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)     

球状星团的天体测量(英)

球状星团是银河系中最年老的天体之一，是储存着银河系早期演化珍贵信息的“化石”．球状星团的天体测量，主要包括球状星因天区内恒星相对自行的测定，并由这些相对自行数据采用适当方法定出星团的绝对自行，或者直接测定绝对自行．利用这些自行数据，或者进一步与测光和视向速度数据结合，可以开展与球状星团的距离、运动、动力学状况、质量、年龄、演化等等以及银河系的结构和演化等有关的一系列重要的研究．在本文中对本世纪70年代中期以来在球状星团相对自行测定和成员概率估计、内部运动检测、绝对自行测定和空间运动研究这三方面取得的成果和进展以及存在的问题作了评述．     

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。     

Implications of low-pass filtering on power spectra and autocorrelation functions of turbulent velocity signals

Filtering either through the electronics of an instrument or through digital procedure is performed routinely on geophysical data. When velocity fluctuations are measured in turbulent flows using electromagnetic current meters (ECMs), a builtin lowpass Butterworth filter of order n usually attenuates fluctuations at high frequencies. However, the effects of this filter may not be acknowledged in turbulence studies, thus impeding comparisons between data collected with different ECMs. This paper explores the implications of the filters on the characteristics of velocity signals, mainly on variance, power spectra, and correlation analyses. Variance losses resulting from filtering can be important but will vary with the order n of the Butterworth filter, decreasing as n increases. Knowing the filter response, it is possible to reconstruct the original signal spectrum to evaluate the effect of filtering on variance and to allow comparisons between data collected with different instruments. The autocorrelation function also is affected by filtering which increases the value of the coefficients in the first lags, resulting in an overestimation of the integral length scale of coherent structures. These important effects add to those related to size and shape differences in ECM sensors and must be taken into account in comparative studies.     

首都圈地区现今断层活动的数学模拟及地震危险性讨论

以首都圈地区现今活动断层上近２０年的位移测量资料为依据，用二维线弹性有限元对该区断层的活动特征进行了拟合，并结合有关资料讨论了该区的地震危险性。结果表明：１９７７－１９８６年间该区主压应力优势方位与华北较一致，约为Ｎ４５°－８０°Ｅ；１９８６－１９９０年其主压应力方向向北偏转，约为Ｎ５°－６０°Ｅ；１９９０年至现在其主压应力又向东偏转，角度大于第一阶段，约为Ｎ８０°－９５°Ｅ。该区的张家口－延庆一带近期有发生中强震的可能；丰镇－阳高－大同地区和凉城－古营盘地区应力较高，也应引起注意。