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 new strategy for the atmospheric gravity effect in gravimetric geoid determination

Prior to Stokes integration, the gravitational effect of atmospheric masses must be removed from the gravity anomaly g. One theory for the atmospheric gravity effect on the geoid is the well-known International Association of Geodesy approach in connection with Stokes integral formula. Another strategy is the use of a spherical harmonic representation of the topography, i.e. the use of a global topography computed from a set of spherical harmonics. The latter strategy is improved to account for local information. A new formula is derived by combining the local contribution of the atmospheric effect computed from a detailed digital terrain model and the global contribution computed from a spherical harmonic model of the topography. The new formula is tested over Iran and the results are compared with corresponding results from the old formula which only uses the global information. The results show significant differences. The differences between the two formulas reach 17 cm in a test area in Iran.     

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…     

平原储灰库区地下潜水位影响评价模式探讨

以山东华能德州发电厂现役储灰库“灰水”对潜水位的影响和水量均衡原理 ,确定其对库区潜水位影响范围 ;对拟建储灰库区根据水文地质条件 ,采用非稳定流基本方程对库区潜水水位进行预测 ,得出平原储灰库区地下潜水位最大影响范围为 75 0m。     

质量吸收因子的经验公式

采用非线性最小二乘法拟合获得了生物学、地学和化学上重要的18种元素的质量吸收因子经验公式μ/ρ=cλ3-dλ4-aλ2+bλ+e,其R2比0.9999更精确。并给出了系数及其适用的波长或能量范围,简单讨论了各系数与原子序数Z和原子量之间的关系。     

Assessment of Discharge through a Dike Breach and Simulation of Flood Wave Propagation

This paper presents a simple and fast method to calculate flow through a dike breach. The approach was based on two-dimensional numerical simulations of idealized dike breakages at straight river-sections. As a result, computation of discharge through a breach can be achieved by use of the new developed formula (denoted as dike break formula). Furthermore, a methodology that combines one-dimensional hydrodynamic modelling, the dike break formula and a simple GIS-based method to estimate inundation areas is described. This fast and easy-to-handle tool can be utilized for near real-time forecasting or evacuation decisions. Detailed predictions were made for a number of flood and dike break scenarios at the River Rhine to prove the accuracy of the new method compared with two-dimensional numerical models.     

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。     

β分布的参数确定及其在岩土工程中的应用

对岩土工程中随机变量的空间概率特征进行了统计分析,介绍了确定β分布各参数的迭代方法,提出了经验公式简化迭代过程,有效地处理了随机变量分布范围的估计问题,并阐明了β分布在可靠度领域中的适用性。作为对比,对同一样本采用了其他分布进行拟合。分析结果表明,β分布拟合精度高于其他分布。     

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。