水准椭球密度问题研究

本文总结了作者等最近十年来对地球重力学"水准椭球密度问题"进行研究的初步结果,首次提出了"密度水准椭球"概念,给出了从"匀质椭球"、"参数椭球"、"纬向密度椭球"、"似水准椭球"到"密度水准椭球"的研究路线,并对该问题的研究前景进行了讨论.     

Parameters of the Earth's tri-axial level ellipsoid

Summary Four parameters defining the Earth's tri-axial ellipsoid (E) have been derived on the basis of the condition that the gravity potential on E be constant and equal to the actual geopotential value (W₀) on the geoid. The geocentric gravitational constant, the angular velocity of the Earth's rotation, the actual 2nd degree geopotential Stokes parameters and W₀ are taken to be the primary geodetic constants defining E and its (normal) gravity field.     

Lame surfaces as a generalisation of the triaxial ellipsoid

In modern geodesy the triaxial ellipsoid as a generalisation of the ellipsoid of revolution has a significant position in studying the figure of the Earth. Lame surfaces represent a generalisation of the triaxial ellipsoid. The following paragraphs are devoted to curvatures of the Lame surfaces.     

An optimized method to transform the Cartesian to geodetic coordinates on a triaxial ellipsoid

Studia Geophysica et Geodaetica - A general triaxial ellipsoid is suitable to represent the reference surface of the celestial bodies. The transformation from the Cartesian to geodetic coordinates...     

Improved expressions for the ellipsoidal harmonic series representing the Earth gravitational potential and its first and second derivatives on and outside the reference ellipsoid of revolution

The Legendre functions of the second kind, renormalized by Jekeli, are considered in the external space on a set of ellipsoids of revolution which are confocal with respect to the normal ellipsoid. Among these ellipsoids a reference one is chosen which bounds the Earth. New expressions for the first and second order derivatives of the Legendre functions are derived. They depend on two very quickly convergent Gauss hypergeometric series which are obtained by transforming the slowly convergent initial hypergeometric series. The derived expressions are applied for constructing the ellipsoidal harmonic series for the Earth disturbing gravitational potential and its derivatives of the first and second orders. Since outside the chosen reference ellipsoid there are no Earth masses (as compared to the normal ellipsoid) then it is more appropriate for constructing the boundary-value equation and solving it on the basis of surface gravity data reduced to this ellipsoid.     

On the solution of the reverse problem of geodesics with the help of the chord

Резюме Дается вывод формул для вычислений длины хорды, длины и азимутов нормаляных сечений и длины геодезической линии эллипсоида. Применяются тригонометрические функции данных величин и постоянные принятого ргфгргнц-эллипсоида, что является целесообразным при использовании вычислителQjных машин, особенно автоматов. Рабочие формулы рекомендуются в форме (8–11).

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Dedicated to Professor František Fiala on His 85th Birthday

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Address: Veveři 95, Brno.     

由震中迁移交汇预测大震的讨论

地壳内部的情况是复杂的,特别是当今地下的情况,而震中迁移交汇的现象可暗示构造运动加力速度快的地区,因此与大震位置的预测有关。     

Two modified algorithms to transform Cartesian to geodetic coordinates on a triaxial ellipsoid

The paper presents modified Lin and Wang??s (1995) and Hedgley??s (1976) algorithms to tackle the problem of transforming Cartesian to geodetic coordinates on a triaxial ellipsoid. Originally, the methods were developed for an ellipsoid of revolution but due to their universality, they may be adapted to the more complicated problem stated on a triaxial ellipsoid what is in fact done in this work. Two modified methods are compared to the vector method recently introduced by Feltens. The modified methods turn out to be more accurate and faster than the algorithm presented by Feltens.     

半拉格朗日模式风的半解析解及与差分解的比较试验

质点的轨迹计算是半拉格朗日模式的重要基础,传统的数值计算方法由于采用时间差分代替微分,只能得到质点运动轨迹终点的速度,因此质点的移动轨迹（位移）只能靠风速外推的方法计算,导致了模式计算不稳定等问题.借鉴精细积分法中使用半解析解的思路,利用正压原始方程研究了用运动方程的半解析解构建数值模式的可能性.求解了运动方程的一阶和二阶微分方程组的半解析解,通过时间积分半解析解计算质点运动轨迹.数值试验表明,一阶微分方程组的半解析解比差分解略有优势.二阶微分方程组的半解析解在时间步长增大时优势非常明显,而且在保证计算精度的前提下,节省计算时间,这对提高模式性能有重要作用.     

Compact non-singular expansions in the exterior space of a reference ellipsoid for the gravitational gradients in the local north-oriented ellipsoidal and spherical reference frames

Due to the complicated structure of their expressions, the ellipsoidal harmonic series for the derivatives of the Earth’s gravitational potential are commonly applied only on a reference ellipsoid. They depend on the first- and second-order derivatives of the associated Legendre functions of both kinds and contain a few singular terms. We construct ellipsoidal harmonic expansions in the exterior space for the first and second potential derivatives, which are similar to the series on the reference ellipsoid enveloping the Earth. We take a point P at an arbitrary altitude above the reference ellipsoid and construct the ellipsoid of revolution confocal to it, which passes through this point. The conventional complicated singular expressions for the first and second potential derivatives in the local north-oriented ellipsoidal reference frame, with the origin at the point P, are transformed into non-singular ellipsoidal harmonic series, which do not contain the first- and second-order derivatives of the associated Legendre functions. The resulting series have an accuracy of the squared eccentricity. These series can be applied for constructing a geopotential model, which is based, simultaneously, on the surface gravity data and the data of satellite missions, which provide measurements of the accelerations and/or the gravitational gradients. When the eccentricity of the considered external ellipsoid is equated to zero, the ellipsoid becomes an external sphere passing through the point P and the constructed ellipsoidal harmonic expansions are converted into non-singular spherical harmonic series for the first and second potential derivatives in the local north-oriented spherical reference frame.     

Approximate solutions for the formation of the lithosphere

The lithosphere is interpreted as a thermal boundary layer. Approximate solutions of the boundary layer cooling problem are developed which include mantle radioactivity, partial melt in the asthenosphere, a temperature gradient in the asthenosphere, and a non-zero lithospheric thickness at the ridge crests. The cooling history of oceanic lithosphere is found to be remarkably insensitive to assumptions about the amount of radioactivity in the upper mantle and the extent of melting in the asthenosphere. Determinations of the thickness of oceanic lithosphere and the depths of oceans as a function of age are in excellent agreement with boundary layer predictions which include a heat flux from the asthenosphere. However, the determinations do not resolve how much of the total asthenospheric heat flux might be caused by a temperature gradient in the asthenosphere. Simple thermal arguments indicate that the initial lithospheric thickness, L₀, at ridge crests should depend on the local half-spreading rate, V, as L₀ = 3 km/V(cm/year).     

Directions of axes of the Earth's ellipsoid of inertia derived from satellite orbit dynamics

Studia Geophysica et Geodaetica - Обсуж¶rt;aеmся 3 возможносmь...     

Existence of the solutions and the attractors for the large-scale atmospheric equations

The atmosphere is a kind of fluid surrounding therotating earth, and its state can be described by thevelocity vector v, the temperature T, the density ρ, andthe pressure p at each point. Its evolution process isessentially governed by the Navier-Stockes equationand the temperature equation. Due to the specialty andthe complexity of the atmospheric problem, althoughsome modified and simplified work have made onthese fluid mechanics and temperature equations, theyare still a very complex forc…     

A consideration of Hayford's best fitting ellipsoid data using the differential change equations of Vening Meinesz

Summary The relations of the defining parameters of a geodetic system to the deflections of the vertical in this system given byVening Meinesz have been used in the computation of a best fitting ellipsoid. The data was that used byHayford in the computation of the resulting International Ellipsoid. Assuming the undulation (N ₀) at Meades Ranch to be zero, the results are: a=6,378,194 m and l/f=299.9. This a is much nearer to modern values than that of the Internaitonal Ellipsoid. If a flattening of 1/298.24 is fixed andN ₀=+3m,a=6,378,164 m which differs by one meter from a recent determination given byKaula.     

基于InSAR技术的喀什-乌恰交汇区地壳垂直形变特征分析

利用喀什-乌恰交汇区2004—2010年间的ENVISAT ASAR数据,采用层叠InSAR技术获得了喀什-乌恰交汇区地壳垂直形变速度场,并结合研究区GPS观测数据结果,分析了喀什-乌恰交汇区地壳形变特征。结果显示,喀什-乌恰交汇区地壳垂直形变速率约为?1—2mm/a,其中,乌恰南边的山区形变量最大,形变速率达到2mm/a,是整个研究区中隆升最明显的区域;而喀什、阿图什一带形变量比较小,基本在0—1mm/a。卡兹克阿尔特和阿图什南翼断裂为乌恰以南的隆升区域到喀什、阿图什垂直形变平稳区域的梯度带,这个区域吸收了1—2mm/a的垂直形变能量和7—9mm/a的水平形变能量,是喀什-乌恰交汇区中主要的地壳形变能量消耗地带。     

Numerical and approximate solutions for lithospheric thickening and thinning

Lithospheric thickness, surface heat flow and subsidence are calculated numerically as functions of time since the formation of oceanic lithosphere at a ridge crest. These numerical results confirm the validity of a previously derived approximate solution to the same problem. A numerical solution is also calculated for lithospheric thinning due to a sudden increase of heat flux into the base of the lithosphere. With this solution as a standard, an approximate solution is derived which can accurately predict thickness, heat flow, and uplift as functions of time. Lithospheric thinning and surface uplift begin immediately with the increase of heat flux at depth, but the increase in surface heat flow begins 20–40 m.y. later.