Estimation of regionalized compositions: A comparison of three methods

A regionalized composition is a random vector function whose components are positive and sum to a constant at every point of the sampling region. Consequently, the components of a regionalized composition are necessarily spatially correlated. This spatial dependence—induced by the constant sum constraint—is a spurious spatial correlation and may lead to misinterpretations of statistical analyses. Furthermore, the cross-covariance matrices of the regionalized composition are singular, as is the coefficient matrix of the cokriging system of equations. Three methods of performing estimation or prediction of a regionalized composition at unsampled points are discussed: (1) the direct approach of estimating each variable separately; (2) the basis method, which is applicable only when a random function is available that can he regarded as the size of the regionalized composition under study; (3) the logratio approach, using the additive-log-ratio transformation proposed by J. Aitchison, which allows statistical analysis of compositional data. We present a brief theoretical review of these three methods and compare them using compositional data from the Lyons West Oil Field in Kansas (USA). It is shown that, although there are no important numerical differences, the direct approach leads to invalid results, whereas the basis method and the additive-log-ratio approach are comparable.     

Groebner-basis solution of the three-dimensional resection problem (P4P)

The three-dimensional (3-D) resection problem is usually solved by first obtaining the distances connecting the unknown point P{X,Y,Z} to the known points P_i{X_i,Y_i,Z_i}i=1,2,3 through the solution of the three nonlinear Grunert equations and then using the obtained distances to determine the position {X,Y,Z} and the 3-D orientation parameters {,, }. Starting from the work of the German J. A. Grunert (1841), the Grunert equations have been solved in several substitutional steps and the desire as evidenced by several publications has been to reduce these number of steps. Similarly, the 3-D ranging step for position determination which follows the distance determination step involves the solution of three nonlinear ranging (`Bogenschnitt') equations solved in several substitution steps. It is illustrated how the algebraic technique of Groebner basis solves explicitly the nonlinear Grunert distance equations and the nonlinear 3-D ranging (`Bogenschnitt') equations in a single step once the equations have been converted into algebraic (polynomial) form. In particular, the algebraic tool of the Groebner basis provides symbolic solutions to the problem of 3-D resection. The various forward and backward substitution steps inherent in the classical closed-form solutions of the problem are avoided. Similar to the Gauss elimination technique in linear systems of equations, the Groebner basis eliminates several variables in a multivariate system of nonlinear equations in such a manner that the end product normally consists of a univariate polynomial whose roots can be determined by existing programs e.g. by using the roots command in Matlab.Acknowledgments.The first author wishes to acknowledge the support of JSPS (Japan Society of Promotion of Science) for the financial support that enabled the completion of the write-up of the paper at Kyoto University, Japan. The author is further grateful for the warm welcome and the good working atmosphere provided by his hosts Professors S. Takemoto and Y. Fukuda of the Department of Geophysics, Graduate School of Science, Kyoto University, Japan.     

空间墨卡托投影研究

主要研究适合星下点轨迹是赤道的卫星数据投影选择的空间墨卡托投影,推导了空间墨卡托投影公式,研究了其变形情况,并证明了该投影是等角空间投影,最后给出了算例。     

对施奈德等积多面体投影的研究

提出了先确定边界、再逐步精化的研究思路，系统、直观地阐述了投影的基本原理，并推导了严密的变换公式，在此基础上给出了详细算法和部分实验结果。     

济源市独立坐标与国家坐标的转换

介绍了济源市独立坐标系的建立过程,阐述了济源市独立坐标系椭球参数的计算方法,实现了独立坐标与国家坐标的转换关系.     

基于逐次投影寻踪的高光谱影像降维方法研究

提出了一种新的逐次投影寻踪方法,对高光谱数据进行降维处理,采用定量化的指标,通过对高光谱数据的多次一维投影,逐步选取有效成分,构建新的低维正交空间.     

中国古代地图的数学基础与地理空间维度认知

从几个典型的中国古地图的数学基础出发,结合相关的数学方法,探讨了中国古人在地理空间维度认知方面走过的历程。认为,当中国古代地图发展到以"计里画方"进行地图绘制时,已经实现了3维地理空间的科学认知。这也是"计里画方"的制图方法可以持续1 000多年的理论依据。     

Reservoir induced earthquakes analyzed via radial basis function networks

Estimation of the magnitude of reservoir induced seismicity is essential for seismic risk analysis of dam sites. Different geological and empirical methods dealing with the mechanism or magnitude of such earthquakes are available in the literature. In this study, a method based on an artificial neural network utilizing radial basis functions (RBF network) was employed to analyze the problem. The network has only two input neurons, one representing the maximum depth of the reservoir and the other being a comprehensive parameter representing reservoir geometry. Magnitudes of the induced earthquakes predicted using the RBF network were compared with the actual recorded data. Compared with the conventional statistical approach, the proposed method gives a better prediction, both in terms of coefficients of correlation and error rates.     

一种基于正交投影的波束形成算法

提出了一种基于正交投影的波束形成算法.首先由MVDR算法确定初始权向量;其次根据该权向量与其它用户波达角方向的关系,建立干扰信号的导向矢量矩阵;然后通过正交投影原理,将期望信号的导向矢量投影到干扰信号的零空间上,从而求得最优权值.仿真结果证明了该算法的有效性.