An analytical approach to small amplitude solutions of the extended nearly circular Sitnikov problem

The model of extended Sitnikov Problem contains two equally heavy bodies of mass m moving on two symmetrical orbits w.r.t the centre of gravity. A third body of equal mass m moves along a line z perpendicular to the primaries plane, intersecting it at the centre of gravity. For sufficiently small distance from the primaries plane the third body describes an oscillatory motion around it. The motion of the three bodies is described by a coupled system of second order differential equations for the radial distance of the primaries r and the third mass oscillation z. This problem which is dealt with for zero initial eccentricity of the primaries motion, is generally non integrable and therefore represents an interesting dynamical system for advanced perturbative methods. In the present paper we use an original method of rewriting the coupled system of equations as a function iteration in such a way as to decouple the two equations at any iteration step. The decoupled equations are then solved by classical perturbation methods. A prove of local convergence of the function iteration method is given and the iterations are carried out to order 1 in r and to order 2 in z. For small values of the initial oscillation amplitude of the third mass we obtain results in very good agreement to numerically obtained solutions.     

Approximate soil–structure interaction analysis by a perturbation approach: The case of soft soils

An approximate solution of the classical eigenvalue problem governing the vibrations of a relatively stiff structure on a soft elastic soil is derived through the application of a perturbation analysis. The full solution is obtained as the sum of the solution for an unconstrained elastic structure and small perturbing terms related to the ratio of the stiffness of the soil to that of the superstructure. The procedure leads to approximate analytical expressions for the system frequencies, modal damping ratios and participation factors for all system modes that generalize those presented earlier for the case of stiff soils. The resulting approximate expressions for the system modal properties are validated by comparison with the corresponding quantities obtained by numerical solution of the eigenvalue problem for a nine-story building. The accuracy of the proposed approach and of the classical normal mode approach is assessed through comparison with the exact frequency response of the test structure.     

Oblique wave scattering by undulating porous bottom in a two-layer fluid: Fourier transform approach

The problem involving scattering of oblique waves by small undulation on the porous ocean bed in a two-layer fluid is investigated within the framework of linearised theory of water waves where the upper layer is free to the atmosphere. In such a two-layer fluid, there exist waves with two different wave numbers (modes): wave with lower wave number propagates along the free surface whilst that with higher wave number propagates along the interface. When an oblique incident wave of a particular mode encounters the undulating bottom, it gets reflected and transmitted into waves of both modes so that some of the wave energy transferred from one mode to another mode. Perturbation analysis in conjunction with Fourier transform technique is used to derive the first-order corrections of velocity potentials, reflection and transmission coefficients at both modes due to oblique incident waves of both modes. One special type of undulating bottom topography is considered as an example to evaluate the related coefficients in detail. These coefficients are shown in graphical forms to demonstrate the transformation of water wave energy between the two modes. Comparisons between the present results with those in the literature are made for particular cases and the agreements are found to be satisfactory. In addition, energy identity, an important relation in the study of water wave theory, is derived with the help of the Green’s integral theorem.     

地震散射波的高精度数值模拟与振幅分析

随着地震勘探要求和技术的不断提高,散射波地震勘探方法逐渐引起人们的重视,尤其在构造复杂地区的高精度勘探中,散射波理论具有广泛的应用前景.本文在讨论了现阶段几种散射波数值模拟方法的利弊后,设计了一种基于微扰论的FK域积分法,在散射场的二次震源和空间能量衰减处理两方面做了改进,其计算精度和效率均得到了提高.此外,采用该算法针对散射波动力学进行了正演模拟试算,从扰动介质空间分布和扰动量两个角度定量地分析了散射波振幅动力学方面的特征.在此基础上得到了五个经验常数,并给出了对应的计算公式和物理意义,通过这五个常数可以划分散射波不同形态的动力学特征.     

各向异性双相介质中多极源声波测井理论研究

将各向异性地层模拟为横向各向同性双相介质 ,使其对称主轴与井孔中心轴线相垂直 .本文针对井孔模型下的多极源声波测井问题提出了一种解析的摄动方法 .将各向异性双相介质看作是由对应的各向同性双相介质加上摄动部分而组成 ,并引入 5个关于弹性模量偏离各向同性时的摄动量 ,对对称主轴与井轴垂直的各向异性双相介质的多极源声波测井问题进行了系统的理论研究和分析 ,严格求解了井孔内外的零级和一级近似声波场 .发现在n级多极源激发下 ,井孔中不仅出现n级多极声场 ,而且还能激发出与各向同性地层时不相同的高于和低于n级的多极声波场     

基于扰动模式的四维变分资料同化系统框架的设计完善和数值试验

为了建立一个应用于区域数值预报的四维变分资料同化（4DVar）系统,在近期开发的扰动预报模式GRAPES_PF基础上,开发完善增量四维变分同化系统框架。该框架中暂不包含物理过程（长短波辐射、边界层过程、对流参数化和云微物理等）。对比业务使用的GRAPES 3DVar系统,增加了温度控制变量。将无量纲Exner气压与流函数的线性风压平衡方程直接在地形追随垂直坐标面上求解,且通过广义共轭余差法（GCR）求解扰动亥姆霍兹（Helmholtz）伴随方程。利用人造“探空”资料对2015年10月台风“彩虹”进行了理想数值试验。试验结果表明,所开发的扰动四维变分同化框架得到了预期的结果,即同化更多资料并反复受到模式约束的四维变分同化系统能有效改善初值质量,进而改善区域数值预报。建立的区域四维变分同化框架合理可行,为进一步发展包含完整物理过程的区域四维变分同化系统奠定了研究基础。      

基于CNOP方法的台风目标观测中三种敏感区 确定方案的比较研究

在目标观测中,敏感区的确定是个关键性的问题。本文详细研究了如何用条件非线性最优扰动（CNOP）方法确定敏感区。提出了三种确定敏感区的方案:水平投影方案、单点能量投影方案以及垂直积分能量方案。比较了三种方案确定的敏感区的差异,分析了它们所阐释的物理意义,讨论了它们的优缺点,并通过理想回报试验考查了不同方案确定的敏感区的有效性。对六个台风个例的应用结果显示,单点能量投影方案与垂直积分能量方案下识别的敏感区较为相似,二者与水平投影方案确定的敏感区则有较大的区别。两种能量方案确定的敏感区更多地反映了环境场对台风的影响,而水平投影方案则反映了台风自身对流不对称性结构对台风发展变化的影响。理想回报试验结果表明,由两种能量方案确定的敏感区对预报误差能量的减小程度以及路径预报的改善程度都要大于水平投影方案确定的敏感区的效果,且垂直积分能量方案确定的敏感区的有效性最高。而在强度预报方面,三种方案对预报效果的改善程度相当。因此,总的说在台风目标观测研究中,利用CNOP方法确定敏感区时,垂直积分能量方案是较佳的方案。     

Analytic continuation of quasi-periodic orbits from non-linear periodic modes

A new theory is formulated for the analytic continuation of quasi-periodic orbits from non-linear, periodic modes of a two degree-of-freedom system in rotating coordinates. Formal solutions of the equations of motion are developed in series expansions, with the non-linear modes as reference solutions. Conditions are determined on the existence and boundedness of the time-dependent coefficients of the velocity field. Boundedness properties of the orbits are specified by an orbit function derived from the Jacobi integral.     

传输铁塔对地磁观测台站影响的实验与排除

本文总结了地面上铁磁性物质感应磁场现场测量结果,较详细地描述其感应磁场的分布特征。它对地磁台站的建设与环境保护,分析与排除人为干扰因素有一定的参考意义。文中还分析菏泽地震遥测传输铁塔对地磁观测的干扰情况。结果认为,该铁塔的感应磁场没有影响到地磁观测台。     

粘弹性拉张型地震破裂过程的解析解

本文应用包括地壳破裂发震过程中具有激发及衰减的非线性Rayleigh阻尼,用Voigt粘弹性模型表示地壳,它能更全面地反映地壳介质分子之间的内摩擦造成的粘滞性阻尼,在数学方法上,用解非线性问题解析法的摄动理论结合动坐标的富氏级数,把问题的非线性控制方程组化为各阶线性化的控制方程组后,再简化为标准的Mathieu方程构成的耦连方程组,再用WKBJ方法,给出其在稳定区域的近似解,从而得出了问题的解析解。