重力场数学拟合模型解的影响因素探究

为了提高地球重力场模型不适定方程求解的精度,该文采用谱分析方法从级数展开阶数、数据采样率及数据缺失量3个方面探索影响数学拟合效果的根本因素:从常用的三角级数及勒让德级数模型出发,引出重力场拟合模型球谐函数模型,观察在改变级数展开阶数、数据采样率及数据缺失量等情况下所对应设计矩阵谱结构的变化,并从微观上研究影响误差分配的有关因素及最小奇异值对误差的决定性作用,为探求重力场模型解不准的原因及实现更高精度的全球重力场模型的建立提供参考。     

Defining the Potential of Nanoscale Re‐Os Isotope Systematics Using Atom Probe Microscopy

Atom probe microscopy (APM) is a relatively new in situ tool for measuring isotope fractions from nanoscale volumes (< 0.01 μm³). We calculate the theoretical detectable difference of an isotope ratio measurement result from APM using counting statistics of a hypothetical data set to be ± 4δ or 0.4% (2s). However, challenges associated with APM measurements (e.g., peak ranging, hydride formation and isobaric interferences), result in larger uncertainties if not properly accounted for. We evaluate these factors for Re‐Os isotope ratio measurements by comparing APM and negative thermal ionisation mass spectrometry (N‐TIMS) measurement results of pure Os, pure Re, and two synthetic Re‐Os‐bearing alloys from Schwander et al. (2015, Meteoritics and Planetary Science, 50, 893) [the original metal alloy (HSE) and alloys produced by heating HSE within silicate liquid (SYN)]. From this, we propose a current best practice for APM Re‐Os isotope ratio measurements. Using this refined approach, mean APM and N‐TIMS ¹⁸⁷Os/¹⁸⁹Os measurement results agree within 0.05% and 2s (pure Os), 0.6–2% and 2s (SYN) and 5–10% (HSE). The good agreement of N‐TIMS and APM ¹⁸⁷Os/¹⁸⁹Os measurements confirms that APM can extract robust isotope ratios. Therefore, this approach permits nanoscale isotope measurements of Os‐bearing alloys using the Re‐Os geochronometer that could not be measured by conventional measurement principles.     

Moritz解析延拓解与Bjerhammar虚拟球面解的等价性

利用调和函数的性质以及球谐函数展开理论,并根据实数域上函数的幂级数展开式证明了Moritz解析延拓解与Bjerhammar虚拟球面解的等价性,同时分析了两种解的内在区别。     

椭球谐和球谐系数之间一个简单的转换关系

本文推导的椭球谐系数和球谐系数相互之间转换关系的核心思想是在ε~2量级下利用Legendre函数的正交性,从球谐系数求解的积分表示出发,将积分中的椭球坐标变量与球坐标变量相互转换,从而得出椭球谐系数与球谐系数之间的转换关系。本文导出的转换关系有以下优点:①对于第二类Legendre函数的计算采用Laurent级数表示,使计算第二类Legendre函数更为简单;②保留了ε~2量级下,导出的转换关系相比文献[2]的形式更简单,满足物理大地测量边值问题线性化的要求;③顾及了余纬和归化余纬的区别。     

拖缆式验潮仪结构设计和实现

以2003年完成定型生产并投入使用的新型号拖缆式验潮仪为例,简要介绍了设备的设计思想、实现方法和新特技术的应用,涉及到嵌入式计算机的选型、智能探头、汉字和图形人机界面、多路串行通讯、潮汐数据实时获取和系统在应用升级等设计细节。