An efficient optimum interpolation scheme for objective analysis over Indian region

In the optimum interpolation scheme, the weights for the observations are computed by solving a set of linear equations for every grid point. As the number of observations increases particularly over data-rich regions, the matrix dimension increases and the computer time required to solve these equations to determine weights increases considerably. In order to reduce the computer time for computing the weights, Tanguay and Robert suggested schemes in which the gaussian function representing the autocorrelation function has been approximated by a second-order and also by a fourth-order Taylor series expansion. This resulted in the solution of matrices of order 4 or 9 respectively to obtain weighting functions irrespective of the number of observations used in the analysis. In the present study, the analyses of mean sea level pressure and geopotential height at 700 mbar level have been carried out for five days using the above two schemes and the regular OI scheme. The analyses are found to be similar in all the three cases suggesting that a lot of computer time could be saved without sacrificing the analysis accuracy by using the modified scheme in which the second-order approximation is utilized.     

A study of slope stability prediction using neural networks

The determination of the non-linear behaviour of multivariate dynamic systems often presents a challenging and demanding problem. Slope stability estimation is an engineering problem that involves several parameters. The impact of these parameters on the stability of slopes is investigated through the use of computational tools called neural networks. A number of networks of threshold logic unit were tested, with adjustable weights. The computational method for the training process was a back-propagation learning algorithm. In this paper, the input data for slope stability estimation consist of values of geotechnical and geometrical input parameters. As an output, the network estimates the factor of safety (FS) that can be modelled as a function approximation problem, or the stability status (S) that can be modelled either as a function approximation problem or as a classification model. The performance of the network is measured and the results are compared to those obtained by means of standard analytical methods. Furthermore, the relative importance of the parameters is studied using the method of the partitioning of weights and compared to the results obtained through the use of Index Information Theory.     

基于Wigner双谱对角切片的谱分解技术在油气检测中的应用

谱分解技术作为一种解释性处理技术得到了地质、地球物理工作者的广泛关注,如何有效地利用其分频显示功能进行油气检测也成为人们关注的一个焦点。利用Wigner高阶谱具有高时频聚集性的特点,提出了一种基于改进核函数的Wigner双谱对角切片的谱分解技术。即在分析指数型核函数与锥形核函数优缺点的基础上,给出了改进的新核函数,进而采用模糊域核函数滤波法抑制Wigner双谱对角切片的交叉项,并解决了Wigner双谱对角切片的模糊函数中心点校正问题。通过对新的核函数交叉项抑制能力的数值模拟,验证新的核函数对时延轴上的交叉项也能抑制。最后对实际地震数据进行了分频处理,在20 Hz低频剖面内的油气有利区表现为强能量显示,与井的钻遇结果一致。     

Deformation of a layered half-space due to a very long tensile fault

The problem of the coseismic deformation of an earth model consisting of an elastic layer of uniform thickness overlying an elastic half-space due to a very long tensile fault in the layer is solved analytically. Integral expressions for the surface displacements are obtained for a vertical tensile fault and a horizontal tensile fault. The integrals involved are evaluated approximately by using Sneddon’s method of replacing the integrand by a finite sum of exponential terms. Detailed numerical results showing the variation of the displacements with epicentral distance for various source locations in the layer are presented graphically. The displacement field in the layered half-space is compared with the corresponding field in a uniform half-space to demonstrate the effect of the internal boundary. Relaxed rigidity method is used for computing the postseismic deformation of an earth model consisting of an elastic layer of uniform thickness overlying a viscoelastic half-space.     

用线性数字滤波法计算大回线源在地下形成的瞬变电磁场

本文讨论了地面大回线源在地下形成瞬变电磁场的正演计算方法。其正演计算是将频率域中相同模型、相同装置条件下的谐变场结果转换到时间域来。计算方法上采用了安德森等人提出的线性数字滤波法。计算过程中采用了三次样条函数插值法，提高了计算速度。通过均匀半无限空间解析解与数值解的计算结果比较表明，两者吻合很好，说明计算方法是可信的。     

掺砾心墙料拉裂力学特性试验研究

研究掺砾心墙料的拉裂特性对深入研究高土石坝水力劈裂、坝顶裂缝以及坝肩横缝等问题至关重要,但目前已有的研究尚不够深入。基于自主研制的单向拉伸试验装置,对不同掺砾量下的心墙料进行了系列的单向拉伸试验,依据试验结果分析了掺砾心墙料拉裂破坏的机制。在此基础上得到以下结论：在试样各自最大干密度及最优含水率下,随着掺砾量的增加,心墙料的抗拉强度和拉应变呈线性递减关系;所有试样的拉应力?应变曲线呈分段指数关系,极限拉应力前后试验曲线可分别采用正负指数关系来描述;进行了系列三轴排水剪试验,分析各试样抗拉强度与强度指标的关系发现,对于所研究的掺砾心墙料,抗拉强度与其黏聚力呈较好的线性关系,在不具备试验条件的情况下,此关系可用来大致估算心墙料的抗拉强度。相关试验结果可为实际土心墙坝抗裂设计提供参照。     

Exact formulas for approximating variogram function integrals

The application of regionalized variables requires the estimation of the variogram function and the evaluation of its integral. By representing the variogram by a polygonal function the integral may be easily approximated by closed form representations of polygonal integrals. This approach provides a basis for more extensive statistical evaluation not evident in existing approximation methods. This paper provides the closed form representations for two-dimensional variogram functions whose domain is represented by a finite collection of rectangles.     

时间域航空电磁系统探测深度研究

时间域航空电磁系统探测深度与采样时间、发射磁矩、大地电导率、仪器背景噪声和灵敏度等诸多因素相关。本文基于时间域航空电磁一维正演对时间域航空电磁系统探测深度进行研究。正演算法从麦克斯韦方程出发,结合准静态近似条件,得到一维层状介质上空中心回线频率域电磁场响应的垂直分量,并采用汉克尔积分进行计算,进而通过时-频变换获得时间域电磁场响应。探测深度研究参考仪器背景噪声水平,通过设定最小可识别信号阈值（本文设定为系统背景噪声三倍）获取最大可探测分离时间,进而利用该分离时间结合平均电导率求取最大探测深度。最后本文以VTEM系统为例,对不同层状介质模型以及不同发射磁矩、背景噪声、发射脉宽和飞行高度下的时间域航空电磁系统最大探测深度进行分析和讨论。     

Fabric-diagram contour precision and size of counting element related to sample size by approximation theory methods

Density estimation on the unit sphere by kernel methods may be conceived as a process of approximation by singular integrals. This concept aids in the solution of the main problems concerning the contouring of fabric diagrams. The optimal size of the counting element in Schmidt's method with respect to the mean integrated square error (MISE)of the density estimation is given. It proved that the optimal size is not only a function of the sample size but seriously depends on the smoothness of the density of directions on the sphere. In the light of approximation theory the Schmidt method of contouring is qualified as a moving average process; an example of a more refined density estimator is given.     

低频谐变电偶极源激发的地下电磁场的闭式解

研究偶极子源产生的电磁场在地下或水下无线电通信和地球物理勘探领域有着重要的应用价值。偶极子和介质的作用往往导致Sommerfeld型积分的解。为了深入揭示电磁波在地下的分布与传播规律,本文针对有耗媒质中为获得大探测深度和长距离通信使用的低频发射天线,在准静态近似条件下导出了水平电偶极子产生的下电磁场Sommerfeld型积分解的闭式表达式。这些公式适用于任意场区和除奇异点以外的任何场点,与数值积分相比,可显著提高计算速度。利用闭合表达式,本文还提出了一种新的场区划分方法。      

An approximate analytical solution for calculating ground surface settlements due to diaphragm walling

This paper focuses on the derivation of an approximate analytical solution to predict ground surface settlements along the centre-line perpendicular to a slurry-supported diaphragm wall panel. An analytical model of trench excavation is constructed by applying linearly-distributed total earth pressure changes on the sidewalls and the base of the trench in a homogeneous, isotropic, elastic half-space. By applying the principle of superposition appropriately, an explicit solution to calculate ground surface settlements is derived by integrating Mindlin’s displacement formulae. The validity of the solution is verified by three-dimensional finite-element analyses and case studies. Based on the results obtained from a parametric study using the newly derived solution, an algebraic formula is obtained as a first approximation for calculating ground surface settlements.     

电偶源瞬变电磁测深研究（三）——大地表面瞬变电磁场

由逆拉普拉斯变换将均匀大地面上的电偶极子源谐变电磁场转换为瞬变电磁场,并计算出B_z(t)/t瞬态曲线;对分层大地面上的瞬变电磁场,采用折线逼近法计算余弦变换得出H_z(t)瞬态曲线。从计算结果分析可知,瞬变电磁测深可实现较小极距探测较大深度。      

Distribution of suspended sediment concentration in wide sediment‐laden streams: A novel power‐law theory

The diffusion equation of suspended sediment concentration in a wide sediment‐laden stream flow is dependent on the vertical gradient of streamwise velocity and the sediment diffusivity. This study aims at investigating the influence of the streamwise velocity laws on the suspended sediment concentration distributions, resulting from the solution of the diffusion equation. Firstly, the sediment concentration distributions are obtained numerically from the solution of the diffusion equation using different velocity laws and compared with the experimental data. It is found that the power‐law approximation produces good computational results for the concentration distributions. The accuracy of using a power‐law velocity model is comparable with the results obtained from other classical velocity laws, namely log‐law, log wake‐law and stratified log‐law. Secondly, a novel analytical solution is proposed for the determination of sediment concentration distribution, where a power‐law, wall‐concentration profile is coupled with a concentration wake function. The power‐law model (for velocity and concentration) is calibrated using the experimental data, and then a generalized wake function is obtained by choosing a suitable law. The developed power‐law model involving the wake function adjusted by an exponent predicts the sediment concentration distributions quite satisfactorily. Finally, a new explicit formula for the suspended‐load transport rate is derived from the proposed theory, where numerical computation of integrals, as needed in the Einstein theory, is avoided.     

有耗分层媒质上瞬变电磁测深的联合时-频解释

时-频分析是信号分析中非常有力的工具,近年来在处理非稳态信号方面获得了很大的成功。本文将联合时-频分析 (JTFA)用于处理地球物理勘探中具有扩散性质的瞬变电磁场信号。首先用数字滤波和逆拉氏算法模拟了分层大地表面上中心回线装置的瞬变响应,然后用Gabor展开研究它们的时-频谱,结果将地层序列成功地区分开来,为瞬变电磁法勘探提供了新的解释手段。      

On Visualization for Assessing Kriging Outcomes

Extant opinion about kriging is that all weights should be positive. Visualizations rendered by converting kriged grids to digital images are presented to show that negative weights may be beneficial to some spatial problems. In particular, variogram models with zero-valued nuggets, already well known to minimize smoothing through kriging, result in a visual resolution substantially superior to that from kriging with a variogram model having a nonzero nugget value in application to satellite acquired data. Negative weights are more likely when using variogram models with zero-valued nuggets, but resultant visualizations often show a smoother transition between extreme data values. This is true even when a variogram model having a nugget value of zero is not optimum with respect to mean square error, as is demonstrated using a nitrate data set. An analogy to digital image processing is used to suggest that the influence of negative weights in kriging is similar to a high-boost kernel.     

Pseudo-dynamic methods for seismic passive earth pressure behind a cantilever retaining wall with inclined backfill

The designing of retaining walls requires the complete knowledge of earth pressure distribution. Under earthquake conditions the design needs special attention to reduce the devastating effect, but under seismic conditions, the available literature mostly uses the pseudo-static analytical solution as an approximate to the real dynamic nature of the complex problem. This paper shows a detailed study on the seismic passive earth thrust behind a cantilever retaining wall with inclined backfill surface by pseudo-dynamic analysis. A planar failure surface has been considered. The effect of variation of parameters such as soil friction angle, wall friction angle and back fill inclination have been explored. A complete analysis shows that the time dependent non-linear behaviour of the pressure distribution obtained in the present method results in more realistic design values of earth pressures under earthquake conditions. Results are provided in tabular and graphical non-dimensional form and compared thoroughly with the existing values in the literature.     

Multi-Collector SIMS Determination of Trace Lanthanides in Zircon

A method is presented for the determination of rare earth elements (REE) in zircon (ZrSiO₄) using a multi-collector equipped ion-microprobe operating at moderately high mass resolution (M/ΔM ˜ 3900). The low abundance light REE (La-Eu) were measured simultaneously in six ion counting electron multipliers, reducing analytical time to less than half of that in a monocollection routine. Effective mass filtering, moderate energy filtering and careful set up of detector parameters in order to minimise background counts, yielded a highly coherent set of analyses from the 91500 zircon reference sample.     

Analytical solution of advection–diffusion equation in heterogeneous infinite medium using Green’s function method

Some analytical solutions of one-dimensional advection–diffusion equation (ADE) with variable dispersion coefficient and velocity are obtained using Green’s function method (GFM). The variability attributes to the heterogeneity of hydro-geological media like river bed or aquifer in more general ways than that in the previous works. Dispersion coefficient is considered temporally dependent, while velocity is considered spatially and temporally dependent. The spatial dependence is considered to be linear and temporal dependence is considered to be of linear, exponential and asymptotic. The spatio-temporal dependence of velocity is considered in three ways. Results of previous works are also derived validating the results of the present work. To use GFM, a moving coordinate transformation is developed through which this ADE is reduced into a form, whose analytical solution is already known. Analytical solutions are obtained for the pollutant’s mass dispersion from an instantaneous point source as well as from a continuous point source in a heterogeneous medium. The effect of such dependence on the mass transport is explained through the illustrations of the analytical solutions.     

Comparing GIS-based support vector machine kernel functions for landslide susceptibility mapping

This study compares the predictive performance of GIS-based landslide susceptibility mapping (LSM) using four different kernel functions in support vector machines (SVMs). Nine possible causal criteria were considered based on earlier similar studies for an area in the eastern part of the Khuzestan province of southern Iran. Different models and the resulting landslide susceptibility maps were created using information on known landslide events from a landslide inventory dataset. The models were trained using landslide inventory dataset. A two-step accuracy assessment was implemented to validate the results and to compare the capability of each function. The radial basis function was identified as the most efficient kernel function for LSM with the resulting landslide susceptibility map showing the highest predictive accuracy, followed by the polynomial kernel function. According to the obtained results, it concluded that using SVMs can generally be considered to be an effective method for LSM while it demands careful consideration of kernel function. The results of the present research will also assist other researchers to select the best SVM kernel function to use for LSM.