A note on the noise amplitudes in some strong motion accelerographs

The amplitudes of digitization and processing noise in strong motion digital and analog accelerographs are discussed and compared with those for hand and automatic digitization. By finding the period bands for which the signal-to-noise ratio in recorded accelerograms is greater than one, the values for the pass-band cutoff periods for data processing are presented. The Empirical scalings for amplitudes in terms of: (1) earthquake magnitude and epicentral distance and, (2) Modified Mercalli Intensity at the recording site have been employed.     

Rocking strong earthquake accelerations

In this paper, the method presented by Lee and Trifunac (1985) for generating synthetic torsional accelerograms has been extended to the estimation of synthetic rocking accelerograms and of their response spectra. Results from our previous regression analyses for the characterization of strong shaking in terms of (1) earthquake magnitude and epicentral distance, or (2) Modified Mercalli Intensity at the site are utilized here again. The effects of geologic environment, in terms of site parameters or the representative depth of sediments, which influence amplification, and the dispersive properties of ground motion are also included. The synthetic rocking accelerogram is then constructed from the horizontal and vertical acceleration components.     

Generation of artificial strong motion accelerograms

A method for generating synthetic strong motion accelerograms for use in engineering design is presented. This method utilizes the model proposed by Trifunac in 1971²⁷ in conjunction with the recent empirical scaling functions for characterization of amplitudes and duration of strong shaking in terms of (i) earthquake magnitude, M, and epicentral distance, R, or (ii) Modified Mercalli Intensity (MMI) at the recording station. The method also enables one to consider the desired levels of confidence that the synthetic motion will not be exceeded, direction of ground motion (horizontal or vertical) and the dispersive properties of geologic environment beneath and surrounding the station. The principal features of this approach are that the resulting accelerograms have non-stationary frequency and amplitude characteristics which are in full agreement with known principles of wave propagation through a stratified medium, and that the Fourier amplitudes and the frequency-dependent duration are scaled in accordance with known trends as in recorded accelerograms.     

Preliminary empirical model for scaling fourier amplitude spectra of strong ground acceleration in terms of modified mercalli intensity and recording site conditions

This paper presents an empirical model for scaling Fourier amplitude spectra of ground acceleration during strong earthquake shaking in terms of the reported Modified Mercalli Intensity (MMI) and the simplified characteristics of the geologic environment at the recording station. This analysis shows that (i) for the intermediate and high-frequency motions the spectral amplitudes approximately double for every level of the MMI; that (ii) the uncertainties associated with estimation of Fourier spectral amplitudes in terms of MMI are not greater than the uncertainties associated with similar estimation in terms of earthquake magnitude and epicentral distance; that (iii) the high frequency spectral amplitudes tend to be greater on basement rock sites relative to alluvium sites, with this trend being reversed for the low-frequency spectral amplitudes; and that (iv) the spectral amplitudes of very high-frequency vertical shaking are equal to or higher than the corresponding spectral amplitudes for horizontal shaking.     

Seismic motion and response prediction alternatives

Statistical methods are available which predict the maximum response of simple oscillators given the peak acceleration (A_p), peak velocity (V_p) or peak displacement (D_p) of seismic ground motions. An alternative parameter, namely an ordinate (or ordinates) of the Fourier amplitude spectrum of ground motion acceleration, FS(f), may in fact be a preferred predictor of peak response, especially in a frequency range close to f. Other statistical methods (attenuation laws) use distance R and other parameters such as magnitude (M), Modified Mercalli epicentral Intensity (I_o) and Modified Mercalli site Intensity (MMI or I_s) to predict spectral velocity (S_v(f)), etc. In using such approaches, it is most desirable to know the total uncertainty in the predicted peak response of the system given the starting parameter values. An extensive strong motion data set is used to study these questions, The most direct prediction models are found to be preferable (have lower prediction dispersion) but data may not be available in all regions to permit their use.     

A note on computing uniform risk spectra from intensity data on earthquake occurrences

Reliability of uniform risk Fourier and response spectra, derived from Modified Mercalli Intentsity data, on earthquake occurrences has been investigated by comparing these spectra with the corresponding spectra based on magnitude data. By treating the site intensity from ab earthquake, with given maximum intensity and epicentral distance, as a random variable, a Bayesian probability approach is suggested to compute the intensity spectra, in the present study. Examples of comparison of the intensity and the magnitude spectra for two typical sites in the highly seismic northeast Indian region have shown very good consistency and agreement between the two spectra. Thus, in the proposed approach, intensity data can be used to get quite reliable design spectra for regions where the history of instrumentally recorded data is not sufficient for engineering seismic risk analysis.     

The Modified Mercalli intensity and the geometry of the sedimentary basin as scaling parameters of the frequency dependent duration of strong ground motion

Several new empirical equations of the frequency dependent duration of strong earthquake ground motion are presented. The duration is considered as being composed of two parts: (1) the duration of stong motion as it is observed at recording stations located on basement rocks, and (2) the prolongation of this duration for stations located on sediments. The first part, called the ‘basic duration’, is modelled in terms of the Modified Mercalli intensity and (in some cases) the hypocentral distance. The depth of the sediments under the station, the distance from the station to the rocks surrounding it, and the angular measure of the size of those rocks (as seen from the station) are chosen as the parameters for modelling the prolongation of the duration. The new empirical equations are compared (a) with each other, (b) with our previous models which used similar ‘prolongation’ terms, but the ‘basic duration’ was expressed in terms of the magnitude of the earthquake and the source-to-station distance, and (c) with models with ‘intensity-type’ ‘basic duration’, but with a simplified ‘prolongation’ term (the geological conditions at the stations are modeled by lumping all the sites into three groups: basement rock, sediments and intermediate geology). This collection of models is found to have good internal consistency. The choice of the proper model depends on the availability of the earthquake and site parameters. The residuals of the empirical regression equations are found to have similar distribution functions for all the models. An explicit functional form for such distributions is proposed, and the frequency dependent coefficients are found for all the models of duration. This allows one to predict (for each set of earthquake and site parameters) the probability of exceedance of any given level of duration of strong ground motion at a given frequency.     

Empirical criteria for liquefaction in sands via standard penetration tests and seismic wave energy

Five empirical equations are presented, describing initiation of liquefaction in fully saturated sands, in terms of standard penetration values and initial overburden stress on level ground. These equations are based on 90 case histories of liquefaction, and relate empirically the pore pressure increase to earthquake magnitude, epicentral distance, energy of strong motion at the site, peak ground velocity, Fourier amplitude of velocity and duration of strong motion. The results are given in terms of raw standard penetration values corrected for overburden pressure. For all the models presented, the standard deviation of the residuals, representing the differences between the observed and predicted penetration values is less than six blow counts.     

拉萨地震台PET重力仪同震响应特征

从面波延迟时间、初动方向、波幅、同震持续时间等4个方面研究拉萨台PET重力仪的同震响应特征,结果表明：（1）同震响应的面波延迟时间与地震震中距离具有较好正相关性;（2）初动方向没有规律;（3）同震响应的波幅不仅与地震震级大小有关,还与震中距远近有关;（4）远震的同震波一般表现为脉冲形式,近震除了脉冲外,还有阶跃;（5）同震波的延续时间与震级没有明确的比例关系.这有助于对重力仪器进行深入的了解,可以为未来西藏地区监测台网布设方案提供参考数据.     

基于EPA的重大工程设计地震动确定

根据第四代《中国地震动参数区划图》编制中采用有效峰值加速度(EPA)的特点,结合概率性方法和确定性方法优点,建议了确定重大工程场点设定地震的原则和方法。该方法根据危险一致的原则选定最大贡献潜源,利用震级空间联合分布函数确定设定地震震级、震中距,最后根据震级、震中距和地震动衰减关系确定设计地震动反应谱。     

基于卷积神经网络的地震预警震级持续估算方法研究

为提高地震预警震级快速持续估算结果的准确性,本文构建了基于多种地震动特征参数的卷积神经网络震级估算CNN-M模型.该模型基于日本KiK-net强震动观测记录,利用其P波触发后3～ 10s时间窗内的幅值参数、周期参数、烈度参数、信噪比参数共11种地震波特征参数以及震中距参数作为输入.本文所建立的CNN-M模型随着地震发生...     

基于工程应用的频率时变模型研究

对美国NGA数据库中的3551组地震记录按场地条件、震级、震中距进行了分组,采用一维连续小波变换得到每条记录的小波功率谱。研究任意时间处小波功率谱最大值所对应的主频率,并对每个地震动分组内的主频率值做一定时间窗内的均方根处理,分别采用线性函数、指数函数和指数三角函数模型来拟合得到的主频率随时间变化的曲线,最后分析了场地条件、震级和震中距对频率时变曲线的影响,并给出了每个分组内水平向和竖直向地震动主频率随时间变化的模型参数。结果表明:地震动主频率随时间的增大逐渐减小,但是竖直向要比水平向衰减得快一些。     

Prediction of the number of equivalent cycles for earthquake motion

This paper addresses new prediction models for computing the number of equivalent cycles in liquefaction analyses. Three models are presented for the Italian seismicity as a function of synthetic ground motion parameters that are often available from earthquake data web-sites immediately after events. In particular, it is observed that the number of earthquake cycles can be best estimated from the five following parameters: peak ground acceleration; epicentral distance; Arias Intensity; the mean period; and, the frequency of zero crossings. However, strong estimations can be obtained from the first three parameters only. We use statistical indicators to determine the goodness of the models and the usefulness of the selected independent variables, and we present a comparative analysis to validate our predictive equations. Moreover, this paper describes the existing correlation between magnitude and cycle numbers. The study is primarily based on Italian acceleration records, even if the database is also expanded to recorded European, Japanese and American events to amplify the magnitude values range. These simplified models are useful in addressing practical earthquake engineering problems which require the knowledge of number of equivalent cycles.     

Order statistics of functionals of strong ground motion for a class of renewal processes

In this paper, probability distribution functions are derived for the order statistics of various functionals of strong ground motion at a site. These functionals can be: Modified Mercalli Intensity (MMI), peak ground acceleration (PGA), Fourier spectral amplitudes of acceleration, response spectrum amplitudes (spectral displacement, pseudo-spectral velocity and pseudo-spectral acceleration), and amplitudes of the peaks (local maxima and local minima) in the time historyof the response of SDOF and MDOF structures at the site. Three parameters of the response of a structure are considered: displacement, shear force and bending moment at each level (storey) of the structure. The earthquake sources contributing to the risk of ground motion at the site are a number of point, area or volume sources, each with defined frequency of occurence-magnitude relationship. The magnitudes of the possible events at these sources are discretized, and the occurrence of events of different magnitudes are assumed to be statistically independent. For each magnitude, it is assumed that the eartquakes occur in a Poissonian sequence or in a renewal process which is a generalization of the Poissonian. For these assumptions, the probability distribution functions are presented for the number of earthquakes, n, during which a given level of site or structural response is exceeded during the exposure time, and for the return period of the exceedances. For example, for single-degree- of-freedom: (SDOF) or multi-degree-of-freedom structures, (MDOF) n can be the number of earthquakes during which the response of a storey will exceed a given level at least m times(m = 1, 2, 3,…) during the exposure time. These probability distribution functions can be used to extend the concept of uniform probability functionals to more than one exceedance. A more important application is to generalize the uniform probability functionals method of site response (uniform probability Fourier or response spectra) to uniform probability envelopes of displacement, shears and bending moments of a given structure. The uniform probability envelopes can be for exceedance at least once during at least one earthquake, or, in general, for exceedance at least m times per earthquake (m = 1, 2,…) during at least n earthquakes. In other words, during at least n earthquakes at least m peaks in the response can be higher than the specified level. Such uniform probability envelopes can be used (1) to define new design guidelines for building codes based on cost-benefit analysis; (2) to construct more refined probability distribution functions for the damage and total economic losses caused by earthquakes; and (3) to develop planning and decision strategies on strengthening and retrofitting existing buildings.     

基于人工神经网络的仪器地震烈度预测模型研究

地震发生后,针对能够快速预测震中附近的烈度分布情况的问题,首先对632次地震触发的台站进行筛选,对2 231个台站触发后20 s内有效的7个地震动参数以及震级和震源距的信息进行提取,并利用人工神经网络对所选数据样本进行训练,建立三种有效的预测模型。研究结果显示模型一所选的输入参数为7个,不利用震源参数,在预测中有着较好的时效性,从第1 s到20 s,预测的平均烈度差值逐渐减小到0.45;模型二所选的输入参数为8个,利用了震源距信息,可以用于烈度级别的预测,预测的平均烈度差值逐渐减小到0.36;模型三所选的输入参数为9个,预测结果较好,可用于震后烈度场的实时预测,平均烈度差值逐渐减小到0.31。利用提出的3种模型对两次地震事件进行烈度预测,预测烈度差值取整后分别有95%和76%以上在1以内,有着较好的结果,可以用于地震预警当中。     

Earthquake ground motion modeling of induced seismicity in the Groningen gas field

A physics‐based numerical approach is used to characterize earthquake ground motion due to induced seismicity in the Groningen gas field and to improve empirical ground motion models for seismic hazard and risk assessment. To this end, a large‐scale (20 km × 20 km) heterogeneous 3D seismic wave propagation model for the Groningen area is constructed, based on the significant bulk of available geological, geophysical, geotechnical, and seismological data. Results of physics‐based numerical simulations are validated against the ground motion recordings of the January 8, 2018, M_L 3.4 Zeerijp earthquake. Taking advantage of suitable models of slip time functions at the seismic source and of the detailed geophysical model, the numerical simulations are found to reproduce accurately the observed features of ground motions at epicentral distances less than 10 km, in a broad frequency range, up to about 8 Hz. A sensitivity analysis is also addressed to discuss the impact of 3D underground geological features, the stochastic variability of seismic velocities and the frequency dependence of the quality factor. Amongst others, results point out some key features related to 3D seismic wave propagation, such as the magnitude and distance dependence of site amplification functions, that may be relevant to the improvement of the empirical models for earthquake ground motion prediction.     

Correlation of pseudo relative velocity spectra with site intensity, local soil classification and depth of sediments

Empirical regression equations are presented for scaling Pseudo Relative Velocity Spectra, PSV(T), in terms of the Modified Mercalli Intensity M.M.I., local soil classification at the recording site (‘rock’, stiff or deep soil), and local geological condition (depth of sediments). It is shown that both the local soil classification and the local geological depth of sediments should be used simultaneously in the evaluation of site specific response spectra.     

基于小波变换的地震动时-频特性研究

对美国NGA,采用一维连续小波变换得到每条记录的小波功率谱。研究了任意时间处小波功率谱最大值所对应的主频率。结果表明:地震动主频率随时间的增大逐渐减小;竖向地震动分量的主频比水平向分量随时间减小更快。分别采用线性函数模型、指数函数模型和指数三角函数模型,分析了场地、震级和震中距对主频变化曲线的影响,拟合了主频率在不同场地条件、震级、震中距等情况下随时间的变化曲线,水平向和竖向的频率时变曲线整体上都是随时间递减的,且竖向衰减得更快些,大多数情况下竖向记录的高频成分比水平向记录的相应成分要多。