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.     

Modeling of spatially correlated,site-reflected,and nonstationary ground motions compatible with response spectrum

Seismic risk analysis and mitigation of spatially extended structures require the synthesis of spatially varying ground motions in the response history analysis of these structures. These synthetic motions are usually desired to be spatially correlated, site reflected, nonstationary, and compatible with target design response spectra. In this paper, a method is presented for simulating spatially varying ground motions considering the nonstationarity, local site effects, and compatibility of response spectra. The scheme for generating spatially varying and response spectra compatible ground motions is first established for spatial locations on the ground surface with varying site conditions. The design response spectrum is introduced as the “power” spectrum at the base rock. The site amplification approach is then derived based on the deterministic wave propagation theory, by assuming that the base rock motions consist of out-of-plane SH wave or in-plane combined P and SV waves propagating into the site with assumed incident angles, from which tri-directional spatial ground motions can be generated. The phase difference spectrum is employed to model ground motions exhibiting nonstationarity in both frequency and time domains with different site conditions. The proposed scheme is demonstrated with numerical examples.     

A stochastic model of the Fourier phase of strong ground motion

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四川汶川8．0级地震山西数字强震动记录特征与分析

对2008年5月12日四川汶川8．0级地震,山西数字强震动台网27个台的地震加速度记录,进行了处理和分析,包括对加速度波形数据的基线校正,滤波,加速度傅立叶和反应谱计算,以及速度和位移计算。结果表明：局部场地的介质特性对地震动特征有相当大的影响,较厚的覆盖土层对较长周期的地震波有明显的放大作用。厚覆盖土层场地的强震动观测对自振周期较长建筑物的抗震设计具有重要的意义。     

长周期地震动频谱特征周期研究

长周期地震动的频谱特性是影响长周期结构动力响应的重要因素,目前关于其频谱特征周期参数的研究尚有欠缺.根据长周期地震动的界定方法,选取65条远场长周期地震动和50条近场脉冲型地震动,计算各条地震动的10个频谱特征周期参数,通过分析各周期参数与长周期地震动低频特性指标的相关性和离散性,探讨合适的长周期地震动频谱特征周期表征...     

Ground Motion Modeling for Seismic Hazard Analysis in the Near-source Regime: An Asperity Model

—A new, yet simple, method using the asperity model to estimate ground motion in the near-source regime for probabilistic seismic hazard analyses is proposed in this study. This near-source model differs from conventional empirical attenuation equations. It correlates peak ground motions with the local contributing source in terms of the static stress drop released non-uniformly on the causative fault plane rather than with the whole seismic source in terms of magnitude. Here the model is simplified such that ground motions at a rock or firm soil site near extended vertical strike-slip faults are dominated by direct shear waves. The proposed model is tested by comparing its predictions with strong ground motion observations from the 1979 Imperial Valley and the 1984 Morgan Hill earthquakes. The results have revealed that ground motions in the near-source region can be adequately predicted using the asperity model with appropriate calibration factors. The directivity effect of ground motion in the near-source region is negligible for high-frequency accelerations. The cut-off frequency (?_max?) at a site is an important parameter in the near-source region. Higher values of ?_max yield higher estimates of peak ground accelerations. For high-frequency structures, ?_max should be carefully estimated. In the near- source region both non-uniform and uniform source models can produce non-stationary high-frequency ground motions. Peak motions may not be caused by the nearest sections of the fault (even if the uniform source model is considered).     

准稳态地震动模拟和场地放大率的计算

本文讨论的是没有强震资料的地区在做地震动模拟时遇到的一些问题。模拟的地震动时程曲线基于统计的衰减数据,如地面加速度峰值或速度反应谱。由于这些数据并不包含有关地震频率成分的信息,要使用相同的统计反应谱对地震动可以随机模拟为稳态或准稳态的设想加以证明。     

Coherence of dispersed synthetic strong earthquake ground motion at small separation distances

It is shown that the observed loss of coherency of synthetic strong motion on ground surface for separation distances less than about 100 m can be described in terms of the dispersion of strong motion waves. Additional contributions to the loss of coherency from variations of material properties in the soil and from geometrical departures from perfectly flat ground surface and irregular layer geometries are not considered in this paper. It is also shown that the synthetic surface displacements over a large rectangular area (100×100 m) on ground surface can be described well by a flat surface undergoing translations and rotations only, and with only minor departures from the plane flat surface.     

Simulation of multi-support depth-varying earthquake ground motions within heterogeneous onshore and offshore sites

This paper presents a novel approach to model and simulate the multi-support depth-varying seismic motions (MDSMs) within heterogeneous offshore and onshore sites. Based on 1D wave propagation theory, the three-dimensional ground motion transfer functions on the surface or within an offshore or onshore site are derived by considering the effects of seawater and porous soils on the propagation of seismic P waves. Moreover, the depth-varying and spatial variation properties of seismic ground motions are considered in the ground motion simulation. Using the obtained transfer functions at any locations within a site, the offshore or onshore depth-varying seismic motions are stochastically simulated based on the spectral representation method (SRM). The traditional approaches for simulating spatially varying ground motions are improved and extended to generate MDSMs within multiple offshore and onshore sites. The simulation results show that the PSD functions and coherency losses of the generated MDSMs are compatible with respective target values, which fully validates the effectiveness of the proposed simulation method. The synthesized MDSMs can provide strong support for the precise seismic response prediction and performance-based design of both offshore and onshore large-span engineering structures.     

汶川地震远场地震动场地相关性与分析方法评价

为考查远场地震动的场地相关性并评价一些场地特性分析方法的适用性,采用不同方法对汶川地震山东省12个远场台站的强震记录进行了分析.选取台站分别位于按建筑抗震设计规范(CBC)场地划分中的Ⅰ—Ⅲ类场地上.地震动记录的分析方法包括傅里叶幅值谱法,地震反应谱法,水平与竖向谱比率法,参考点谱比率法,以及尾波分析等.结果表明,按傅里叶幅值谱法,地震反应谱法,水平与竖向谱比法计算得到的卓越周期均远大于台站场地的卓越周期,不同方法得到的结果之间也有较大差别,且主要反映长周期地震动的卓越频率;参考点谱比率法的结果未反映地震动的卓越周期,也与场地的卓越周期差别较大;对完整记录尾波分析所得的结果比较接近场地的卓越周期.希望本文能为考虑远场地震作用时设计谱的建立,以及场地特性估计时地震动分析方法的选取提供参考依据.     

Effect of topography and subsurface inhomogeneity on seismic rayleigh waves

The effect of topography and subsurface inhomogeneity on surface motion is investigated in the case of Rayleigh waves. In the previous paper, the same effect was investigated in the case of SV waves. Several types of topography, such as cliffs both with and without a soft layer at the foot of the slope, are considered. Computations are made using a new hybrid method combining a particle model with a finite element method. In cases of harmonic Rayleigh waves, surface motions with amplitudes as large as 1.5 to 5 times the horizontal surface displacement of the incident Rayleigh waves are produced near the slope and the sloping interface. When a Rayleigh wave propagating through a hard single-layered ground encounters a sloping interface where hard ground and soft ground make contact with each other, Rayleigh waves having two different, phase velocities are produced and they correspond to the fundamental mode, and the first mode determined by Haskell's method. In addition, the transient response when Rayleigh waves propagate through the cliff is also simulated. Assuming the vertical component of the Tokachi-oki Earthquake (1968) measured on the surface to be a Rayleigh wave, the incident Rayleigh wave can be obtained by a Fourier synthesis of eigenfunctions of Rayleigh waves.     

Effects of random variations of soil properties on site amplification of seismic ground motions

This paper investigates the effects of random variations of soil properties on site amplification of seismic waves. First, based on attenuation laws and the filtered Tajimi–Kanai spectrum, seismic motion at the base rock of a soil site is stochastically generated according to an assumed earthquake with a given magnitude and epicentral distance. Motions on the surface of this layered random soil site are calculated by nonlinear wave propagation methods, and by assuming the incoming seismic wave consisting of SH wave or combined P and SV waves. Soil properties, including shear modulus, damping ratio and mass density, as well as ground water level are considered as random in the numerical calculation. The Rosenblueth method is used to solve the random dynamic responses of the soil site. Parametric calculations are performed to investigate the effects of various parameters on site amplification of seismic waves. The mean and maximum ground motions on surface of the site are estimated. Numerical results indicate that the estimated surface motions differ substantially if the random variations of soil properties and soil saturation level are taken into consideration in the analysis.     

Scattering and diffraction of earthquake motions in irregular elastic layers,I: Love and SH waves

We describe the wave propagation through an irregularly layered, elastic medium for incoming body (SH) and surface (Love) waves. As a result of irregular geometry, each layer generates additional waves by scattering and diffraction. These additional waves modify the input motions and locally may lead to larger motions and concentrations of stresses, strains, and rotations on or below the ground surface. For engineering design, and in particular for analyses of soil-structure interaction, it is important to understand the nature and the consequences of such motions.The scattering and diffraction of Love and SH waves by irregular layers will be investigated by the weighted-residuals method. The scattered and diffracted mode shapes and spectral amplification characteristics at different frequencies will be examined and discussed.     

ANALYSIS OF AMPLIFICATION CHARACTERISTICS OF GROUND MOTIONS IN THE HEAVILY DAMAGED BELT ZONE DURING THE 1995 HYOGO-KEN NANBU EARTHQUAKE

To estimate the amplification characteristics of ground motions in the heavily damaged belt zone in Kobe City during the 1995 Hyogo-ken Nanbu earthquake, 3D wave propagation analyses of a 2D deep irregular underground structure model with a vertical discontinuity were performed at an early stage as a preliminary and qualitative study. The hyperelement method was applied to the analyses for incident plane waves expected from the wavefields due to the source mechanism. The observation records at Kobe University of the rock site were used as control motions. The ground motions on the engineering bedrock (assumed to be on the free surface of the Osaka group layers having a shear velocity of 500 m/s) and at ground surface were calculated. The effects of the deep irregular underground structure and shallow surface layers on the ground motion amplification are discussed. Although there are qualifications due to the uncertain characteristics of the input rock motion and shear wave velocities of the underground structure, the analytical results show that the ground motion in the heavily damaged belt zone were amplified due to the focusing effect of the deep irregular underground structure as well as the shallow surface layers, and that the calculated peak ground acceleration (PGA) distribution coincided closely with the distributions of structural damage. © 1997 by John Wiley & Sons, Ltd.     

台湾费丛峡谷对强地面运动的影响研究──利用单台资料及2．5维SH混合方法

本文通过格林函数反褶积方法，由台湾峡谷附近的记录资料预测峡谷区的强地面运动的时程曲线．峡谷区的理论格林函数应用２．５维ＳＨ混合方法求解．通过格林函数反褶积方法得到的峡谷区费丛１及费丛２台的位移、速度、加速度和实际资料对比，取得了满意结果．计算结果表明，峡谷底部的峰值加速度相对峡谷边缘为最小；在靠近震中的一侧，峡谷的加速度的最大振幅相对比另一侧大．还给出了其余３个台的预测结果，研究了它们的加速度傅里叶谱和反应谱．     

台湾费丛峡谷对强地面运动的影响研究──利用单台资料及2．5维SH混合方法

本文通过格林函数反褶积方法，由台湾峡谷附近的记录资料预测峡谷区的强地面运动的时程曲线．峡谷区的理论格林函数应用２．５维ＳＨ混合方法求解．通过格林函数反褶积方法得到的峡谷区费丛１及费丛２台的位移、速度、加速度和实际资料对比，取得了满意结果．计算结果表明，峡谷底部的峰值加速度相对峡谷边缘为最小；在靠近震中的一侧，峡谷的加速度的最大振幅相对比另一侧大．还给出了其余３个台的预测结果，研究了它们的加速度傅里叶谱和反应谱．     

Analysis of the spatial variation of seismic waves and ground movements from smart-1 array data

Specially designed arrays of strong motion seismographs located near earthquake sources are required for engineering studies of the near-source properties and the spatial variation of seismic waves. The SMART-1 array in Taiwan provides good records for this type of study. Careful study of the observed strong motion data permits the identification of wave types, directions and apparent wave velocities. In this paper, a principal direction ratio R (f,α) is defined; this indicates the principal direction of the motion (along a nearly straight line) within the range 0 < R < 1. Vertical motion of the ground is also included in this study. Orbit spectrum analysis is used to verify the identification of wave directions and wave types. The spatial variation of seismic waves along the principal direction is studied. From frequency-domain analysis, mathematical models of the spatial variation of ground displacement are developed using a wave-number spectrum and the cross-spectral density function between two spatial coordinates; these models in turn can provide two alternative models for the random vibration analysis of extensive structures subject to multiple point seismic excitation. The SMART-1 array data gathered during the January 29, 1981 earthquake also are used to demonstrate calculation of the ground strains and differential movements of the array site. From time-domain analysis, the spatial variation of seismic waves is defined for ground motion along the identified principal direction. The time variation of evolutionary spectra characterized by frequency-dependent parameters is used for this formulation. The SMART-1 array data again form the basis for discussion of the spatial variation of model parameters.     

Site dependence of far-source ground motions during the Wenchuan earthquake

This paper aimed to examine the site dependence and evaluate the methods for site analysis of far-source ground motions. This was achieved through the examination of frequency content estimated by different methods based on strong ground motions recorded at twelve far-source stations in Shandong province during the Wenchuan earthquake. The stations were located in sites with soil profiles ranging from code classes Ⅰ to Ⅲ. Approaches used included the Fourier amplitude spectrum (FAS), the earthquake response spectrum (ERS), the spectral ratio between the horizontal and the vertical components (H/V), the spectral ratio between the spectra at the site and at a reference site (SRRS), and coda wave analysis (CWA). Results showed that major periods of these ground motions obtained by FAS, ERS and H/V ratio methods were all evidently larger than site dominant periods; the periods were also different from each other and mainly reflected the frequency content of long period components. Prominent periods obtained by the SRRS approach neither illuminated the long period aspect nor efficiently determined site features of the motions. The CWA resulted in a period close to site period for stations with good quality recordings. The results obtained in this study will be useful for the evaluation of far-source effect in constructing seismic design spectra and in selecting methods for ground motion site analysis.     

HORIZONTAL-TO-VERTICAL SPECTRUM RATIO OF EARTHQUAKE GROUND MOTION FOR SITE CHARACTERIZATION

Nakamura's method, which uses a horizontal-to-vertical Fourier spectrum ratio of microtremor, has become popular to determine the predominant period and amplification of a site. In this study, this method is extended for earthquake ground motion recordings using new strong motion data recorded by JMA-87-type accelerometers. From the analysis of these accelerograms, horizontal-to-vertical Fourier spectrum ratios of a site for different earthquakes are also found to be stable irrespective of magnitude, distance and depth. To establish this fact, attenuation relations of velocity response spectra for horizontal and vertical components are derived for three damping ratios (0, 2 and 5 per cent) using the JMA data. Then the horizontal-to-vertical ratios of the velocity response spectra are obtained. The results show that the horizontal and vertical velocity response spectra are dependent on magnitude, distance and depth, but that their ratios are almost independent of magnitude, distance and depth. However, since the current data set consists of mostly intermediate to far field data, this observation should be limited to records of these distance ranges. Introducing station coefficients, representing site amplification, to this relation yields the value comparable to the horizontal-to-vertical Fourier spectrum ratio at a specific site. The stability of the spectrum ratio is explained by the transfer function between the ground surface and stiff-soil outcrop due to S-wave propagation. These results suggest that site amplification characteristics can be evaluated by one-point two-component surface recordings of earthquake ground motion, in a similar manner as proposed by Nakamura for microtremor. © 1997 by John Wiley & Sons, Ltd.