Seismic rays in an ellipsoidal earth model: theoretical analysis and estimation of deviations due to the ellipticity

Summary. A first-order form of the Euler's equations for rays in an ellipsoidal model of the Earth is obtained. The conditions affecting the velocity law for a monotonic increase, with respect to the arc length, in the angular distance to the epicentre, and in the angle of incidence, are the same in the ellipsoidal and spherical models. It is therefore possible to trace rays and to compute travel times directly in an ellipsoidal earth as in the spherical model. Thus comparison with the rays of the same coordinates in a spherical earth provides an estimate of the various deviations of these rays due to the Earth's flattening, and the corresponding travel-time differences, for mantle P -waves and for shallow earthquakes. All these deviations are functions both of the latitude and of the epicentral distance. The difference in the distance to the Earth's centre at points with the same geocentric latitude on rays in the ellipsoidal and in the spherical model may reach several kilometres. Directly related to the deformation of the isovelocity surfaces, this difference is the only cause of significant perturbation in travel times. Other differences, such as that corresponding to the ray torsion, are of the first order in ellipticity, and may exceed 1 km. They induce only small differences in travel time, less than 0.01s. Thus, we show that the ellipticity correction obtained by Jeffreys (1935) and Bullen (1937) by a perturbational method can be recovered by a direct evaluation of the travel times in an ellipsoidal model of the Earth. Moreover, as stated by Dziewonski & Gilbert (1976), we verify the non-dependence of this correction on the choice of the velocity law.     

THE EVOLUTION OF SERVICE ECONOMIES: A GEOGRAPHICAL PERSPECTIVE1

Of the several classifications of services, each emphasizes different characteristics. The International Standard Industrial Classification (ISIC) is used for a comparative study on the transformation into service economies of the U.S., Canada, Great Britain, France, West Germany, Italy and Japan. Service economies are defined as national economies in which employment in services surpassed that in manufacturing. The pace of the evolution of service economies has been rapid with North America leading, followed in order by Great Britain, France, Italy, Japan and West Germany. Service economies have important implications for urban growth, intercity competition, and international trade.     

A warped m= 2 water maser disc in V778 Cyg?

The silicate carbon star V778 Cyg is a source of 22-GHz water maser emission which was recently resolved by MERLIN. Observations revealed an elongated     -like structure along which the velocities of the maser features show a linear dependence on the impact parameter. This is consistent with a doubly warped   m = 2  disc observed edge-on. Water masers and silicate dust emission (detected by the Infrared Astronomical Satellite and Infrared Space Observatory ) have a common origin in O-rich material and are likely to be co-located in the disc. We propose a detailed self-consistent model of a masing gas–dust disc around a companion to the carbon star in a binary system, which allows us to estimate the companion mass of  1.7 ± 0.1 M_⊙  , the disc radius of  40 ± 3  au and the distance between companions of ∼80 au. Using a dust–gas coupling model for water masing, we calculate the maser power self-consistently, accounting for both the gas and the dust energy balances. Comparing the simulation results with the observational data, we deduce the main physical parameters of the masing disc, such as the gas and dust temperatures and their densities. We also present an analysis of the stability of the disc.     

REVIEWS OF GEOGRAPHIC SOFTWARE

Reviews of geographic software in this article: DEMO-GRAPHICS: WORLD POPULATIONS AND PROJECTIONS. ESP GAUSS. CEMODEL S. Damus LIMDEP. William H. Greene MICROSTAT 4.1 OTIS PCIPS. (Personal Computer Image Processing System) . H.J. Meyers and R. Bernstein. REGRESSION ANALYSIS OF TIME SERIES (RATS) SPSS/PC+ URBAN DATA MANAGEMENT SOFTWARE (UDMS)     

地球化学景观吸引子的发现及其意义

勘查地球化学对异常评价的最大不确定性源于对地球化学景观特性的认识不够。我们应用构造相空间的方法分析了浙江儒岙幅（1:5万）水系沉积物测量的Ag含量数据，揭示了地球化学景观是具有低维吸引子（DZ≈2．9）的混饨系统。这一发现将对勘查地球化学中采样密度的选择、地球化学场模拟、异常评价等根本性问题产生重大影响。     

地形面方法在渭河盆地活断层研究中的应用

本文主要依据地形图和航空照片解译，并经已有地质、钻孔资料验证及野外实地考察的方法来研究地形面及其变形特征，由此确定渭河盆地活断层的分布、最新活动特征及活动规律，为地震预报及地震危险性分析提供依据。     

中国东部第四纪自然环境演化及庐山“冰碛层”堆积时期的自然环境研究

根据第四纪地层内孢粉组合和动物群等新资料恢复了我国东部各大区域第四纪各个时期的自然环境特征,其温暖期与干冷期的交替与深海沉积O~(18)温度变化趋势大致对应。庐山三次“冰期冰碛层”内孢粉组合表明均为温暖湿润针阔叶混交林景观,而不是寒冷的冰川环境。     

论裸眼井中的“共振纵波”和“共振横波”

一、引言 文献[1]和[2]指出,充流体裸眼井中存在频率确定、波速恒定、且沿传播方向不衰减的“共振纵波”和“共振横波”。本文的目的在于论证并指出,这两种波是不存在的。 二、论证 设一点源位于z=0的井轴上,则井轴上z处的声波频率响应为