Calculation of vibration transmission over bedrock using a waveguide finite element model

A finite element method is developed for the study of elastic wave propagation in layered ground environments. The formulation is based on a spectral finite‐element approach using a mixture of high‐order element shape functions and wave solutions. The numerical method provides solutions to vibration transmission on and within layered elastic waveguides. Examples of its use include the theoretical analysis of transmission of vibrations in the vicinity of the surface of the ground. The mathematical model is two dimensional, and the interior of the ground is modelled as an elastic layer overlying a rigid foundation. An analysis of the natural modes of free vibration in a single layer and two layers is presented and compared with known results. In addition the forced response of the layers, for which the surface is assumed to be subjected to a harmonic point force load is shown. These results also include an illustration of the attenuation of surface vibration due to ‘wave impedance blocks’ in the ‘near field’ of the source up to a frequency of 200 Hz for two soil types. Copyright © 2007 John Wiley & Sons, Ltd.     

Karhunen-Loeve展开在土性各向异性随机场模拟中的应用研究

研究了Karhunen-Loeve(简称KL)展开在土性参数随机场模拟中的应用,分析了KL展开的特点,针对不规则区域和任意类型协方差函数提出了积分方程的Galerkin数值解法,模拟了土壤渗透系数各向异性随机场。分析结果表明：较低阶Karhunen-Loeve展开能够较好描述随机场的空间结构,与转动带法相比,KL展开法在模拟随机场的各向异性特性方面更具优势;与谱展开法相比,KL展开法具有更优的收敛性。     

交错网格有限差分法模拟微动信号

为了较好地模拟给定模型在随机源激发下产生的稳定波场信息,为微动信号的检验和数据特征分析等提供理论依据,采用交错网格有限差分方法模拟微动信号,并根据瑞雷波和勒夫波的产生机理,通过测区内震源的分布情况估测微动信号中面波的组成成分。首先建立交错网格有限差分法模拟微动信号的数值模型,然后给出估测微动信号中面波组成成分的算式,最后采用典型方法数值模拟微动信号,应用空间自相关方法提取模拟信号中面波的频散曲线进行分析对比。结果表明,交错网格有限差分方法模拟得到的微动信号更符合实测结果。     

复杂地表地震资料叠前深度偏移成像

分析了复杂地表地区复杂地震波场的形成原因,探讨了基于高角度时空域单程波动方程适用于起伏地表之下构造成像的逆时叠前深度偏移方法。从声波方程有限差分法合成起伏地表上的炮集记录知,当激发点位于低速层中,共炮点道集中低速层表面和高速层表面接收到的信号强度相差较大:低速层表面的信号很强,而高速层表面的信号很弱,低速层中产生了较强的槽波。将该逆时叠前深度偏移方法应用于起伏地表地震波场的偏移处理。虽然在偏移成像前既没有压制与低速层有关的槽波,又没有压制随机噪声,但偏移剖面上界面清晰、位置正确,断层面也得到了很好的聚焦。     

表面波有效相速度近似分析方法

分层介质中瑞利面波有多个模态,表面瞬态响应是多个模态响应的叠加。在近场,面波模态响应传播速度随传播距离而变化;在远场,其趋于模态相速度。由分层介质表面两不同点响应互谱分析(SASW)得到的有效相速度并不对应于面波基阶模态相速度,它与波场中高阶模态能量分配比例有关。有效相速度随传播距离而变化,近场体波对有效相速度影响较大。对分层介质在简谐荷载下表面质点位移响应进行了互谱分析,得到了有效相速度理论值,通过理论值与测试值匹配分析可估算分层参数,该分析方法考虑了近场及高阶面波模态对有效相速度的影响。     

Digital simulation of multivariate two- and three-dimensional stochastic processes with a spectral turning bands method

The space domain version of the turning bands method can simulate multidimensional stochastic processes (random fields) having particular forms of covariance functions. To alleviate this limitation a spectral representation of the turning bands method in the two-dimensional case has shown that the spectral approach allows simulation of isotropic two-dimensional processes having any covariance or spectral density function. The present paper extends the spectral turning bands method (STBM) even further for simulation of much more general classes of multidimensional stochastic processes. Particular extensions include: (i) simulation of three-dimensional processes using STBM, (ii) simulation of anisotropic two- or three-dimensional stochastic processes, (iii) simulation of multivariate stochastic processes, and (iv) simulation of spatial averaged (integrated) processes. The turning bands method transforms the multidimensional simulation problem into a sum of a series of one-dimensional simulations. Explicit and simple expressions relating the cross-spectral density functions of the one-dimensional processes to the cross-spectral density function of the multidimensional process are derived. Using such expressions the one-dimensional processes can be simulated using a simple one-dimensional spectral method. Examples illustrating that the spectral turning bands method preserves the theoretical statistics are presented. The spectral turning bands method is inexpensive in terms of computer time compared to other multidimensional simulation methods. In fact, the cost of the turning bands method grows as the square root or the cubic root of the number of points simulated in the discretized random field, in the two- or three-dimensional case, respectively, whereas the cost of other multidimensional methods grows linearly with the number of simulated points. The spectral turning bands method currently is being used in hydrologic applications. This method is also applicable to other fields where multidimensional simulations are needed, e.g., mining, oil reservoir modeling, geophysics, remote sensing, etc.     

Practical second‐order reliability analysis applied to foundation engineering

A practical and efficient approach of implementing second‐order reliability method (SORM) is presented and illustrated for cases related to foundation engineering involving explicit and implicit limit state functions. The proposed SORM procedure is based on an approximating paraboloid fitted to the limit state surface in the neighborhood of the design point and can be easily carried out in a spreadsheet. Complex mathematical operations are relegated to relatively simple user‐created functions. The failure probability is calculated automatically based on the reliability index and principal curvatures of the limit state surface using established closed‐form SORM formulas. Four common foundation engineering examples are analyzed using the proposed method and discussed: immediate settlement of a flexible rectangular foundation, bearing capacity of a shallow footing, axial capacity of a vertical single pile, and deflection of a pile under lateral load. Comparisons with Monte Carlo simulations are made. In the case of the laterally loaded pile, the friction angle of the soil is represented as a one‐dimensional random field, and pile deflections are computed based on finite element analysis on a stand‐alone computer package. The implicit limit state function is approximated via the response surface method using two quadratic models. Copyright © 2011 John Wiley & Sons, Ltd.     

Free field ground motions at various depths derived from actual seismograph records by using elastodynamic infinite elements

This paper presents a method for the analysis of free field ground motions at various depths from actual seismograph records. The proposed method replaces the propagating rupture on the fault surface by a fictitious focal point and a seismograph station in the vicinity of the given soil site. A fictitious focal point and seismograph station scheme is used to calibrate the free field ground motion of the soil site. The harmonic vibration analysis of the half space, which elastodynamic infinite elements are adopted in the far field and finite elements in the near field, yields the Fourier transform of any constituent wave in terms of the amplitude of the forces applied at the focal point, thus in terms of the Fourier transforms of the accelerations in three orthogonal directions recorded at a seismograph station. If a seismograph station is in the far field (as it is usually), the recorded values there can be transformed into the values at the infinite element node by means of appropriate shape functions. The results can be more refined in case of the availability of simultaneous records at more seismograph stations. In case of N stations, we assume N fictitious focal points, and solve a set of 3N simultaneous equations of 3N forces, three orthogonal forces at each focal point. Naturally, only the results by the present method were ‘exact’ at the calibrated points, and should be accurate in-between and near those points. The accelerations at the points near seismograph stations at various depths can also be obtained. An appropriate inverse Fourier transform algorithm will properly yields all results as time functions.     

基于点云密度特征的滑坡位移监测方法

激光扫描仪对同一目标两次采集的点并不重合,无法通过点云的直接比较快速确定滑坡位移。考虑到单个点云位置的不确定性和区域点云密度的稳定性,将点云的密度作为滑坡表面变形的表征,提出了基于点云密度特征的滑坡位移监测方法。将离散的三维点云转化为二维的密度图像,再利用粒子图像测速技术分析位移前后两幅点云密度图像的相关性,从而计算栅格图像中各子集的相对位移值;当各子集的位移全部计算完成后,得到目标区域的平面位移场。室内块体移动试验表明该方法的计算精度受变形梯度的影响,在地表变化剧烈处会产生一定程度的误差,且子集相关性系数无法达到1。在黄藏寺滑坡的位移监测中,利用本方法识别出了边坡的变动区域,计算出了滑坡的平面位移场,直观地反映了滑坡表面变形状况,验证了该方法的实用性。     

基于面波模拟和曲波变换的去噪技术

面波是陆上地震资料的主要干扰噪声,目前主要采用基于十字交叉排列的FKK（频率-波数-波数）面波压制技术;但其效果不理想,会损害部分有效信号的低频能量。针对此问题,提出一种面波模拟和曲波变换联合压制面波的技术。首先利用面波模拟逐级压制基阶、一阶和二阶面波;然后,再采用曲波变换方法压制残余面波。实际地震资料的处理结果表明：与三维FKK滤波相比,本文所述方法在压制面波的同时,能够保持反射波的低频信息,提高了信噪比。该技术是一种相对保幅的压制面波方法。     

Seismic response of 3D topographical irregularities under incoming elastic waves from point sources

We study some effects that produce 3D topographical irregularities under incoming elastic waves from point sources using the indirect boundary element method. This technique is based on the representation of elastic waves in terms of single-layer boundary sources. In this way reflected and diffracted waves are constructed at the boundaries from where they are radiated by means of boundary sources. The field emited from the point source is computed with the moment tensor for a shear dislocation and analytical expressions of the elastodynamic 3D Green's functions. In this way we can construct a double couple with variable orientation. We compare the technique with that of Bouchon, who used the discrete wave number method for a shear dislocation in a halfspace with a triangular source function. We subsequently apply our method to simulate the seismic response of a mountain of ellipsoidal geometry. The source function that we have considered is a triangular pulse and we show results corresponding to the velocity registered over the surface of the irregularity and that of the halfspace. This motion is presented by means of snapshots showing the evolution of the wavefields that are present in the problem.     

地震勘探基于波场分离的逆时偏移去噪方法

基于双程波动方程的逆时偏移（RTM）具有原理简单、无倾角限制、可以适用于速度任意变化的模型,并具有对各类波正确成像等优点,是当今最好的偏移方法之一.本文阐述了逆时偏移存在的缺陷并分析了低频噪声的产生机制,重点探讨了使用波场分离的逆时偏移去噪方法,并通过模型的试算证明了该方法的有效性.     

基于饱和渗透系数空间变异结构的斜坡渗流及失稳特征

以往研究一般采用单随机变量方法（SRV）或基于水平或垂直方向波动范围生成的空间变异随机场来模拟岩土参数的空间变异性,对具有倾斜定向特征的空间变异随机场未有涉及.基于条件模拟相关理论和非侵入式随机有限元的理论框架,提出了利用序贯高斯模拟方法进行斜坡参数条件随机场模拟并运用有限元方法进行斜坡渗流和稳定性分析的方法.针对理想边坡,对各向同性和几何各向异性的共7种空间变异结构的饱和渗透系数（K_s）各进行了200次条件随机场模拟,基于条件随机场模拟结果进行了有限元渗流和稳定性计算,对每种空间变异结构多次计算结果进行了统计分析.结果表明:本文所提出的方法不仅再现了研究区域参数的空间二阶统计特性,通过设定变异函数参数进行不同空间变异类型、变异程度、变异定向性的随机场模拟,同时利用现场观测数据对随机场模拟结果进行条件限制,从而提高了随机场的赋值精度;K_s的空间变异结构对孔隙水压力的分布规律、地下水位线变化范围、稳定性系数和最危险滑动面分布特征均有一定程度的影响.本研究为库岸斜坡稳定性评价提供方法支撑.      

Gravity inversion in Qinghai-Tibet Plateau

Due to its high elevation and high seismicity the Qinghai-Tibet plateau takes a primary position on the earth surface. The inaccessibility of the region makes geophysical studies difficult. Active seismic sounding is available along essentially one line crossing the eastern part of the plateau. In such a situation gravity is a powerful method to obtain information on the crustal structure. We apply an inversion of the gravity field throughout the entire plateau. The inversion is limited to the long-wavelength band of the field, which has been shown by spectral analysis to be generated at lower crustal levels. The field is inverted in terms of the oscillation of a boundary layer with strong density contrast. This boundary is identified with the crust-mantle discontinuity (Moho). A map of the 3D oscillations of the Moho is presented and the properties discussed along 4 profiles cutting the plateau longitudinally and transversally.     

Transient solution for multilayered poroviscoelastic media obtained by an exact stiffness matrix formulation

The authors propose a semi‐analytical approach to studying wave propagation in multilayered poroviscoelastic grounds due to transient loads. The theoretical development is based on the exact stiffness matrix method for the Biot theory coupled with a matrix conditioning technique. It is developed in the wavenumber frequency domain after a Fourier transform on the surface space variables and the time variable. The usual methods yield a poorly conditioned numerical system. This is due in particular to the presence of mismatched exponential terms. In this article, increasing exponential terms are eliminated and only decreasing exponential terms remain. Consequently, the method can be applied to a large field of configurations without restriction concerning high frequencies, large Fourier transform parameters or large layer thicknesses. Validation and efficiency of the method are discussed. Effects of layering show that the layer impedance influence on solid and fluid displacements. Moreover, this approach can be of interest for the validation of numerical tools. Copyright © 2009 John Wiley & Sons, Ltd.     

Source signature and elastic waves in a half‐space under a sustainable line‐concentrated impulsive normal force

First, the response of an ideal elastic half‐space to a line‐concentrated impulsive normal load applied to its surface is obtained by a computational method based on the theory of characteristics in conjunction with kinematical relations derived across surfaces of strong discontinuities. Then, the geometry is determined of the obtained waves and the source signature—the latter is the imprint of the spatiotemporal configuration of the excitation source in the resultant response. Behind the dilatational precursor wave, there exists a pencil of three plane waves extending from the vertex at the impingement point of the precursor wave on the stress‐free surface of the half‐space to three points located on the other two boundaries of the solution domain. These four wave‐arresting points (end points) of the three plane waves constitute the source signature. One wave is an inhibitor front in the behaviour of the normal stress components and the particle velocity, while in the behaviour of the shear stress component, it is a surface‐axis wave. The second is a surface wave in the behaviour of the horizontal components of the dependent variables, while the third is an inhibitor wave in the behaviour of the shear stress component. An inhibitor wave is so named, since beyond it, the material motion is dying or becomes uniform. A surface‐axis wave is so named, since upon its arrival, like a surface wave, the dependent variable in question features an extreme value, but unlike a surface wave, it exists in the entire depth of the solution domain. It is evident from this work that Saint‐Venant's principle for wave propagation problems cannot be formulated; therefore, the above results are a consequence of the particular model proposed here for the line‐concentrated normal load. Copyright © 2002 John Wiley & Sons, Ltd.     

基于数字表面模型的岩体结构面产状获取

针对传统现场接触式测量获取岩体结构面参数效率低、工作量大、结果精确性受人为因素影响等问题,本文结合数字摄影测量技术与运动法（structure from motion,SFM）进行岩体三维数字表面模型重建,并在此基础上建立了岩体结构面自动识别方法。岩体数字表面模型重建步骤主要为岩体影像资料采集,基于尺度不变特征变换（Scale-Invariant Feature Transform,SIFT）算法进行图像特征匹配、稀疏点云构建、点云稠密化以及岩体曲面模型重构。结构面识别方法流程主要为:首先平滑岩体数字表面模型;通过改变搜索半径和角度阈值实现模型平面分割;基于区域生长原理进行结构面搜索;最后基于随机采样一致性拟合结构面得到结构面产状。将该方法应用于甘肃北山地下实验巷道,实现了巷道三维数字表面模型的重建与结构面产状数据获取,最后将识别到的结构面分组表征在模型表面。与人工实地测量方法以及现有的结构面识别软件相比,本文提出的方法具有良好的准确性,可为工程应用提供一定的参考。     

Stochastic finite element methods for the seismic response of soils

Some of the available stochastic finite element methods are adapted and evaluated for the analyses of response of soils with uncertain properties subjected to earthquake induced random ground motion. In this study, the dynamic response of a soil mass, with finite element discretization, is formulated in the frequency domain. The spectral density function of the response variables are obtained from which the evaluation of the root-mean-squared and the most probable extreme values of the response are made. The material non-linearities are incorporated by using strain compatible moduli and damping of soils using an equivalent linear model for stress–strain behaviour of soils and an iterative solution of the response. The spatial variability of the shear modulus is described through a random field model and the earthquake included motion is treated as a stochastic process. The available formulations of direct Monte-Carlo simulation, first-order perturbation method, a spectral decomposition method with Neumann expansion and a spectral decomposition method with Polynomial Chaos are used to develop stochastic finite element analyses of the seismic response of soils. The numerical results from these approaches are compared with respect to their accuracy and computational efficiency. © 1998 John Wiley & Sons Ltd.     

基岩表面地脉动谱比研究

目前,场地影响评价方法可以分为理论法和经验法。地脉动水平分量与竖向分量谱比法属经验法。这种方法将地脉动水平分量与竖向分量谱比的最大值对应的频率和幅值分别看作是观测场地的卓越频率和放大因子。虽然该法在国内外很多工程实例中得到了理想的结果。但由于这种方法建立过程中应用了许多假设,所以很多地震工程学家对这种方法持怀疑态度。本文讨论了基岩地脉动水平分量与竖向分量谱比为1这一假定的合理性。并采用泊松弹性半空间模型,应用概率分析方法考虑地脉动的随机性,推导了地下体波斜入射弹性半空间自由表面形成地脉动的水平分量与竖向分量谱比表达式。通过计算论证体波斜入射泊松弹性半空间形成的地脉动水平分量与竖向分量谱比特性。结果表明：当地脉动主要成分为体波时,基岩表面地脉动水平分量与竖向分量谱比接近于1;当地脉动主要成分为面波时,基岩表面地脉动水平分量与竖向分量谱比介于0.54～0.79之间。对泊松基岩,该比值是0.68。     

天然源面波频率-波数法的应用

在借鉴国外资料的基础之上,通过分析面波的基本特性,成功开发了天然源面波频率-波数法野外采集观测系统及数据处理系统,并通过大量已知孔的试验,在检验该方法的同时,确立了随机布阵的野外观测方法。