Strong ground motion prediction using macro–micro analysis method

The authors propose a new analysis method, called the macro–micro analysis method (MMAM) in a companion paper. (Earthquake Engng. Struct. Dyn., this issue) for strong motion prediction with higher resolution and accuracy. The MMAM takes advantage of the bounding medium theory to obtain optimistic and pessimistic estimates of the expected strong motion and the singular perturbation expansion that leads to an efficient multi‐scale analysis. The results of the numerical simulation with the MMAM are given as the sum of waves of low resolution covering the whole city and waves of high resolution for each part of the city. While the huge computation amount is reduced by the MMAM, the computation amount is huge still. For resolving this problem, this paper applies the finite element method with voxel element to numerical simulation tools after some numerical verification. To reproduce complicated material properties of surface soft deposits, fundamental hysteresis attenuation is implemented in the three‐dimensional simulation code. The proposed method is verified by carrying out the strong motion prediction with MMAM and comparing with measured data. In addition, the effect of three‐dimensional soil–structure and frequency component on the maximum velocity distribution, which is simulated by proposed method with high spatial resolution, is discussed. Copyright © 2005 John Wiley & Sons, Ltd.     

Current state of integrated earthquake simulation for earthquake hazard and disaster

This paper presents the current state of integrated simulation for earthquake hazard and disaster. This simulation takes advantage of the macro–micro analysis method; this method estimates an earthquake’s strong motion with high spatial and temporal resolution, using the bounding medium theory to obtain optimistic and pessimistic estimates of expected strong motion distribution and the singular perturbation expansion that results in an efficient multi-scale analysis. Integrated earthquake simulation calculates seismic responses for all structures in a target area, inputting simulated strong ground motion to a structure analysis method that is plugged into the system by means of a wrapper; a suitable method, linear or nonlinear, is chosen depending on the type of the structure. The results of all simulations are visualized so that residences and government officials can share a common recognition of earthquake hazard and disaster. Two examples of this integrated earthquake simulations are presented; one is made by plugging nonlinear structure analysis methods into the system, and the other is made for an actual city, the computer model of which is constructed with the help of available geographical information systems.     

Studies on seismic waves

The development of seismic wave study in China in the past four years is reviewed. The discussion is divided into several aspects, including seismic wave propagation in laterally homogeneous media, laterally heterogeneous me-dia, anisotropie and porous media, surface wave and seismic wave inversion, and seismic wave study in prospect-ing and logging problems. Important projects in the current studies on seismic wave is suggested as the develop-ment of high efficient numerical methods, and applying them to the studies of excitation and propagation of seis-mic waves in complex media and strong ground motion, which will form a foundation for refined earthquake haz-ard analysis and prediction.     

地震波研究://car

回顾了近4年来中国地球物理学家在地震波研究方面取得的主要进展. 分别简要地讨论了层状均匀介质、横向不均匀介质和多孔介质中的地震波传播，地震面波及波形反演，以及地震勘探、测井问题中的地震波研究方面取得的新成果. 指出当前地震波研究的重要课题是发展高效的数值方法，并利用该方法开展复杂介质中的地震波激发和传播，以及强地面运动的研究，为精细的地震危险分析与预测奠定基础.      

Studies on seismic waves

The development of seismic wave study in China in the past four years is reviewed. The discussion is divided into several aspects, including seismic wave propagation in laterally homogeneous media, laterally heterogeneous media, anisotropic and porous media, surface wave and seismic wave inversion, and seismic wave study in prospecting and logging problems. Important projects in the current studies on seismic wave is suggested as the development of high efficient numerical methods, and applying them to the studies of excitation and propagation of seismic waves in complex media and strong ground motion, which will form a foundation for refined earthquake hazard analysis and prediction.     

含裂隙介质中地震波传播的振幅异常

本文首先利用两相介质模型从理论上简要分析了地震波在含裂隙介质中的传播特性.由初步理论研究结果与简单计算实例可以看出,在含裂隙介质或两相介质中有可能发现并观测到地震波形状与振幅的某些变化.其次,利用马鞍山矿区爆破及唐山、松潘、马边、康定等地区小地震的观测资料,着重提出了研究大震前振幅异常或振幅比异常的一些实际方法,认为大震前外围介质已属于微破裂介质或两相介质.得出并详细研究了震前振幅异常,尤其是振幅比异常的一些基本特性.最后,本文对影响到振幅异常的发现与分析的某些因素作了简要的讨论.文中所得结果与初步结论可能有助于地震预报的研究工作.      

Ground motion characteristics of the Chi‐Chi earthquake of 21 September 1999

The purpose of this paper is to investigate the ground motion characteristics of the Chi‐Chi earthquake (21 September 1999) as well as the interpretation of structural damage due to this earthquake. Over 300 strong motion records were collected from the strong motion network of Taiwan for this earthquake. A lot of near‐field ground motion data were collected. They provide valuable information on the study of ground motion characteristics of pulse‐like near‐field ground motions as well as fault displacement. This study includes: attenuation of ground motion both in PGA and spectral amplitude, principal direction, elastic and inelastic response analysis of a SDOF system subjected to near‐field ground motion collected from this event. The distribution of spectral acceleration and spectral velocity along the Chelungpu fault is discussed. Based on the mode decomposition method the intrinsic mode function of ground acceleration of this earthquake is examined. A long‐period wave with large amplitude was observed in most of the near‐source ground acceleration. The seismic demand from the recorded near‐field ground motion is also investigated with an evaluation of seismic design criteria of Taiwan Building Code. Copyright © 2000 John Wiley & Sons, Ltd.     

Estimation of rocking and torsion associated with surface waves extracted from recorded motions

By exploiting the capability of identifying and extracting surface waves existing in a seismic signal, we can proceed to estimate the angular displacement (rotation about the horizontal axis normal to the direction of propagation of the wave; rocking) associated with Rayleigh waves as well as the angular displacement (rotation about the vertical axis; torsion) associated with Love waves.For a harmonic Rayleigh (Love) wave, rocking (torsion) would be proportional to the harmonic vertical (transverse horizontal) velocity component and inversely proportional to the phase velocity corresponding to the particular frequency of the harmonic wave (a fact that was originally exploited by Newmark (1969) [15] to estimate torsional excitation). Evidently, a reliable estimate of the phase velocity (as a function of frequency) is necessary. As pointed out by Stockwell (2007) [17], because of its absolutely referenced phase information, the S-Transform can be employed in a cross-spectrum analysis in a local manner. Following this suggestion a very reliable estimate of the phase velocity may be obtained from the recordings at two nearby stations, after the dispersed waves have been identified and extracted. Synthesis of the abovementioned harmonic components can provide a reliable estimate of the rocking (torsional) motion induced by an (extracted) Rayleigh (Love) wave.We apply the proposed angular displacement estimation procedure for two well recorded data sets: (1) the strong motion data generated by an aftershock of the 1999 Chi-Chi, Taiwan earthquake and recorded over the Western Coastal Plain (WCP) of Taiwan, and (2) the strong motion data generated by the 2010 Darfield, New Zealand earthquake and recorded over the Canterbury basin. The former data set is dominated by basin-induced Rayleigh waves while the latter contains primarily Love waves.     

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.     

断层区强余震波传播及影响的动态模拟研究

本文用动态光弹性技术模拟研究了强震发生时,强余震波在断层区内的传播、对江川县城区等关注位置的影响,以及断层对地震波的阻隔作用。结果表明,研究方法实用有效,结果直观,对地震分析具有参考价值。     

Reflection and transmission of attenuated waves at the boundary between two dissimilar poroelastic solids saturated with two immiscible viscous fluids

The phenomenon of reflection and transmission of plane harmonic waves at the plane interface between two dissimilar poroelastic solids saturated with two immiscible viscous fluids is investigated. Both porous media are considered dissipative due to the presence of viscosity in pore‐fluids. Four attenuated (three dilatational and one shear) waves propagate in such a dissipative porous medium. A finite non‐dimensional parameter is used to define the effective connections between the surface‐pores of two media at their common interface. Another finite parameter represents the gas‐share in the saturation of pores. An attenuated wave in a dissipative medium is described through the specification of directions of propagation and maximum attenuation. A general representation of an attenuated wave is defined through its inhomogeneous propagation, i.e., different directions for propagation and attenuation. Incidence of an inhomogeneous wave is considered at the interface between two dissipative porous solids. This results in four reflected and four transmitted inhomogeneous waves. Expressions are derived for the partition of incident energy among the reflected and transmitted waves. Numerical examples are studied to determine the effects of saturating pore fluid, frequency, surface‐pore connections and wave inhomogeneity on the strengths of reflected and transmitted waves. Interaction energy due to the interference of different (inhomogeneous) waves is calculated in both the dissipative porous media to verify the conservation of incident energy.     

三维层状孔隙介质中弹性波的一种积分表达式I：理论

孔隙介质弹性波传播理论在地球物理勘探、地震工程和岩土动力学等领域有着广泛的应用.而孔隙介质中的弹性波受孔隙度、渗透率、流体黏滞系数等参数的影响,因此研究波场的传播特征将有助于分析和提取这些信息.本文在Biot理论的基础上,针对三维层状孔隙介质模型,利用在合成理论地震图的研究中已经被证实具有稳定、高效且适用范围较广的Luco-Apsel-Chen（LAC）广义反透射方法,给出了弹性波场的一种积分形式的半解析解,可通过数值方法高效、准确地计算层状孔隙介质中的理论波场,所以该积分形式的半解析解可为三维层状孔隙介质波场传播特征的理论数值模拟研究提供一种新的途径和手段.     

Parallel PSM/FDM Hybrid Simulation of Ground Motions from the 1999 Chi-Chi,Taiwan, Earthquake

-- A new technique for the parallel computing of 3-D seismic wave propagation simulation is developed by hybridizing the Fourier pseudospectral method (PSM) and the finite-difference method (FDM). This PSM/FDM hybrid offers a good speed-up rate using a large number of processors. To show the feasibility of the hybrid, a numerical 3-D simulation of strong ground motion was conducted for the 1999 Chi-Chi, Taiwan earthquake (M_w 7.6). Comparisons between the simulation results and observed waveforms from a dense strong ground motion network in Taiwan clearly demonstrate that the variation of the subsurface structure and the complex fault slip distribution greatly affect the damage during the Chi-Chi earthquake. The directivity effect of the fault rupture produced large S-wave pulses along the direction of the rupture propagation. Slips in the shallow part of the fault generate significant surface waves in Coastal Plain along the western coast. A large velocity gradient in the upper crust can propagate seismic waves to longer distances with minimum attenuation. The S waves and surface waves were finally amplified further by the site effect of low-velocity sediments in basins, and caused the significant disasters.     

Comprehensive numerical analysis of fault‐structure systems – Computation of the large‐scale seismic structural response to a given earthquake scenario –

The seismic structural response is affected by temporal and spatial variations in strong ground motion. It can be evaluated through the fault‐structure system: the fault mechanism, wave propagation through the crust, amplification near the surface, and soil‐structure interaction. To analyze this system at high resolution and accuracy, we previously proposed a new multiscale analysis method and numerically verified its validity. However, the problem of the extremely large computation cost of constructing a three‐dimensional numerical model and solving the discretized governing equations still remains. Here, we introduce a new method to resolve these difficulties. By combining this new method with our multiscale analysis, we developed a tool for fault‐structure system analysis. The accuracy of this tool is verified by comparing it to a Green's function solution. Finally, we demonstrate the potential utility of the method by estimating the seismic response of a large and complex underground highway junction in a given earthquake scenario. Copyright © 2011 John Wiley & Sons, Ltd.     

Spatial variation and stochastic modelling of seismic differential ground movement

Specially designed arrays of strong motion seismographs located near earthquake sources are required for engineering studies of near-source earthquake properties as well as spatial variation of seismic waves. The SMART-1 array in Tath provides good records for this type of study. Based on the SMART-1 array data, the analysis of the principal direction wave propagation and the space-time correlation of some events recorded by SMART-1 have been studied. A stoce model for predicting the differential ground movement was also developed. This stochastic model includes the effect of source characteristics, attenuation of wave passage and spatial correlation characteristics. The performance of this more discussed and compared with the ground movement recorded by the SMART-1 array. From the present study, it is that spatial correlations do exist as seismic waves propagate across the array site. Generally, the loss of coherence is direction of propagation can be explained by energy at the same frequency exhibiting a slightly different velocity with the measurement intervals. It is also concluded that the phase velocity of seismic waves and the corner frequency of the grep displacement spectrum are controlling factors in the prediction of the root mean square of differential grep displacement.     

Simplification of strong ground motion considering inelastic responses of structures

Simplification of strong ground motions to 1 cycle sine waves was investigated from the elastic and inelastic earthquake response analyses and response analyses under sine wave input using single‐degree‐of‐freedom systems. Strong ground motions could be simplified to 1 cycle sine waves if large plastic deformations, with ductility factor more than 2, were assumed. This is because the approximate maximum responses from input sine waves are determined by the initial response cycle, due to period elongation and plastic energy dissipation of the systems. A sine wave whose acceleration amplitude is the peak ground acceleration (PGA) and whose period is that of an equivalent 1 cycle sine wave is proposed. The period of an equivalent sine wave is easily obtained from the elastic response acceleration spectrum of a seismic record. This means that the inelastic responses are approximately determined by the PGA and an equivalent 1 cycle sine wave period. Therefore, an equivalent 1 cycle sine wave period provides a single index to express the frequency characteristics of a strong ground motion. Copyright © 2000 John Wiley & Sons, Ltd.     

Pure acoustic wave propagation in transversely isotropic media by the pseudospectral method

Seismic wave propagation in transversely isotropic (TI) media is commonly described by a set of coupled partial differential equations, derived from the acoustic approximation. These equations produce pure P‐wave responses in elliptically anisotropic media but generate undesired shear‐wave components for more general TI anisotropy. Furthermore, these equations suffer from instabilities when the anisotropy parameter ε is less than δ. One solution to both problems is to use pure acoustic anisotropic wave equations, which can produce pure P‐waves without any shear‐wave contaminations in both elliptical and anelliptical TI media. In this paper, we propose a new pure acoustic transversely isotropic wave equation, which can be conveniently solved using the pseudospectral method. Like most other pure acoustic anisotropic wave equations, our equation involves complicated pseudo‐differential operators in space which are difficult to handle using the finite difference method. The advantage of our equation is that all of its model parameters are separable from the spatial differential and pseudo‐differential operators; therefore, the pseudospectral method can be directly applied. We use phase velocity analysis to show that our equation, expressed in a summation form, can be properly truncated to achieve the desired accuracy according to anisotropy strength. This flexibility allows us to save computational time by choosing the right number of summation terms for a given model. We use numerical examples to demonstrate that this new pure acoustic wave equation can produce highly accurate results, completely free from shear‐wave artefacts. This equation can be straightforwardly generalized to tilted TI media.     

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.     

S‐wave kinematics in acoustic transversely isotropic media with a vertical symmetry axis

Acoustic transversely isotropic models are widely used in seismic exploration for P‐wave processing and analysis. In isotropic acoustic media only P‐wave can propagate, while in an acoustic transversely isotropic medium both P and S waves propagate. In this paper, we focus on kinematic properties of S‐wave in acoustic transversely isotropic media. We define new parameters better suited for S‐wave kinematics analysis. We also establish the travel time and relative geometrical spreading equations and analyse their properties. To illustrate the behaviour of the S‐wave in multi‐layered acoustic transversely isotropic media, we define the Dix‐type equations that are different from the ones widely used for the P‐wave propagation.     

张北地震在北京市激发的二维强地面运动的模拟

张北县距离北京市约200多km,1998年1月的张北地震是近期北京周边地区发生的一次较强规模的地震,研究它在北京地区引起的强地面运动,有助于分析首都圈内的地震危害性,为地震减灾提供理论帮助.本文利用新的计算工具-局域离散波数法,模拟了张北地震激发的包括来自上地壳、moho面反射波、首播等在内的全波场在北京西部引起的2D强地面运动,分析了该区内第三纪、第四纪沉积地层对于地震的放大效应,得出的主要结论有,薄的第四纪沉积盖层的地点放大效应比厚的第三纪盖层的大很多,说明介质物性是决定地点放大效应的根本原因;不同物性的沉积盖层,在R、Z分量上的放大作用不一样,体现了地点放大效应的复杂性,值得在今后的研究中继续探讨.