On estimating the hydraulic properties of soil,Part 2. A new empirical equation for estimating hydraulic conductivity for sands

A new empirical equation to estimate hydraulic conductivity is proposed, based on a large set of measured data for hydraulic properties of soil. The equation is simpler and more accurate than the series-parallel model. Under conditions of insufficient data, the new equation provides a good estimation of hydraulic conductivity for sands. For the same class of soils, another empirical equation is proposed to estimate the power N in the Averjanov-Irmay function.     

A varying time-step explicit numerical inte-gration algorithm for solving motion equa-tion

Introduction In linear elastic medium,motion equation for lumped-mass finite element simulation of wave motion is expressed as(LIAO,2002)∑=+lililii ttGtM)()()(FUU&&(1)where Mi is lumped-mass at node i,Gil is stiffness coefficient of node i with respect to node l,üi(t)is acceleration vectors at node i,Ul(t)is displacement vectors at node l,Fi(t)is the external nodal force vectors acting at node i.If acceleration vectorsüi(t),displacement vectors Ul(t)and the external nodal force vectors…     

适用于声波方程数值模拟的时间-空间域隐式有限差分算子优化方法

声波方程数值模拟已广泛应用于理论地震计算,同时构成了地震逆时偏移成像技术的基础.对于有限差分法而言,在满足一定的稳定性条件时,普遍存在着因网格化而形成的数值频散效应.如何有效地缓解或压制数值频散是有限差分方法研究的关键所在.有限差分格式分为显式有限差分和隐式有限差分.隐式有限差分能够进一步压制数值频散效应.因此本文提出了给定频率范围满足时间-空间域隐式有限差分频散关系的方法,并根据震源频率、波速和网格间距确定波数范围,在此基础上建立方程确定了相应的隐式有限差分系数,使得差分系数能在更大频率范围符合波场传播规律.通过频散分析和正演模拟,验证了本文方法的有效性.     

漾濞MS6.4地震长周期强地震动的有限差分初步模拟

根据我国川滇地区的地质地貌特征、前人地质资料和2021年漾濞M_S6.4地震的震源参数初步反演结果,建立三维速度结构模型,采用三维有限差分法对漾濞地震的长周期地震动进行研究.对实际地震烈度和模拟烈度进行对比,同时在区域附近布置了36个观测点,给出其中6个观测点的三分量速度时程,并给出所有观测点阻尼比为5%的速度反应谱,结果表明:(1)模拟的速度峰值已超过25 cm/s,与实际漾濞地区附近的烈度为8度吻合;(2)受断层滑动分布影响,速度水平分量在西北方向分布范围更广,衰减速度明显慢于东南方向,并且在极震区,东北—西南方向的地震动衰减也较慢.方向性效应对峰值大小及其分布范围的影响显著;(3)观测点速度反应谱的特征周期分布在1~3 s范围内,可能会因为共振效应对区域附近的大型建筑物产生较为严重的破坏.需要对漾濞地震进行进一步研究,以期对漾濞地震的长周期地震动有更为细致的认识.     

用于弹性波方程数值模拟的有限差分系数确定方法

有限差分方法是波场数值模拟的一个重要方法,交错网格差分格式比规则网格差分格式稳定性更好,但方法本身都存在因网格化而形成的数值频散效应,这会降低波场模拟的精度与分辨率.为了缓解有限差分算子的数值频散效应,精确求解空间偏导数,本文把求解波动方程的线性化方法推广到用于求解弹性波方程交错网格有限差分系数;同时应用最大最小准则作为模拟退火(SA)优化算法求解差分系数的数值频散误差判定标准来求解有限差分系数.通过上述两种方法,分别利用均匀各向同性介质和复杂构造模型进行了数值正演模拟和数值频散分析,并与传统泰勒展开算法、最小二乘算法进行比较,验证了线性化方法和模拟退火方法都能有效压制数值频散,并比较了各个算法的特点.     

Numerical method of moments for solute transport in a nonstationary flow field conditioned on hydraulic conductivity and head measurements

The unconditional stochastic studies on groundwater flow and solute transport in a nonstationary conductivity field show that the standard deviations of the hydraulic head and solute flux are very large in comparison with their mean values (Zhang et al. in Water Resour Res 36:2107–2120, 2000; Wu et al. in J Hydrol 275:208–228, 2003; Hu et al. in Adv Water Resour 26:513–531, 2003). In this study, we develop a numerical method of moments conditioning on measurements of hydraulic conductivity and head to reduce the variances of the head and the solute flux. A Lagrangian perturbation method is applied to develop the framework for solute transport in a nonstationary flow field. Since analytically derived moments equations are too complicated to solve analytically, a numerical finite difference method is implemented to obtain the solutions. Instead of using an unconditional conductivity field as an input to calculate groundwater velocity, we combine a geostatistical method and a method of moment for flow to conditionally simulate the distributions of head and velocity based on the measurements of hydraulic conductivity and head at some points. The developed theory is applied in several case studies to investigate the influences of the measurements of hydraulic conductivity and/or the hydraulic head on the variances of the predictive head and the solute flux in nonstationary flow fields. The study results show that the conditional calculation will significantly reduce the head variance. Since the hydraulic head measurement points are treated as the interior boundary (Dirichlet boundary) conditions, conditioning on both the hydraulic conductivity and the head measurements is much better than conditioning only on conductivity measurements for reduction of head variance. However, for solute flux, variance reduction by the conditional study is not so significant.     

Geostatistical analysis and conditional simulation for estimating the spatial variability of hydraulic conductivity in the Choushui River alluvial fan,Taiwan

This work evaluated the spatial variability and distribution of heterogeneous hydraulic conductivity (K) in the Choushui River alluvial fan in Taiwan, using ordinary kriging (OK) and mean and individual sequential Gaussian simulations (SGS). A baseline flow model constructed by upscaling parameters was inversely calibrated to determine the pumping and recharge rates. Simulated heads using different K realizations were then compared with historically measured heads. A global/local simulated error between simulated and measured heads was analysed to assess the different spatial variabilities of various estimated K distributions. The results of a MODFLOW simulation indicate that the OK realization had the smallest sum of absolute mean simulation errors (SAMSE) and the SGS realizations preserved the spatial variability of the measured K fields. Moreover, the SAMSE increases as the spatial variability of the K field increases. The OK realization yields small local simulation errors in the measured K field of moderate magnitude, whereas the SGS realizations have small local simulation errors in the measured K fields, with high and low values. The OK realization of K can be applied to perform a deterministic inverse calibration. The mean SGS method is suggested for constructing a K field when the application focuses on extreme values of estimated parameters and small calibration errors, such as in a simulation of contaminant transport in heterogeneous aquifers. The individual SGS realization is useful in stochastically assessing the spatial uncertainty of highly heterogeneous aquifers. Copyright © 2004 John Wiley & Sons, Ltd.     

基于Remez迭代算法求解差分系数的双相介质自适应有限差分正演模拟

利用传统有限差分方法对基于Biot理论的双相介质波动方程进行数值求解时,由于慢纵波的存在,数值频散效应较为明显,影响模拟精度.相对于声学近似方程及普通弹性波方程,Biot双相介质波动方程在同等数值求解算法和精度要求条件下,其地震波场正演模拟需要更多的计算时间.本文针对Biot一阶速度-应力方程组发展了一种变阶数优化有限差分数值模拟方法,旨在同时提高其正演模拟的精度和效率.首先结合交错网格差分格式推导Biot方程的数值频散关系式.然后基于Remez迭代算法求取一阶空间偏导数的优化差分系数,并用于Biot方程的交错网格有限差分数值模拟.在此基础上把三类波的平均频散误差参数限制在给定的频散误差阈值和频率范围内,此时优化有限差分算子的长度就能自适应非均匀双相介质模型中的不同速度区间.数值频散曲线分析表明：基于Remez迭代算法的优化有限差分方法相较传统泰勒级数展开方法在大波数范围对频散误差的压制效果更明显;可变阶数的优化有限差分方法能取得与固定阶数优化有限差分方法相近的模拟精度.在均匀介质和河道模型的数值模拟实验中将本文变阶数优化有限差分算法与传统泰勒展开算法、最小二乘优化算法进行比较,进一步证明其在复杂地下介质中的有效性和适用性.

     

有限元算法在声波方程数值模拟中的频散分析

针对有限元算法在地震波数值模拟中的数值频散问题,利用集中质量矩阵双线性插值有限元算法,推导了二维声波方程的频散函数.在此基础上采用定量分析方法,对比分析了网格纵横长度比变化时的入射方向、空间采样间隔、地震波频率以及地层速度对数值频散的影响.数值算例和模型正演结果表明：当采用集中质量矩阵双线性插值有限元算法时,为了有效地压制数值频散,在所使用震源子波的峰值频率对应的波长内,采样点数目应不少于20个;减小网格长度的纵横比可以有效地抑制入射角(波传播方向与z轴的夹角)较小的地震波的数值频散;地震波频率越高,传播速度越慢,频散越严重,尤其是当相速度与其所对应的频率比值小于2倍空间采样间隔时,不仅会出现严重的数值频散,还会出现假频现象.