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.     

Tectonic relation between northeastern China and the Korean peninsula revealed by interpretation of GRACE satellite gravity data

The major continental blocks in northeastern Asia are the North China block and the South China block, which have collided starting from the Korean peninsula. Geologic and geophysical interpretations reveal a well defined suture zone in northeastern China from Qinling through Dabie to Jiaodong. The discovery of high-pressure metamorphic rocks in the Hongseong area of the Korean peninsula, prominent evidence for the collision zone, indicates extension of the collision zone in northeastern China into the Korean peninsula. Interpretation of the GRACE satellite gravity dataset shows two prominent structural boundaries in the Yellow Sea. One extends from the Jiaodong Belt in eastern China to the Imjingang Belt in the Korean peninsula. The other extends from near Nanjing, eastern China, to Hongseong. Tectonic movement in or near the suture zone may be responsible for seismic activity in the western Korean peninsula and the development of the Yellow Sea sedimentary basin.     

Compression of the North Hemisphere derived from space geodesy

Introduction With the development of global tectonics and overall detections for global tectonics with multi-geophysical methods, ones can roundly study on the geological tectonics of sampling and magnetic stripe image, so as to summarize and interpret the geometrical and kinematical charac-teristics for the distribution of the ocean and the land, and spreading state of the global tectonics in a global scale. From a comprehensive view, the South and North hemispheres are clearly unsym-metrical…     

全球观测应力场的短波分量分析

世界应力图(WSM，World Stress Map)计划的应力指标，目前已累积数据共计10 920个，这些应力指标代表了该地区最大水平主应力的实际观测方向；与此同时，可以假定全球各个板块的绝对运动方向表征了相应各板块的最大水平主应力方向的长波分量．根据应力场的叠加原理，得到由该地区局部构造运动等因素贡献的短波分量的相对大小和方向．将全球划分成2.52.5的基本单元，对每个单元的WSM数据进行加权统计分析，得到其平均应力观测取向，利用HS2-NUVEL1全球绝对板块运动模型计算应力场的长波分量；平均观测应力取向和长波分量取向之间的夹角，决定了相应短波分量相对于观测应力场的大小及其取向的范围，并反映了特定研究地区局部应力场对总应力场的贡献程度．本文的计算结果表明，全球板块的绝大部分地区及各板块的平均效果，长波分量与短波分量对观测应力场的贡献程度相当．对于某些大陆板块内部，局部构造活动对观测应力场的贡献起到重要作用，因而控制着地震的孕育与发生．      

基于空间技术实测数据的板块构造运动研究

将ITRF2008解算结果 GPS、SLR、VLBI实测站速度信息和北美CORS网络、中国陆态网络、欧洲CORS网络站速度信息进行基准统一,联合解算IERS组织划定的全球14个主要大陆板块的欧拉矢量,对原有的板块运动参数进行精化;提出了基于最小二乘法的海量台站选择方法,实验结果表明,该台站选取方法能够有效提高海量台站的筛选效率和可靠性。稳定台站的数量越多,分布越均匀,越能够体现板块运动的现势性。     

基于欧拉反褶积法的无人机航磁找矿应用

无人机航磁测量以其高效、安全、低成本等优点逐渐应用到中小面积大比例尺资源勘探领域。本文针对安徽芜湖市三山区22 km²区域构造刻画和找矿前景预测,开展1∶20 000高精度无人机航磁测量工作;推导了欧拉反演求解过程,并分析对比构造指数选取,使用构造指数为0的欧拉反褶积对航磁数据进行反演求解,获得地下磁异常体构造边界解集信息;将其应用到研究区域航磁数据反演,根据反演得到的边界位置和深度信息圈定了18处断裂,并结合异常特征给出了8.7 km²岩浆岩分布区,根据宁芜区域铁矿成矿特点,圈定岩浆分布区及边界为成矿详查区。     

中国西部活动地块运动模型的建立及其运动学分析

中国西部的青藏和新疆地区现代构造变形活动非常强烈, 业已证实该区可以进一步划分为塔里木、 阿拉善、 天山、 柴达木和西藏5个活动地块。 利用GPS观测资料得到的中国大陆地壳水平运动的速度场, 借鉴全球板块运动模型的建模方法, 将其视为刚性的地块系统, 反演得到各地块相对欧亚板块运动的欧拉矢量, 进而求得各地块两两之间相对运动的欧拉矢量, 并计算出沿地块边界的相对运动速率。 结果显示, 与地块边界上的地震滑移矢量, 由地质学资料得到的滑移速率, 以及GPS数据本身均有较好的一致性, 从而也说明了将该地区划分为若干活动地块并视为刚性地块的合理性。     

利用多面函数拟合和欧拉矢量法建立福建省GPS速度场模型

通过处理福建省卫星导航定位基准服务系统(FJCORS)2013-2015年观测资料,获得GPS站实测运动速度值,在此基础上,分别利用多面函数拟合法和欧拉矢量法构建了福建省及周边区域GPS速度场模型.内符合精度方面,多面函数拟合的速度精度南北分量为1.06 mm/a、东西分量为2.00 mm/a;欧拉矢量法得到的速度精度南北分量为1.36 mm/a、东西分量为1.22 mm/a.外符合精度方面,两种方法模拟得到的检核点速度值与实测速度值的较差均在±2.28 mm/a以内.在福建省陆域内,两种方法得到的速度场具有高度的一致性,运动速度均为35 mm/a左右,运动方向为SE-E向.     

A Time-Domain Coupled Model for Nonlinear Wave Forces on A Fixed Box-Shaped Ship in A Harbor

A 2-D time-domain numerical coupled model is developed to obtain an efficient method for nonlinear wave forces on a fixed box-shaped ship in a harbor.The domain is divided into an inner domain and an outer domain.The inner domain is the area beneath the ship and the flow is described by the simplified Euler equations.The other area is the outer domain and the flow is defined by the higher-order Boussinesq equations in order to consider the nonlinearity of the wave motions.Along the interface boundaries between the inner domain and the outer domain,the volume flux is assumed to be continuous and the wave pressures are equal.Relevant physical experiment is conducted to validate the present model.It is shown that the numerical results agree with the experimental data.Compared with the coupled model with the flow in the inner domain governed by the Laplace equation,the present coupled model is more efficient and its solution procedure is more simple,which is particularly useful for the study on the effect of the nonlinear wave forces on a fixed box-shaped ship in a large harbor.     

Calculating actual crop evapotranspiration under soil water stress conditions with appropriate numerical methods and time step

Calculation of actual crop evapotranspiration under soil water stress conditions is crucial for hydrological modeling and irrigation water management. Results of actual evapotranspiration depend on the estimation of water stress coefficient from soil water storage in the root zone, which varies with numerical methods and time step used. During soil water depletion periods without irrigation or precipitation, the actual crop evapotranspiration can be calculated by an analytical method and various numerical methods. We compared the results from several commonly used numerical methods, including the explicit, implicit and modified Euler methods, the midpoint method, and the Heun's third‐order method, with results of the analytical method as the bench mark. Results indicate that relative errors of actual crop evapotranspiration calculated with numerical methods in one time step are independent of the initial soil water storage in the range of soil water stress. Absolute values of relative error decrease with the order of numerical methods. They also decrease with the number of time step, which can ensure the numerical stability of successive simulation of soil water balance. Considering the calculation complexity and calculation errors caused by numerical approximation for different time step and maximum crop evapotranspiration, the explicit Euler method is recommended for the time step of 1 day (d) or 2 d for maximum crop evapotranspiration less than 5 mm/d, the midpoint method or the modified Euler method for the time step of up to one week or 10 d for maximum crop evapotranspiration less than 5 mm/d, and the Heun's third‐order method for the time step of up to 15 d. Copyright © 2011 John Wiley & Sons, Ltd.