Comparison of methods to model the gravitational gradients from topographic data bases

A number of methods have been developed over the last few decades to model the gravitational gradients using digital elevation data. All methods are based on second-order derivatives of the Newtonian mass integral for the gravitational potential. Foremost are algorithms that divide the topographic masses into prisms or more general polyhedra and sum the corresponding gradient contributions. Other methods are designed for computational speed and make use of the fast Fourier transform (FFT), require a regular rectangular grid of data, and yield gradients on the entire grid, but only at constant altitude. We add to these the ordinary numerical integration (in horizontal coordinates) of the gradient integrals. In total we compare two prism, two FFT and two ordinary numerical integration methods using 1" elevation data in two topographic regimes (rough and moderate terrain). Prism methods depend on the type of finite elements that are generated with the elevation data; in particular, alternative triangulations can yield significant differences in the gradients (up to tens of Eötvös). The FFT methods depend on a series development of the topographic heights, requiring terms up to 14th order in rough terrain; and, one popular method has significant bias errors (e.g. 13 Eötvös in the vertical–vertical gradient) embedded in its practical realization. The straightforward numerical integrations, whether on a rectangular or triangulated grid, yield sub-Eötvös differences in the gradients when compared to the other methods (except near the edges of the integration area) and they are as efficient computationally as the finite element methods.     

Traction image method for irregular free surface boundaries in finite difference seismic wave simulation

In this study, we propose a new numerical method, named as Traction Image method, to accurately and efficiently implement the traction-free boundary conditions in finite difference simulation in the presence of surface topography. In this algorithm, the computational domain is discretized by boundary-conforming grids, in which the irregular surface is transformed into a 'flat' surface in computational space. Thus, the artefact of staircase approximation to arbitrarily irregular surface can be avoided. Such boundary-conforming gridding is equivalent to a curvilinear coordinate system, in which the first-order partial differential velocity-stress equations are numerically updated by an optimized high-order non-staggered finite difference scheme, that is, DRP/opt MacCormack scheme. To satisfy the free surface boundary conditions, we extend the Stress Image method for planar surface to Traction Image method for arbitrarily irregular surface by antisymmetrically setting the values of normal traction on the grid points above the free surface. This Traction Image method can be efficiently implemented. To validate this new method, we perform numerical tests to several complex models by comparing our results with those computed by other independent accurate methods. Although some of the testing examples have extremely sloped topography, all tested results show an excellent agreement between our results and those from the reference solutions, confirming the validity of our method for modelling seismic waves in the heterogeneous media with arbitrary shape topography. Numerical tests also demonstrate the efficiency of this method. We find about 10 grid points per shortest wavelength is enough to maintain the global accuracy of the simulation. Although the current study is for 2-D P-SV problem, it can be easily extended to 3-D problem.     

A traveltime reciprocity discrepancy in the Podvin & Lecomte time3d finite difference algorithm

We have found that the extensively used finite difference scheme time3d produces time fields which are 'asymmetric' in the sense that traveltimes computed to the right of the source are faster than traveltimes computed to the left. All finite difference schemes will, as they are approximations to the wave equation, to some extent fail to obey reciprocity perfectly. We show, however, that the errors in time3d may be significant—and unnecessarily large. An asymmetry in the point source initialization has been identified, and after correction time3d produces time fields with an improved reciprocity.     

Dissolved trace elements in river water: spatial distribution and the influencing factor, a study for the Pearl River Delta Economic Zone, China

Twenty-nine water samples were collected from different river channels of the Pearl River Delta Economic Zone, China. An inductively coupled plasma-mass spectromonitor (ICP-MS) was used to measure concentrations of the trace elements in these samples. The results suggest that the average concentrations of rare earth elements in river water show an increasing trend from the West River, the North River, the rivers of the Pearl River Delta, and the Shenzhen River to the East River. Relatively high concentrations of heavy metals appear in the East River, the rivers of the Pearl River Delta and the Shenzhen River, while the West River and the North River have relatively low heavy metal concentrations. Trace element concentrations in samples collected near urban or industrial areas are much higher than those of samples collected from distant areas, away from urban and industrial areas. After natural conditions, human activities have significant influence on the trace element concentrations in river water. This trace element concentration’s spatial distribution in the river water from the Pearl River Delta Economic Zone is actually an integrated effect of natural conditions and human activity.     

基于有限差分法的抗滑桩计算机辅助设计

基于地基系数“m-m”法、“m-k”法、“k-k”法的原理,考虑桩顶和桩底边界条件以及桩在滑动面处位移、转角、弯矩和剪力的连续条件,可解得桩身各节点的位移和内力,提出了进行抗滑桩全桩内力计算的有限差分法。根据差分方程并用VB6.0编制了实用的计算程序,既可避免繁琐的查表计算,提高计算速度,又可提高计算精度,直观生动,真正实现了人机交互,在界面的引导下,设计人员可完成全部计算,并绘出内力图形和抗滑桩截面配筋图,使设计更方便快捷,该软件可以极大地提高生产效率,降低工程造价,从而实现抗滑桩的优化设计。最后采用上述方法对某滑坡的悬臂抗滑桩进行了设计与计算。     

要十分重视另一类型地质灾害的防治

文章提出另一类型地质灾害,即化学型地质灾害的定义及其分类。并认为化学型地质灾害不像物理型地质灾害那样发生瞬时灾害,而有一个延缓过程,但是一旦发生,难于挽救。化学型地质灾害体的主体是化学元素,开展地球化学调查,研究化学元素的赋存规律、土壤及沉积物承受各类元素的极限、各类元素活化的条件是揭示诱发化学型地质灾害机理的关键。因此要十分重视与加强化学型地质灾害的调查、研究、监测与治理工作。     

Petrogenesis and geotectonic setting of the PanAfrican basement rocks in Bamenda Massif, Obudu Plateau, southeastern Nigeria： Evidence from trace element geochemistry

1 IntroductionThe study area is part of the Obudu Plateau,which forms part of the Precambrian Pan-African tec-tonothermal belt, lying between the West African Cra-ton and the Gabon-Congo Craton ( Fig. 1). It isbounded by the Benue Trough, in the NE-SW axi…     

REE/trace element characteristics of sandstone-type uranium deposits in the Ordos Basin

1 Introduction The Ordos Basin is the second largest sedimentary basin in China. During the last 10 years, a great progress has been achieved in the aspects of tectonic evolution, dynamics process, inner and outer geological processes during Mesozoic-Cen…