The development of stochastic space transformation and diagrammatic perturbation techniques in subsurface hydrology

This paper develops concepts and methods to study stochastic hydrologic models. Problems regarding the application of the existing stochastic approaches in the study of groundwater flow are acknowledged, and an attempt is made to develop efficient means for their solution. These problems include: the spatial multi-dimensionality of the differential equation models governing transport-type phenomena; physically unrealistic assumptions and approximations and the inadequacy of the ordinary perturbation techniques. Multi-dimensionality creates serious mathematical and technical difficulties in the stochastic analysis of groundwater flow, due to the need for large mesh sizes and the poorly conditioned matrices arising from numerical approximations. An alternative to the purely computational approach is to simplify the complex partial differential equations analytically. This can be achieved efficiently by means of a space transformation approach, which transforms the original multi-dimensional problem to a much simpler unidimensional space. The space transformation method is applied to stochastic partial differential equations whose coefficients are random functions of space and/or time. Such equations constitute an integral part of groundwater flow and solute transport. Ordinary perturbation methods for studying stochastic flow equations are in many cases physically inadequate and may lead to questionable approximations of the actual flow. To address these problems, a perturbation analysis based on Feynman-diagram expansions is proposed in this paper. This approach incorporates important information on spatial variability and fulfills essential physical requirements, both important advantages over ordinary hydrologic perturbation techniques. Moreover, the diagram-expansion approach reduces the original stochastic flow problem to a closed set of equations for the mean and the covariance function.     

Errors Due to the Common Ray Approximations of the Coupling Ray Theory

The common ray approximation considerably simplifies the numerical algorithm of the coupling ray theory for S waves, but may introduce errors in travel times due to the perturbation from the common reference ray. These travel-time errors can deteriorate the coupling-ray-theory solution at high frequencies. It is thus of principal importance for numerical applications to estimate the errors due to the common ray approximation.We derive the equations for estimating the travel-time errors due to the isotropic and anisotropic common ray approximations of the coupling ray theory. These equations represent the main result of the paper. The derivation is based on the general equations for the second-order perturbations of travel time. The accuracy of the anisotropic common ray approximation can be studied along the isotropic common rays, without tracing the anisotropic common rays.The derived equations are numerically tested in three 1-D models of differing degree of anisotropy. The first-order and second-order perturbation expansions of travel time from the isotropic common rays to anisotropic-ray-theory rays are compared with the anisotropic-ray-theory travel times. The errors due to the isotropic common ray approximation and due to the anisotropic common ray approximation are estimated. In the numerical example, the errors of the anisotropic common ray approximation are considerably smaller than the errors of the isotropic common ray approximation.The effect of the isotropic common ray approximation on the coupling-ray-theory synthetic seismograms is demonstrated graphically. For comparison, the effects of the quasi-isotropic projection of the Green tensor, of the quasi-isotropic approximation of the Christoffel matrix, and of the quasi-isotropic perturbation of travel times on the coupling-ray-theory synthetic seismograms are also shown. The projection of the travel-time errors on the relative errors of the time-harmonic Green tensor is briefly presented.     

Improved First-Order Approximation of Group Velocities in Weakly Anisotropic Media

A first-order approximation of the group velocity is derived for qP and qS waves in weakly anisotropic media. The formula gives an explicit expression of the group velocity in terms of elastic parameters and wave normal and is independent of any reference isotropic media. The approximated group velocity differs from the first order phase velocity in direction and in magnitude, the difference being of the first order in direction and the second order in magnitude. The accuracy of the approximate formula is tested on two examples of TI media. The formula well approximates the qS-waves group velocity surface even in the presence of triplications.     

Landsat 7图像快速几何校正方法研究

Landsat 7采用双向扫描的方式，由于扫描非线性及卫星姿态和轨道的波动，使得建立卫星视线的计算量增大。引入一种求视线的快速方法，将图像上的扭曲分解为标称扫描镜及卫星运动引起的和7个偏离标称运动的微扰量引起的两个部分，详细分析了各个微扰量造成的影响，建立了一个新的视线求解方程。最后用实际的数据验证了方法的速度和精度。     

西藏高原地形扰动对其降水分布影响的研究

利用离散谱空间变换中谱能不变性约束下的谱分析方法和引进相对地形高程(地形扰动)概念,研究了西藏高原地形强迫对该区降水分布的影响机制。研究表明,在相对最大降水高度之下,所谓地形-降水分布剖面一致性(即降水分布曲线相似于地形起伏曲线,雨峰雨谷和山峰山谷基本一一对应)的经典结论在西藏高原不能完全满足。频谱空间中的地形-降水锁相关系能够更本质地反映出地形性降水分布的物理特征。揭示出,两种不同的地形-降水锁相关系即分别对应西藏高原的两种地形-降水分布形态,即雨峰雨谷和山峰山谷基本一一对应的共振分布型;降水随地形增高或增或减的漂移分布型。     

基于摄动有限元方法对梁结构损伤的识别

结构损伤的定量识别是工程技术中急待解决的问题。利用矩阵摄动和结构有限元动力学理论推出梁结构损伤程度定量识别的公式和方法,该方法仅需要在役结构的固有频率测量值就可识别结构的损伤位置和损伤程度,而且可以识别结构的老化程度,避免了由模态振型识别损伤,因测量自由度不足带来的误差,通过对一钢悬臂梁损伤识别的数值仿真,证明了该方法的有效性。该方法具有较大的工程应用价值。