卫星测高混合边值问题的球谐级数解法

研究了球界面下卫星测高问题的解法,利用有限逼近方法得到了下列结论：若陆地部分是球冠,则卫星测高问题的解可以转换成关于球谐级数位系数的线性方程组,并且位系数的阶和次是以分离形式出现的,从而确保该解法具有实用意义. 利用重力场360阶模型进行模拟计算的结果表明：该解法得到的位系数的相对精度达到了10－１１. 同时证明了常用的Stokes问题、Dirichlet问题、Neumann问题可以看成卫星测高问题的特殊情况.     

有限差分格式与物理量守恒性

为了成功地开展大气数值模拟,如何构造相应的离散格式是一项十分重要的工作.本文以大气球面浅水方程为例,从不同形式的微分方程组出发,分别构造了能量守恒格式、准辛格式和多守恒格式,并作相应的数值检验和比较,从中可以清楚地看到三类格式的优劣.这三类格式构造方法不同,所保持的物理守恒性不完全相同,数值计算时所需机时也不同,这些比较结果为实际工作的不同使用需求提供了选择依据.     

京津冀地区地磁场球冠谐分析

2002年在京津冀地区进行了45个测点的地磁三分量测量,对测量资料进行通化处理,通化时间为2002年5月5日16～18时（世界时）. 通化后的观测均方差分别优于1.5nT（地磁场总强度F）,0.5′(磁偏角D和磁倾角I). 将国际参考地磁场（IGRF2000）作为地磁正常场,建立了京津冀地区地磁异常场的球冠谐模型（BTHASCH）. 球冠极的空间位置坐标为39.5°N和117.0°E,球冠半角为4°. 在模型计算过程中,球冠谐函数的截断阶数分别取为1～10. 经综合比较, 最终采用的截断阶数为5. 建立了京津冀地区参考地磁场的球冠谐模型（BTHGRF）.根据模型,绘制了京津冀地区地磁异常场图(ΔX、ΔY、ΔZ、ΔF、ΔD、ΔI)和京津冀地区地磁图(X、Y、Z、F、D、I).     

Thomsen's parameters from p‐wave measurements in a spherical sample‡

The aim of this paper is to understand the seismic anisotropy of the overburden shale in an oilfield in the North West Shelf of Western Australia. To this end, we first find the orientation of the symmetry axis of a spherical shale sample from measurements of ultrasonic P‐wave velocities in 132 directions at the reservoir pressure. After transforming the data to the symmetry axis coordinates, we find Thomsen's anisotropy parameters δ and ? using these measurements and measurements of the shear‐wave velocity along the symmetry axis from a well log. To find these anisotropy parameters, we use a very fast simulated re‐annealing algorithm with an objective function that contains only the measured ray velocities, their numerical derivatives and the unknown elasticity parameters. The results show strong elliptical anisotropy in the overburden shale. This approach produces smaller uncertainty of Thomsen parameter δ than more direct approaches.     

球体位错理论计算程序的总体设计与具体实现

本文详细介绍了球体位错理论计算程序的总体设计思想、 各类配套文件的具体内涵以及各类输出文件的物理含义, 同时介绍了程序的使用方法和注意事项, 为读者独立使用该程序提供参考。 球体位错理论计算程序主要由三部分组成: ① 位错格林函数计算程序, 基于具体的球对称地球模型提供离散的二维格林函数数值框架; ② 积分计算程序, 对离散的格林函数数值框架进行双二次样条插值运算, 并对四类独立位错源对应的格林函数进行适当组合, 从而计算出任意位置任意类型震源在地表产生的同震变形(含位移、 应变、 重力变化和大地水准面变化); ③ 辅助文件, 用于提供发震断层模型和计算点位信息。 一般情况下, 读者不需要理解位错格林函数计算程序和积分计算程序, 只需要对辅助文件提供的信息进行针对性改动, 就可以计算目标地震在目标观测站引起的同震变形。     

Nonmodal Growth on a Sphere at Various Horizontal Scales

Nonmodal growth (NG) and unstable normal mode growth are considered in spherical geometry. Two groups of initial conditions (IC) are studied: "connected" IC (common in Cartesian studies) and "separated" IC (based on observed conditions prior to cyclogenesis). Time series of growth rates are emphasized in conjunction with eigenmode projections. Projections show that early on normal mode growth was much stronger for connected IC and that NG caused negative growth early on of some variables for separated IC. Projections explain why amplitude, kinetic energy (KE), and potential vorticity have more NG than available potential energy (APE). Though varying between ICs and with initial phase shift, NG increases with wavenumber. For middle wavelengths, NG is significant and positive using connected IC but negative or small using separated IC. Total energy and KE growth rates of short waves are very similar during the first 2 days for both ICs. Amplitude time series closely follow KE in all cases studied. APE has less overlap than does KE between the main modes present, so less NG occurs for APE than for KE. In separated IC cases, APE growth rates evolve consistent with emergence of an unstable normal mode and little NG.     

The temporal variation of the spherical and Cartesian multipoles of the gravity field: the generalized MacCullagh representation

 The Cartesian moments of the mass density of a gravitating body and the spherical harmonic coefficients of its gravitational field are related in a peculiar way. In particular, the products of inertia can be expressed by the spherical harmonic coefficients of the gravitational potential as was derived by MacCullagh for a rigid body. Here the MacCullagh formulae are extended to a deformable body which is restricted to radial symmetry in order to apply the Love–Shida hypothesis. The mass conservation law allows a representation of the incremental mass density by the respective excitation function. A representation of an arbitrary Cartesian monome is always possible by sums of solid spherical harmonics multiplied by powers of the radius. Introducing these representations into the definition of the Cartesian moments, an extension of the MacCullagh formulae is obtained. In particular, for excitation functions with a vanishing harmonic coefficient of degree zero, the (diagonal) incremental moments of inertia also can be represented by the excitation coefficients. Four types of excitation functions are considered, namely: (1) tidal excitation; (2) loading potential; (3) centrifugal potential; and (4) transverse surface stress. One application of the results could be model computation of the length-of-day variations and polar motion, which depend on the moments of inertia. Received: 27 July 1999 / Accepted: 24 May 2000     

地磁场模型和冠谐分析

地磁场是由内源场(地核场和地壳场)和外源场(电离层场和磁层场)组成的,地磁场模型是表示地磁场时空分布的数学表达式.本文简述了地磁场全球模型和区域模型的计算方法和应用;评述了冠谐分析方法及其在地磁学中的应用;介绍了地磁场模型误差的主要来源.     

长江主干流的球面重心计算及其尺度效应分析

长江不仅具有长度这一非空间属性,还具有重心、方位、密度以及形状等多种空间分布属性。为了对长江的空间分布特征进行统计分析,提出了一种基于球面坐标的空间分布统计方法。采用空间随机抽样的方法,通过对组成长江水系的2种有限线段(即原始数据线段和等长切分线段)进行了不放回空间随机抽样,估计了长江球面重心位置的不确定性。为了解长江水系空间数据固有的多尺度特性,还研究了长江水系不同分辨率的空间切分(1 000 m、100 m、10 m)条件下的球面重心的规律。长江球面重心的计算方法不仅适用于球面线状物体球面重心的计算,也适用于球面面状物体重心的计算。研究长江水系的空间分布特征可以增加人们对长江水系的认知,为研究长江流域的经济、政治等相关的研究提供重要的地理参考信息或背景信息。     

Spherical harmonic analysis of earth’s conductive heat flow

A reappraisal of the international heat flow database has been carried out and the corrected data set was employed in spherical harmonic analysis of the conductive component of global heat flow. Procedures used prior to harmonic analysis include analysis of the heat flow data and determination of representative mean values for a set of discretized area elements of the surface of the earth. Estimated heat flow values were assigned to area elements for which experimental data are not available. However, no corrections were made to account for the hypothetical effects of regional-scale convection heat transfer in areas of oceanic crust. New sets of coefficients for 12° spherical harmonic expansion were calculated on the basis of the revised and homogenized data set. Maps derived on the basis of these coefficients reveal several new features in the global heat flow distribution. The magnitudes of heat flow anomalies of the ocean ridge segments are found to have mean values of less than 150 mW/m². Also, the mean global heat flow values for the raw and binned data are found to fall in the range of 56–67 mW/m², down by nearly 25% compared to the previous estimate of 1993, but similar to earlier assessments based on raw data alone. To improve the spatial resolution of the heat flow anomalies, the spherical harmonic expansions have been extended to higher degrees. Maps derived using coefficients for 36° harmonic expansion have allowed identification of new features in regional heat flow fields of several oceanic and continental segments. For example, lateral extensions of heat flow anomalies of active spreading centers have been outlined with better resolution than was possible in earlier studies. Also, the characteristics of heat flow variations in oceanic crust away from ridge systems are found to be typical of conductive cooling of the lithosphere, there being little need to invoke the hypothesis of unconfined hydrothermal circulation on regional scales. Calculations of global conductive heat loss, compatible with the observational data set, are found to fall in the range of 29–34 TW, nearly 25% less than the 1993 estimate, which rely on one-dimensional conductive cooling models.