VTI介质qP波方程高精度有限差分算子

波动方程有限差分法是一种使用广泛的地震波数值模拟方法.但是有限差分法本身固有存在着数值频散问题,会降低地震波场模拟的精度与分辨率.为了克服常规有限差分算子的数值频散,本文针对VTI介质地震波数值模拟问题,构造了频率-空间域qP波波动方程高精度有限差分优化算子,根据最优化理论中高斯-牛顿法确定了高精度有限差分算子的优化系数.利用常规差分算子和高精度优化差分算子对归一化相速度的频散关系精度进行了对比分析,并对均匀各向同性介质和均匀VTI介质中的qP波地震波场进行了有限差分数值模拟,通过频散关系精度分析和波场数值模拟结果表明：有限差分优化算子具有较高的波场数值模拟精度,有效压制了传统有限差分算子数值模拟中的数值频散现象,提高了有限差分算子精度,为VTI介质频率-空间域qP波正演模拟奠定了基础.     

非线性波消波及波场分布研究

本文基于雷诺平均N-S方程,并结合RNG k-e方程建立了粘性数值波浪水槽,对不同波陡、不同相对水深、不同相对波高的非线性规则波的阻尼消波问题和波场分布进行研究。文中提出了两种描述消波区内部阻尼变化的阻尼函数,分别适用于小波陡情形和高波陡情形。研究结果表明,小波陡组消波区可设为一个波长,阻尼系数取10~4～10~5即可满足消波要求,计算结果与实验结果及造波理论吻合良好;高波陡组消波区可设为两个波长,阻尼系数取10~4～10~5亦可满足消波要求,计算结果与实验结果吻合良好。此外,当波陡较小时,波场内反射情况的小幅改变即可对整个波场造成影响,特别是当水深较浅时这种影响极为明显,需谨慎考虑。当波陡较大时,水波能量较高,整个波场沿水波传播方向可观测到明显的衰减现象,在具体试验中需进行考虑。     

基于粒径分维值检验的松散介质渗透系数空间估值——以河北平原为例

为了克服松散含水介质非均质性各向异性对介质渗透系数的求取所带来的困难,以水动力条件为线索,利用互相关法寻找同一时代地层及同一时代地表水的主、次流方向.在主流方向上,建立了石家庄-束鹿-衡水段介质颗粒粒径随距离递变的数学模型,并以此为基础推求无钻孔地段的粒径.同时,运用分形理论,计算了中、上更新统地层主流方向平均粒径空间分布的分维值,并将其作为检验粒径估值正确与否的判据.通过不同岩性的渗透系数-深度模型,实现了用平均粒径预测渗透系数的全过程.     

One‐dimensional dynamics of saturated incompressible porous media: analytical solutions and influence of inertia terms

The complexity of formulations for the hydromechanical coupled mechanics of porous media is typically minimised by simplifying assumptions such as neglecting the effect of inertia terms. For example, three formulations commonly employed to model practical problems are classified as fully dynamic, simplified dynamic and quasi‐static. Thus, depending on the porous media conditions, each formulation will have advantages and limitations. This paper presents a comprehensive analysis of these limitations when solving one‐dimensional fully saturated porous media problems in addition to a new solution that considers a more general loading situation. A phase diagram is developed to assist on the selection of which formulation is more appropriate and convenient regarding particular cases of porosity and hydraulic conductivity values. Non‐dimensional formulations are proposed to achieve this goal. Results using the analytical solutions are compared against numerical values obtained with the finite element method, and the effect of porosity is investigated. Copyright © 2016 John Wiley & Sons, Ltd.     

Numerical analysis of frost effects in porous media. Benefits and limits of the finite element poroelasticity formulation

The aim of this paper is to analyse the performance of a finite element formulation usable for predicting the mechanical consequences of frost effects on porous media. It considers the characteristics of porous media and how the frost action can be assessed. The problem is then separated into two parts: thermal and poromechanical calculations. The constitutive equations developed in the framework of poromechanics are presented and the implementation in a usual finite element poroelasticity formulation based on Zuber's method is adopted. An analysis of the time‐step influence on the convergence rate is given and leads us to propose a simple method in order to obtain objectivity of the finite element response and avoid over‐long calculations. Frost effect simulations are carried out on real porous media (two fired clays) as a case study. Although the experimental behaviour of the porous media subjected to frost action is in accordance with some observations, the calculated strains appear to be overestimated compared with measurements. The problem could be largely attributable to the difficulty of assessing permeability evolution during frost development. Copyright © 2011 John Wiley & Sons, Ltd.     

Constitutive approach for rate‐sensitive anisotropic structured clays

This paper describes a constitutive approach to model the behavior of rate‐dependent anisotropic structured clay. Rate‐sensitivity is modeled using overstress viscoplasticity. Clay structure is treated as a viscous phenomenon whereby the viscosity of the undisturbed structured clay is initially very high and the viscosity degrades or decreases with plastic straining until the intrinsic or residual viscosity is reached. A microstructure tensor approach is used to make the structured viscosity anisotropic; whereas, the intrinsic viscosity is assumed to be isotropic. The behavior of the constitutive model is compared with the measured response of two clays (Gloucester and St. Vallier clay) from Eastern Canada during triaxial compression tests on specimens trimmed at different orientations to the vertical. The comparisons show that the constitutive framework is able to describe the anisotropic and rate‐sensitive response of both clays. The response of the model is also examined for the more general case of anisotropic consolidated triaxial compression and extension. Copyright © 2010 John Wiley & Sons, Ltd.     

Dynamics of unsaturated poroelastic solids at finite strain

We derive the governing equations for the dynamic response of unsaturated poroelastic solids at finite strain. We obtain simplified governing equations from the complete coupled formulation by neglecting the material time derivative of the relative velocities and the advection terms of the pore fluids relative to the solid skeleton, leading to a so‐called u^s ? p^w ? p^a formulation. We impose the weak forms of the momentum and mass balance equations at the current configuration and implement the framework numerically using a mixed finite element formulation. We verify the proposed method through comparison with analytical solutions and experiments of quasi‐static processes. We use a neo‐Hookean hyperelastic constitutive model for the solid matrix and demonstrate, through numerical examples, the impact of large deformation on the dynamic response of unsaturated poroelastic solids under a variety of loading conditions. Copyright © 2011 John Wiley & Sons, Ltd.     

二维不均匀介质中点源P-SV波响应的有限差分近似算法

本文从一阶方程组形式的波动方程出发,发展了一种计算二维不均匀介质中点源P-SV波响应的近似方法。该方法通过引入线分布的应力作为震源,利用二维有限差分方法计算出线源响应,然后再经过波形校正和几何扩散校正得出相应的近似点源响应。通过把波形和振幅与精确解比较表明,该方法具有较好的精度。由于有限差分方法对于介质中速度和密度的分布没有特殊要求,另一方面,本文所给出的震源可以适用于位错点源、爆炸源或集中力源,因此上述方法十分适合于研究横向不均匀介质中的近场强地运动、爆炸振动或地震勘探等问题。     

Seismic wave attenuation in fluid-saturated porous media

Contrary to the traditional view, seismic attenuation in Biot's theory of fluid-saturated porous media is due to viscous damping of local (not global) pore-fluid motion. Since substantial inhomogeneities in fluid permeability of porous geological materials are to be expected, the regions of highest local permeability contribute most to the wave energy dissipation while those of lowest permeability dominate the fluid flow rate if they are uniformly distributed. This dichotomy can explain some of the observed discrepancies between computed and measured attenuation of compressional and shear waves in porous earth. One unfortunate consequence of this result is the fact that measured seismic wave attenuation in fluid-filled geological materials cannot be used directly as a diagnostic of the global fluid-flow permeability.