Numerical analysis of the symmetric methods

Aimed at the initial value problem of the particular second-order ordinary differential equations,y =f(x, y), the symmetric methods (Quinlan and Tremaine, 1990) and our methods (Xu and Zhang, 1994) have been compared in detail by integrating the artificial earth satellite orbits in this paper. In the end, we point out clearly that the integral accuracy of numerical integration of the satellite orbits by applying our methods is obviously higher than that by applying the same order formula of the symmetric methods when the integration time-interval is not greater than 12000 periods.     

Low-low satellite-to-satellite tracking: a comparison between analytical linear orbit perturbation theory and numerical integration

Low-low satellite-to-satellite tracking (ll-SST) range-rate observations have been predicted by two methods: one based on a linear perturbation theory in combination with the Hill equations, and one based on solving the equations of motion of two low-flying satellites by numerical integration. The two methods produce almost equivalent Fourier spectra of the range-rate observations after properly taking into account a few resonant terms. For a typical GRACE-type configuration, where the two satellites trail each other at a distance of 300 km at an altitude of 460 km, and in the presence of the EGM96 gravity field model, complete to spherical harmonic degree and order 70, the agreement between the Fourier spectra is about 1 mm/s compared to a root-mean-square (RMS) value of more than 220 mm/s for the range-rate signal. The discrepancy of 1 mm/s can be reduced significantly when not taking into account perturbations caused by the J₂ term. Excluding the J₂ term, the agreement between the two methods improves to 0.4 mm/s compared to a RMS value of 6 mm/s for the range-rate signal. These values are 0.01 and 2.3 mm/s when ignoring the spectrum for frequencies below two cycles per orbital revolution, reducing the discrepancy even further to about 0.5% of the signal. The selected linear perturbation theory is thus capable of modeling gravity field induced range-rate observations with very high precision for a large part of the spectrum.     

Analysis and classification of hyperspectral data for mapping land degradation: An application in southern Spain

Desertification is a severe stage of land degradation, manifested by “desert-like” conditions in dryland areas. Climatic conditions together with geomorphologic processes help to mould desert-like soil surface features in arid zones. The identification of these soil features serves as a useful input for understanding the desertification process and land degradation as a whole. In the present study, imaging spectrometer data were used to detect and map desert-like surface features. Absorption feature parameters in the spectral region between 0.4 and 2.5 μm wavelengths were analysed and correlated with soil properties, such as soil colour, soil salinity, gypsum content, etc. Soil groupings were made based on their similarities and their spectral reflectance curves were studied. Distinct differences in the reflectance curves throughout the spectrum were exhibited between groups. Although the samples belonging to the same group shared common properties, the curves still showed differences within the same group.Characteristic reflectance curves of soil surface features were derived from spectral measurements both in the field and in the laboratory, and mean reflectance values derived from image pixels representing known features. Linear unmixing and spectral angle matching techniques were applied to assess their suitability in mapping surface features for land degradation studies. The study showed that linear unmixing provided more realistic results for mapping “desert-like” surface features than the spectral angle matching technique.     

Application of Linear Thermodynamics to the Atmospheric System. Part Ⅰ: Linear Phenomenological Relations and Thermodynamic Property of the Atmospheric System

从一般的热力学原理或其它自然原理对唯象关系所强加的限制，能够演绎出大气系统的一系列热力学性质。利用非平衡态线性热力学导出了湍流K闭合理论中湍流交换系数同唯象系数的关系，从理论上证明大气系统热量湍流输送同水泡之间存在交叉耦合，还导出了湍流强度同速度和位温梯度的关系，从而证明速度和位温空间分布的非均匀性是湍流之源。并证明湍流强度定理，不可压缩气体和各向同性湍流大气中，湍流强度正比于速度与位温梯度的标积。进而证明大气涡旋定理，位温的切变将导致涡旋运动或各种环流运动，速度涡度等于速度同位温相对梯度的矢积。展现了线性热力学在大气系统的应用前景。     

Dynamic processes of a simple linear dune—a study in the Taklimakan Sand Sea, China

Samples of dune sands, surveys of the morphology and field measurements of wind velocity and direction of a simple linear dune in Taklimakan Sand Sea show that the airflow and sand flux vary with the change of wind direction on the dune surface. Decrease of the airflow stress on the lee flank does not result in much decrease of the sand flux because of the low threshold shear velocities and the airflow conditions. There are no significant relations between the sand flux on the lee flank and the angle of incidence of the airflow. The low threshold shear velocities and the maintenance of the sand flux at the lee flank are the main mechanisms keeping the linear shape of the dunes. Measurements of the sand flux shows that it reaches a maximum on the crest of the dune. The grain size of the transported sands has some differences compared to that of the dune surface. The sands transported are finer than that on the dune surface, but better sorted under the influence of the medium to low wind activity. The field experiment results exhibit that it is possible for the dunes to be shaped as linear dunes during the processes of accumulation and elongation.     

滑带土动力学性质试验研究

为了研究地震高烈度区老滑坡的复活变形原因,本文对滑坡滑带土的动力学特性进行了系列研究。本次试验采用扰动土样,制样基本物理指标按滑带土的现场测试指标确定,在不固结不排水条件下,运用MTS810Teststar程控液压伺服土动三轴仪对单个样品逐级放大动应力的分级试验方法进行。侧向压力 (围压 )分别采用 100kPa、20 0kPa、300kPa三级,通过施加轴向振动荷载 (力 )模拟地震作用,振动波形为正弦波,频率为 1Hz,振幅随试样性质确定。研究结果表明,滑带土在动荷载作用下的动力学性质与其静荷载作用下的力学性质有着较大的差异,主要表现在滑带土的动应力与动应变关系的非线性、滞后性及变形积累特点,动弹性模量与动强度的显著降低以及动阻尼比的显著增大特性。这揭示了动力作用下的滑坡复活原因之一,同时为滑坡稳定性评价和动力作用下的变形机制模拟分析提供了基础资料,也为分析滑带土动力本构模型提供了基本内容。     

Scattering of elastic waves by a general anisotropic basin. Part 2: a 3D model

Scattering of plane harmonic waves by a three‐dimensional basin of arbitrary shape embedded within elastic half‐space is investigated by using an indirect boundary integral equation approach. The materials of the basin and the half‐space are assumed to be the most general anisotropic, homogeneous, linearly elastic solids without any material symmetry (i.e. triclinic). The unknown scattered waves are expressed in terms of three‐dimensional triclinic time harmonic full‐space Green's functions. The results have been tested by comparing the surface response of semi spherical isotropic and transversely isotropic basins for which the numerical solutions are available. Surface displacements are presented for a semicircular basin subjected to a vertical incident plane harmonic pseudo‐P‐, SV‐, or SH‐wave. These results are compared with the motion obtained for the corresponding equivalent isotropic models. The results show that presence of the basin may cause significant amplification of ground motion when compared to the free‐field displacements. The peak amplitude of the predominant component of surface motion is smaller for the anisotropic basin than for the corresponding isotropic one. Anisotropic response may be asymmetric even for symmetric geometry and incidence. Anisotropic surface displacement generally includes all three components of motion which may not be the case for the isotropic results. Furthermore, anisotropic response strongly depends upon the nature of the incident wave, degree of material anisotropy and the azimuthal orientation of the observation station. These results clearly demonstrate the importance of anisotropy in amplification of surface ground motion. Copyright © 2003 John Wiley & Sons, Ltd.     

APPLICATION OF SOME MECHANICAL CONCEPTS TO STRUCTURAL GEOLOGY

This paper discusses some mechanical concepts that have been largely applied to structural geology and tectonics, and addresses the problems and misunderstandings in use of these mechanical terms. The purpose is to stimulate the interests for structural geologists in using the mechanical principles and methods correctly to solve the geodynamic problems.     

宜兴抽水蓄能电站试验洞的反分析研究

结合江苏宜兴抽水蓄能电站地下厂房试验洞量测资料的分析,研究了成层各向异性岩体中洞室工程问题的反分析方法。采用分层均质模型进行反分析计算。计算区域的各层岩层均被分别视为均质各向同性体,初始地应力假设呈线性分布。有限元分析中,对倾斜成层的岩层、软弱夹层及断层节理等分别划分了单元,据以模拟成层岩体的各向异性特征。为使计算过程简化,对离洞室较远的岩层拟按地质资料对材料特性参数赋值,反分析计算的目标未知数为初始地应力和试验洞相邻围岩的弹性模量。结果表明,与工程实践符合较好。