Amplification of elastic waves by a three dimensional valley. Part 2: Transient response

Transient response of three dimensional dipping layers of different shapes subjected to incident P, SV, SH and Rayleigh waves is investigated. The time domain response is constructed from steady state solutions through the Fourier synthesis. An indirect boundary integral equation method is applied to calculate the required steady state solutions. The material of the half-space and the layer is assumed to be linear, weakly inelastic, homogeneous and isotropic. Numerical results show that the maximum amplification of motion is strongly dependent upon the type of incident wave, the shape of the basin and signal frequency. The change in the shape of the valley from hemispherical to semi-prolate causes a significant increase in the amplitude of surface waves near the edges; however, the maximum amplification of motion near the centre of the valley decreases. This phenomenon is especially apparent for the case of an incident P wave. In comparison to the corresponding two dimensional responses, the amplitude of motion near the centre of the valley is in general higher for three dimensional models.     

弹性波逆散射微扰论

本文将普遍声逆散射微扰论应用于弹性波层析成像问题,在Born变换下推出了以旋转角为补偿参数的各阶微扰重建公式,实现了对非均匀各向同性散射体内3个参数（质量密度ρ和两个Lamé系数λ,μ）的同时重建. 对于层析成像问题,在弹性波的传播过程中P波与SV波有耦合,但它们不会和SH波发生耦合,于是可以得到3个形式相对简单的标量方程. 在Born变换下,在散射波中引入微扰参数,将散射体的3个参数分别按该微扰参数展开,然后利用二维自由空间的Green函数分别得到散射的P波、SV波和SH波的积分表示. 最后,经一维傅氏变换后,得到Born变换下散射体3个参数的各阶微扰重建公式.     

Scattering of elastic waves by a general anisotropic basin. Part 1: a 2D model

Scattering of incident plane harmonic pseudo P‐, SH‐, and SV‐waves by a two‐dimensional basin of arbitrary shape is investigated by using an indirect boundary integral equation approach. The basin and surrounding half‐space are assumed to be generally anisotropic, homogeneous, linearly elastic solids. No material symmetries are assumed. The unknown scattered waves are expressed as linear combinations of full‐space time‐harmonic two‐dimensional Green functions. Using the Radon transform, the Green functions are obtained in the form of finite integrals over a unit circle. An algorithm for the accurate and efficient numerical evaluation of the Green functions is discussed. A detailed convergence and parametric analysis of the problem is presented. Excellent agreement is obtained with isotropic results available in the literature. Steady‐state surface ground motion is presented for semi‐circular basins with generally anisotropic material properties. The results show that surface motion strongly depends upon the material properties of the basin as well as the angle of incidence and frequency of the incident wave. Significant mode conversion can be observed for general triclinic materials which are not present in isotropic models. Comparison with an isotropic basin response demonstrates that anisotropy is very important for assessing the nature of surface motion atop basins. Copyright © 2001 John Wiley & Sons, Ltd.     

Scattering of plane harmonic SH,SV, P and rayleigh waves by non-axisymmetric three-dimensional canyons: A wave function expansion approach

Scattering of elastic waves by three-dimensional canyons embedded within an elastic half-space is investigated by using a wave function expansion technique. The geometry of the canyon is assumed to be non-axisymmetric. The canyon is subjected to incident plane Rayleigh waves and oblique incident SH, SV and P waves. The unknown scattered wavefield is expressed in terms of spherical wave functions which satisfy the equations of motion and radiation conditions at infinity, but they do not satisfy stress-free boundary conditions at the half-space surface. The boundary conditions are imposed locally in the least-squares sense at several points on the surface of the canyon and the half-space. Through a comparative study the validity and limitations of two-dimensional approximations (antiplane strain and plane strain models) have been examined. It is shown that scattering of waves by three-dimensional canyons may cause substantial change in the surface displacement patterns in comparison to the two-dimensional models. These results emphasize the need for three-dimensional modelling of realistic problems of interest in strong ground motion seismology and earthquake engineering.     

Soil amplification of plane seismic waves

Amplitudes of surface particle velocities are calculated when time-harmonic seismic waves of uniform amplitude are incident upon an arbitrary stratified elastic soil layer from the underlying bedrock. Whereas previous workers have mainly treated normally incident S waves, we allow the waves to be of SV, P, or SH types and to have arbitrary angles of incidence. Following standard practice the problem is set up as a matrix differential system, but in such a way that incident SV and P waves may be treated together (the system for SH decoupling). Though complicated, the 4 × 4 SVP system has considerable structure which is elucidated in Appendices 1 and 2. These results, though not altogether new, are of independent interest, and are gathered together in concise form for reference. The theory for low- and for high-frequency approximations is given. The main results of the work are illustrated by two numerical examples: Model 1 where the soil layer is homogeneous; and Model 2 where the soil layer has a linear velocity profile.     

The free surface response of a subsurface anomaly to an SH wave with source on the surface

The response of a shallow subsurface anomaly to an SH wave with source on the surface is computed by using a two dimensional finite element technique. It is demonstrated that the effects of the depth and relative material composition of the anomaly can be identified in the power spectra. The behaviour of the response agrees with principles established from investigating cases where the SH wave is incident from below.     

含黏滞流体各向异性孔隙介质中弹性波的频散和衰减

基于Biot理论,考虑液相的黏弹性变形和固液相接触面上的相对扭转,提出了含黏滞流体VTI孔隙介质模型.从理论上推导出,在该模型中除存在快P波、慢P波、SV波、SH波以外,还将存在两种新横波－慢SV波和慢SH波.数值模拟分析了6种弹性波的相速度、衰减、液固相振幅比随孔隙度、频率的变化规律以及快P波、快SV波的衰减随流体性质、渗透率、入射角的变化规律.结果表明慢SV波和慢SH波主要在液相中传播,高频高孔隙度时,速度较高;大角度入射时,快P波衰减表现出明显的各向异性,而快SV波的衰减则基本不变;储层纵向和横向渗透率存在差异时,快SV波衰减大的方向渗透率高.     

Reflection and Transmission Coefficients for an Incident Plane Shear Wave at an Interface Separating Two Dissimilar Poroelastic Solids

Using Biot’s poroelasticity theory, we derive expressions for the reflection and transmission coefficients for a plane shear wave incident on an interface separating two different poroelastic solids. The coefficients are formulated as a function of the wave incidence angle, frequency and rock properties. Specific cases calculated include the boundary between water-saturated sand and water-saturated sandstone and the gas–water interface in sand. The results show a very different interface response to that of an incident P wave. Plane SV wave incidence does not significantly excite the Biot slow P wave if the frequency of the wave is below the transition frequency. Above this frequency, an incident plane SV wave can generate a mode-converted slow Biot P wave which is actually a normal propagating wave and not highly attenuating as in the usual (diffusive) case. For an incident SV wave onto a gas–water interface, even at very high frequency, there is no significant Biot second P wave produced. For small incident angles, the gas–water interface is essentially transparent. With increasing angles, there can arise an unusual "definitive angle" in the reflection/transmission coefficient curves which is related to the change of fluid viscosity on both sides of the interface and provides a possible new means for underground fluid assessment.     

基于地震波叠加模式的空间域划分及质点运动空间差异——以SV波入射为例

针对地震动空间差异问题,以半无限空间内平面SV波入射为例,采用波动理论和叠加原理相结合的方法研究地震动的空间特征。首先,分析入射波和反射波在空间内形成质点运动的叠加模式差异,并依此对空间域进行划分;其次,针对不同泊松比和SV波入射角情形研究叠加区与分离区的分界线控制情况;最后,对比分析不同空间域内的质点运动在峰值、持时等方面的特征。研究结果显示:当SV波入射时,叠加区与分离区的分界线通常由z₃ （反射P波与反射SV波的分离线）控制;同时存在两种特殊情况,当SV波垂直入射时,分界线由z₁ （入射SV波与反射SV波的分离线）控制,当反射SV波幅值为零时,分界线由z₂ （入射SV波与反射P波的分离线）控制。在入射波和反射波的影响下,质点运动时程的形状具有水平不变性。三波贡献时段只出现在深度小于z₁的质点的运动时程中,且持时随着深度的增加线性减少;双波贡献时段出现在位于叠加区内的质点的运动时程中,持时沿深度先增加后减少;单波贡献时段随着深度的增加而逐渐加长,在分离区达到最大值。质点运动总持时随深度逐渐增加,在分离线z₂和z₃深度处存在两个拐点。在质点运动峰值方面,靠近自由面的叠加区质点运动峰值变化较大,深度较大的叠加区和分离区的质点运动峰值一般不变。      

Prevailing-frequency approximation of the coupling ray theory along the SH and SV reference rays in a heterogeneous generally anisotropic medium which is approximately uniaxial

The behaviour of the actual polarization of an electromagnetic wave or elastic S–wave is described by the coupling ray theory, which represents the generalization of both the zero–order isotropic and anisotropic ray theories and provides continuous transition between them. The coupling ray theory is usually applied to anisotropic common reference rays, but it is more accurate if it is applied to reference rays which are closer to the actual wave paths. In a generally anisotropic or bianisotropic medium, the actual wave paths may be approximated by the anisotropic–ray–theory rays if these rays behave reasonably. In an approximately uniaxial (approximately transversely isotropic) anisotropic medium, we can define and trace the SH (ordinary) and SV (extraordinary) reference rays, and use them as reference rays for the prevailing–frequency approximation of the coupling ray theory. In both cases, i.e. for the anisotropic–ray–theory rays or the SH and SV reference rays, we have two sets of reference rays. We thus obtain two arrivals along each reference ray of the first set and have to select the correct one. Analogously, we obtain two arrivals along each reference ray of the second set and have to select the correct one. In this paper, we suggest the way of selecting the correct arrivals. We then demonstrate the accuracy of the resulting prevailing–frequency approximation of the coupling ray theory using elastic S waves along the SH and SV reference rays in four different approximately uniaxial (approximately transversely isotropic) velocity models.     

太平洋盆地勒夫波与瑞利波不一致性的研究

在勒夫波及瑞利波频散反演的基础上,本文分析了太平洋盆地水平剪切波速度SH与垂直剪切波速度SV之间的不一致性,并对其成因及与地球各向异性之间的关系进行了探讨。我们发现:除最顶部一二十公里处的SH小于SV之外,在几乎整个太平洋岩石圈内,SH都大于SV。此外,在占太平洋大约2/3的区域下面的软流圈内,SH略高于SV。如此广泛存在的SH与SV的不一致性可能是与大规模地质及构造过程有关的太平洋地壳及上地幔的固有各向异性的一个证据。     

地震体波斜入射下的断层台阶地震反应分析

应用显式有限元法对倾斜断层台阶在地震体波斜入射下的地震反应进行了数值模拟。模拟结果表明，P波入射时的竖向运动分量和SV波入射时的水平向运动分量在台阶上角点处存在极大值、在台阶下角点处存在极小值，同时在上下台面还出现由角点激发、向台阶外传播的转换体波与面波。这一结果说明，在断层台阶场地建设重大工程时应离开上角点一定距离，并考虑上下水平表面地面运动的差异性。     

使用SV/P,SH/P和SV/SH振幅比确定震源机制解

为了准确确定地震的震源机制解，引入了用SV／P，SH／P和SV／SH振幅比修正使用P波、SV波和SH波极性所得到的震源机制解的方法，采用解析法在震源空间内寻找符合地震波观测极性和振幅比的解。该方法能够降低单纯使用初动极性确定震源机制解的不确定性，提高震源机制解的求解精度。     

场地钻井台阵观测中斜入射P波和SV波的近似剥离方法

通常认为,成层介质中P波和SV波互相转化、耦合交织而不可以解耦得到单独的P和SV波入射场.针对钻井台阵的两处三分量加速度记录,根据反向方位角将两水平分量分解为径向水平分量和横向水平分量,假设横向水平分量由SH波系组成,竖向分量和径向分水平量由P-SV波系组成.本文提出在频域内解联立方程组的方法,并结合遗传算法-单纯形法混合优化策略,对P-SV耦合场包括SH波系进行了联合剥离反演,最终得到了基岩斜入射P、SV和SH波.最后,通过场地条件差别较大的另一附近钻井台站的联合反演结果,初步验证了其合理性.该项研究对于断层特征和震相特性研究、近地表“软”基岩或土层介质参数研究、场地效应的细致评价具有一定意义.     

利用井中偶极声源远场辐射特性的远探测测井

远探测声波测井技术近年来的一个重要进展是利用偶极声波探测仪器来发射和接收地层深部的反射信号.本文论述了这种偶极声波远探测技术的基本原理和方法,并结合数值模拟计算验证了该方法的可行性及灵敏度.具体来说,井中偶极声源向地层深部辐射出纵波、SH和SV型横波,其中SH型横波具有很宽的辐射覆盖及较高的反射灵敏度,是偶极横波远探测...     

Scattering of obliquely incident seismic waves by a cylindrical valley in a layered half-space

Three-dimensional scattering of seismic waves by a cylindrical alluvial valley embedded in a layered half-space is investigated by using the combination of the boundary integral representation and the finite element method. The surface displacements due to incident plane harmonic body waves (P, SV and SH) propagating at an arbitrary angle to the axis of the cylindrical valley are evaluated numerically for two semi-elliptical alluvial valleys. The presence of the layer is found to have a strong effect on the amplification of the surface displacements in some cases. The three-dimensional motion seems to be quite critical and may cause large amplification. The surface ground motion becomes significant when compared with corresponding free-field motion as the wavelengths become comparable to the characteristic length of the valley. The maximum amplification always occurs atop the valley. Numerical results show that the amplitude and the amplification pattern of the surface displacement strongly depend upon the frequency, the angle and the type of the incident waves.     

SV波在饱和土体自由表面的反射

基于饱和两相介质弹性波动方程分析SV波在饱和土体自由表面的反射问题,引入波动方程的势函数解答,求解出二维问题中SV波入射情况下饱和土体自由场的位移、速度、加速度和应力响应。在饱和土体自由场响应解析解基础上,建立SV波入射下饱和土体自由场静、动力有限元模型。建模中考虑了如下几方面因素:(1)在不同分析步,对土体单元赋予不同材料本构。通过*model change命令进行单元生死设定,从而实现在初始应力场平衡的静力状态下采用DuncanChang本构模型,而地震波动输入时采用Davidenkov动力本构模型;(2)采用多孔介质黏弹性人工边界条件,在人工边界上分别施加固相和液相介质的弹簧和阻尼来模拟饱和土体中能量的传播;(3)将地震波转化为作用在人工边界上的等效地震荷载,施加到人工边界节点上;(4)土体单元采用4结点平面应变孔压单元(CPE4P)。有限元计算与解析解比较结果表明:SV波在垂直入射和掠入射时,竖向位移响应为零;在45°左右入射时,水平位移响应最大;60°左右入射时,竖向位移响应最大。这些结论与解析解吻合较好,本文模型为建立土-结构动力相互作用模型打下良好的基础。     

非对称圆弧片状声源在井旁地层中产生的声场

提出了一种可用于随钻三维反射声波成像测井的圆弧片状声源,推导了该声源声学性质在波数-频率域内的数学描述,并利用实轴积分的方法对该声源在井旁地层中产生的声场进行求解,考察了声源的线度、频率等因素对该声源向地层中辐射的声场的影响.研究结果表明,特定尺寸和特定频率下的圆弧片状声源产生的纵波场的水平和垂直指向性图中仅具有一个明显的主瓣,且主瓣三分贝角宽较窄,方位分辨率较高,指向性良好,适用于随钻三维反射成像测井;SV波场和SH波场的指向性图中存在两个或者多个角瓣,SV波场在垂直于井轴方向上辐射的能量为0,另外在井中发射和接收的反射SH波场和SV波场会相互干扰,所以难以利用SV波场和SH波场进行三维反射声波成像;声源的线度和频率等因素对其辐射声场影响较大,考虑到激励效率和方位分辨率等因素,对于本文描述的井孔模型,选择圆周角在75°和90°之间, 主频为12 kHz左右的声源是合适的.     

Elastic wave mode separation for tilted transverse isotropy media

Seismic waves propagate through the earth as a superposition of different wave modes. Seismic imaging in areas characterized by complex geology requires techniques based on accurate reconstruction of the seismic wavefields. A crucial component of the methods in this category, collectively known as wave‐equation migration, is the imaging condition that extracts information about the discontinuities of physical properties from the reconstructed wavefields at every location in space. Conventional acoustic migration techniques image a scalar wavefield representing the P‐wave mode, in contrast to elastic migration techniques, which image a vector wavefield representing both the P‐ and S‐waves. For elastic imaging, it is desirable that the reconstructed vector fields are decomposed into pure wave modes, such that the imaging condition produces interpretable images, characterizing, for example, PP or PS reflectivity. In anisotropic media, wave mode separation can be achieved by projection of the reconstructed vector fields on the polarization vectors characterizing various wave modes. For heterogeneous media, because polarization directions change with position, wave mode separation needs to be implemented using space‐domain filters. For transversely isotropic media with a tilted symmetry axis, the polarization vectors depend on the elastic material parameters, including the tilt angles. Using these parameters, we separate the wave modes by constructing nine filters corresponding to the nine Cartesian components of the three polarization directions at every grid point. Since the S polarization vectors in transverse isotropic media are not defined in the singular directions, e.g., along the symmetry axes, we construct these vectors by exploiting the orthogonality between the SV and SH polarization vectors, as well as their orthogonality with the P polarization vector. This procedure allows one to separate all three modes, with better preserved P‐wave amplitudes than S‐wave amplitudes. Realistic synthetic examples show that this wave mode separation is effective for both 2D and 3D models with strong heterogeneity and anisotropy.     

Influences of type of wave and angle of incidence on seismic bending moments in pile foundations

When analysing the seismic response of pile groups, a vertically‐incident wavefield is usually employed even though it does not necessarily correspond to the worst case scenario. This work aims to study the influences of both the type of seismic body wave and its angle of incidence on the dynamic response of pile foundations. To this end, the formulation of SV, SH and P obliquely‐incident waves is presented and implemented in a frequency‐domain boundary element‐finite element code for the dynamic analysis of pile foundations and piled structures. Results are presented in terms of bending moments at cap level of single piles and 3 × 3 pile groups, both in frequency and in time domains. It is found that, in general, the vertical incidence is not the most unfavourable situation. In particular, obliquely‐incident SV waves with angles of incidence smaller than the critical one, a situation in which the mechanism of propagation of the waves in the soil changes and surface waves appear, yield bending moments much larger than those obtained for vertically‐incident wavefields. It is also shown that the influence of pile‐to‐pile interaction on the kinematic bending moments becomes significant for non‐vertical incidence, especially for P and SV waves. Copyright © 2013 John Wiley & Sons, Ltd.