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     

Numerical and experimental studies of a floating and liquid-filled membrane structure in waves

Linear theories to analyse a floating and liquid-filled membrane structure in head- and beam-sea waves have been presented. The dynamic solutions are based on a small perturbation of the static solution, and the hydroelastic deformation has been taken care of correctly to the first order of the incident wave amplitude. A new experiment has been carried out for measuring the dynamic tensions of a membrane. A comparison between the theories and experiment are presented for the dynamic hoop tension.     

Direct Calculation Methods of Hansen Coefficients and Their Derivatives

Seven direct calculation methods of Hansen coefficients and their derivatives are reviewed. The computational efficiencies of these methods are compared, and their computational stabilities are analyzed. We show that the recursion relations of Hansen coefficients can be used to determine the stabilities of calculation results. Finally, it is pointed out that Wnuk's method (double precision computation) and McClain's methods (quadruple precision computation) are stable, which can be used to calculate orbit perturbations. Because of small orbital eccentricities of most satellites, the perturbation calculations without singularities are required, and McClain's first method (quadruple precision computation) is recommended.     

Perturbed Robe’s circular restricted three-body problem under an Oblate Primary

This paper examines the existence and linear stability of equilibrium points in the perturbed Robe’s circular restricted three-body problem under the assumption that the hydrostatic equilibrium figure of the first primary is an oblate spheroid. The problem is perturbed in the sense that small perturbations are given to the Coriolis and centrifugal forces are being considered. Results of the analysis found two axial equilibrium points on the line joining the centre of both primaries. It is further observed that under certain conditions, points on the circle within the first primary are also equilibrium points. And a special case where the density of the fluid and that of the infinitesimal mass are equal (D = 0) is discussed. The linear stability of this configuration is examined; it is observed that the first axial point is unstable while the second one is conditionally stable and the circular points are unstable.     

稳定的保幅高阶广义屏地震偏移成像方法研究

以先进的波动理论为基础的波动方程保幅地震偏移成像是在给出正确位置的同时也给出真实振幅的一种特殊完善.作者从保幅单程波动方程的非稳态相移公式出发,基于反问题求解中常用的摄动理论,利用单平方根算子的渐进展开,从而推导出保幅叠前深度偏移方程的高阶广义屏形式;针对散射波场计算项对于横向变速介质的不稳定性,通过数学近似提出一个有效提高稳定性的策略,应用到波场递归外推过程中,从而得到一种稳定的保幅高阶广义屏叠前深度偏移算子.理论模型试算和实际资料处理表明,该方法不但可以更精确地使散射能量聚焦、归位,提高成像精度;而且可以输出正确反映地下反射系数的振幅信息,使AVO响应更加清晰,提高了AVO资料的分析精度.     

Oblique surface wave propagation over a small undulation on the bottom of an ocean

The problem of oblique water wave diffraction by small undulation of the bottom of a laterally unbounded ocean is considered using linear water wave theory. A perturbation analysis is employed to obtain the velocity potential, the reflection and the transmission coefficients up to the first order in terms of integrals involving the shape functions c(x) representing the bottom undulation. Finite cosine transform is used to find the first order potential, and this potential is utilised in obtaining the first order reflection and transmission coefficients. Some particular forms of the shape function representing an exponentially damped undulation, a single hump and a patch of sinusoidal ripples are considered and the integrals for the reflection and transmission coefficients are evaluated. For the exponentially damped undulation, it is observed that the reflection ceases much before transmission while for the single hump, reflection and transmission go hand in hand up to a certain value of the wavenumber, after which they vanish. For the patch of sinusoidal ripples having the same wavenumber, the reflection coefficient up to the first order is found to be an oscillatory function in the quotient of twice the component of the wavenumber along x-axis and the ripple wavenumber. When this quotient becomes one, the theory predicts a resonant interaction between the bed and free surface, and the reflection coefficient becomes a multiple of the number of ripples. High reflection of the incident wave energy occurs if this number is large. Also, when a patch of ripples having different wavenumbers is considered the same result follows. Known results for the normal incidence are recovered as special cases for the patch of sinusoidal ripples. The theoretical observations are shown computationally.     

非静力平衡下中小尺度扰动的不稳定发展

本文采用非静力平衡模式,使用摄动方法研究了里查逊数与中小尺度扰动的稳定性的关系。在零级近似和一级近似下,对称不稳定判据依次为RiF;在零级近似下斜压不稳定判据为Ri<-_(k2)~8     

Perturbations of the Kepler Problem in Global Coordinates

The usual action-angle variables for the Kepler Problem (the Delaunay variables) are not globally defined, leaving out some orbits (circular orbits or those lying on the xy-plane). Moreover they are trascendental functions of the physical variables, making it quite difficult to write the perturbed Hamiltonian. The way-out proposed here is to pass to a 8-dimensional rank-6 Poisson manifold, that is, to parametrize the state of the Kepler Problem with two 4-dimensional vectors mutually orthogonal and of equal norm. This revised version was published online in July 2006 with corrections to the Cover Date.     

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