primary objective of this study was to develop a robust MTI method to estimate the moment tensors of clusters of seismic events recorded in the underground environment. To achieve this, three hybrid MTI methods were developed by the author. These methods involve different iterative weighting schemes designed to enhance the accuracy of the computed moment tensors by decreasing the effect of outliers (data points whose residuals lie far from the mean or median error). The additional information required for hybrid methods is obtained by considering a spatial cluster of seismic events and assuming that the waves generated by each event in the cluster follow a similar path through the rockmass and allowing a common ray-path to be assumed. Hence the unknown effect of the heterogeneous rockmass on the waveform is similar for all the events in the cluster.The final objective was to determine whether the techniques developed could be successfully applied to real data. The hybrid MTI methods using the median and the weighted mean correction were applied to a cluster of 10 events, having remarkably similar waveforms, recorded at Oryx Gold Mine. For comparative purposes, the more conventional absolute method was also applied. The solutions computed using the hybrid MTI with a median correction displayed a distinct improvement after the iterative residual correction procedure was applied, in contrast to the solutions obtained from the absolute method. The radiation patterns and fault-plane solutions from the hybrid method showed a high degree of similarity, and were probably more accurate reflections of reality. These observations are very encouraging and point towards the potential for using the hybrid MTI method with a median correction as a standard processing tool for mine seismicity.The implications of this work are that a robust method for calculating the focal mechanisms of clusters of seismic events induced by mining activities has been developed. Regular application will lead to a better understanding of rock fracture processes and to improved safety underground.     

岩体破裂矩张量反演方法及其应用

地震及岩体失稳破裂过程中,破裂机制、震源参数及破裂能量等信息均可通过矩张量方法求解,文中详细介绍了矩张量基本理论,对比分析了绝对矩张量反演法、相对矩张量反演法、混合型矩张量反演法等3种常用方法的优缺点。在详细归纳、总结国内外相关文献的基础上,就水压致裂、采矿及深埋隧道等工程领域综述了矩张量反演理论在岩体工程中的应用现状,并结合其在德国黑林根矿区微震事件震源机制分析中的应用实例,表明通过矩张量反演获取的震源机制解及震源参数等信息,在岩体工程灾害预警及防治、水压致裂过程监测和控制等领域具有重要作用。最后分析了影响矩张量反演精度的因素及应用于岩体工程领域时存在的不足,包括定位精度低、波形识别及处理困难等问题,并对其在采矿、石油等岩体工程领域的应用前景、改进措施及需进一步研究的问题等进行了探讨,为矩张量反演方法的推广应用提供重要的参考。     

多维分形理论和地球化学元素分布规律

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.      

利用惯量椭圆进行岩石有限应变分析

提出了利用惯量椭圆对任意形状矿物颗粒进行描述的方法，并利用惯量椭圆理论，计算了岩石薄片中任意形状矿物颗粒的惯量椭圆，通过颗粒面积对椭圆参数进行标准化，得到每一矿物颗粒的等效应变椭圆。等效应变椭圆能够有效地反映对应矿物颗粒的优选方位以及变形特征，进而利用椭圆的矩阵参数形式对等效应变椭圆进行统计分析，获得岩石的有限应变椭圆；同时给出了相应的数值计算方法，编制了软件Straindesk，并得到了成功的应用。该方法克服了先前应变测量中的局限性，方便实现计算机的自动分析，具有较强的有效性和广泛的适用性。