Computational properties of a new horizontal staggered grid

On variable configuration in the horizontal direction, Winninghoff[1] had some discussions in the 1960s. Subsequently, according to the thoughts of Winning- hoff, Liu Yudi[2―9] has widely and deeply studied al- most all the existing horizontal grids from the fre- quency and group velocity of inertia gravity and Rossby waves. Results show that although Arakawa C grid is the best one among all existing horizontal grids, it also has some shortcomings. For example, there is still an “average…     

A Relative Moment Tensor Inversion Technique Applied to Seismicity Induced by Mining

Summary. Studies of source mechanisms of mining-induced seismic events play an important role in understanding the various modes of failure observed around underground excavations and enable the geometry of likely planes of failure to be determined. These planes can be mapped using conventional techniques, for example, geological fracture mapping. However, such an approach is often problematical due to limited access to the site and/or poor exposures (if any) of the failure plane. An added difficulty is that planes of failure often do not follow faults of geological origin, but are related to the geometry of the advancing stope face. For example, the development of face-parallel shear zones ahead of deep-level stope faces. In such cases, the stresses induced by mining dominate over the geological structure in the critical region close to the stope face. Seismic methods therefore have the potential of being a practical method of studying the development of seismic shear zones underground.Slip on such a failure plane generates a three dimensional elastic wave that propagates through the rockmass, carrying a wealth of information regarding the source rupture process. The ground motions caused by the passage of the wave can be recorded by arrays of sensitive instruments called seismometers. These sets of recordings (seismograms) provide the basic data that seismologists use to study these elastic waves as they propagate through the Earth. Conventional seismic analyses provide scalar measurements of the rupture size and intensity. However, through a process known as moment tensor inversion (MTI), the seismograms recorded from a seismic event can be used to calculate a moment tensor that describes the three dimensional nature of the source mechanism. Interpretation of the moment tensor gives insight into whether the rockmass failed in tension, compression or shear and indicates the direction of movement and the failure plane.Moment tensor solutions computed using conventional MTI methods are sensitive to noise and may be biased due to systematic errors in the measurements. The primary objective of this study was to develop a robust MTI method to estimate the moment tensors of clusters of seismic events recorded in the underground environment. To achieve this, three hybrid MTI methods were developed by the author. These methods involve different iterative weighting schemes designed to enhance the accuracy of the computed moment tensors by decreasing the effect of outliers (data points whose residuals lie far from the mean or median error). The additional information required for hybrid methods is obtained by considering a spatial cluster of seismic events and assuming that the waves generated by each event in the cluster follow a similar path through the rockmass and allowing a common ray-path to be assumed. Hence the unknown effect of the heterogeneous rockmass on the waveform is similar for all the events in the cluster.The final objective was to determine whether the techniques developed could be successfully applied to real data. The hybrid MTI methods using the median and the weighted mean correction were applied to a cluster of 10 events, having remarkably similar waveforms, recorded at Oryx Gold Mine. For comparative purposes, the more conventional absolute method was also applied. The solutions computed using the hybrid MTI with a median correction displayed a distinct improvement after the iterative residual correction procedure was applied, in contrast to the solutions obtained from the absolute method. The radiation patterns and fault-plane solutions from the hybrid method showed a high degree of similarity, and were probably more accurate reflections of reality. These observations are very encouraging and point towards the potential for using the hybrid MTI method with a median correction as a standard processing tool for mine seismicity.The implications of this work are that a robust method for calculating the focal mechanisms of clusters of seismic events induced by mining activities has been developed. Regular application will lead to a better understanding of rock fracture processes and to improved safety underground.     

关于矩阵A~(-1)B的一个注记

本文讨论了对求解差分方程有用的矩阵A~(-1)B的范数。胡家赣曾于1983年给出一个关于‖A~(-1)B‖的估计的定理。然而,这里给出一个比原来的证明更为简单的新的证明。     

The mimetic finite difference method on polygonal meshes for diffusion-type problems

New mimetic discretizations of diffusion-type equations (for instance, equations modeling single phase Darcy flow in porous media) on unstructured polygonal meshes are derived. The first order convergence rate for the fluid velocity and the second-order convergence rate for the pressure on polygonal, locally refined and non-matching meshes are demonstrated with numerical experiments. The work was partly performed at Los Alamos National Laboratory operated by the University of California for the US Department of Energy under contract W-7405-ENG-36. The U.S. Government’s right to retain a non-exclusive, royalty free license in and to any copyright is acknowledged. The research of the first author was supported by a grant from the Los Alamos Computer Science Institute (LACSI).     

Comparison between TVD-MacCormack and ADI-type solvers of the shallow water equations

A total variation diminishing (TVD) modification of the MacCormack scheme is developed for simulating shallow water dynamics on a uniform Cartesian grid. Results obtained using conventional and deviatoric forms of the conservative non-linear shallow water equations (SWEs) are compared for cases where the bed has a varying topography. The comparisons demonstrate that the deviatoric form of the SWEs gives more accurate results than the conventional form, in the absence of numerical balancing of the flux-gradient and source terms. A further comparison is undertaken between the TVD-MacCormack model and an alternating direction implicit (ADI) model for cases involving steep-fronted shallow flows. It is demonstrated that the ADI model is unable to predict trans-critical flows correctly, and artificial viscosity has to be introduced to remove spurious oscillations. The TVD-MacCormack model reproduces all flow regimes accurately. Finally, the TVD-MacCormack model is used to predict a laboratory-scale dyke break undertaken at Delft University of Technology. The predictions agree closely with the experimental data, and are in excellent agreement with results from an alternative Godunov-type model.     

几种台风初始化方法及其对比实验

利用中尺度MM5V3模式及其伴随系统，运用四维变分同化方法，将Bogus台风作为观测资料进而优化台风初始场，对0422号台风个例进行了数值模拟和试验，并与传统Bogus方法和Nudging方法进行比较。结果表明，经过BDA方案优化的台风初始场更加接近实际台风的结构，有效地提高了台风路径和强度预报的准确率。     

北京市人工增雨效果评估方法分析

用序列试验法、回归分析法、双比分析法和区域回归数值模拟试验方案4种效果评估方法对北京地区2001~2004年6~9月的37次火箭、高炮催化作业进行效果评估,并比较各种方法的优缺点。结果表明:①这4种方案统计结果均得到显著的增雨效果,平均增雨分别为:用序列试验的方法6.99%,用回归分析法30.68%,双比分析法20.11%,区域回归数值模拟试验方案13.37%。②误差分析表明,区域回归数值模拟试验方案产生的绝对误差仅为2.1%~2.2%,是一种较科学的评价方法。     

基于提升格式小波包变换的SAR图像去噪

基于信号和噪声在提升格式小波分解中呈现出的不同特性，提出了一种新的小波包去噪算法。该算法采用提升格式小波对SAR图像进行最优小波包分解，并计算每个子频带的能量范数，然后根据软阈值法和能量范数区分信号和噪声，达到去除噪声的目的。试验结果表明，该算法对SAR图像具有较好的去噪效果，不仅可以去除图像中的大部分噪声，而且可以较好地保留图像纹理的细节信息。与传统小波包算法相比，其计算速度快了一倍左右。     

Scattering of elastic waves in cracked media using a finite difference method

This paper presents a simple, flexible way of introducing stress-free boundary conditions for including cracks and cavities in 2D elastic media by a finite difference method (FDM). The surfaces of cracks and cavities are discretized in a staircase on a rectangular grid scheme. When zero-stress is applied to free surfaces, the resulting finite difference schemes require a set of adjacent fictitious points. These points are classified based on the geometry of the free surface and their displacement is computed as a prior step to later calculation of motion on the crack surface. The use of this extra line of points does not involve a significant drain on computational resources. However, it does provide explicit finite difference schemes and the construction of displacement on the free surfaces by using the correct physical boundary conditions. An accuracy analysis compares the results to an analytical solution. This quantitative analysis uses envelope and phase misfits. It estimates the minimum number of points per wavelength necessary to achieve suitable results. Finally, the method is employed to compute displacement in various models with cavities in the P-SV formulation. The results show suitable construction of the reflected P and S waves from the free surface as well as diffraction produced by these cavities.     

An efficient discontinuous Galerkin method for advective transport in porous media

We consider a discontinuous Galerkin scheme for computing transport in heterogeneous media. An efficient solution of the resulting linear system of equations is possible by taking advantage of a priori knowledge of the direction of flow. By arranging the elements in a suitable sequence, one does not need to assemble the full system and may compute the solution in an element-by-element fashion. We demonstrate this procedure on boundary-value problems for tracer transport and time-of-flight.