Minimum conformal mapping distortion according to Chebyshev’s principle: a case study over peninsular Spain

Defining the distortion of a conformal map projection as the oscillation of the logarithm of its infinitesimal-scale σ, Chebyshev’s principle states that the best (minimum distortion) conformal map projection over a given region Ω of the ellipsoid is characterized by the property that σ is constant on the boundary of that region. Starting from a first map of Ω, we show how to compute the distortion δ₀(Ω) of this Chebyshev’s projection. We prove that this minimum possible conformal mapping distortion associated with Ω coincides with the absolute value of the minimum of the solution of a Dirichlet boundary-value problem for an elliptic partial differential equation in divergence form and with homogeneous boundary condition. If the first map is conformal, the partial differential equation becomes a Poisson equation for the Laplace operator. As an example, we compute the minimum conformal distortion associated with peninsular Spain. Using longitude and isometric latitude as coordinates, we solve the corresponding boundary-value problem with the finite element method, obtaining δ₀(Ω)=0.74869×10⁻³. We also quantify the distortions δ_l and δ_utm of the best conformal conic and UTM (zone 30) projections over peninsular Spain respectively. We get δ_l=2.30202×10⁻³ and δ_utm=3.33784×10⁻³.     

Two deterministic and three stochastic modifications of Stokes’s formula: a case study for the Baltic countries

In regional gravimetric geoid determination, it is customary to use the modified Stokes formula that combines local terrestrial data with a global geopotential model. This study compares two deterministic and three stochastic modification methods for computing a regional geoid over the Baltic countries. The final selection of the best modification method is made by means of two accuracy estimates: the expected global mean square error of the geoid estimator, and the statistics of the post-fit residuals between the computed geoid models and precise GPS-levelling data. Numerical results show that the modification methods tested do not provide substantially different results, although the stochastic approaches appear formally better in the selected study area. The 2.8–5.3 cm (RMS) post-fit residuals to the GPS-levelling points indicate the suitability of the new geoid model for many practical applications. Moreover, the numerical comparisons reveal a one-dimensional offset between the regional vertical datum and the geoid models based upon the new GRACE-only geopotential model GGM01s. This gives an impression of a greater reliability of the new model compared to the earlier, EGM96-based and somewhat tilted regional geoid models for the same study area.     

基于World Wind的鄱阳湖水位动态变化仿真系统研究

World Wind是由美国宇航局(NASA)开发的三维地理信息系统,也是一款可提供丰富数据的数字地球平台,如何将多源数据实现紧密型二三维耦合是基于World Wind开发专业系统需要解决的重要问题.在.NET开发环境下,以World Wind为仿真内核,开发了水位仿真系统,研究了二三维数据耦合技术,实现了环鄱阳湖生态经济开发区的湖区与航道淹没分析和三维漫游.结果表明,仿真系统流畅地实现了任意点地形高程、水位、水深和航道级别等信息的实时查询,仿真了不同控制水位条件下的鄱阳湖区淹没范围,仿真结果能够服务于鄱阳湖水利枢纽的水位调控决策;该仿真系统在湖泊干旱特征水位等确定中也具有重要的应用价值.     

地球化学的空间自相关异常信息提取方法

针对地球化学数据存在的空间分布相关性特征,该文提出了一种基于空间自相关统计的地球化学异常提取方法。以内蒙古浩布高矿床外围的土壤地球化学数据为例,通过对Sn、Cu元素地球化学数据在不同空间间隔上的全局自相关计算,测算其空间聚集的程度,选取聚集程度最高时的间隔距离作为局部空间自相关的参数,通过局部Moran’s I值研究元素的空间分布特征,分析空间聚类和异常值,从而提取地球化学异常。结果表明,局部空间自相关分析可以揭示Sn、Cu地球化学数据的空间分布特征,能够更好地提取地球化学弱缓异常,说明空间自相关是一种有效的地球化学异常识别方法。     

观测点的变形过程曲线“三点法”修匀通用计算公式

本文推导了“三点法”修匀通用计算公式．采用该公式便于计算机编程自动处理，计算结果精度比图解法精度高．     

论三角测量单位权方差的先验估计与后验估计

三角洲量单位权方差的先验估值一般用经典菲列罗公式计算。实践中，经常出现三角测量单位权方差的先验估值不等于后验估值的情形．本文根据条件平差的原理，证明了单位权方基的先验估值是有偏估计，经典菲列罗公式是后验估计公式的特殊形式，并推导出了广义菲列罗公式。     

HYOROTRAC单频测深仪在二滩水电站库区泥沙淤积监测中的应用

迄今为止，声纳技术应用于江、河、湖、海水下地形测量，特别在大面积、深水域是最便捷、最有效的方法。本文着重阐述了HYOROTRAC单频测深仪在二滩水电站库区泥沙淤积监测中的应用，并解决了长期以来数据处理中忽视的问题。     

模糊聚类的DEM确定耕地坡度方法

针对实际应用的坡度计算中没有考虑DEM高程精度影响这一状况,提出采用模糊聚类法进行坡度分级,给出了具体的精度评定方法,并采用我国南方某地区一个镇的第二次土地调查耕地成果数据进行了分析,与传统的直接计算方法进行了比较。结果表明,两种方法得到的图斑坡度级别基本相同;从总体分类精度与Kappa系数计算来看,两者基本接近,模糊聚类法略微优于直接计算法,而且由于其顾及了DEM高程精度的影响,得到的分级结果可靠性更高。     

Earth’s precession–nutation motion: the error analysis of the theories IAU 2000 and IAU 2006 applying the VLBI data of the years 1984–2006

The long-term systematic errors of the analytical theories IAU 2000 and IAU 2006 of the Earth’s precession–nutational motion are studied making use of the VLBI data of 1984–2007. Several independent methods give indubitable evidence of the significant quadratic error in the IAU 2000 residuals of the precessional angle while the adopted value of the secular decrease /cy of the Earth’s ellipticity e (derived from Satellite Laser Ranging data) should manifest itself in the residuals of as the negative quadratic trend . The problem with the precession of the IAU 2006 theory adopted as a new international standard and based on the precession model P03 (Capitaine et al., Astron Astrophys 432:355–367, 2005) appears to be even more serious because the above mentioned quadratic term has already been incorporated into the P03 precession. Our analysis of the VLBI data demonstrates that the quadratic trend of the IAU 2006 residuals does amount to the expected value (30.0 ± 3) mas/cy². It means, first, that the theoretical precession rate of IAU 2006 should be augmented by the large secular correction and, second, that the available VLBI data have potentiality of estimating the rate . And indeed, processing these data by the numerical theory ERA of the Earth’s rotation (Krasinsky, Celest Mech Dyn Astron 96:169–217, 2006, Krasinsky and Vasilyev, Celest Mech Dyn Astron 96:219–237, 2006) yields the estimate /cy statistically in accordance with the satellite-based . On the other hand, applying IAU 2000/2006 models, the positive value /cy is found which is incompatible with the SLR estimate and, evidently, has no physical meaning. The large and steadily increasing error of the precession motion of the IAU 2006 theory makes the task of replacing IAU 2006 by a more accurate model be most pressing.     

Kriging方法在GPS速度场网格化和应变率场计算中的适用性

目的 从Kriging方法的基本原理出发,推导了 Kriging球面应变计算公式,通过在模拟和实际 GPS数据中的试算,讨论了该方法在区域 GPS速度场网格化和应变率计算中的适用性。结果表明 Kriging方法对 GPS速度场滤波和网格插值是可行的,交叉检验及残差分析结果亦表明了 Kriging方法的有效性。对比 Kriging方法与最小二乘配置方法对中国大陆1999～2004期 GPS速度场处理结果,发现两种方法的滤波和网格化效果相当;而应变率场结果总体分布相近,但 Kriging结果自身一致性不佳,最大剪应变率的高值区是一致的,但量级上差别显著;Kriging应变率计算方法在抗差性和边缘效应处理方面不如最小二乘配置方法。