含流体层的河谷场地对地震波散射的间接边界元法模拟

结合单相介质动力格林函数和流体域格林函数,将间接边界元方法拓展到含流体层河谷对地震波散射的求解,并结合具体算例进行大量参数分析。研究结果表明,含流体层河谷地形对平面P波、SV波入射时的地震响应受控于入射波频率、入射波角度及流体深度等多种因素。总体来看:① 在低频域内,含流体河谷底部及附近地表的频谱特性与不含流体的河谷反应基本一致;② P波入射时在水层体系共振频率处,河谷底部位移缩小效应显著,而此频率处流体表面位移达到最大;③ 流体层具有吸收地震波能量的作用,流体深度越大,河谷表面及附近地表的地震动位移越小。研究成果可在一定程度上为河谷地形附近地震动效应的评估及防震减灾工作提供理论依据。      

Transient Scattering of Elastic Waves by Dipping Layers of Arbitrary Shape Part 1: Antiplane Strain Model

Scattering of elastic waves by two dimensional multilayered dipping sediments of arbitrary shape embedded in an elastic half-sapce is investigated by using a bondary method. The displancement field is evaluated throughout the elastic media for both steady state and transient incident SH waves. The unknown scattered field is expressed in terms of wave functions which satisfy the equation of motion, traction-free boundary condition and appropariate radiation conditions. The transient response is constructed from the steady state solution by using the fast Fourier transform technique. The numerical results presented demonstrate that scattering of waves by subsurface irregularities may cause locally very large amplification of surface ground motion. The motion can be affected greatly by the scattered surface waves in the sediments. The results clearly indicate that the surface ground motion depends upon a number of parameters present in the problem, such as frequency and the angle of incidence of the incoming wave, impedance contrast between the layers and location of the observation point.     

岩土介质随机性对沉积河谷地震动放大效应的影响

基于间接边界元法计算沉积河谷对平面P波和SV波的二维散射,着重考察沉积介质波速比和材料阻尼比的随机性对河谷地震动放大效应的影响.利用蒙特卡罗方法随机模拟产生了波速比样本和阻尼样本各30组,给出了不同入射角度和频率的P波和SV波入射下河谷随机响应的单频和频谱结果.算例分析结果表明:①地表位移响应幅值的变异系数极值均显著大于波速比变异系数,且波速比的随机性对地表位移的影响在体系共振频率处最为显著,地表位移的标准差最大可达7.168;低频情况下,沉积中部地震动反应的变异性更显著,高频情况下则在沉积河谷边缘变异性最大;②入射角对地表位移响应变异系数极值的影响不大,但对变异系数空间变化的影响显著;③阻尼比随机性对地表位移的影响在低频情况下较小,在高频情况下则较明显,尤其是在沉积河谷的体系自振频率处,其影响最为显著.      

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。      

Scattering of elastic waves by a general anisotropic basin. Part 2: a 3D model

Scattering of plane harmonic waves by a three‐dimensional basin of arbitrary shape embedded within elastic half‐space is investigated by using an indirect boundary integral equation approach. The materials of the basin and the half‐space are assumed to be the most general anisotropic, homogeneous, linearly elastic solids without any material symmetry (i.e. triclinic). The unknown scattered waves are expressed in terms of three‐dimensional triclinic time harmonic full‐space Green's functions. The results have been tested by comparing the surface response of semi spherical isotropic and transversely isotropic basins for which the numerical solutions are available. Surface displacements are presented for a semicircular basin subjected to a vertical incident plane harmonic pseudo‐P‐, SV‐, or SH‐wave. These results are compared with the motion obtained for the corresponding equivalent isotropic models. The results show that presence of the basin may cause significant amplification of ground motion when compared to the free‐field displacements. The peak amplitude of the predominant component of surface motion is smaller for the anisotropic basin than for the corresponding isotropic one. Anisotropic response may be asymmetric even for symmetric geometry and incidence. Anisotropic surface displacement generally includes all three components of motion which may not be the case for the isotropic results. Furthermore, anisotropic response strongly depends upon the nature of the incident wave, degree of material anisotropy and the azimuthal orientation of the observation station. These results clearly demonstrate the importance of anisotropy in amplification of surface ground motion. Copyright © 2003 John Wiley & Sons, Ltd.     

Amplification of elastic waves by a three dimensional valley. Part 1: Steady state response

Steady state scattering of incident P, SV, SH and Rayleigh waves by general non-axisymmetric three dimensional dipping layers is investigated by using an indirect boundary integral equation method. Material of the half-space and the layer is assumed to be linear, weakly anelastic, homogeneous and isotropic. Systematic comparisons between three dimensional and two dimensional models demonstrate that the validity of a two dimensional approximation for a given basin shape may be affected strongly by changes in azimuthal angle of incidence, type of incident wave and frequency. The discrepancies of two dimensional modelling appear to be much more pronounced for the case of an incident SH wave. Another important feature of the results is the existence of strong coupling between P/SV and SH modes, which has no correspondence in two dimensional models. Such off-azimuthal mode conversions are particularly strong for an incident SH wave.     

Transient scattering of elastic waves by dipping layers of arbitrary shape. Part 2: Plane strain model

Scattering of elastic waves by dipping layers of arbitrary shape embedded within an elastic half-space is investigated for a plane strain model by using a boundary method. Unknown scattered waves are expressed in the frequency domain in terms of wave functions which satisfy the equations of motion and appropriate radiation conditions at infinity. The steady state displacement field is evaluated throughout the elastic medium for different incident waves so that the continuity conditions along the interfaces between the layers and the traction-free conditions along the surface of the half-space are satisfied in the least-squares sense. Transient response is constructed from the steady state one through the Fourier synthesis. The results presented show that scattering of waves by dipping layers may cause locally very large amplification of surface ground motion. This amplification depends upon the type and frequency of the incident wave, impedance contrast between the layers, component of displacement which is being observed, location of the observation station and the geometry of the subsurface irregularity. These results are in agreement with recent experimental observations.     

地震体波斜入射情形下台阶地形引起的波型转换

本文首次对地震体波斜入射情形下竖直、倾斜台阶地形引起的波型转换进行了数值模拟，结果表明：地震波的斜入射会使台阶上角点引起更强的转换面波；转换Rayleigh面波最大振幅可达弹性半空间表面自由场位移的1.1倍左右。     

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.     

圆弧状沉积盆地与软土单覆盖层出平面地表运动对比

采用解析方法，通过圆弧状沉积盆地与同样参数的软土均匀单覆盖层的对比，研究沉积盆地对平面SH波二维散射效应和其出平面地表运动。数值对比结果表明：（1）波垂直入射时盆地中央地表位移幅值反应，其随频率变化形式与软土单覆盖层的地表运动有较强的对应性，且此时单覆盖层地表位移幅值为其下降；（2）盆地的二维散射效应特点显著波的汇聚作用使盆地中的地表运动显著放大，总体上较软土单覆盖层的地表位移幅值要大，其频域内的最大反应则明显大于单覆盖层情况，但最大反应在盆地表面出现的位置依赖于入射波角度、盆地深宽比和盆地的软硬程度；（3）沉积盆地中地表位移运动有强烈扭转效应，且随盆地变软和入射波频率增高而增强。     

三维沉积盆地对地震动的放大效应间接边界元法模拟

基于一种高精度间接边界元法(IBEM), 实现了沉积盆地三维地震响应的频域、 时域精细求解, 并以半空间中椭球形沉积盆地对平面P波和SV波的散射为例, 着重探讨了入射角度、 入射波型、 入射频率、 盆地长宽比和深宽比对沉积盆地地震动放大效应的影响规律． 结果表明: 盆地形状对地震波的放大效应和空间分布状态具有显著影响, 且具体规律受控于入射波频段． ① 随着盆地深度增大, 盆地边缘面波发育更为充分, 在较宽频段内均会出现显著的地震动放大效应, 且深盆地的放大区域集中于盆地中部． ② 圆形盆地对地震波的汇聚效应最为显著, 而狭长盆地对地震波的汇聚作用相对较弱, 高频情况下可在盆地内部形成多个聚焦区域． ③ 不同波型入射下, 盆地对地震动放大效应的机制有所差异: P波入射下, 竖向位移放大主要是由于盆地边缘面波由四周向中部汇聚所致; SV波入射下, 边缘面波汇聚效应相对较弱, 而当盆地较深时, 底部透射体波和边缘面波易形成同相干涉从而显著放大地震动． 按盆地内外介质波速比为1/2, P波和SV波垂直入射下频域最大放大倍数分别为25和15, 时域放大倍数约为4.0和3.7(雷克子波)． ④ 低频波入射下, 位移从盆地中部向边缘逐渐减小, 且浅层沉积盆地对地表位移幅值的放大作用不明显． ⑤ P波和SV波的入射角度对盆地地震动放大幅值及空间分布特征也具有显著影响．      

岩土介质随机性对沉积河谷地震动放大效应的影

基于间接边界元法计算沉积河谷对平面P波和SV波的二维散射,着重考察沉积介质波速和材料阻尼的随机性对河谷地震动放大效应。利用蒙特卡罗方法随机模拟产生了波速样本和阻尼样本各30组,给出了不同入射角度和频率P波和SV波入射下河谷随机响应的单频和频谱结果。算例分析结果表明:(1)地表位移响应幅值的变异系数极值均显著大于波速比变异系数,且波速比的随机性对地表位移的影响在体系共振频率处最为明显,地表位移的最大标准差可达7.168;低频情况下,沉积中部地震反应变异性更显著,高频情况下则在沉积河谷边缘变异性最大;(2)入射波角度对地表位移响应变异系数极值的影响不大,但对变异系数空间变化的影响显著;(3)阻尼的随机性对地表位移的影响在低频情况下较小,在高频情况下则较明显,尤其是在沉积河谷的体系自振频率处,其影响最为显著。      

黄土丘陵河谷场地地震动特征研究

研究黄土丘陵河谷场地在地震作用下强地面运动特征的变化情况,可以揭示强震对该类场地上震害的触发机理。结合黄土高原的地貌特征,建立具有代表性的动力数值分析模型,通过输入不同幅值、频谱特性和持续时间的地震波,对起伏地形和覆盖黄土层共同影响下的黄土河谷场地进行地震反应分析。结果表明:黄土层和地形耦合作用控制了地表的PGA变化,使其趋于复杂,在同一输入波不同振幅作用下,与基岩河谷各测点相比,黄土覆盖河谷场地的地震动频谱幅值均有所增加,并且频谱主峰均向高频移动。在不同地震波输入下,场地不同部位的固有频率受地形高程和土层影响;而地震动大小和频谱幅值不仅与场地的基本频谱和地形起伏有关,也与输入地震波的频谱成分相关。输入波PGA与地震频谱特征都不变时,同一场地输出的地震频谱形状具有相似的特征,随着地震持时增长,能量向场地基本频率附近集中,从而可能导致场地上相应频率建筑物震动幅值增加,造成累积破坏。     

Peak surface motion due to scattering of plane harmonic P,SV, or Rayleigh waves by a rough cavity embedded in an elastic half-space

Scattering of plane harmonic P, SV, or Rayleigh waves by a two-dimensional rough cavity completely embedded in an isotropic elastic half-space is investigated by using a direct boundary integral equation method. The cavity’s roughness is assumed to be in the form of periodic or random perturbations of arbitrary amplitude superimposed to a smooth elliptical shape. For the randomly corrugated cavities the normal or the uniform probability distribution functions are assumed. Based on multiple random cavity results, the corresponding average surface response is computed. These are compared with the corresponding periodically corrugated and smooth cavity responses. The surface response is evaluated for different cavity shapes and incident waves and for a range of frequencies. The surface motion results are used to determine the peak surface motion frequencies. They depend strongly upon the basic inclusion shape (the principal axes) and the nature of the incident wave. Strong similarity in the peak surface motion frequencies can be observed for the rough and smooth cavity models for both circular and elliptical shapes. In order to quantify the importance of the cavity corrugation upon the surface motion, a roughness influence factor is defined in terms of the rough and smooth cavity surface responses. This factor strongly depends upon the type of the incident wave, the nature of the cavity corrugation, the basic cavity shape, and the frequency. The factor clearly shows the effect of the cavity roughness upon the surface motion.     

圆弧状多层沉积谷地在平面SV波入射下的动力响应

利用波函数的Fourier-Bessel级数展开法,推导出了含任意多个圆弧状沉积层的谷地在平面SV波入射下稳态动力响应的解析解,并分析了该级数形式的解析解随着截断项数的收敛问题.其结果表明,该级数解能够在一个非常宽的频带范围内收敛;通过在简化条件下与现有其他解析解的比较,验证了该解析解的正确性;并利用该解析解,以稳态地面运动的位移幅值和相位差为基本参数,在一个较宽的频带范围内讨论了谷地中沉积介质的成层性对地面运动的影响,其结果表明对于多层谷地而言,当入射波频率较高时,散射波之间的干涉显著并且出现了能量聚焦现象.     

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.     

圆弧状多层沉积谷地在平面P波入射下稳态响应的解析解

利用波函数的FourierBessel级数展开法,给出了含任意多个圆弧状沉积层的谷地在平面P波入射下稳态动力响应的解析解.并以具有三个沉积层的谷地为例,在宽频范围内,利用稳态地面运动幅值的空间分布,讨论了谷地中沉积介质的成层性对地面运动的影响.     

Numerical investigation of infragravity wave amplifications during harbor oscillations influenced by variable offshore topography

The infragravity (IG) period oscillations inside an elongated rectangular harbor near the offshore fringing reef induced by normal-incident bichromatic short wave groups are simulated using a fully nonlinear Boussinesq model, FUNWAVE 2.0. Based on an IG wave separation procedure, this article presents a systematical investigation on how the maximum IG period component amplitude, the bound and free IG waves, and their relative components inside the harbor change with respect to the plane reef-face slope and the incident short wave amplitude under the condition of the 2nd to the 5th modes. For the given harbor and the ranges of the reef-face slope and the incident short wave amplitude studied in this paper, it is shown that both the maximum IG period component amplitude and the free IG wave component amplitude inside the harbor fluctuate widely with the reef-face slope, and their changing trends with the reef-face slope are almost identical with each other, while the bound IG waves inside the harbor seem insensitive to it. Both the maximum IG period component amplitude and those of the bound and free IG standing waves inside the harbor change cubically with the incident short wave amplitude.     

青藏高原东缘地震波数字资料几种振幅比的前兆测定

根据兰州数字遥测地震台网记录的祁连山中东段的地震资料,利用近震的几种体波及地震波初动的3种振幅比:尾波振幅比、纵波与横波振幅比、初动纵波与横波最大振幅的振幅比的4个振幅比参数rco、Rco、Sco1、Sco2,对该区的2000年6月6日景泰MS5.9地震、2001年7月11日肃南MS5.3地震和2000年9月12日兴海MS6.6地震及余震群进行分析研究。结果表明中强震前各类振幅比会出现高值异常,振幅比参数出现异常后大部分大约1~4个月发震。振幅比参数Sco1、Sco2对应地震关系更明显,说明初动纵波的振幅比由于最先到达,它不受其他波迭加的干扰,能较好的反映孕震区的信息。     

P波入射下断层参数对地表地震动的影响

基于应用透射人工边界条件的显式有限元法计算断层破碎带宽度及力学参数变化、地震动入射角变化时二维断层场地模型P波入射下地表地震动场的分布。结果表明:(1)低速度破碎带的存在导致整个场地都有P波转换为SV波的分量,且在断层破碎带的区域出现断层陷波;(2)低速度破碎带的存在使输入场地恒定的能量向破碎带集聚放大,随着破碎带宽度增大或其介质波速降低集聚放大效应增大;(3)场地放大效应是频率相关的,宽度较宽或介质波速较低的断层破碎带对输入地震动中较低的频率成份放大显著;(4)竖向断层破碎带能阻隔斜入射地震P波,随着入射角增加隔震效应更显著。