球坐标系下谱元法三维地震波场模拟

谱元法已成为区域性乃至大陆性尺度地震波场模拟的重要工具.对于区域或大陆尺度层析成像而言,地球曲率不可忽略,此时模拟地震波传播采用球坐标系更为合适.本文从球坐标系下弹性波动方程弱形式出发,基于球坐标系变分原理给出了球坐标系下求解三维地震波方程的谱元法.另一方面,计算Fréchet敏感核是进行全波形反演的关键,本文借助伴随原理,推导了全波走时层析成像三维Fréchet敏感核表达式.为了验证球坐标系下谱元法的精度,我们将数值模拟结果与normal mode方法得到的解析解在1-D PREM模型下进行了对比.同时,我们将此方法应用到华北克拉通区域,以期获得地球内部结构精确成像.基于3-D全球径向各向异性地幔模型S362ANI和3-D地壳模型Crust1.0,我们建立了华北克拉通初始3-D背景模型,并将数值模拟结果与实际观测台站记录波形资料进行对比分析,利用互相关方法提取走时残差,最后给出了Fréchet敏感核在3-D空间中的分布,这些工作为下一步开展球坐标系下三维大尺度全波形反演奠定了基础.

     

Numerical Modeling of the Hyperbolic Mild-Slope Equation in Curvilinear Coordinates

The mild-slope equation is familiar to coastal engineers as it can effectively describe wave propagation in nearshore regions. However,its computational method in Cartesian coordinates often renders the model inaccurate in areas with irregular shorelines,such as estuaries and harbors. Based on the hyperbolic mild-slope equation in Cartesian coordinates,the numerical model in orthogonal curvilinear coordinates is developed. The transformed model is discretized by the finite difference method and solved by th...     

Applying invariant eigen-operator method to deriving normal coordinates of general classical Hamiltonian

For classical Hamiltonian with general form we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator (IEO) method (Fan et al. 2004 Phys. Lett. A 321 75) to derive them. The general matrix equation, which relies on M and L, for obtaining the normal coordinates of H is derived.     

起伏地表组合震源地震波场定向方法

多个震源组合激发通过改变激发延时,可以得到沿某方向传播的地震波场,即定向地震波场激发技术,它可用于特定目标体的照明与探测之中.本文以水平地表的组合震源定向激发原理为基础,推导了倾斜地表情况下的组合震源定向激发公式,并计算绘制了其理论方向图.另外本文将组合震源波场定向方法推广至任意起伏地表,根据惠更斯菲涅尔原理,提出了旋转坐标方法,即将水平坐标旋转至定向波场传播方向法向的倾斜坐标,可方便地计算震源传播至定向波场波前面的走时,作为组合震源的激发延时.根据本文提出的方法,我们分别计算了倾斜地表条件与复杂地表条件定向地震波场的组合震源延时参数,通过波动方程数值模拟技术得到的波场快照验证了本文方法的有效性.     

IMU/GPS组合导航系统自适应Kalman滤波算法

给出了IMU在地固坐标系中的误差方程,介绍并分析了自适应滤波和渐消Kalman滤波算法原理,然后将渐消因子引入到自适应滤波算法中,并将其应用到IMU/GPS松组合导航系统中,最后利用一个实际算例证明了该组合导航系统的有效性。     

彩色CRT显示器呈色域的确定

彩色显示器呈色域的确定是彩色管理系统中实现颜色空间转换的前提。不考虑亮度因素Y而仅把在CIE1931色度图上连接R、G、B三原色点形成的三角形区域认为是彩色显示器的呈色域,尚不能全面地描述显示器的呈色域。如果考虑亮度因素Y,那么,在不同的呈色亮度下,其呈色域的形状与大小是不同的。本文就彩色显示器在不同呈色亮度下呈色域的确定问题进行实验研究,得出相应结论。     

变形监测点三维坐标获取系统

从摄像机获取的图像信息出发计算三维空间中物体的几何信息,标志点像片上的二维平面坐标的与其三维空间位置是一一对应的。相片立体量测系统的主要目标就是通过像点计算机图像坐标的量测与相机姿态参数来求解相应物方三维坐标,并对误差来源和精度进行分析,最后讨论了监测点变形值的确定方法。详细研究了相机姿态参数确定的方法、目标点的准确定位和像点坐标的求取,根据前方交会得出监测点的物方坐标。通过研究和分析,近景摄影测量在建筑物等小变形体上应用,基本上能达到精度规定要求。     

Fast transform from geocentric to geodetic coordinates

 A new iterative procedure to transform geocentric rectangular coordinates to geodetic coordinates is derived. The procedure solves a modification of Borkowski's quartic equation by the Newton method from a set of stable starters. The new method runs a little faster than the single application of Bowring's formula, which has been known as the most efficient procedure. The new method is sufficiently precise because the resulting relative error is less than 10⁻¹⁵, and this method is stable in the sense that the iteration converges for all coordinates including the near-geocenter region where Bowring's iterative method diverges and the near-polar axis region where Borkowski's non-iterative method suffers a loss of precision. Received: 13 November 1998 / Accepted: 27 August 1999     

A new solution to the lagrange's case of the three‐body problem

The motion of three particles, interacting by gravitational forces, is studied in a new coordinate system given by the principal axes of inertia, as determined by Euler angles, and using the inertia principal moments and an auxiliar angle as coordinates. The solution to the particular Lagrange case of the three‐body problem is reviewed and solved in these new coordinates. This revised version was published online in July 2006 with corrections to the Cover Date.