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.     

城市公园的类型划分及其与功能的关系分析——以北京市城市公园为例

城市公园是城市人居环境的重要组成,也是宜居城市建设的重要内容。通过对中国现行城市公园分类标准的回顾与探讨,提出城市公园可以划分为5种类型:文化遗址公园、游乐公园、综合性公园、社区公园、生态公园。北京市六环以内城市公园共计148处,总面积7293.9 hm²,平均面积49.28 hm²,各个类型公园有着不同的分布特征。城市公园至少具有四种重要功能:旅游休闲、生态价值、防灾减灾和教育科普。城市公园类型与功能之间有着密切联系,每个公园复合了多种功能,但是各个类型城市公园有不同的主导功能。文化遗址公园以旅游休闲和教育科普为主导功能,游乐公园相对单一的旅游休闲功能,综合性公园的功能比较全面,社区公园除科普功能较弱外,具有其它几项功能的中等水平,生态公园则以生态价值为主。对城市公园进行细化分类,识别主导功能,有助于科学指导城市公园建设,实现城市公园的合理配置。