Bayesian methods for estimating multi-segment discharge rating curves

This study explores Bayesian methods for handling compound stage–discharge relationships, a problem which arises in many natural rivers. It is assumed: (1) the stage–discharge relationship in each rating curve segment is a power-law with a location parameter, or zero-plane displacement; (2) the segment transitions are abrupt and continuous; and (3) multiplicative measurement errors are of equal variance. The rating curve fitting procedure is then formulated as a piecewise regression problem where the number of segments and the associated changepoints are assumed unknown. Procedures are developed for describing both global and site-specific prior distributions for all rating curve parameters, including the changepoints. Estimation and uncertainty analysis is evaluated using Markov chain Monte Carlo simulation (MCMC) techniques. The first model explored accounts for parameter and model uncertainties in the interpolated area, i.e. within the range of available stage–discharge measurements. A second model is constructed in an attempt to include the uncertainty in extrapolation, which is necessary when the rating curve is used to estimate discharges beyond the highest or lowest measurement. This is done by assuming that the rate of changepoints both inside and outside the measured area follows a Poisson process. The theory is applied to actual data from Norwegian gauging stations. The MCMC solutions give results that appear sensible and useful for inferential purposes, though the latter model needs further efforts in order to obtain a more efficient simulation scheme.     

Statistics for Twenty-first Century Astrometry

H. K. Eichhorn had a lively interest in statistics during his entire scientific career, and made a number of significant contributions to the statistical treatment of astrometric problems. In the past decade, a strong movement has taken place for the reintroduction of Bayesian methods of statistics into astronomy, driven by new understandings of the power of these methods as well as by the adoption of computationally-intensive simulation methods to the practical solution of Bayesian problems. In this paper I will discuss how Bayesian methods may be applied to the statistical discussion of astrometric data, with special reference to several problems that were of interest to Eichhorn.     

贝叶斯统计方法在海浪方向谱研究中的应用

较详细介绍了贝叶斯统计方法在海浪方向谱估计中的应用,指出先验分布的不同对估计结果没有影响,由于均匀分布与最大熵原则相对应,使其具有某种特殊性.数值模拟表明贝叶斯方法对双峰方向分布估计的有效性,将其应用于黑海实测资料,证明双峰方向分布的出现依赖于估计方法分辨力的大小,而用最大似然法得到的双峰方向分布值得怀疑.最后给出出现双峰方向分布的一种可能物理解释.     

位场各阶垂向导数换算的新正则化方法

位场垂向导数大量应用于位场数据处理与解释中.当前广泛采用的位场各阶垂向导数换算方法为基于Laplace方程并结合波数域和空间域方法的具有递推特性的ISVD(integrated second vertical derivative)算法.本文在位场垂向导数换算的正则化方法和径向平均功率谱的基础上,提出一种位场各阶垂向导数换算的新正则化方法.新正则化方法仅需通过分析位场径向平均功率谱来确定一个截止波数,即可稳定换算位场各阶垂向导数.理论模型和实测数据实验结果表明:(1)新正则化方法物理意义明确、计算简单,且各阶垂向导数换算的稳定性和精度明显优于ISVD算法;(2)在用新正则化方法求得各阶垂向导数的基础上,利用泰勒级数法可以获得大深度、高精度的位场向下延拓结果.     

基于改进全变差正则化的GPR多尺度全波形双参数同步反演

针对探地雷达（GPR）双参数全波形反演中电导率反演精度差、双参数存在串扰现象、反演计算量大、易陷入局部极值等问题.作者将具有多参数调节功能的L-BFGS算法引入到GPR时间域全波形反演中,它避免了对Hessian矩阵的直接存储与精确求解,减小了存储量和计算量.结合参数调节因子的选取,有效减小了同步反演时介电常数与电导率的串扰影响,在不降低介电常数反演精度的前提下,提高电导率参数的反演精度.通过在反演目标函数中加载改进全变差正则化方法,提高了反演的稳定性,使目标体边缘轮廓更加清晰.首先以简单模型为例,对比了单尺度反演与多尺度串行反演策略的优劣,说明多尺度串行反演有利于逐步搜索全局最优解;而开展参数调节因子的选取实验,说明合适的参数调节因子可以有效改善介质电导率的反演精度;测试了不同正则化的反演效果,表明改进全变差正则化能提高反演稳定性,显著降低模型重构误差.最后,分别对含噪合成数据和实测数据进行了反演测试,说明本文提出的多尺度、双参数反演具有较强的鲁棒性,能提供更丰富的信息约束,重构图像界面清晰、反演效果好.     

Effect of loading duration on uncertainty in creep analysis of clay

Some studies suggest that creep parameters should be determined using a greater quantity of creep test data to provide more reliable prediction regarding the deformation of soft soils. This study aims to investigate the effect of loading duration on model updating. One‐dimensional consolidation data of intact Vanttila clay under different loading durations collected from the literature is used for demonstration. The Bayesian probabilistic method is used to identify all unknown parameters based on the consolidation data during the entire consolidation process, and their uncertainty can be quantified through the obtained posterior probability density functions. Additionally, the optimal models are also determined from among 9 model candidates. The analyses indicate that the optimal models can describe the creep behavior of intact soft soils under different loading durations, and the adopted method can evaluate the effect of loading duration on uncertainty in the creep analysis. The uncertainty of a specific model and its model parameters decreases as more creep data are involved in the updating process, and the updated models that use more creep data can better capture the deformation behavior of an intact sample. The proposed method can provide quantified uncertainty in the process of model updating and assist engineers to decide whether the creep test data are sufficient for the creep analysis.     

空间归一化边界识别方法用于判断地质体的水平位置及深度(英文)

边界识别是重磁数据解释中的常用方法之一,依据其结果可划分出地质体的水平范围。边界识别结果受地质体埋深及导数计算误差的影响所识别边界与真实边界之间存在一定的差距,且边界识别法无法直观地给出地质体的深度信息。为了获得异常体的水平位置和深度信息,本文提出空间归一化边界识别方法,其对不同深度的边界识别函数进行归一化计算,空间归一化边界识别法的最大值对应于异常体的水平位置和深度。常规边界识别结果的误差随理深的减小而减小,而空间归一化边界识别法是通过最大值来判断地质体的位置,最大值是在地质体处获得,因此归一化边界识别方法所获得的结果是准确的。通过理论模型试验证明归一化边界识别方法能有效地完成异常体的水平位置和深度的计算,所获得的水平位置和深度信息与理论值相一致,为下一步的勘探计划提供了更加可靠的依据。将其应用于实际航磁数据的解释,获得了断裂的具体分布形式。     

基于等效源的重力异常空间导数计算方法及其在川滇地区的应用

在综合分析前人研究成果的基础上,采用基于贝叶斯准则的等效源模型滤波增强方法来识别地质体边界。通过理论模型实验讨论了在相同的噪声水平情况下,不同算法对于计算结果的影响,模型实验结果表明,与直接计算和传统高斯滤波增强技术相比,新算法可以有效消除传统算法中普遍存在的对于噪声的过度敏感问题,所得到的地质体边界形态失真更小。随后,利用此方法对川滇地区的重力数据进行了处理,并对该地区的重力水平总梯度(THD)、重力垂直梯度模(AVG)、重力解析信号模量(AAS)、重力水平梯度垂向导数(VGHD)应用效果进行了对比分析。研究结果提供了川滇地区的构造分区信息,对该地区构造演化、边界定位及动力学过程分析具有重要的指导意义。     

扰动重力梯度的球冠谐分析建模

从球冠谐理论出发,详细推导了球冠坐标系下扰动重力梯度的无奇异性计算公式。基于Tikhonov正则化方法,利用GOCE卫星实际观测数据解算局部重力场球冠谐模型。数值计算表明,基于扰动重力梯度的球冠谐分析建模方法能够有效地恢复局部重力场中的短波信号,与GO_CONS_GCF_2_DIR_R5模型的差异在±0.3×10~(-5) m/s~2水平。     

基于贝叶斯层次时空模型的甘肃省土地利用程度演变分析

以甘肃省为例,在基于Google Earth Engine (GEE)平台实现1995年、2000年、2005年、2010年、2015年和2020年土地变化监测的基础上,利用贝叶斯层次时空模型(BHM)分析土地利用程度的时空变化特征。结果表明：① 研究期间内甘肃省土地利用程度呈增长趋势,其中1995―2000年和2010―2015年增长速度较明显;② 土地利用程度空间格局“东高西低”,热点区域主要分布在陇中、陇东和陇南地区;③ 土地利用程度局部变化呈现明显区域差异,整体表现为“东弱西强”,局部变化热点区域主要分布在河西地区;④ 影响土地利用程度变化的主要因素是经济规模和产业结构,其中经济因素影响程度最高。