The analytical continuation bias in geoid determination using potential coefficients and terrestrial gravity data

One important application of an Earth Gravity Model (EGM) is to determine the geoid. Since an EGM is represented by an external-type series of spherical harmonics, a biased geoid model is obtained when the EGM is applied inside the masses in continental regions. In order to convert the downward-continued height anomaly to the corresponding geoid undulation, a correction has to be applied for the analytical continuation bias of the geoid height. This technique is here called the geoid bias method. A correction for the geoid bias can also be utilised when an EGM is combined with terrestrial gravity data, using the combined approach to topographic corrections. The geoid bias can be computed either by a strict integral formula, or by means of one or more terms in a binomial expansion. The accuracy of the lowest binomial terms is studied numerically. It is concluded that the first term (of power H²) can be used with high accuracy up to degree 360 everywhere on Earth. If very high mountains are disregarded, then the use of the H² term can be extended up to maximum degrees as high as 1800. It is also shown that the geoid bias method is practically equal to the technique applied by Rapp, which utilises the quasigeoid-to-geoid separation. Another objective is to carefully consider how the combined approach to topographic corrections should be interpreted. This includes investigations of how the above-mentioned H² term should be computed, as well as how it can be improved by a correction for the residual geoid bias. It is concluded that the computation of the combined topographic effect is efficient in the case that the residual geoid bias can be neglected, since the computation of the latter is very time consuming. It is nevertheless important to be able to compute the residual bias for individual stations. For reasonable maximum degrees, this can be used to check the quality of the H² approximation in different situations.Acknowledgement The author would like to thank Prof. L.E. Sjöberg for several ideas and for reading two draft versions of the paper. His support and constructive remarks have improved its quality considerably. The valuable suggestions from three unknown reviewers are also appreciated.     

A probabilistic investigation of infiltration in the vadose zone: proposal for a new formula of infiltration rate

The infiltration rate in the unsaturated zone is analysed from a probabilistic point of view. It is shown that the empirical formulas of Horton and Kostiakov, without apparent physical basis, are explained in a probabilistic approach. Horton's formula reflects a Markovian process contrary to Kostiakov's formula. This approach made it possible to explain why Kostiakov's formula is more powerful than that of Horton. A new equation of infiltration is proposed. The three formulas were compared, for four types of soil, with the model of van Genuchten based on the Richards equation. Copyright © 2006 John Wiley & Sons, Ltd.     

以建成区面积表征的中国城市规模分布

选择1990~2000年中国城市用地面积位于前200位的地级及地级以上的城市用地资料,把运用在城市人口规模上的位序-规模法则移植到城市用地上,分析了城市土地利用规模的变化规律。然后运用分形理论,阐释了城市用地的位序-规模曲线。结果显示：(1)以建成区面积作为衡量城市规模的指标,中国城市规模分布符合位序-规模法则,拟合曲线的判定系数都在0.95以上;(2)根据位序-规模曲线的形态,中国城市按建成区面积可分为3类：用地面积>200 km²的大城市,50~200 km²的中等城市和<50 km²的小城市;(3)城市建成区用地的位序-规模曲线有平行向前推进的特点,这为预测我国未来城市建成区用地规模提供很好的基础;(4)中国位于前200位的城市用地规模分布的均衡度不断增强,城市建成区用地规模总量持续增加。     

平行剖面法用棱柱和截锥公式计算块段体积注意的问题

用平行剖面法计算资源/储量时,若矿体块段在相邻两剖面上均有面积,且控制两面积的工程间距或控制每个剖面面积的工程见矿平均厚度不相等的情况下,使用棱柱体公式计算块段体积,或相邻两剖面上面积形状不相似的情况下,使用截锥体公式计算块段体积,均存在一定的误差。而拟柱体公式则是精确计算块段体积的通用公式,其使用不受上述条件的限制。因此,在这种情况下,建议限制或停止使用棱柱体和截锥体公式,提倡统一使用拟柱体公式来计算矿体块段的体积。     

导水裂隙带高度研究方法概述

导水裂隙带高度的确定是水下采煤工作之重点,目前并没有一个完全可以精确确定的方法。主要的研究方法有经验公式法、物理模拟、数值模拟和现场实测。单靠其中的一种也不能确定,将几种方法相互结合则是准确得到导水裂隙带高度计算方法的重要途径。     

Deduction and application of generalized Euler formula in topological relation of geographic information system (GIS)

Topological relation is one important characteris-tics of spatial data, and reflects the structural relation-ships among geographical objects, and is regarded as the core of spatial data processing[1,2]. Topological transformation has been widely used in diverse spatial studies, and in fact, the processing of geographical data is a kind of topological transformations[3]. There-fore, it is of significance to study the mathematical theory of generating and checking topological rela-tions in GIS…     

平面Radon变换的反演公式

本文借助球面平均法和Ｈｉｌｂｅｒｔ空间算子理论,给出了平面上Ｒａｄｏｎ变换的反演公式,此公式是具体的、构造性的,便于数值计算,或者进一步探讨重建图象的性质。     

轴角描述的光束法平差新方法

建立了一种基于轴角描述的光束法平差新方法。与传统基于欧拉角的光束法平差理论相比,基于轴角法在平差过程免去了大量冗杂的三角函数运算,平差模型系数矩阵和迭代过程全部采用线性运算,结构简洁。试验表明,基于轴角描述的光束法平差解算速度较快,为欧拉角平差方法的两倍左右,并且具有较好的稳定性,为影像区域网平差稳定快速求解提供了一套新方法,对于多定向参数数据快速处理具有一定借鉴价值。     

重力场向下延拓的三阶Adams-Bashforth公式法

重力场向上延拓是稳定且收敛的过程,而向下延拓是不稳定且发散的过程。为此,本文提出一种重力场向下延拓新方法。首先,对重力场及其垂向一阶导数向上延拓,得到不同高度的重力场垂向导数;然后,基于求解微分方程的三阶Adams-Bashforth多步法,推导出稳定的向下延拓公式;最后,为验证本文方法,将其分别应用于模型数据和实际数据。理论模型试验及误差曲线表明,相对于经典下延方法——傅里叶变换下延法和积分迭代下延法,新方法三阶Adams-Bashforth公式法下延过程稳定,边界效应不明显,下延深度可达5倍点距,下延结果与真实值的相对误差更小,结果更准确。将本文方法应用于加拿大某区实测航空重力数据,得到有效且准确的下延结果,能够识别和圈定一些细小异常特征。     

基岩中高精度钻孔施工技术

在总结多项工程实践和查阅大量相关资料基础上，以倒垂孔为例，全面系统地介绍了基岩中高精度钻孔施工各项技术和最新工艺。