单程波方程偏移算子高阶辛格式

针对地震偏移算法中单程波算子中e指数项的近似，提出一种高阶辛格式算法. 与非辛格式的近似、一阶辛格式近似和两步法进行数值对比表明，文中提出的高阶辛格式具有更高的精度. 脉冲响应的计算也表明文中的近似方法具有降低频散效应和适应横向变速的能力. 用Marmousi模型验证了对复杂构造的成像的能力，实际资料计算表明本文方法适合于较大深度的稳定准确成像.     

Three‐parameter discontinuous distributions for hydrological samples with zero values

A consistent approach to the frequency analysis of hydrologic data in arid and semiarid regions, i.e. the data series containing several zero values (e.g. monthly precipitation in dry seasons, annual peak flow discharges, etc.), requires using discontinuous probability distribution functions. Such an approach has received relatively limited attention. Along the lines of physically based models, the extensions of the Muskingum‐based models to three parameter forms are considered. Using 44 peak flow series from the USGS data bank, the fitting ability of four three‐parameter models was investigated: (1) the Dirac delta combined with Gamma distribution; (2) the Dirac delta combined with two‐parameter generalized Pareto distribution; (3) the Dirac delta combined with two‐parameter Weibull (DWe) distribution; (4) the kinematic diffusion with one additional parameter that controls the probability of the zero event (KD3). The goodness of fit of the models was assessed and compared both by evaluation of discrepancies between the results of both estimation methods (i.e. the method of moments (MOM) and the maximum likelihood method (MLM)) and using the log of likelihood function as a criterion. In most cases, the DWe distribution with MLM‐estimated parameters showed the best fit of all the three‐parameter models. Copyright © 2005 John Wiley & Sons, Ltd.     

间断有限元方法的数值频散分析及其波场模拟

数值求解波动方程是大尺度正演波场模拟、基于波动方程的地震偏移和反演成像的关键.本文针对求解二维声波方程的Runge-Kutta 间断有限元（RKDG）方法的数值频散问题,从理论推导和数值分析的角度进行了深入研究,并将其与近似解析离散化方法（Optimal Nearly Analytic Discrete Method,简称ONAD 方法）、Lax-Wendroff 修正方法、交错网格（Staggered-Grid,简称SG）方法的数值频散进行了比较研究.结果表明：RKDG方法以及近似解析离散化方法在压制数值频散方面要好于上述其他方法,特别是空间精度为3阶的RKDG方法,即使当空间步长取波长的一半,即一个波长内取2个网格点时,最大的频散误差也不超过1.67%.同时,我们也通过波场模拟对比研究了不同数值方法的数值频散问题,进一步直观地验证了数值频散的理论分析结果.     

非连续变形分析中块体大转动问题研究

原有非连续变形分析（DDA）采用一阶近似后的位移增量表达式更新块体构形,推导相关子矩阵,且对不同时步计算出的应变增量直接叠加,当模拟的块体发生大转动时往往会产生较大误差。为考虑块体转动与变形的耦合作用,引入先变形、后转动的块体位移增量表达式。重新推导了惯性力子矩阵,将块体转动时的离心力与科氏力加到荷载矩阵中。计算时对应变分量及其相关变量进行坐标变换与修正,并采用新引入的位移增量表达式计算块体顶点位移,进行后接触修正与更新块体构形。数值算例表明,改进后的程序能够消除转动带来的误差,自动考虑了块体转动时离心力和科氏力引起的变形,应变计算精度更高。改进方法克服了块体体积自由膨胀、应变场畸变等问题,给出了合理的块体应变。     

A discontinuous finite element suspended sediment transport model for water quality assessments in river networks

Suspended sediment plays an important role in the distribution and transport of many pollutants (such as radionuclides) in rivers. Pollutants may adsorb on fine suspended particles (e.g. clay) and spread according to the suspended sediment movement. Hence, the simulation of the suspended sediment mechanism is indispensable for realistic transport modelling. This paper presents and tests a simple mathematical model for predicting the suspended sediment transport in river networks. The model is based on the van Rijn suspended load formula and the advection–diffusion equation with a source or sink term that represents the erosion or deposition fluxes. The transport equation is solved numerically with the discontinuous finite element method. The model evaluation was performed in two steps, first by comparing model simulations with the measured suspended sediment concentrations in the Grote Nete–Molse Nete River in Belgium, and second by a model intercomparison with the sediment transport model NST MIKE 11. The simulations reflect the measurements with a Nash‐Sutcliffe model efficiency of 0.6, while the efficiency between the proposed model and the NST MIKE 11 simulations is 0.96. Both evaluations indicate that the proposed sediment transport model, that is sufficiently simple to be practical, is providing realistic results.     

Investigation of highly efficient algorithms for solving linear equations in the discontinuous deformation analysis method

Large‐scale engineering computing using the discontinuous deformation analysis (DDA) method is time‐consuming, which hinders the application of the DDA method. The simulation result of a typical numerical example indicates that the linear equation solver is a key factor that affects the efficiency of the DDA method. In this paper, highly efficient algorithms for solving linear equations are investigated, and two modifications of the DDA programme are presented. The first modification is a linear equation solver with high efficiency. The block Jacobi (BJ) iterative method and the block conjugate gradient with Jacobi pre‐processing (Jacobi‐PCG) iterative method are introduced, and the key operations are detailed, including the matrix‐vector product and the diagonal matrix inversion. Another modification consists of a parallel linear equation solver, which is separately constructed based on the multi‐thread and CPU‐GPU heterogeneous platforms with OpenMP and CUDA, respectively. The simulation results from several numerical examples using the modified DDA programme demonstrate that the Jacobi‐PCG is a better iterative method for large‐scale engineering computing and that adoptive parallel strategies can greatly enhance computational efficiency. Copyright © 2015 John Wiley & Sons, Ltd.     

Three-dimensional discontinuous deformation analysis (3-D DDA) using a new contact resolution algorithm

This paper presents a new contact calculating algorithm for contacts between two polyhedra with planar boundaries in the three-dimensional discontinuous deformation analysis (3-D DDA). In this algorithm, all six type contacts in 3-D (vertex-to-face, vertex-to-edge, vertex-to-vertex, face-to-face, edge-to-edge, and edge-to-face) are simply transformed into the form of point-to-face contacts. The presented algorithm is a simple and efficient method and it can be easily coded into a computer program. In this paper, formulations of normal contact, shear contact and frictional force submatrices based on the new method are derived and the algorithm has been programmed in VC⁺⁺. Examples are provided to demonstrate the new contact rule between two blocks.     

Finite cube elements method for calculating gravity anomaly and structural index of solid and fractal bodies with defined boundaries

In this paper, we present the finite cube elements method (FCEM); a novel numerical tool for calculating the gravity anomaly g and structural index SI of solid models with defined boundaries and variable density distributions, tilted or in normal position (e.g. blocks, faulted blocks, cylinders, spheres, hemispheres, triaxial ellipsoids). Extending the calculation to fractal objects, such as Menger sponges of different orders and bodies defined by polyhedrons, demonstrates the robustness of FCEM. In addition, approximating the cube element by a sphere of equal volume makes the calculation of gravitation and related derivatives much simpler. In gravity modelling of a sphere, cubes with edges of 100 m and 200 m achieve a good compromise between running time and overall error.
Displaying the distribution of SI of the studied models on contour maps and profiles will have a strong impact on the forward and inverse modelling of potential field data, especially for Euler deconvolution.
For Menger sponges, plots of gravity elements g and its derivatives show similar patterns independent of fractal order. Moreover, both the pattern and magnitude of SI are independent of fractal order, allowing the use of SI as a new invariant measure for fractal objects. However, SI pattern and magnitude strongly depend on the depth to the buried bodies as do other elements
In this study, we also present a new type of plot; the structural index against distance variation diagrams from which we extract the three critical SI ( CSI ) values, one per axis. The inversion of gravity anomaly data at CSI values gives the optimal mean location of the buried body.     

中国大陆及其周边块体的现时运动、变形及其动力学解释

运用块体不连续变形分析方法 ,对利用GPS测量数据解算中国大陆及其周边块体的位移进行分析。结果显示 ,除块体 2、10、13为近东西方向的运动 ,块体 15为近北东向的运动外 ,其余块体均朝南东或南东东方向运动。同时 ,各块体还以各自的角速度绕其重心旋转。整个研究区在南北方向是压缩的 ,所得的最大主应力方向与利用震源机制解与原地应力测量的结果总的来说大体一致。最后 ,对产生中国大陆及周边块体运动与变形的动力源进行了讨论