重力场的潮汐变化观测及其研究

基于我国武汉超导重力仪长周期序列潮汐观测数据,研究了重力场潮汐变化特征,精密确定了地球潮汐常数,讨论了重力观测中的海潮负荷和大气效应问题;根据地球自由核章动在周日重力潮汐观测中的共振效应确定了自由核章动的复本征周期和品质因子Q值,研究了极移重力效应;并对进一步利用重力潮汐观测研究地球物理问题进行了讨论。     

饱和土中弹性波在双椭圆孔洞周围的散射

利用复变函数法和多极坐标法,研究了饱和土中弹性波在双椭圆孔洞周围的散射及动应力集中的问题。首先通过引入位移势函数,将二维稳态条件下Biot波动方程解耦成势函数所满足的3个Helmholtz方程, 根据分离变量方法即可得Helmholtz方程在柱坐标下势函数的通解。利用土骨架和孔隙水的边界条件,确定波函数展开式中的未知系数,进而得到位移、应力和孔压的表达式。给出了弹性波对2个椭圆形孔洞的动应力集中系数的数值结果,并讨论了波数和孔距变化对动应力集中系数和孔压集中系数的影响。     

传统和旋转交错网格有限差分在双相介质中的模拟对比

以Biot双相介质模型为背景,笔者推导了双相各向同性介质二维三分量一阶速度——应力弹性波方程方程,建立了各向同性双相介质波动方程的二维三分量有限差分格式。分别采用传统交错网格有限差分技术和旋转交错网格有限差分技术对均匀和非均匀双相各向同性介质进行了波场模拟。结果表明,旋转交错网格有限差分技术能够有效模拟双相各向同性介质中弹性波的传播情况;通过传统和旋转交错网格有限差分技术的对比,说明了旋转交错网格有限差分算法的稳定性更强,避免了插值带来的误差,是一种有效的地震波场模拟方法。     

SH波对无限介质土中衬砌结构的动应力集中

运用复变函数法和保角映射法对无限介质土中的衬砌结构进行分析.通过引入两个势函数将弹性介质的控制方程解耦成两个Helmholtz方程.利用所得势函数的通解,得到无限土介质和衬砌结构的位移和应力的表达式,利用无限介质与衬砌结构之间的连续性条件和衬砌结构内边界上的边界条件,可确定波函数展开式中的末知系数,并给出动应力集中系数的数值结果.     

祁连山老虎沟12号冰川冰内结构特征分析

利用探地雷达(Ground Penetration Radar,GPR)调查冰川冰内结构和冰层厚度是一种监测冰川变化常用手段.应用麦克斯维(Maxwell)方程的二维时域有限差分(FDTD)方法,通过将模拟图像与老虎沟12号冰川的实测图像的对比,分析了雷达剖面中的几种反射特征,如冰裂隙、融洞、暖冰等.对比结果表明,GP...     

波动方程差分法正演的频散与分辨率

通过一维波动差分方程分析了合成记录中产生频散及分辨率低的原因,定义了差分算子Dzz与Dtt,确定了无频散条件Dtt/Dzz=C~2,并提出了提高合成记录分辨率的方法.     

2.5维声波数值模拟

利用Liner的2.5-D时间域声波方程和高阶有限差分近似,研究了2.5维声波方程在时间-空间域中的衰减特性。简单地质模型(水平二层介质)的数值计算结果证实了下列事实:在Liner的声波方程中的最后一项,即含有1/t2的一项对整个计算结果没有影响,因此可以忽略。这一结论与文献中已经发表的数值结果相吻合。同样的结论对于由Williamson和Pratt提出的2.5-D声波方程也适用。     

有限差分算法求解砂岩型铀矿体氡气场分布初探

介绍了有限差分方法的原理,叙述了砂岩型铀矿体上氡气场的分布,并建立了氡气场分布的理论方程,通过有限差分算法求解氡气场分布方程,为砂岩型铀矿体上氡气场的正演研究提供了数值计算方法。针对砂岩型铀矿体上氡气场低值区对应矿体而高值异常场对应矿体两端的特点,以矿体端点高值异常峰值点为中心进行二维等步长剖分,得出差分方程,为问题的进一步研究提供一种算法思路。     

复杂地表起伏多重变加密网格有限差分法波动方程数值模拟

常规变加密网格有限差分波动方程数值模拟方法采用水平分层加密网格,该网格剖分策略在适应地形起伏和近地表速度结构变化特征方面效果较差。针对该问题,提出一种起伏多重变加密网格有限差分波动方程数值模拟方法。该方法根据地形起伏和近地表低速层到高速层的速度分布特征进行网格加密;采用不同网格中的变系数差分格式离散声波方程,在保证波场模拟精度的同时兼顾计算效率;同时,为了进一步保障地表附近波场模拟的精度,地表附近最细网格中的差分格式不做降阶处理,针对位于地表以上的虚像点的波场值,提出一种融入自由地表边界条件的法向虚像外推法。算例分析验证该算法对速度模型不同区域进行的网格多次加密显著提高了计算效率,以黄土塬实际模型为例,耗时为常规1 m×1 m网格耗时的43.3%,并可达到和细网格基本一致的模拟精度,模拟误差控制在10^-12范围内,同时表现出很好的近地表散射压制和边界吸收效果,且算法能稳定地适应实际复杂地表介质。     

基于NAD算法的声波方程时间四阶差分解法

波动方程数值模拟是研究地震波传播机理的重要工具,有限差分求解波动方程是当前地震波数值模拟的主要方法之一。当地下介质中的地震波速度较低或地震波高频成分丰富时,常规有限差分技术常常产生严重的数值频散误差,这种误差会降低数值模拟的精度,影响对地震波传播机理的分析。为压制地震波数值模拟时产生的数值频散误差,提高波场模拟精度,提出了基于NAD算子的时间四阶精度波动方程差分格式。根据对应的差分格式,分析了该差分格式的数值频散关系。与常规四阶精度差分算法的频散曲线相比,基于NAD时间四阶精度差分方法不但能够实现时间频散的有效压制,同时其基于更多网格点的位移分量和位移梯度分量空间微分求解方法还能够实现空间频散的有效压制。另外在相同模型条件下,基于NAD算法的声波方程时间四阶差分解法可采用大网格对模拟空间进行差分离散,减少网格数,提高计算效率。     

剪切对非饱和土土-水特征曲线影响的探讨

用净平均应力和吸力等于常数、偏应力增大的三轴排水剪切试验，探讨了剪切对非饱和土水量变化的影响。试验结果表明，土-水特征曲线依赖于偏应力，改进了非饱和土中水量变化的本构关系，建立了含水量．吸力．净平均应力．偏应力形式的土．水特征曲线。     

The mean and turbulence structure simulation of the monsoon trough boundary layer using a one-dimensional model withe-l ande-ε closures

An attempt has been made here to study the sensitivity of the mean and the turbulence structure of the monsoon trough boundary layer to the choice of the constants in the dissipation equation for two stations Delhi and Calcutta, using one-dimensional atmospheric boundary layer model withe-ε turbulence closure. An analytical discussion of the problems associated with the constants of the dissipation equation is presented. It is shown here that the choice of the constants in the dissipation equation is quite crucial and the turbulence structure is very sensitive to these constants. The modification of the dissipation equation adopted by earlier studies, that is, approximating the Tke generation (due to shear and buoyancy production) in theε-equation by max (shear production, shear + buoyancy production), can be avoided by a suitable choice of the constants suggested here. The observed turbulence structure is better simulated with these constants. The turbulence structure simulation with the constants recommended by Aupoixet al (1989) (which are interactive in time) for the monsoon region is shown to be qualitatively similar to the simulation obtained with the constants suggested here, thus implying that no universal constants exist to regulate dissipation rate. Simulations of the mean structure show little sensitivity to the type of the closure parameterization betweene-l ande-ε closures. However the turbulence structure simulation withe-ε. closure is far better compared to thee-l model simulations. The model simulations of temperature profiles compare quite well with the observations whenever the boundary layer is well mixed (neutral) or unstable. However the models are not able to simulate the nocturnal boundary layer (stable) temperature profiles. Moisture profiles are simulated reasonably better. With one-dimensional models, capturing observed wind variations is not up to the mark.     

Hypoplastic constitutive equation with internal variables

A new version of a hypoplastic constitutive equation is presented which is characterized by the introduction of a stress-like internal parameter called back stress. The back stress is a function of the void ratio and of the hydrostatic stress. Using a unique set of material constants, the new constitutive equation describes many aspects of the behaviour of cohesionless soils including the influence of density and stress level. This is demonstrated by a series of verification tests. The determination of the material constants from laboratory tests is described analytically.     

Cosmological parameters and the large numbers of Eddington and Dirac

Cosmological large numbers are studied using dimensional analysis. Expressions linking cosmological parameters with fundamental constants of the microworld are proposed. The Zel’dovich formula for the cosmological constant is generalized, and a series of characteristic masses of the Universe is derived.     

An Analytical Investigation of a Variable-Compliance-type Constitutive Equation

Summary. A constitutive equation is proposed in which the compliance is assumed to monotonically increase as a load is applied. The primary feature of the constitutive equation is that the equation can be applied to various loading conditions such as constant stress rate, constant strain rate, creep, or relaxation. The second feature is that the equation has exact solutions under many loading conditions. The present paper shows the exact solutions for the constitutive equation and investigates the mutual relationships between the exact solutions for the different loading conditions. The third feature is that it is comparatively easy to find the constants in the constitutive equation. The present paper shows how to solve the constitutive equation for the constants, and the constants for some native Japanese rocks. The constitutive equation used in the present paper is extremely simple. Therefore, the equation can be easily implemented in almost any FEM code. It is likely that additional terms of the constitutive equation will prove necessary for practical usage. However, additional terms can be found very easily by finding higher-order approximations of experimental data.     

Calculation of head difference at two sides of a cut-off barrier during excavation dewatering

This paper proposed a series of simple equations to calculate the head difference at the two sides of waterproof curtain. The barrier effect of waterproof curtain is considered from two situations with respect to without barrier case: (i) groundwater head difference below the barrier and (ii) groundwater head difference by convergence into the opening. The solution for the first situation can be derived from hydraulic analyses and the second situation can be obtained using a numerical analysis. The final groundwater head difference is the sum of these two situation according to the superposition principal. In the proposed equations, the head difference is expressed as a function of the inserted depth of the barrier into confined aquifer, the ratio of the hydraulic conductivity of the aquifer, the thickness of the aquifer, and hydraulic gradient under normal conditions. Finally, the proposed equation was applied to a field case to verify the validity of the proposed approach. Compared with the field data, the results show that the proposed method is reasonable.     

赣中南产铀钨系列花岗岩岩石化学数值多元判别及地质效果

由于赣中南及邻区地壳初始物质应分的不均匀性而导致的地壳重熔型花岗岩岩石化学成分和成矿元素的差异,以及U、W-Sn、TR、Nb-Ta等与壳型花岗岩有关的成矿元素地球化学性质的差异,决定了这些元素的不共生性,而各自有其成矿专属岩体。按成矿专属性可将本区燕山期花岗岩划分为产U系列花岗岩和产TR、W-Sn、Nb-Ta系列花岗岩。二系列岩体的岩石化学成分和副矿物组合有明显的差别。据此建立的岩石化学数值多元线性判别函数式能判别二系列岩体;对产W-Sn、TR、Nb-Ta系列岩体能进行二级判别,同时能判别壳源型花岗质侵出岩的产矿性,以及区分加里东期交代花岗岩及混熔过渡型Cu花岗若。     

准P波方程紧致交错网格井间地震波场模拟及边界条件

研究井间地震波场的形成过程以及波场的传播机理、规律,对于指导实际井间地震勘探有着重要的意义.基于具有垂直对称轴的横向各向同性(VTI)介质中的一阶准P波方程,应用具有无条件稳定性质的紧致交错网格隐式差分格式求解该方程.重点研究了紧致交错网格求解该方程的完全匹配层(PML)吸收边界条件,在此基础上实现了VTI介质中一阶准P波方程的井间地震波场的正演模拟.数值算例表明:紧致交错网格能精准模拟VTI介质中准P波的传播过程,得到高精度的正演结果.一阶准P波方程能以足够的精度描述VTI介质中准P波特征.完全匹配层吸收边界能有效地解决人工边界问题,是一种高效的边界吸收算法.     

基于混合遗传算法估计van Genuchten方程参数

van Genuchten(VG)方程是最常用的土壤水分特征曲线方程,其参数取值的精度直接影响到土壤水分运动方程计算的精度.该文建立了VG方程参数的优化模型,构建遗传算法与Levenberg-Marquardt算法相结合的混合遗传算法对其进行求解,并进行了数值试验.结果表明采用混合遗传算法比普通遗传算法不但提高了收敛效率,而且收敛迭代次数也大大减少;采用混合遗传算法估计参数的精度比非线性单纯形法和阻尼最小二乘法要高一些,而且不需要给参数初值.因此,混合遗传算法可以作为估计VG方程参数的一种新方法.