Scattering of a spherical pulse from a small inhomogeneity: Dilatation and rotation

Perturbations in elastic constants and density distinguish a volume inhomogeneity from its homogeneous surroundings. The equation of motion for the first order scattering is studied in the perturbed medium. The scattered waves are generated by the interaction between the primary waves and the inhomogeneity. First order scattering theory is modified to include the source term generating the primary waves. The body force equivalent to the scattering source is presented in a convenient form involving the perturbations in wave velocities and gradient of density perturbation. A procedure is presented to study the scattering of a spherical pulse from a small inhomogeneity, in time domain. The size of inhomogeneity is assumed small as compared to its distance from source and receiver. No restrictions are placed on the positions of source, receiver and inhomogeneity. The dilatation and rotations are calculated for a pulse scattered from an arbitrary point in a spherical volume. The aggregate of the scattered phases from all the points of the inhomogeneity, reaching at a fixed receiver, gives the amount of scattering from the inhomogeneity. The interaction of bothP andS waves with inhomogeneity are considered. Dilatation and rotations for scattering are obtained as integral expressions over the solid angle of inhomogeneity. These expressions are computed numerically, for hypothetical models. The effects of source (unit force) orientations, velocity and density perturbations, and size of inhomogeneity, on the scattered phases, are discussed.     

Clast Fabric in Relict Periglacial Colluvium, Salamanca Re-Entrant, Southwestern New York, USA

Samples of macrofabric data obtained from colluvial deposits near the late-Wisconsinan glacial margin display widely divergent characteristics. Those from highly weathered and jointed sandstone plot as girdle distributions. Samples from red colluvium of early-Wisconsinan age form moderately strong clusters. Fabrics from shallow depth in medium-textured brown colluvium of late-Wisconsinan age generally have modes aligned with the local slope but are weak, and appear to have been modified by frost heaving. Clasts in the basal layers of an overlying loess unit were emplaced by frost heaving from the brown colluvium and have very weak or uniform fabrics. Particle shape exerts an influence on fabric strength in the brown colluvium, with samples composed of more elongated clasts displaying stronger fabrics. Fabrics from near-surface deposits show generally weaker shape and strength characteristics and higher inclinations than those at depth. Calculated seasonal frost penetration is consistent with the depth to which weaker, more steeply inclined fabrics are found. Sampling in relict periglacial deposits should be performed only below the level of disturbance by seasonal frost.     

理论变异函数球状模型的加权线性规划法似合

对理论变异函数球状模型及其套合结构拟合这一问题作了探讨，提出了加权线性规划拟合法。同于该法在目标函数中既可考虑到对不同滞后h下所得实验变异函数值进行加权，又可保证拟合成功，同时还可进行人工干预，因此，方法综合了现有加权多项式拟合法及线性规划拟合法的各自优点，且在计算上较目标规划拟合法更为简单。     

掺Zn球形氢氧化镍的研究

采用化学沉淀法制备球形氢氧化镍,通过对制备条件pH值、添加剂量、搅拌强度的研究,探讨了其对掺Zn球形氢氧化镍     

论用球谐函数拟合地幔地震波品质因数Q值空间分布

本文引用S.J.Duda所导出的吸收特征时间t~*与震中距离△的关系,由地震台网观测的地震波振幅A和周期T,求得观测的t_0~*,及t_0~*～△的关系函数,用以拟合不同周期范围地震波品质因数Q 值随深度的分布Q(h),从而计算理论的t~*,再由t~*的残差δt~*与δQ 的关系参照A.M.Dzjewonskj 拟合地幔地震波速度三维分布的方法运用球谐函数的关系拟合地幔地震波品质因数Q 值的三维空间分布。     

Spectral analysis using orthonormal functions with a case study on the sea surface topography

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Spherical harmonics are orthonormalized using the Gram-Schmidt process in a function space. The problem of linear dependence of spherical harmonics over the oceans is studied using the Gram matrices and consequently three sets of orthonormal (ON) functions have been constructed. For the process an efficient formula for computing inner products of spherical harmonics has been developed. Important spectral properties of the ON functions are addressed. The ON functions may be used for representing the sea surface topography (SST) in the analysis of satellite altimeter data. The geoid error can be transformed to a representation by the ON functions and hence the comparison of powers of the geoid error and the SST signal only over the oceans is possible, leading to a better way of determining the cut-off frequency of the SST in the simultaneous solution using satellite altimeter data. As a case study, the modified Levitus SST is expanded into the ON functions. The results show that 99.90 per cent of that signal's energy is contained within degree 24 of the orthonormal functions. Such expansions also render better spectral behaviour of oceanic signals as compared to that from spherical harmonic expansions. The study shows that these generalized Fourier functions are suitable for spectral analyses of oceanic signals and they can be applied to future altimetric mission where the geoid and the SST are to be recovered.     

关于Stokes公式的球面卷积和平面卷积的注记

讨论了Stokes公式球面卷积和平面卷积形式的近似性和严密性问题,分析了Stokes函数球面卷积形式和平面卷积形式的关系,推导了其间的差值表达式,估算了最大差值及其对计算大地水准面差距的误差影响。同时指出,将顾及Stokes函数全项的平面卷积公式称为严密公式的提法,仅仅是相对仅顾及Stokes函数首项的简单平面卷积公式而言,认为更合理的提法应该是“高精度Stokes平面近似卷积公式”。理论分析表明,球面卷积不可能严格转化为等效的平面卷积。     

NOC model of the earth's main magnetic field

The international geomagnetic reference field (IGRF) is a standard model for describing the spatial structure and temporal variation of the earth抯 main magnetic field[1—3]. The first IGRF model, designated IGRF 1965, was adopted by IAGA in 1968[4]. In l…