Eulerian spatial moments for solute transport in three-dimensional heterogeneous,dual-permeability media

A Eulerian analytical method is developed for nonreactive solute transport in heterogeneous, dual-permeability media where the hydraulic conductivities in fracture and matrix domains are both assumed to be stochastic processes. The analytical solution for the mean concentration is given explicitly in Fourier and Laplace transforms. Instead of using the fast fourier transform method to numerically invert the solution to real space (Hu et al., 2002), we apply the general relationship between spatial moments and concentration (Naff, 1990; Hu et al., 1997) to obtain the analytical solutions for the spatial moments up to the second for a pulse input of the solute. Owing to its accuracy and efficiency, the analytical method can be used to check the semi-analytical and Monte Carlo numerical methods before they are applied to more complicated studies. The analytical method can be also used during screening studies to identify the most significant transport parameters for further analysis. In this study, the analytical results have been compared with those obtained from the semi-analytical method (Hu et al., 2002) and the comparison shows that the semi-analytical method is robust. It is clearly shown from the analytical solution that the three factors, local dispersion, conductivity variation in each domain and velocity convection flow difference in the two domains, play different roles on the solute plume spreading in longitudinal and transverse directions. The calculation results also indicate that when the log-conductivity variance in matrix is 10 times less than its counterpart in fractures, it will hardly influence the solute transport, whether the conductivity field is matrix is treated as a homogeneous or random field.     

Determining the equivalent permeability tensor for fractured rock masses using a stochastic REV approach: Method and application to the field data from Sellafield,UK

A numerical procedure to determine the equivalent permeability tensor of a fractured rock is presented, using a stochastic REV (Representative Elementary Volume) concept that uses multiple realizations of stochastic DFN (Discrete Fracture Network) models. Ten square DFN models are generated using the Monte Carlo simulations of the fracture system based on the data obtained from a site characterization program at Sellafield, Cumbria, UK. Smaller models with varying sizes of from 0.25 m×0.25 m to 10 m×10 m are extracted from the generated DFN models and are used as two-dimensional geometrical models for calculation of equivalent permeability tensor. The DFN models are also rotated in 30º intervals to evaluate the tensor characteristics of calculated directional permeability. Results show that the variance of the calculated permeability values decreases significantly as the side lengths of the DFN models increase, which justifies the existence of a REV. The REV side length found in this analysis is about 5 m and 8 m with 20% and 10% acceptable variations, respectively. The calculated directional permeability values at the REV size have tensor characteristic that is confirmed by a close approximation of an ellipse in a polar plot of the reciprocal of square roots of the directional permeability.

Duality properties of Gorringe–Leach equations

In the category of motions preserving the angular momentum direction, Gorringe and Leach exhibited two classes of differential equations having elliptical orbits. After enlarging slightly these classes, we show that they are related by a duality correspondence of the Arnold–Vassiliev type. The specific associated conserved quantities (Laplace–Runge–Lenz vector and Fradkin–Jauch–Hill tensor) are then dual reflections of each other.     

复杂条件二维重力场及重力张量场空间波数域正演方法

随着传感器技术的发展,重力场与重力张量场测量技术发展迅速,为实现地下密度分布精细反演提供了数据保障。正演是反演的基础,解决任意密度分布复杂地质体重力场与重力张量正演高效、高精度计算问题,是实现重力高效、精细反演、人机交互反演解释的关键。针对起伏地形和任意密度分布这种复杂条件下二维重力场及重力张量场高效高精度正演问题,这里提出了一种空间波数混合域正演算法,其关键环节包括:①结合新的矩形二度体组合模型波数域表达式和一维Gauss-FFT算法,提出了一种任意密度分布和起伏地形下重力场及重力张量高效、高精度正演算法;②采用新的二维正演算法,计算观测最高点和最低点之间多个不同高度水平网格重力场及重力张量,结合三次样条插值方法,实现了起伏地形上重力场及重力张量场高效、高精度正演。模型算例结果表明,新方法具有高效、高精度的显著特点。     

地下目标体重力张量数据的边界识别与增强算法的研究

边界增强与识别在重力数据处理中占据重要地位,与传统重力异常数据相比,重力张量及其高阶分量对于直接反映异常体的边界具有更高的精度。当异常数据中的所有网格点的值均较低时,通过Sigmoid变换,可以实现高异常值网格数据的拉升,同时压缩低灰度级像素,从而凸显地质体边界,提高边界增强后图像的识别效果。文中利用张量及其分量构建常用的边界识别算法,通过组合体模型进行多种边界识别算法的试算,以比较分析各自的效果,并对结果进行Sigmoid变换。结果表明:对于张量高阶分量组合形式,水平梯度模、解析信号能基本反映浅异常体的边界,gzz水平梯度模能较好反映浅异常体边界,但三者均不能识别深异常体边界;Tilt梯度、Theta和ITA3效果不理想;ITA2能在有效均衡不同强度异常信号的同时,清晰地识别不同深度异常体的边界;采用Sigmoid变换,可以明显提高边界识别的识别效果。     

An analysis of horizontal dispersion due to the drift current with an Ekman layer

An analytical method for describing horizontal matter dispersion in shear currents is presented using a tensor expression from the point of view that matter dispersion due to the shear effect should be one of the principal mixing dilution processes. Although the behavior of horizontal dispersion is considerably more complicated than common longitudinal dispersion, the present study elucidates the vertical structure of dispersion and the dispersing process from the initial to the stationary stage, besides the usual depth-averaged dispersion coefficient at the stationary stage. As one of the typical applications of horizontal dispersion, dispersion due to the pure drift current with an Ekman layer is examined theoretically using the present method. This examination reveals that the displacement of the centroid and the major axis of dispersion are twisted in the vertical direction more than the direction of the current vector forming the Ekman spiral; that the variance increases in proportion to the third power of the elapsed time; and that the dispersion coefficient at the stationary stage remains constant, independent of the depth normalized by an Ekman layer thickness. Such dependence of the dispersion coefficient in the steady current is shown to be different from that in the oscillatory current, which is inversely proportional to the depth normalized by a Stokes layer thickness. This is considered to be induced by the difference of the vertical profiles of the first order moment in both currents, that is, the shear region of the first order moment is restricted around the floor by the alternation of the current shear in the oscillatory current while it is diffused in the whole depth in the steady current.     

用不完整的地震资料估计地震矩年变化率

在充分考虑现有地震资料的不完备性和震级服从两端截去泊松分布的条件下,建立了用历史地震资料和现代地震资料及考古地震资料计算地震矩年变化率的方法。计算了西南地区几个地震带的地震矩年变化率,并与地质资料得到的结果进行了比较,结果表明该方法是切实可行的     

Some aspects of head‐variance evaluation

We compare two methods of evaluating head covariance for two‐dimensional steady‐state flow in mildly heterogeneous bounded rectangular aquifers. The quasi‐analytical approach, widely used in stochastic subsurface hydrology, is based on the Green's function representation, and involves numerical four‐fold integration. We compare this approach with a numerical solution of the two‐dimensional boundary‐value problem for head covariance. We show that the finite differences integration of this problem is computationally less expensive than numerical four‐fold integration of slowly‐convergent infinite series. This revised version was published online in July 2006 with corrections to the Cover Date.     

地壳介质各向异性电性本构关系讨论

讨论了地壳介质中常见的两类电性各向异性。推导了长波长条件下薄中向异性电导率张量;提出了一种新的电导率物理模型并由此推导了与ＥＤＡ裂隙相适应的各向异性电导率张量。从直流电法和大地电磁测深法的角度分别讨论了这两种电性各向异性所显现的地表视电阻率、阻抗和电位特征。     

武定地震序列的震源参数与频率特征

利用武定地震序列数字化记录地震图资料研究了直接用速度谱和位移谱测定地震矩的方法,结果给出前者的误差比后者小５０％,两者无系统差。对序列地震震源参数的研究结果给出,地震矩Ｍ０在１０１２～１０１６（Ｎ·ｍ）之间,震源破裂半径ａ在１００～３５０ｍ范围,震源距ｒ或震级ＭＬ与近场波谱拐角频率ｆ０相关性不明显,序列地震应力降Δσ多数在１０～８０ＭＰａ的范围,表明武定地震序列是在高应力背景下发生的爆发性地震群。