Amplification of waves by an orthotropic basin: sagittal plane motion

Scattering of elastic waves by an orthotropic basin of arbitrary shape embedded in a half-space is investigated for the sagittal plane motion using an indirect boundary integral equation approach. Steady-state results were obtained for incident plane harmonic pseudo P-, S-, and Rayleigh waves. Detailed convergence analysis of the method is presented. Green's functions are evaluated by using adaptive Newton–Cotes or Filon quadratures. Surface ground motion is presented for semicircular and semielliptical basins with different material properties and various angles of incidence. The results show that surface motion strongly depends upon nature of incident wave, geometry and material properties of the basin, and location of the observation point. Comparison with isotropic basin response demonstrates that anisotropy is very important in amplification of surface ground motion. Copyright © 1999 John Wiley & Sons, Ltd.     

Scattering of elastic waves by a 3D anisotropic basin

Scattering of elastic waves by a three‐dimensional transversely isotropic basin of arbitrary shape embedded in a half‐space is considered using an indirect boundary integral equation approach. The unknown scattered waves are expressed in terms of point sources distributed on the so‐called auxiliary surfaces. The sources are expressed in terms of the full‐space Green's functions with their intensities determined from the requirement that the boundary and the continuity conditions are to be satisfied in the least‐squares sense. Steady‐state results were obtained for incident plane pseudo‐P‐, SH‐, SV‐, and Rayleigh waves. Using the Radon transform the Green's functions are obtained in the form of finite integrals over a unit sphere or a unit circle which can be numerically evaluated very efficiently. Detailed analysis of the method includes the discussion on the shape of the auxiliary surfaces and the distribution of the collocation points and sources. The convergence criteria is defined in terms of transparency tests, isotropic limit test, and minimization of a certain norm. The isotropic limit tests show excellent agreement with the isotropic results available in literature. For anisotropic materials the numerical results are given for a semispherical basin. The results show that presence of an anisotropic basin may result in significant amplification of surface motion atop the basin. While the amplitude of peak surface motion may be similar to the corresponding isotropic results, the difference in the displacement patterns may be quite different between the two. Therefore, this study clearly demonstrates that material anisotropy may be very important for accurate assessment of surface ground motion amplification atop basins. Copyright © 2000 John Wiley & Sons, Ltd.     

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.     

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.     

层状半空间中洞室对平面SH波的放大作用

利用间接边界元法,求解了弹性层状半空间中洞室对入射平面SH波的放大作用问题,并以基岩上单一土层中洞室对入射平面SH波的放大作用为例进行了数值计算分析。本文模型的特点之一是考虑了层状场地的动力特性,因而更接近于实际工程;特点之二是计算精度非常高。研究表明,层状半空间中洞室对波的放大作用与均匀半空间中情况有着本质的差别;层状半空间中洞室附近地表动力响应由土层动力特性和洞室对波的散射二者共同决定。土层动力特性不仅影响洞室附近地表位移的幅值,还会影响地表位移的频谱。在土层的前几阶共振频率附近,随着基岩与土层剪切波速比的增大,土层的影响随之增大,而随着土层厚度的增加,土层的影响随之减小,并逐渐趋于均匀半空间情况。     

含断层破碎带场地对平面SH波的放大作用

借助wolf的土层和半空间精确动力刚度矩阵和斜线荷载格林函数,采用间接边界元法在频域内求解了含断层破碎带场地对SH波的放大作用,着重分析了破碎带较窄断层两侧围岩动力响应的基本规律及场地动力特性对散射的影响.结果表明,断层破碎带对SH波有显著的影响,即使破碎带很窄,也可对SH波产生很大的放大作用;层状场地动力特性对放大作用有显著的影响.     

Response of sedimentary basin to obliquely incident SH waves

This research studies the impact of the incident angle of SH waves on the seismic response of two-dimensional sedimentary basins by using a nonlinear method. At first Ricker wavelet is input for a detailed analysis, followed by a statistical analysis based on a total of 100 real earthquake motions recorded at rock sites. The results show that the incident angle has a significant implication on the basin ground motion. First, the incident angle affects the short-period components more than the long-period ones of the spectral response acceleration, but the dominant period of the spectral response acceleration is insensitive to incident angle and location. Second, the MDIA of a basin is not necessarily 0° (vertical incidence) but in the range of approximately 0°–30°, and hence due attention should be paid to the influence of incident angle in seismic response analysis. Third, basin central areas are seismically preferable to edge regions for short-period buildings located on the basin, while, for long-period buildings, the edge areas become preferable. However, with the increase in incident angle, the difference between edge and central areas diminishes gradually. Finally, given that the dimensions of a basin are perceivable to incidence waves, the slope angle has a considerable impact on the PGA distribution pattern by controlling whether or not peak appears in the edge area. The MDP is most likely to be in the edge area of a basin with small slope angle when subjected to excitation with small incident angle (including vertical incidence).     

四川盆地场地土动力学参数统计研究

四川盆地地震构造环境相对稳定,主要遭受近场中强地震和外围大地震的影响。盆地内第四系主要为河流相的砂卵石层夹粘土、粉土层,分布于成都平原及盆地内外河流两岸。这种地层在土层地震反应计算时往往产生一个峰值,具有显著的放大作用。本文收集共计123组土动力学参数的实验资料,统计分析了淤泥质土、粉质粘土、粘土、粉土、细砂和全风化泥岩等6种土类实测土动力学参数,给出了它们在不同深度下的动剪切模量比和阻尼比的统计值。并且将统计值和"94"规范值与袁晓铭推荐值[9]进行了对比分析,结果表明在盆地内使用规范值和推荐值会对工程的抗震设防产生不利影响。该研究成果对盆地内各类工程建设的工程场地地震安全性评价工作具有一定的借鉴和参考价值。     

渭河盆地中土层场地对地震动的放大作用

土层场地对地震动的影响较大,建(构)筑物的选址及其抗震设防必须考虑土层场地的放大作用,以避免或减轻其震害.汶川地震中,布设在渭河盆地中的数字强震动台网共有27个台站(包括2个基岩台站和25个土层台站)获得良好的主震加速度时程.利用这些加速度时程,选择汤峪台做为参考场地,基于考虑几何衰减的传统谱比法分析研究了25个土层场地的放大作用.结果表明:(1)汶川地震中渭河盆地土层场地上的加速度峰值(PGA)有随震中距增加而减小的趋势,且与土层的厚度无关.(2)根据汶川地震中渭河盆地土层场地的加速度反应谱特征及其对地震动的放大作用特征,渭河盆地的土层场地可分为3类:深厚、中厚和薄土层场地.而且,深厚、中厚和薄土层场地分别对地震动的低频、1 Hz附近和高频分量放大作用显著;值得注意的是,深厚土层对地震动的高频分量也有一定程度的放大,只不过相对于低频分量的放大作用较小.(3)汶川地震中渭河盆地的土层场地对不同方向地震动的放大作用不同,且有EW＞NS＞UD的关系.(4)汶川地震中从宝鸡到眉县沿着盆地边缘分布的Ⅶ度烈度异常区是盆地边缘效应和土层场地对地震动放大作用共同作用的结果.     

北京盆地结构对长周期地震动反应谱的影响

建立了北京盆地含起伏地形的地下介质三维速度结构模型, 以有限差分方法对盆地内的3次地震动进行了数值模拟． 计算了地表加速度反应谱, 论证了反应谱的有效周期范围, 从而获得了盆地结构对长周期段反应谱的平均放大系数, 并对不同周期时反应谱的平均放大系数进行了分区, 为今后城市的合理规划和长周期建筑物的建设提供了抗震设防参考． 最后对反应谱平均放大系数与等效沉积物厚度之间的关系进行了回归, 得出了反应谱放大系数随沉积物厚度增大而增强, 以及随周期增大而减弱等结论．      

MT测深结果对松辽盆地西缘可能存在前陆盆地的认识

前陆盆地是一种较为特殊的沉积盆地,是位于造山带前沿和相邻克拉通之间的沉积盆地,是在板块会聚或碰撞条件下,靠近克拉通(或大陆)一侧形成的盆地.我们通过MT测深结果分析,直观地看到了松辽盆地西缘存在着前陆盆地的电性异常特征.本文通过MT测深结果,结合构造动力学环境、地质构造现象分析,认为松辽盆地西缘可能存在前陆盆地(松辽西前陆盆地).这个前陆盆地的存在,可以合理地解释大杨树盆地与其东部松辽盆地主体深度上的重大差异;可以解释利用传统的断陷盆地无法解释的松辽盆地中“凹中隆”的问题;无疑会对目前的研究理论注入新的内涵,从而更有助于指导松辽盆地及其外围的油气勘探与开发.     

Scattering of SH waves by a scalene triangular hill

<正>The influence of local landforms on ground motion is an important problem.The antiplane response of a scalene triangular hill to incident SH waves is studied in this paper by using a complex function,moving coordinates and auxiliary functions.First,the model is divided into two domains:a scalene triangular hill with a semi-circular bottom;and a half space with a semi-circular canyon.Wave functions that satisfy the zero-stress condition at the triangular wedges and at the horizontal surface are constructed in both domains.Then,considering the displacement continuity and stress equilibrium, algebraic equations are established.Finally,numerical examples are provided to illustrate the influence of the geometry of the hill and the characteristics of the incident waves on the ground motions.     

Anti-plane （SH） waves diffraction by cavity： analytical an underground semi-circular solution

Diffraction of a two-dimensional (2D) semi-circular cavity in a half-space under incident SH-waves is studied using the classic wave function expansion method with a new de-coupling technique. This so-called “improved cosine halfrange expansion” algorithm exhibits an excellent performance in reducing displacement residual errors at two rim points of concern. The governing equations are developed in a manner that minimizes the residues of the boundary conditions. Detailed derivation and analysis procedures as well as truncation of infinite linear governing equations are presented. The semi-circular cavity model presented in this paper, due to its simple profile, is expected to be used in seismic wave propagation studies as a benchmark for examining the accuracies of various analytical or numerical methods for mixed-boundary wave propagation problems.     

浅埋圆柱形弹性夹杂附近等腰三角形凸起地形引起的SH波的散射

文章利用“契合”思想,给出了地下弹性夹杂与地面上的等腰三角形凸起地形引起的SH波散射问题的解析解答。利用复平面下坐标移动,通过区域Ⅰ和区域Ⅱ以及区域Ⅱ和区域Ⅲ的“公共边界”位移应力连续条件,建立起求解该问题的无穷代数方程组并截断有限项进行求解,最后通过具体算例及结果分析得出相应结论。     

北京地区中硬场地对地震动加速度反应谱的放大效应研究

当前,合理确定地震动峰值加速度与反应谱特征周期是工程场地地震动参数确定工作的主要内容。本文以北京地区典型中硬场地为研究对象,分析场地条件对不同周期地震动反应谱值的影响。首先,计算不同震级、震中距条件下的基岩地震动加速度反应谱,合成基岩输入地震动时程;再利用110个工程场地的钻孔资料进行土层地震反应计算,分析中硬场地条件对不同输入环境下的地震动加速度反应谱值的放大效应。结果表明,中硬场地对高、中频震动放大效应明显,尤其是对0.2-0.5s周期段地震动加速度反应谱值的放大倍数大多在1.3以上;场地覆盖层厚度变化对不同频段地震动加速度反应谱值的放大倍数所产生的影响是不同的,与场地自振周期的相关性很强;在不同的地震动输入环境下,中硬场地对不同频段地震动加速度反应谱的影响是不同的,这一结论对实际的抗震设防工作具有一定参考价值。     

胶东地区地壳S波衰减系数和台站场地响应的研究

根据山东数字地震台网7个地震台的118条波形资料,采用Atkinson方法（1992）,研究了胶东地区的非弹性衰减系数;采用Moya方法（2000）,研究了各台的场地响应。得到胶东地区非弹性衰减Q值随频率,的关系为Q（f）=249×f^0.596;得到的7个台站的场地响应均没有显示出明显的放大效应,这与胶东地区台站均处于岩石地基相符。     

Diffraction of anti-plane SH waves by a semi-circular cylindrical hill with an inside concentric semi-circular tunnel

A closed-form analytic solution of two-dimensional scattering and diffraction of plane SH waves by a semicylindrical hill with a semi-cylindrical concentric tunnel inside an elastic half-space is presented using the cylindrical wave functions expansion method. The solution is reduced to solving a set of infinite linear algebraic equations. Fourier expansion theorem with the form of complex exponential function and cosine function is used. Numerical solutions are obtained by truncation of the infinite equations. The accuracy of the presented numerical results is carefully verified.     

A site effect study of the Adapazari basin,Turkey, from strong- and weak-motion data

Approximately 4000 people were killed due to collapse of buildings in downtown Adapazari during the 1999 Izmit, Turkey earthquake (Mw = 7.4). The downtown is located on a deep sedimentary basin, so-called Adapazari basin. We study site effects of the Adapazari basin based on strong- and weak-motion data obtained by a temporary array observation deployed in and around the Adapazari basin after the earthquake. Four moderate-size aftershocks (M4.6–M5.8) are selected in our study. We evaluate the S-wave amplifications in the basin by using the traditional spectral ratio method. The spectral ratios show that the S waves are considerably amplified in the frequency range of 0.5 to about 5 Hz at the basin sites, but are apparently de-amplified at frequencies higher than about 10 Hz. We make a quantitative interpretation of the empirical amplifications based on the S-wave velocity structures at the stiff-soil reference site as well as at the basin sites; these structures were estimated by the microtremor array measurements. Through the interpretation, we confirm that the amplifications at low frequencies are attributed to the thick sedimentary layers in the Adapazari basin and that the apparent de-amplifications at high frequencies are partly due to the reference site response. In addition to the considerable S-wave amplifications, the basin site records show long-period (about 2 sec) later phases after the S-wave arrival; these later phases are basin-transduced surface waves that are originated from the source and transmitted into the basin. The predominant period of these waves apparently depends on the earthquake magnitude. We conclude that heavy damage in downtown Adapazari during the 1999 Izmit earthquake was caused not only by strongly amplified S-waves but also by long-period basin surface waves of long duration.