一种求解应变软化岩体中球腔问题的数值方法

均匀地应力场中球形洞室开挖问题可以简化为空间轴对称问题,为分析和评价球形洞室开挖的稳定性,采用有限差分方法对平衡方程与变形协调方程进行离散,将洞室围岩潜在塑性区划分为一系列的球壳,并考虑岩体的应变软化行为,可以得到满足线性Mohr-Coulomb（H-C）准则和非线性Hoek-Brown（H-B）屈服准则的围岩体塑性区范围及相应的应力与变形分布。计算结果表明,随着离散步的增加,数值解逐渐收敛,文中解与已有文献的结果完全吻合,且计算效率更高。对一组强度参数遵循CWFS（黏聚力弱化与摩擦角强化）规律的围岩体内塑性区范围、变形与应力的分布进行了分析,并与常规的应变软化模型的计算结果进行了对比,CWFS模型的结果更合理一些。     

一种新的基于局部重力图逼近的组合匹配算法

惯性导航系统定位误差随时间积累发散,利用重力场辅助惯性导航已成为组合导航领域的新方向,该技术对实现潜艇无源定位意义重大.首先利用二维高斯基函数对局部离散格网重力异常基准图进行逼近获取其解析表达式,在此基础上对传统相关极值匹配算法进行重新建模,采用拟牛顿BFGS非线性寻优方法对该模型进行解算,最终完成基于连续解析形式重力异常基准图的相关极值匹配算法设计.为进一步提高算法性能进行以下两点改进:(1)采用TERCOM算法进行预匹配以缩小寻优范围提高寻优速度;(2)采用差分法减小实测过程中Eötvös效应对重力匹配的影响.最后在2'×2'卫星测高反演重力异常数据库基础上进行了三组对比仿真实验,从实验结果可以看出,在重力测量误差、系统误差及初始定位误差较大的情况下,通过该组合匹配算法获得的匹配定位仍能以较高的精度跟踪真实航迹,且其性能较传统单一匹配算法有较大提高.     

Elastic wave modelling method based on the displacement–velocity fields: an improving nearly analytic discrete approximation

In this paper, we present an improvement to our previously published nearly analytic discrete method (NADM) to solve acoustic and elastic wave equations. We compare the numerical errors of the improved NADM with the original NADM and also the fourth-order Lax–Wendroff correction and present examples of three-component wave fields in 2D transversely isotropic media with strong velocity contrasts. Comparing with the original NADM, we find that the improved method requires significantly less storage space and can increase the time accuracy from second order of the original NADM to fourth order, while the space accuracy remains the same as that of the original one. Theoretical analyses and numerical results suggest that our improved NADM is suitable for large-scale numerical modelling as it can effectively suppress numerical dispersion and source-generated noises caused by discretising wave equations when too-coarse grids are used.     

High frequency site amplification evaluated from Borehole data in the Taipei Basin

Based on the quarter-wavelength approximation, the frequency-dependent site amplifications, A(f ), at 18 free-field strong-motion stations in and near the Taipei Basin are evaluated from well-logging data. The V ₃₀, which is the average of the S-wave velocities in the topmost 30 m, is a significant factor in classifying the sites. Results show that the site amplifications at all sites in study are larger than 1 and functions of frequency. Compared with the Haskell method, the quarter-wavelength approximation is almost an average and a good representation of overall amplifications. It is noted that the site amplifications evaluated in this study can apply only to frequencies greater than about 1.1 Hz for class C sites and 3.1 Hz for class D.     

离子分布函数的20矩近似在非相干散射谱中的应用

根据Grad理论,以麦克斯韦分布函数为基,将离子分布函数展成20矩近似的形式,讨论了黏滞张量项与热流项对离子分布函数的影响.在电场比较弱的情况下,沿着E×B和E的方向上,热流矢量项和黏滞张量项是可以分别忽略掉的.离子温度的各向异性特征和分布函数的不对称性是由黏滞项和热流项引起的.利用Sheffield理论计算得到了非相干散射谱,并对13矩近似和20矩近似得到的非相干散射谱进行了对比.在电场比较弱的情况下,这两种近似基本一致,而当电场增强时,热流张量项的贡献变得很明显,温度各向异性的特征加剧.此时与13矩近似相比较,20矩近似能够更加准确地描述以温度各向异性为特性的非麦克斯韦分布等离子体.     

利用积分方程的加速迭代算法计算随钻电磁波电阻率测量仪器的响应

采用改进型逐次逼近解法(MSAM)和Aitken加速技术相结合的迭代算法计算二维积分方程.该算法将纵向成层原状地层作为背景地层,将计算区域限制在井眼和侵入带内,具有未知量数目少、收敛速度快、计算精度高的优点.利用该算法对随钻电磁波电阻率测量仪器在轴对称二维地层中的响应进行数值模拟.模拟结果显示,幅度衰减曲线和相位移曲线受井眼、侵入和围岩的影响程度不同,二者径向探测深度和垂向分辨率也有差异,利用补偿后的幅度衰减电阻率曲线和相位移电阻率曲线交叉点的坐标可精确确定地层层界面位置.     

基于GSLS模型TI介质衰减拟声波方程

随着计算机硬件技术的发展以及高分辨率勘探需求的增加,我们希望能够更准确地模拟地下介质,得到更丰富的地层信息.然而,传统的声学假设并不能描述实际地层所存在各向异性和黏滞性,使得成像分辨率较低.为了实现深部储层的高精度成像,本文同时考虑了介质的各向异性和黏滞性,从TI介质弹性波的基本理论出发,结合各向异性GSLS理论,并通过声学近似方法导出基于GSLS模型的各向异性衰减拟声波方程.数值模拟表明该方程既能准确地描述各向异性介质下的准P波运动学规律,又能体现地层的吸收衰减效应;模型逆时偏移结果表明,在实现成像过程中考虑各向异性和黏滞性的影响,能对高陡构造清晰成像,且剖面振幅相对均衡,分辨率较高.     

基于Chebyshev走时逼近的三维多次反射射线计算

在利用有限差分等基于网格的数值分析方法解地震波走时所满足的程函方程时,由于速度模型的网格化离散等原因,会使走时在各网格节点之间不具有计算射线路径所要求的光滑性,即走时在邻近网格节点之间不具有连续的一阶导数。因此,直接利用网格节点走时计算射线路径会使最终的射线路径不光滑。为解决这个问题,已有研究者提出了基于B样条插值的逆向梯度方案（法）。然而,在速度发生突变时,B样条逆向梯度法所计算出的射线路径会具有较大的误差。针对这个问题,首先采用适合于解最小零偏差逼近及最佳平方逼近问题的Chebyshev多项式取代B样条对来自于分区多级计算方案的网格节点走时进行最佳逼近,得到在最小平方意义下的最优走时公式;然后采用与B样条逆向梯度法类似的计算过程得到光滑的射线路径。数值实验表明,利用Chebyshev多项式逼近走时可以得到具有很高精度的多次反射射线路径,在多次波偏移成像研究中具有潜在的价值。     

多重网格准线性近似技术在三维航空电磁正演模拟中的应用

系数矩阵存储和线性方程组求解是限制三维电磁积分方程方法发展的主要因素。Zhdanov提出准线性（QL）近似技术,建立了复杂散射场与背景场的线性关系,有效地避免了积分方程中大型线性方程组的求解,但是该算法用于多源问题航空电磁正演模拟时精度不高。因此,本文提出一种基于多重网格准线性（MGQL）近似的算法,并利用系数矩阵的Toeplitz性质存储矩阵和快速傅里叶变换,实现了矩阵与向量的快速乘积、降低了计算复杂度,采用多重网格结合了积分方程方法和准线性近似解法的优点,在保证精度的条件下提高计算速度、减少存储量。针对不同类型网格的模拟实验表明,相比于传统积分方程方法,本文算法在保证计算精度的同时,可以将计算速度极大地提高（>10倍）。     

Estimation of uncertainty propagation in flood inundation mapping using a 1‐D hydraulic model

A need for more accurate flood inundation maps has recently arisen because of the increasing frequency and extremity of flood events. The accuracy of flood inundation maps is determined by the uncertainty propagated from all of the variables involved in the overall process of flood inundation modelling. Despite our advanced understanding of flood progression, it is impossible to eliminate the uncertainty because of the constraints involving cost, time, knowledge, and technology. Nevertheless, uncertainty analysis in flood inundation mapping can provide useful information for flood risk management. The twin objectives of this study were firstly to estimate the propagated uncertainty rates of key variables in flood inundation mapping by using the first‐order approximation method and secondly to evaluate the relative sensitivities of the model variables by using the Hornberger–Spear–Young (HSY) method. Monte Carlo simulations using the Hydrologic Engineering Center's River Analysis System and triangle‐based interpolation were performed to investigate the uncertainty arising from discharge, topography, and Manning's n in the East Fork of the White River near Seymour, Indiana, and in Strouds Creek in Orange County, North Carolina. We found that the uncertainty of a single variable is propagated differently to the flood inundation area depending on the effects of other variables in the overall process. The uncertainty was linearly/nonlinearly propagated corresponding to valley shapes of the reaches. In addition, the HSY sensitivity analysis revealed the topography of Seymour reach and the discharge of Strouds Creek to be major contributors to the change of flood inundation area. Copyright © 2014 John Wiley & Sons, Ltd.