地质统计学在气象要素场插值的实例研究

对两种气象要素场数据分别用距离平方反比法、三次B样条和克里格（Kriging）法插值计算.比较了三种方法结果的差异和当计算场满足不同类型克里格数学假设前提下,普通克里格法（OK）与泛克里格法（UK）插值结果的异同.结果表明：克里格法的误差普遍偏小,且在插值区域峰值处克里格法的最大绝对误差和残差方差均可能较样条的小,说明只要充分了解研究区域特点,恰当选用参数,克里格法有可能得到优于样条的结果,而距离平方反比法和克里格法用全场数据插值不如使用局部数据插值的精度高,则表明内插计算具有局域性.同时还发现,虽然插值场是否满足克里格法假设对插值结果存在影响,但这种影响有时并不重要,它依赖于插值场的性质.     

基于克里格方法的相空间重构统计特征研究与应用

提高矿藏储量的预测精度是资源评价的难点之一.本文利用地质数据的相关性和变异性,建立了相空间重构的克里格方法,并结合限制性克里格法,给出了带有限制特征的计算理论,并设计出在特定铜矿中的储量计算流程,用阿舍勒铜矿体作为实例模拟了储量估计.数值计算结果表明,相空间重构克里格储量计算方法能够较为理想的预测储量.     

裂隙岩体渗透性空间分布的指示克里格估值

本文较详细介绍了指示克立格估值的基本方法和原理，以指示变异函数为基本工具分析了向家坝坝址区裂隙岩体渗透性空间分布的结构特征，表明该址区裂隙岩体渗透性存在明显的各向异性特征；在此基础上用指示克立格法对未采样点处进行估值，估值结果显示坝址区裂隙岩体渗透性存在明显的壳状渗透结构特征.通过这一实际应用，表明指示克立格法可以较好地描述裂隙岩体渗透性的空间分布规律.     

网格法在煤层地质建模和储量计算中的应用

为了提高煤层地质建模和资源量估算的效率,本文提出了网格法,并以某煤矿为例,在钻孔数据库的基础上,创建了煤矿的地表模型、块模型、断层模型等.本文的主要结论如下:1.通过分析和编辑空间数据,设计并创建了煤矿钻孔数据库.2.基于煤矿钻孔数据库,在三维可视化环境中显示了钻孔轨迹、样品值和其它一些地质信息.3.利用GPS当中存储...     

用地震资料预测孔隙度的广义协克里格法

在Doyen工作的基础上,本文对简单协克里格法作了一些改进,提出了用地震资料预测孔隙度的广义协克里格法,详细推导证明了其基本公式.并分别用3种方法预测了松辽盆地宋站地区扶余油层含气砂岩储层的孔隙度分布.井孔处的交互检验证明,广义协克里格法比线性回归法和简单协克里格法预测孔隙度的均方根误差分别小40％和30％以上.     

岩石圈磁场数据网格化方法研究

选取最小曲率、克里格、改进Shepard、反距离加权和径向基函数等5种网格化数学模型,对小江断裂地磁总强度加密区岩石圈磁场数据进行数据网格化,采用均方根预测误差和插值数据残差均方根等评价指标对网格化结果进行评价,结果表明,克里格插值与反距离加权插值法的精度最高。进一步比较克里格插值与反距离加权插值法的网格化图形质量,结果显示克里格插值网格化过程中兼顾了数据的平滑性和各实测点与待估点之间的空间位置关系,避免了系统误差,得出克里格插值更适用于岩石圈磁场数据网格化的结论。     

基于B spline和正则化算法的低轨卫星轨道平滑

本文提出了一个利用纯几何轨道和力模型的新算法来计算精确且相对平滑的卫星轨道. 该法将一个纯几何轨道表达为一个B spline的线性组合，线性组合的系数可以由最小二乘法估计获得. 力模型通过计算加速度来附加约束. 为了平衡几何轨道的点位误差和加速度的不精确，一个基于“广义交互确认（GCV，generalized cross validation）”的正则化算法运用其中. 由于B spline的本地控制性，该方法的计算效率相当高. 本文的数值分析表明了该法的有效性. 模拟计算的结论是：带加速度约束较不带加速度约束的平滑效果好. 力模型越精确，平滑的轨道就越精确. 三个月的CHAMP实测轨道数据处理结果表明，平滑后的轨道改进了重力场模型.     

基于空间平滑法的武汉城市圈地震危险性概率分析

以武汉城市圈为研究对象,利用空间平滑方法建立了区域的两个地震活动性模型,计算了50年超越概率10％的基岩峰值加速度分布图,与地震动参数区划图的对比表明,其结果能合理反映区域的地震危险性水平.在弱震活动区,基于空间平滑法的地震危险性概率计算能给出可靠的地震动参数.     

基于Bspline和正则化算法的低轨卫星轨道平滑

本文提出了一个利用纯几何轨道和力模型的新算法来计算精确且相对平滑的卫星轨道. 该法将一个纯几何轨道表达为一个Bspline的线性组合，线性组合的系数可以由最小二乘法估计获得. 力模型通过计算加速度来附加约束. 为了平衡几何轨道的点位误差和加速度的不精确，一个基于“广义交互确认（GCV，generalized crossvalidation）”的正则化算法运用其中. 由于Bspline的本地控制性，该方法的计算效率相当高. 本文的数值分析表明了该法的有效性. 模拟计算的结论是：带加速度约束较不带加速度约束的平滑效果好. 力模型越精确，平滑的轨道就越精确. 三个月的CHAMP实测轨道数据处理结果表明，平滑后的轨道改进了重力场模型.     

窗函数对地基阻尼比测试的影响

根据某块体基础的实测数据,讨论了常见平滑方法对时域对数衰减法和频域点峰法竖向阻尼比测试的影响。结果表明,无论采用时域方法还是频域方法,分别对测试曲线进行相邻三点的滑动平均、汉宁窗、哈明窗平滑,阻尼比计算数值差别很小。平滑次数对时域阻尼比结果有影响,平滑次数越多,时域阻尼比有减少的趋势,而频域阻尼比有增大的趋势。滑动平均方法和平滑次数的合理选取,应通过理论和试验方法的研究进一步确定。     

时空Kriging算法在区域地磁场插值中的应用及改进

本文以区域地磁场为应用背景,研究了时间域信息对地磁场插值效果的影响.用时空Kriging算法进行插值时,在时空Kriging变差函数的拟合过程中,将角度信息引入向量距离,定义了新的向量距离形式,提出了改进的时空Kriging算法,并对权重的选取进行讨论.对经度87.2°E—126.6°E,纬度19.0°N—49.6°N范围内的32个台站时均值地磁场数据进行插值实验.在添加了时间信息之后,插值结果在兼顾经度方向和纬度方向变化的同时,边值问题也得以缓解,明显优于传统方法.交叉验证结果表明,随着时间域信息和向量角度的加入,Kriging算法的性能得到改进,地磁场的插值精度依次提高.对比实验中,改进Kriging算法的精度最高、性能最稳定,MAE集中在1nT左右,MSE集中在[0,5]的范围内.     

中国地区电离层foF2重构方法及其在短期预报中的应用

提出了一种适合于中国地区电离层f_oF₂的重构方法——以中国参考电离层为背景的改进克里格法.该方法把f_oF₂的估计值与中国参考电离层模型值之差值的相对值作为区域化变量,引入电离层距离,采用克里格法实现区域电离层重构.与直接利用f_oF₂进行克里格重构相比,以中国参考电离层为背景场保持了电离层的区域特征,提高了重构的准确性和稳定性.利用我国电离层垂测台站网的数据对该方法应用于中国地区的重构精度进行了评估.该方法与单站预报的自相关分析法相结合可实现中国地区电离层f_oF₂短期预报.     

Temporal and spatial rainfall analysis across a humid tropical catchment

Temporal and spatial rainfall patterns were analysed to describe the distribution of daily rainfall across a medium‐sized (379km²) tropical catchment. Investigations were carried out to assess whether a climatological variogram model was appropriate for mapping rainfall taking into consideration the changing rainfall characteristics through the wet season. Exploratory, frequency and moving average analyses of 30 years' daily precipitation data were used to describe the reliability and structure of the rainfall regime. Four phases in the wet season were distinguished, with the peak period (mid‐August to mid‐September) representing the wettest period. A low‐cost rain gauge network of 36 plastic gauges with overflow reservoirs was installed and monitored to obtain spatially distributed rainfall data. Geostatistical techniques were used to develop global and wet season phase climatological variograms. The unscaled climatological variograms were cross‐validated and compared using a range of rainfall events. Ordinary Kriging was used as the interpolation method. The global climatological variogram performed better, and was used to optimize the number and location of rain gauges in the network. The research showed that although distinct wet season phases could be established based on the temporal analysis of daily rainfall characteristics, the interpolation of daily rainfall across a medium‐sized catchment based on spatial analysis was better served by using the global rather than the wet season phase climatological variogram model. Copyright © 2001 John Wiley & Sons, Ltd.     

Present-day horizontal deformation status of continental China and its driving mechanism

Based on velocity data of 933 GPS sites and using the methods of Ordinary Kriging interpolation and shape function derivation, this study has obtained the strain rate field of continental China in the spherical coordinates. In comparison with previous research results, it is found that such a strain rate field can be described by both the continuous deformation and block motions in the continent. The Tibetan Plateau and Tianshan region are characterized by continuous deformation which is distributed across the whole area. Within the blocks of South China, Tarim, Ordos, and Northeast China, little crustal deformation and deformation occurs primarily on the faults along their boundaries, which can be explained by the model of block motion. In other regions, such as the Yinshan-Yanshan block, North China block, and East Shandong-Yellow Sea, deformation patterns can be explained by both models. Besides, from southwest to northeast of continental China, there are three remarkable extensional zones of NW trending. These results imply that the NNE directed push of the India plate is the primary driving force accounting for the internal deformation of continental China. It produces the uplift, hori-zontal shortening and vertical thickening of the Tibetan Plateau as well as radiation-like material extru-sion. Of these extruded materials, one part accommodates the eastward "escape" of other blocks, generating convergence and compression of western China and widespread extension and local com-plicated deformation in eastern China under the joint action of the surrounding settings. The other part opens a corridor between the South China block and Tibetan Plateau, flowing toward southeast to the Myanmar range arc and filling the gap there which is produced by back-arc extension due to plate subduction.     

Calibration of P/S amplitude ratios for seismic events in Xinjiang and its adjacent areas based on a Bayesian Kriging method

Correction maps of P/S amplitude ratios for seismic events distributed in Xinjiang, China and its adjacent areas were established using a Bayesian Kriging method for the two seismic stations WMQ and MAK. The relationship between correction maps and variations of along-path features was analyzed and the validity of applying the cor- rection maps to improve performances of P/S discriminants for seismic discrimination was investigated. Results show that obtained correction maps can generally reflect event-station path effects upon corresponding P/S dis- criminants; and the correction of these effects could further reduce scatters of distance-corrected P/S measurements within earthquake and explosion populations as well as improve their discriminating performances if path effects are a significant factor of such scatters. For example, as corresponding Kriging correction map was applied, the misidentification rate of earthquakes by Pn(2~4 Hz)/Lg(2~4 Hz) at MAK was reduced from 16.3% to 5.2%.     

自适应顺序采样Kriging方法及其在增量动力分析中的应用

复杂结构的增量动力分析（IDA）对于结构的抗震设计和分析有着重要意义,但需对结构进行大量的非线性时程分析,计算量成本高。本文结合Kriging元模型和自适应顺序采样并用于结构增量动力分析以提高其计算效率和精度,其中:Kriging元模型用于预测结构的地震响应,顺序采样根据候选点的熵值补充非线性时程分析逐步增加Kriging模型的预测精度。借助本文方法,IDA曲线可通过少量的时程分析实现较高的精度。为了校验本文方法的可行性与有效性,对二层和九层钢框架结构模型应用直接IDA、hunt&fill方法和本文方法分析并比较了上述三种方法的计算误差、计算效率和IDA曲线差别。在此基础上本文将自适应顺序采样Kriging方法用于考虑结构不确定性参数的IDA分析,并和传统的蒙特卡洛方法进行比较。结果表明:该方法具有较高的计算效率,可以保证IDA曲线的精度。     

贵州百花湖表层水中不同形态汞的分布规律

均匀布点采集百花湖表层水样44个,对水样不同形态汞含量进行了分析,并现场测定水质参数。采用经典统计学与半变异函数拟合相结合的方法,研究了百花湖表层水中不同形态汞含量的空间变异性。根据半变异函数拟合的结果,在ArcGIS软件的支持下进行克立格插值,以此来揭示百花湖表层水中不同形态汞含量的空间分布规律。研究表明:百花湖表层水中的汞污染主要来自上游,随水体流动汞污染减少;但也有一些区域可能因富营养化而使颗粒态汞和总汞含量增加。     

Spatial prediction using bivariate exponential distribution

In this paper, a certain bivariate exponential distribution is used for the spatial prediction. The unobserved random variable is predicted by the projection onto the space of all linear combinations of the powers, up to degree m, of the observed random variables plus the constant 1. We obtain a solution by assuming that all the bivariate distributions follow Gumbel’s type III or logistic form of bivariate exponential. The method is implemented on two data sets and the results are presented. The predictions are compared with the original values through Mean Structural Similarity (MSSIM) index of Wang et al. (IEEE Trans Image Process 13(4):600–612, 2004). Using the MSSIM index the proposed method is also compared with Ordinary Kriging and with Simple Kriging after normal score transform.