Statistics and geometry of the eigenspectra of three-dimensional second-rank symmetric random tensors

Geoscientists have undertaken mapping of the Earth's crustal strain (or stress) fields using a great variety of field data. The output can be represented by a 3-D second-rank symmetric random strain tensor. The random principal strains-land rotations of the random tensor are frequently computed. The accuracy is calculated using a first-order approximation. The distribution aspects of the random principal strains and rotations have received almost no attention in Earth Sciences. A first-order approximation of accuracy may not be sufficient if the signal-to-noise ratio is small, as is often the case for geodetically derived random strain tensors. Therefore, the purpose of this paper is to investigate the distribution and estimation problems of the general 3-D second-rank tensor equation GΛG ^T= T , where T is a given 3-D second-rank symmetric random tensor, Λ a diagonal (3 × 3) random eigenvalue matrix, and G a (3 × 3) random orientation matrix, which is also orthogonal. Λ and G are to be estimated (or solved) from T . If some eigenvalues coincide, additional conditions are imposed on the eigenvectors so that they can be chosen uniquely. The joint probability density function (pdf) of the random eigenvalues and rotations will be worked out, given a joint pdf of the elements of random tensors T. Because the rotations are of special interest in Earth Sciences, we shall also derive the joint marginal pdf of random rotations. The geometry of eigenspectra will be studied. The biases of random eigenvalues and rotations will be derived, which have been neglected in the past. They can be very crucial in interpreting the pattern of a derived strain field, however, when applied to a real Earth Science problem. The variance-covariance matrices will be computed using a second-order approximation.     

Some further clarification on Markov chain random fields and transiograms

The Markov chain random field (MCRF) theory and the transiogram spatial measure were proposed several years ago. Basic sequential simulation algorithms based on simple MCRF models such as the Markov chain sequential simulation algorithm and the Markov chain sequential co-simulation algorithm have been developed and used in a series of application studies. However, misunderstanding of these two ideas and the geostatistical approach built on them arose recently among some researchers in geostatistics. The purpose of this article is to further clarify some issues related to these two ideas, so as to avoid further misunderstanding. For those issues already clarified, trivial, or obviously irrelevant, we do not talk about them here.     

On covariance propagation of eigenparameters of symmetric n-D tensors

Symmetric tensors are typically encountered during investigations associated with stress and strain analysis and, thus, they are of particular interest to geophysicists and geodesists. Furthermore, symmetric tensors are studied using eigentheory analysis which provides the decomposition of the tensor on its principal components (n independent eigenvalues and the corresponding eigenvectors). In this paper, an analytical expression of the covariance matrix of the eigenvalues and eigenvectors of an n-D symmetric tensor is derived based on the principles of linear algebra and differential calculus. Through numerical tests, the proposed formulation is proven to give realistic uncertainty estimates of the determined eigenparameters. The methodology also reveals the significant impact on uncertainty assessments when the parameter dependencies between principal components are neglected.     

土壤氧化铁光谱特征研究

土壤光谱反射特性的研究是土壤遥感的物理基础,土壤氧化铁含量影响土壤反射率。对采集的174个土样350~2 500 nm谱段的光谱数据进行分析,着重探讨下述3类光谱变量,寻找对土壤氧化铁含量敏感的光谱特征。1)原始光谱反射率及其各种变换形式;2)基于光谱吸收峰特征的变量,因为已知三价铁在870 nm附近有吸收峰存在,提取该吸收峰的面积、宽度、深度等变量;3)基于植被指数的变量,构建土壤氧化铁指数。研究结果表明,各类变量中土壤氧化铁指数对土壤氧化铁含量最敏感,建立相应的回归预测模型,模型拟合度R2为0.534。     

Neumann stochastic finite element method for calculating temperature field of frozen soil based on random field theory

To study the effect of uncertain factors on the temperature field of frozen soil, we propose a method to calculate the spatial average variance from just the point variance based on the local average theory of random fields. We model the heat transfer coefficient and specific heat capacity as spatially random fields instead of traditional random variables. An analysis for calculating the random temperature field of seasonal frozen soil is suggested by the Neumann stochastic finite element method, and here we provide the computational formulae of mathematical expectation, variance and variable coefficient. As shown in the calculation flow chart, the stochastic finite element calculation program for solving the random temperature field, as compiled by Matrix Laboratory (MATLAB) software, can directly output the statistical results of the temperature field of frozen soil. An example is presented to demonstrate the random effects from random field parameters, and the feasibility of the proposed approach is proven by comparing these results with the results derived when the random parameters are only modeled as random variables. The results show that the Neumann stochastic finite element method can efficiently solve the problem of random temperature fields of frozen soil based on random field theory, and it can reduce the variability of calculation results when the random parameters are modeled as spatially random fields.     

基于光谱混合分解的民勤生态治理效果评价

作为退化绿洲典型,甘肃民勤生态治理效果的评价对全球干旱区土地退化防治具有重要借鉴作用。使用Landsat系列遥感数据,基于光谱混合分解模型,采用土地覆被/利用分类后比较和端元丰度值差值的方法,对民勤生态工程第二阶段初期(2010—2015年)的治理效果进行了定性和定量研究。结果表明:民勤县土地退化面积为39 712.14hm^2,恢复面积为101 503.44hm^2,恢复面积大于退化面积,呈现出恢复的态势。沙地面积减少,沙地的沙化程度降低;盐碱地面积虽有增加,但盐碱地的盐渍化程度有所下降;林草地相较耕地、夏作耕地相较春作耕地成为当地优势植被地类;水域面积虽有减少,但水域的水含量有所增加。民勤经过近20年的生态修复治理,已经进入良性修复阶段。     

基于混合光谱理论的太湖水体叶绿素a浓度提取

TM图象多波段数据作为遥感监测水体叶绿素a浓度的数据源,已有多种遥感定量模型与之对应,但主要还是以经验模型为主。利用TM数据首先采用特征波段比值方法,建立太湖水体合适的叶绿素a浓度反演的遥感定量模型。由于经验模型的缺陷性,还提出了基于TM数据的水体混合光谱分析模型,同时分析了端元光谱提取方法对模型求解的影响。通过计算叶绿素a浓度模型估算结果与实地测量数据的相关系数和均方根误差(RMSE),可以发现混合光谱分析模型也是水体叶绿素a浓度遥感估算的另一条佳径。     

不同浓度悬浮泥沙水体的光谱吸收特性模拟

悬浮泥沙的光学特性是影响内陆湖泊水色遥感的重要因素。利用光谱吸收衰减仪(AC-S)测得水池中悬浮泥沙浓度为2.13~1 442.40 mg/L的水体光谱吸收。在蓝、绿和红光波段,悬浮泥沙水体的平均比吸收系数分别为0.0161±0.0039 m2.g-1、0.0071±0.0020 m2.g-1和0.0025±0.0007 m2.g-1;指数拟合获得的Sm*值为0.0098±0.0011 nm-1,利用其模拟的比吸收光谱与实测光谱吻合效果较好,说明该Sm*取值对悬浮泥沙水体比吸收光谱的曲线斜率变化具有一定的参考价值。此外,建立了悬浮泥沙水体吸收系数a(440)m与其浓度的关系模型,R2达0.947,拟合精度较高;然而比吸收系数a*(440)m与泥沙浓度几乎无相关性。研究结果可为内陆水色遥感分析模型的建立提供重要的参数保障。     

面向土地资源管理的我国后续资源卫星谱段设置方法研究

谱段设置是资源卫星传感器设计的关键技术之一。该文针对土地资源管理对资源卫星光谱分辨率的需求。详细分析了收集和采集的主要土地利用/覆被光谱数据的特征，从主要地物的光谱可分性出发，提出了满足土地资源管理需要的资源卫星传感器谱段设置方案，并利用机载成像光谱数据进行波段优选和在轨资源卫星数据的模拟验证，分类对比研究表明，该优化谱段模拟图像土地利用／覆被分类效果好于TM和CBERS-1影像。     

基于TM光谱特征的沼泽地定量提取模式研究

要从TM影像上定量提取沼泽地信息就必须首先获取TM数据中的沼泽地波谱信息这个最基本参数。以2000年7月TM数据为数据源,在ERDAS和PCI等遥感软件支持下,运用灰度分析方法分析沼泽地及背景地物光谱特征,并以一条光谱采样剖面线分析沼泽地内部光谱结构。最终,建立了基于前述光谱特征的三个关于沼泽地信息的定量提取模式,定量提取了沼泽地的植被、积水信息以及与水田区别的参数,具有计算机上运算的可行性。     

内陆水体水质参数光谱特征与定量遥感

该文在分析内陆水体及其主要水质参数的光谱特征的基础上 ,讨论了水质遥感监测常用的遥感数据和方法 ,对近年来国内外遥感技术特别是高光谱技术在内陆水体水质监测中的应用研究现状和进展进行了综述 ,并提出未来此领域的发展方向及研究工作的重点     

土地利用变化遥感监测精度评价系统——以随机抽样为基础的方法

中国正在采用遥感技术对 5 0万以上市区非农人口城市的建设用地扩展情况进行分期监测 ,监测结果的精度评价是该项工作的一个重要方面。本文提出以分层随机抽样的方法来获取对遥感监测的精度分析 ,内容包括监测精度评价的指标系统、分层随机抽样样本容量的确定和在各层的分配、抽样评价的工作步骤以及抽样调查的统计分析和结果表达 ,并以北京和重庆 2 0 0 1年的遥感监测数据和实地调查数据为基础进行了精度评价的实际演练。     

基于改进线性光谱解混和 SCS-CN 模型的广州主城区降雨产流模拟

城市降雨产流特征的定量研究对于城市雨水资源开发利用、科学规划和管理具有十分重要的意义。以广州市主城区为研究对象,提出一种改进的线性光谱解混方法提取遥感影像的不透水面、植被和土壤盖度,并结合SCS-CN 产流模型进行城区降雨径流模拟。首先利用线性光谱解混方法提取 2015-10-18 Landsat 8 OLI 遥感影像的不透水面、植被和土壤盖度;然后利用归一化建筑物指数和归一化植被指数进一步优化解混结果;最后结合优化的不透水面、植被和土壤盖度计算合成的 CN 值,并应用 SCS-CN 产流模型分析研究区在不同降雨重现期的降雨产流分布特征。结果表明：改进的线性光谱解混方法能较好地提高不透水面、植被和土壤盖度的提取精度;不透水面盖度越高的区域,CN 值越高;CN 值对地表径流深模拟有显著的影响;在不同重现期降雨条件下,研究区地表径流深空间分布格局差异显著;总体上,降雨量越大,不透水面盖度越高,形成的地表径流深越深,内涝发生的可能性越大。     

半封闭大棚实验下广州市植被滞尘光谱特征分析

基于广州市常见的绿化植物,采用高光谱遥感技术,通过设计半封闭的大棚实验方案,探讨了滞尘污染下不同植物叶片的光谱特征,结果表明：1）滞尘时间是影响绿化植物累积滞尘量的一个重要因子,滞尘量随着时间的增加而增加,但达到饱和之后会呈减少的趋势。2）在可见光波段,受叶面尘影响,叶片光谱反射率升高,且随滞尘量的增加而升高;在近红外波段则相反,光谱反射率随滞尘量的增加而降低。3）叶面尘对植物叶片的光谱特征参数具有直接或间接的影响,其中滞尘量与植物的三边位置无关,与归一化植被指数NDVI呈负相关关系,且不同植物的NDVI受叶面尘影响的程度不同,从大到小依次为：朱蕉>红花檵木>金叶榕。文章设计的半封闭大棚实验方案为植物滞尘效应的长时间可持续性研究提供了新思路。