Using Bayesian Statistics to Capture the Effects of Modelling Errors in Inverse Problems

When the parameters of a numerical model are adjusted, so that the predictions of the model match measurements from the real system, we need to take account of two sources of errors. These being measurement errors and modelling errors. Measurement errors are commonly considered, and a number of different approaches are in general usage, the most common being the weighted sum of squares method. In this paper the standard Bayesian equation, used for inverse problems, is reformulated so as to make it more intuitive to use. This allows the inclusion of both a modelling error and correlations between measurements to be carried out easily. The results are tested on a simple one-parameter numerical model and a cross-sectional model of a petroleum reservoir. In the first case the proposed error model appears to work well. In the second case it appears that the objective function is multimodal, leading to multiple acceptable solutions. The results of this paper are important to those whose numerical models are thought to contain significant modelling error. This encompasses many areas of modelling related to earth science and engineering.     

一元p－范极大似然平差

本文详细推导了一元ｐ－范极大似然平差的计算公式。在观测误差分布单峰、对称的条件下，该法可同时确定参数估值在忽略的随机性影响时，本文还推导了的估算公式。     

Generalized covariance functions in estimation

I discuss the role of generalized covariance functions in best linear unbiased estimation and methods for their selection. It is shown that the experimental variogram (or covariance function) of the detrended data can be used to obtain a preliminary estimate of the generalized covariance function without iterations and I discuss the advantages of other parameter estimation methods.     

二阶导数等值点荧光光度法同时测定岩矿中钨和钼

在W(Mo)-茜素磺酸钠荧光体系中,加入一定量乙醇后,可使W、Mo的荧光强度明显增加,Mo比W的灵敏度提高更加显著,为W、Mo在同一体系中进行测定提供了条件。在λ_(em)=603nm时,W的二阶导数荧光值不随含量变化而变化,成为W等值点,而Mo的二阶导数荧光值则有良好的线性关系。同时,λ_(em)=613nm时成为Mo等值点,而W的二阶导数荧光值有良好的线性关系。基于上述事实,提出用等值点法实现在导数荧光光谱仍相互重叠情况下同时测定W和Mo。方法经标准样品分析验证,结果与推荐值吻合。     

修正等应变假定下刚性桩复合地基固结特性分析

刚性桩复合地基固结特性是影响工程进度的重要因素。为研究外荷载作用下刚性桩复合地基固结特性，结合刚性桩和桩间土应力?应变特点对等应变假定进行修正。在此基础之上，考虑涂抹效应、桩间土和下卧层土体固结特性的影响，推导得到桩间土和下卧层土体固结微分方程。基于双层地基固结理论，考虑单级匀速施加荷载和附加应力沿深度变化等边界条件，推导得到其固结度解析解。最后，利用数值模拟方法对解析解进行验证，并对影响刚性桩复合地基固结特性的因素进行分析。结果表明：理论计算与数值模拟结果较为吻合；刚性桩复合地基固结速率受到贯入比影响较大，当贯入比较小时，与天然地基相比，其固结速率较小，贯入比较大且桩端阻力系数较小时，复合地基固结速率大于天然地基；随着贯入比、桩?土相对刚度和垫层?土体相对刚度的增大，复合地基整体固结速率加快；随着置换率的增大，复合地基整体固结速率降低。     

Development and application of a coupled-process parameter inversion model based on the maximum likelihood estimation method

The coupled flow-mass transport inverse problem is formulated using the maximum likelihood estimation concept. An evolutionary computational algorithm, the genetic algorithm, is applied to search for a global or near-global solution. The resulting inverse model allows for flow and transport parameter estimation, based on inversion of spatial and temporal distributions of head and concentration measurements. Numerical experiments using a subset of the three-dimensional tracer tests conducted at the Columbus, Mississippi site are presented to test the model's ability to identify a wide range of parameters and parametrization schemes. The results indicate that the model can be applied to identify zoned parameters of hydraulic conductivity, geostatistical parameters of the hydraulic conductivity field, angle of hydraulic conductivity anisotropy, solute hydrodynamic dispersivity, and sorption parameters. The identification criterion, or objective function residual, is shown to decrease significantly as the complexity of the hydraulic conductivity parametrization is increased. Predictive modeling using the estimated parameters indicated that the geostatistical hydraulic conductivity distribution scheme produced good agreement between simulated and observed heads and concentrations. The genetic algorithm, while providing apparently robust solutions, is found to be considerably less efficient computationally than a quasi-Newton algorithm.     

古登堡-里希特定律中的b值统计样本量研究

b值是研究地震活动的重要指标,其广泛应用于地震危险性分析和地震预测研究之中,与实际资料的完整性、样本量的大小、计算方法等因素有着重要的关系。常见的b值计算方法有最小二乘法和最大似然法,样本量的大小对这2种方法影响很大。本文利用蒙特卡罗模拟地震目录和汾渭地震带实际目录作为样本,从中抽取不同大小的样本量进行计算,研究不同样本量下这2种方法计算得到的b值与设定值或真实值之间的差别。结果表明,最小二乘法需要的最低样本量为1000,最大似然法为200;当样本量达不到要求时,计算出的b值是不可靠的;由于对样本量的要求不同,前者适用于计算区域的整体b值,而后者在研究某区域b值在时间轴上的变化方面更有优势。本研究为确定2种b值计算方法对样本量的最低要求提供了参考依据。     

山东CORS坐标时间序列周期与噪声特征分析

针对不同区域的周期和噪声特性存在差异,以27个山东连续运行参考站(CORS)2015—2018年的坐标时间序列为研究对象,进行周期和噪声特征分析.结果 表明:坐标时间序列并没有严格的周期信号,U方向的周期运动较为规律;坐标分量的谱指数显示大部分站点可用白噪声(WN)+闪烁噪声(FN)的噪声模型进行描述;采用最大似然估计...     

基于Surfer和Grapher的基坑变形监测数据分析

针对当前基坑变形监测数据分析可视化程度低、分析功能单一的现状,本文提出了一种基坑变形监测数据分析方法。该法在Surfer中将沉降量构建格网数据,通过插值方法绘制等沉降曲线,实现任意点沉降量分析、趋势分析和均匀性分析。通过读取坐标、计算方位角和向量模,在Grapher中构建水平位移向量图,实现水平位移定量精确分析和一致性分析。数据分析实验表明,本文提出的数据分析方法具有较高的可视化效果和较强的分析功能,可进行变形监测整体性分析和趋势分析,且该法具有较高的普适性,是一种可靠的基坑变形监测数据分析方法。     

计算机技术应用于山东地矿工作的回顾与展望

回顾了４０ 多年来计算机技术在山东地矿工作中从无到有,从简单的数据处理到各种各样专用软件的开发应用的发展历程。总结了计算机技术在数据库建设、遥感影像的处理、制图以及地理信息系统等方面取得的主要成果。展望了 Ｇ Ｉ Ｓ 技术和网络技术的广泛应用,以及 Ｇ Ｉ Ｓ 技术与 Ｉ Ｔ 技术相结合应用于地矿事业的广阔前景。