Study of Basin-edge Effects on the Ground Motion Characteristics Using 2.5-D Modelling

This paper presents the role of basin-edge geometry in the generation of surface waves using 2.5-D modelling. The simulated responses of various basin-edge models revealed surface wave generation near the basin edge and their propagation normal to the edge. Seismic responses of basin-edge models using different fundamental frequency of soil along with spectral analysis of differential ground motion confirmed that surface waves start generating near the basin edge when body-wave frequency exceeds the fundamental frequency of soil. Spectral analysis of differential ground motion also confirmed the generation of high frequency surface wave. An increase of surface-wave amplitude with soil thickness was obtained. Large ground displacement observed near the basin edge may be due to the interference of surface/diffracted waves with the direct waves and their multiples. The effect of edge roughness on the surface-wave characteristics was found to be negligible as compared with the edge geometry. Simulated results revealed a decrease of surface-wave amplitude with edge slope, particularly in the case of surface waves caused by S waves. Surface wave generation near the basin edge was obtained for all four considered angles of incidence. At the same time, it was also inferred that the characteristics of these surface waves depend on the angle of incidence to some extent. The findings of this paper reveal that basin-edge effects deserve a particular attention for the purpose of earthquake-resistant design and seismic microzonation.Acknowledgement Financial assistance by the Department of Science and Technology (DST) New Delhi and the Indian National Science Academy (INSA), New Delhi is gratefully acknowledged.     

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．      

2008年青海大柴旦Mw6.3地震地面运动模拟

2008年11月10日在青海柴达木盆地北缘发生了大柴旦M_W6.3地震,为了研究该地震的区域地震波传播与地面运动特征,本文利用地质资料和地壳速度结构研究成果,构建了柴达木盆地及周边区域三维传播介质模型,采用有限差分方法模拟了大柴旦地震波场传播过程以及地面运动分布特征.结果表明,柴达木盆地对波场传播有明显影响,表现为地震波传入盆地后在边界产生次生面波,盆地沉积物对地震波具有围陷作用,地震地面运动在盆地内振幅增大、持时延长.模拟结果给出的地震地面运动峰值速度分布以及理论地震图均和观测结果符合较好,反映数值模拟较好地给出了观测地面运动的主要特征以及传播介质模型的合理性.     

Three-dimensional simulations of strong ground motion in the Shidian basin based upon the spectral-element method

The strong motion of a small long and narrow basin caused by a moderate scenario earthquake is simulated by using the spectral-element method and the parallel computing technique.A total of five different geometrical profiles within the basin are used to analyze the generation and propagation of surface waves and their relation to the basin structures in both the time and frequency domain.The amplification effects are analyzed by the distribution of peak ground velocity(PGV)and cumulative kinetic energy(Ek) in the basin.The results show that in the 3D basin,the excitation of the fundamental and higher surface wave modes are similar to that of the 2D model.Small bowls in the basin have great influence on the amplification and distribution of strong ground motion,due to their lateral resonances when the wavelengths of the lateral surface waves are comparable to the size of the bowls.Obvious basin edge effects can be seen at the basin edge closer to the source for constructive interference between direct body waves and the basin-induced surface waves.The Ek distribution maps show very large values in small bowls and some corners in the basin due to the interference of waves propagating in different directions.A high impedance contrast model can excite more surface wave modes,resulting in longer shaking durations as well as more complex seismograms and PGV and Ek distributions.     

二维梯形沉积盆地放大效应的数值模拟研究

盆地效应作为场地效应的一种特殊类型,其对地震动的影响仍在持续研究当中。建立二维梯形沉积盆地模型,模型边界采用透射人工边界,利用显式有限元法作为求解方法。根据Buckingham提出的π定理定义了多个影响盆地效应的无量纲参数,包括盆地深宽比、介质波速比、盆地深度与入射波长之比、盆地开口宽度与入射波长之比。以Ricker子波作为输入波,研究SH波垂直入射盆地模型时,以上无量纲参数对盆地放大效应的影响。研究发现盆地深宽比越大盆地诱发的聚焦效应越明显,盆地深宽比越小盆地边缘效应越明显。在盆地的深宽比和入射波确定时,随着盆地开口宽度与入射波长之比不断增大盆地的最值放大系数逐渐从盆地中心移向盆地边缘,表现出越来越明显的边缘放大效应。其中波速比差异对放大系数的影响最大,波速比差异越大介质的波阻抗比越大,放大效应越显著。通过将影响盆地放大效应的参数无量纲化,使梯形盆地对地震动放大效应的研究的结论更具有普遍意义。     

考虑土体非线性及倾角影响的盆地地震响应研究

基于二维沉积盆地模型,采用D-P弹塑性模型模拟盆地的非线性特征。利用显式有限元与黏弹性边界结合的方法,通过改变盆地边缘倾角,在时域和频域内分析盆地地表的地震动响应,对比线性与非线性盆地地震反应的差异。结果表明:(1)土体非线性对整个盆地范围内地震动的影响都较显著。考虑非线性时地震动放大系数明显降低,降低幅度在30%~50%。同时,考虑非线性和倾角影响时最强烈放大区域的范围和位置变化,且很小倾角下的分布特征显著不同。(2)两分量的放大系数都有随边缘倾角的增大而增强的趋势,但均是盆地边缘区域受非线性的影响最为显著。此外,真实地震波输入下显著放大区域的范围及线性与非线性结果的差异程度相对更大。(3)考虑非线性时,对于不同频率地震波的放大系数差别明显,但都表现出从低频到高频谱比分布越来越复杂的现象,同时盆地倾角的影响程度随频率的增大更加明显。(4)考虑土体非线性并未改变地震波传播的总体特征,但各震相强度相对降低。     

A numerical study on the influence of geometry on the formation of sandbanks

Applying a two-dimensional, non-linear hydrodynamic numerical model in combination with a semiempirical equation for bedload sediment transport, the influence of geometry on the formation of sandbanks is investigated. In the first experiment, the formation of sandbanks in an ideal rectangular basin, resembling the Taylor’s problem, was calculated. Sandbanks occur in a small area at the closed boundary. Similar experiments were carried out for a range of wavelengths of the incident Kelvin wave. The results reveal that large wavelengths favor the generation of sandbanks. In subsequent calculations, the basin was modified by introducing new geographical features like bays and peninsulas. The numerical experiments show that geometry is a fundamental factor to determine the position where groups of sandbanks appear. The results suggest that in regions where the Kelvin wave is diffracted, the formation of sandbanks occurs. An experiment, in which we applied an ideal geometric configuration representing that of the Southern Bight of the North Sea, generated sandbank patterns resembling those observed in the region.     

表层沉积物特性对地震地面运动的影响研究

建立包含震源、沉积盆地和表层低速沉积层的二维模型,采用交错网格有限差分/伪谱混合方法求解地震波传播,讨论沉积层厚度和速度对地震地面运动的作用。结果表明:沉积层内产生的地震波的多重反射以及转换会引起地面运动持续时间的延长,它们的相干叠加会造成地面运动峰值的放大;随着沉积层速度的增加,多重反射与转换波的能量减小,地面运动持续时间减小,但是不同速度或者不同厚度的低速层模型均显示出一致的地面运动峰值放大特征。结果说明,在包含震源、沉积盆地和沉积层的模型中,沉积层对地面运动的作用机理更复杂。在实际应用中有必要同时考虑这些因素的综合作用。     

Simulating the Taipei basin response by numerical modeling of wave propagation

Taipei, the capital of Taiwan, suffered from destructive earthquakes four times during the 20th century (M _L = 7.3 on April 15, 1909; M _L = 6.8 on November 15, 1986; the Chi–Chi M _L = 7.3 earthquake on September 21, 1999; and M _L = 6.8 on March 31, 2002). Analysis of recorded data shows a strong dependence of spectral amplification in the Taipei Basin on earthquake depth and azimuth. At low frequencies (f < 3 Hz) significant larger amplifications are observed for shallow earthquakes as compared to intermediate depth events. The former ones also display strong azimuthal dependence. As structures with large response periods such as bridges and tall buildings are sensitive to these low frequencies the understanding of the associated wave effects within the basin and their role for site effect amplification is critical. The tool we employ is 3D finite-difference modeling of wave propagation of incident wave fronts. The available detailed model of the basin allows studying the wave effects. Modeling clearly reveals that basin edge effects as observed in data are related to surface wave generation at the basin edges with a high degree of azimuthal dependency. The reproduced site amplification effects are in qualitative agreement with the observations from strong motion data.     

Contributions of Basin-edge-induced Surface Waves to Site Effect in the Dinar Basin,Southwestern Turkey

Ground motion amplifications in the Dinar basin, and contributions of the surface waves generated from basin edges are investigated in frequency and time domains. Amplification functions are computed from the aftershock data of the October 1, 1995 Dinar earthquake (M_W=6.4) using the Standard Spectral Ratio method which requires a pair of instruments; one located at the site under investigation (generally on alluvium) and the other on a reference site, preferably a nearby rock site. First, a time window covering the whole signal is used to compute the amplification function, and, successively, the noise, P wave, S wave and the surface wave time windows are used in computation to observe their contributions to the amplification function. It is seen that the maximum amplifications observed at about 2.0 Hz on the amplification functions of the stations located in the basin are largely due to basin edge induced surface waves. These waves have significantly increased the duration of signals recorded within the basin. Particularly, on the vertical component records, the amplitudes of surface waves are larger than the S-wave amplitudes. The periods of waves amplified maximally due to the basin structure coincide with the natural periods of 4–6-story buildings which were heavily damaged in Dinar. This indicates that the site effects may have been important regarding the damage which occurred during the Dinar earthquake of October 1995.     

Response spectral amplification ratios from 1- and 2-dimensional nonlinear soil site models

In order to determine the effect of geometry on the ground response of 2-dimensional (2-D) basins filled with soils that can develop nonlinear response, we use three basin models with width/depth ratios 3, 6 and 10. The three basins are subjected to a suite of rock site records with various magnitudes and source distances. We compute response spectral amplification ratios at four locations on the surface of the 2-D basins, and determine the average variation of the amplification ratios with respect to excitation spectra, for peak ground acceleration (PGA) and 3 spectral periods of 0.2, 0.5, 1 s. Similarly, we compute the average response spectral amplification ratios for two 1-dimensional (1-D) nonlinear models, one having the soil profile at the basin centre and the other having a soil profile at half the depth of the basin. From the relationship between the average amplification ratios and excitation spectra, we determine the cross-over point in terms of excitation spectral values that separate the amplification range from the deamplification range. Our results show that the cross-over point varies significantly from one location to another on the ground surface and from one basin to another, in a range of 0.3–1.1g for PGA. The effects of basin geometry are very strong at weak and moderate excitation, but decrease with increasing excitation spectra in a significant portion around the basin centre. Our results provide some justification for using 1-D models for 2-D basins with a width/depth ratio ?6 if the soil site is subjected to strong ground shaking.     

基于伪谱和有限差分混合方法的兰州盆地强地面运动二维数值模拟

利用伪谱和有限差分混合方法对兰州盆地进行二维强地面运动模拟.假设3个不同的震源深度5、10、20 km的同一地震下,以一个5层的二维剖面作为模型,以此来研究地震波传播过程并分析复杂的二维非均质路径效应,以及局部地下速度构造对强地面运动振幅加乘的影响,从而了解路径效应对强地面运动最大峰值位移的影响程度.研究结果显示:伪谱和有限差分混合方法模拟地震波场结合了有限差分法和伪谱法的优点,弥补了二者的不足,能较好地处理介质不连续面的计算,同时保证了和伪谱法相当的计算精度.通过地震波场模拟可知沉积盆地的强地面运动较基岩相比具有放大效应,震源深度的不同对兰州盆地垂直分量地面最大峰值位移影响较大,在震源深度为5 km时最小,为0.06 cm;震源深度10 km时在水平剖面30～55 km范围内峰值位移最大,达到0.14 cm;但对水平分量的峰值位移影响较小.     

Directional dependence of site effects observed near a basin edge at Aegion,Greece

We study site effects using 520 weak motion earthquake records from a vertical array in Aegion, Greece. The array is inside a basin, has four stations in soil, and one in bedrock (178 m depth). The site is marked by high seismicity and complex surface geology. We first use the records to establish the downhole accelerometer orientations and their evolution with time. Then we estimate site effects using empirical spectral ratios with and without a reference site (standard and horizontal-to-vertical spectral ratio). We find significant site amplification which cannot be accounted for by 1D model predictions, along with a significant difference in the amplification level between the two horizontal components. These are indications of 2D effects, namely surface waves generated at the basin edge. The difference in amplification between the horizontal components is maximised when these are rotated with respect to the orientation of the basin edge. The strongest amplification takes place in the direction parallel to the basin edge (SH, or out-of-plane motion), and is up to 2 times higher than in the perpendicular direction (SV, or in-plane motion). This directional effect on the amplification is corroborated by numerical 2D modelling using incident SH and SV waves, with the former possibly generating strong Love waves. In the records, the directionality is clear for windows containing the largest amplitudes of the records (S waves and strong surface waves), while it tends to vanish for coda-wave windows. This directionality is also observed when using response spectral ratios rather than Fourier ratios. We compute soil-to-rock amplification factors for peak ground acceleration (PGA) and find it is significantly higher than what is predicted by current design codes. We attribute this difference to the basin edge amplification, linear soil behaviour, and to the inability of simple scalar values like PGA to describe complex amplification effects. Finally, we analyse the earthquake records at a surface station near the slope crest and do not observe significant topographic amplification.     

Effects of Impedance Contrast and Soil Thickness on Basin-Transduced Rayleigh Waves and Associated Differential Ground Motion

This paper presents the effects of impedance contrast (IC) across the basin edge, velocity contrast between the basin and underlying bedrock, Poisson’s ratio and soil thickness on the characteristics of basin-transduced Rayleigh (BTR) waves and associated differential ground motion (DGM). Analysis of simulated results for a two-dimensional (2D) basin revealed complex mode transformation of Rayleigh waves after entering the basin. Excellent correlation of frequencies corresponding to different spectral ratio peaks in ellipticity curves of BTR waves and spectral amplification peaks was obtained. However, such correlation was not observed between values of peaks in ellipticity curves and spectral amplification at the corresponding frequencies. An increase of spectral amplification with IC was obtained. The largest spectral amplification was more than twice the IC in the horizontal component and more than the IC in the vertical component in the case of large and same impedance contrast for P- and S-waves. It was concluded that the frequency corresponding to the largest spectral amplification was greater than the fundamental frequency of soil by around 14% and 44% in the vertical and horizontal components, respectively. Spectral amplification of the vertical component was negligible when soil thickness was less than around 15–20 times the S-wave wavelength in the basin. The largest values of peak ground displacement (PGD) and peak differential ground motion (PDGM) were obtained very near the basin edge, and their values with offset from the edge were strongly dependent on the IC across the basin edge, Poisson’s ratio, velocity contrast between the basin and underlying bedrock (dispersion), damping and soil thickness. The obtained value of PDGM for a span of 50 m in the horizontal and vertical components due to the BTR wave was of the order of 0.75 × 10^?3 and 1.32 × 10^?3 for unit amplitude (1.0 cm) in the horizontal component of the Rayleigh wave at rock very near the basin edge.     

SEISMIC MODEL STUDIES ON DIFFRACTION OF WAVES BY EDGES OF VARYING RADIUS OF CURVATURE AND DEPTH *

Results of studies carried out with the help of a three-dimensional seismic model on waves diffracted from edges of varying radius of curvature R and depth h with respect to wave length λ are described. The amplitude decay, travel time, and apparent velocity of the wave diffracted from a sub-surface edge of semi-infinite length are found to depend on the parameters R, h, and distance from the edge on the surface provided the ratio of the parameters to λ are less than some limiting values. The nature of the amplitude decay is independent of R when the depth exceeds 2λ, and independent of h when R exceeds 1.5λ. When these are below the limiting values (h= 2λ and R= 1.5λ), the nature of the decay depends appreciably on R and h. The apparent decay in amplitude on the surface due to geometrical spreading by the diffracting edge is less than that of a cylindrical secondary wave source and decreases with increase in depth of the edge. The nature of the travel time curves of the diffracted waves near the edge depend on R/λ when the depth is within about one λ. Apparent velocity of the wave depends largely on R/λ in the zone of diffraction up to a distance of about one λ from the edge on the surface. Beyond this distance the velocity is almost the same irrespective of R/λ and depend only on h/λ. The width of the zone of diffraction caused by an edge of finite length comparable to λ is more and more narrow as the ratio of the distance of the edge on the surface to its depth increases.     

Amplification of SH waves by an orthotropic basin

Scattering of elastic waves by an orthotropic sedimentary basin is investigated for antiplane strain model using an indirect boundary integral equation approach. Both steady state and transient response were obtained for semicircular and semielliptical basins with different material properties. The results indicate that the basin geometry and the impedance contrast between the half-space and the basin have similar effects on the surface ground motion amplification as for the isotropic case. However, the material anisotropy may change significantly the fundamental resonant frequencies of the basin, resulting in different surface displacement amplification patterns. In addition, it was observed that the arrival time of the main disturbance on the surface strongly depends on material anisotropy for different angles of incidence. The results demonstrate that material anisotropy may be very important in explaining surface ground motion amplification for sedimentary basins. © 1998 John Wiley & Sons, Ltd.     

Regional seismic responses of shallow basins incorporating site‐city interaction analyses on high‐rise building clusters

This study assesses the 3D amplification effects in shallow basins and quantifies the effects of site‐city interaction (SCI) on high‐rise buildings. A regional‐scale 3D spectral element simulation is conducted on the Tuen Mun‐Yuen Long basin, which contains multiple subbasins with heterogeneous and nonlinear soil profiles, while 3D city models with various building layouts are fully integrated into the basin model for our SCI study. We found a good correlation between spectral amplification factors and soil depths. Site response is significantly amplified at basin edges and centers due to surface waves generated at basin edges and the focusing effects stemming from 3D basin geometry. Transfer functions of 3D basins can be up to fourfold at fundamental frequencies as compared to 1D response, and further amplifications occur at high frequencies due to surface waves. In the SCI simulations, we observe wave trapping in the open space amid buildings resulting in energy concentration and up to twofold PGA amplifications. The wave trapping effect diminishes as the space between buildings increase beyond their range of influence (～100 m). The SCI analyses show that destructive kinetic energy in superstructures increases 28% in one horizontal direction but decreases 22% in the other. Our study concluded that, 1D site response analysis can significantly underestimate the seismic demand in shallow basins. Site‐city interaction of high‐rise buildings increases the short‐period spectra of ground motions, leading to an increase in their story accelerations by up to 50% and to a substantial decrease in the seismic safety of short structures in their vicinity.     

Numerical study on basin-edge effects in the seismic response of the Gubbio valley,Central Italy

The Gubbio basin in Central Italy is a intermountain basin of extensional tectonic origin, typical of Central and Southern Apennines, characterized by moderate seismicity. The strongest recorded event within the area is a magnitude 5.7 earthquake which occurred on 29 April 1984 along the Gubbio fault, bordering the eastern side of the basin. The main objective of this study is to analyze the features of earthquake ground motion as related to basin-edge effects, by performing physics-based numerical simulations of the 1984 earthquake through a high-performance spectral element code. The simulated ground motions are found in reasonable agreement with the recorded motions when using the kinematic source model developed by Ameri et al. (Bull Seismol Soc Am 99:647–663, 2009), with a rise-time equal to 1 s and a nucleation point located in the middle of the fault. Pronounced differences were noted between records from the basin and adjacent sites at outcropping bedrock, owing to both the strong impedance contrast between soft alluvial sites and bedrock formations (lithostratigraphic amplification), as well as lateral discontinuities related to the 2D/3D geometry of the basin (generation of surface waves). Since the fault was located beneath the basin, 1D amplification effects were found to be more relevant than those associated with the generation of surface waves from the basin edge. Finally, an envelope delay spectrum was computed for the simulated ground motions, showing that surface waves are excited in the frequency band of 0.2–0.8 Hz with a significant increase of ground motion duration within the basin.     

Scattering and diffraction of earthquake motions in irregular,elastic layers,II: Rayleigh and body P and SV waves

We present our study of the wave propagation in an irregularly layered, elastic wave-guide excited by incoming Rayleigh surface waves and P and SV body waves. Our aim is to show examples of applying a method that will make it possible to analyze the distribution and amplification of displacements, rotations, curvatures, strains, and stresses on or below the ground surface during passage of strong earthquake ground motion. We employ the weighted-residuals method, which makes it possible to calculate the scattered and diffracted waves, and then we illustrate the amplification of motions in the vicinity of inhomogeneity.