A stochastic model of the Fourier phase of strong ground motion

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利用EMD和子波振幅谱与相位谱关系的时变子波提取方法

本文首先分析了地震波在黏弹介质的传播规律,基于黏弹介质地震波动方程总结了时变子波振幅谱和相位谱的关系,从而得出结论,准确估计子波相位谱初值和不同时刻的子波振幅谱是实现时变子波准确提取的必要条件.在此基础上,针对传统方法限制子波振幅谱形态且受限于分段平稳假设的问题,提出了一种利用EMD(Empirical Mode Decomposition)和子波振幅谱与相位谱关系的时变子波提取方法,根据子波对数振幅谱光滑连续而反射系数对数振幅谱振荡剧烈的特点,采用EMD方法将不同时刻地震记录的对数振幅谱分解为一组具有不同振荡尺度的模态分量,通过滤除振荡剧烈分量、重构光滑连续分量提取时变子波振幅谱;再应用子波振幅谱和相位谱的关系提取时变子波相位谱,将分别提取的振幅谱和相位谱逐点进行合成,最终实现时变子波的准确提取.本文方法不需要求取Q值,适用于变Q值的情况,具有良好的抗噪性能.数值仿真和叠后实际资料处理结果表明,相比传统的分段提取方法,利用本文方法提取的时变子波准确度更高,研究成果对提高地震资料分辨率具有重要意义.     

Theoretical research on intensity envelope function of strong ground motion

（金星，瘳振鹏）Ｔｈｅｏｒｅｔｉｃａｌｒｅｓｅａｒｃｈｏｎｉｎｔｅｎｓｉｔｙｅｎｖｅｌｏｐｅｆｕｎｃｔｉｏｎｏｆｓｔｒｏｎｇｇｒｏｕｎｄｍｏｔｉｏｎ￥ＸｉｎｇＪＩＮａｎｄＺｈｅｎ－ＰｅｎｇＬＩＡＯ（ＩｎｓｔｉｔｕｔｅｏｆＥｎｇｉｎｅｅｒｉｎｇＭｅｃｈ...     

Simulation of digital earthquake accelerograms using the inverse discrete Fourier transform

Acceleration time histories of horizontal earthquake ground motion are obtained by inverting the discrete Fourier transform, which is defined by modelling the probability distribution of the Fourier phase differences conditional on the Fourier amplitude. The Fourier amplitude spectrum is modelled as a scaled, lognormal probability density function. Three parameters are necessary to define the Fourier amplitude spectrum. They are the total energy of the accelerogram, the central frequency, and the spectral bandwidth. The Fourier phase differences are simulated conditional on the Fourier amplitudes. The amplitudes are classified into three categories: small, intermediate and large. For each amplitude category, a beta distribution or a combination of a beta distribution and a uniform distribution are defined for the phase differences. Seven parameters are needed to completely define the phase difference distributions: two for each of the three beta distributions, and the weight of the uniform distribution for phase differences corresponding to small Fourier amplitudes. Approximately 300 uniformly processed horizontal ground motion records from recent California earthquakes are used to develop prediction formulas for the model parameters, as well as to validate the simulation model. The moment magnitude of the earthquakes ranges from 5.8 to 7.3. The source to site distance for all the records is less than 100 km. Copyright © 2002 John Wiley & Sons, Ltd.     

Subsoil structure and site effects: A comparison between results from SPAC and HVSR in sites of complex geology

We present the results of the analysis of array recorded microtremors at 14 sites, close to the edges of the Mygdonian basin in northern Greece (Euroseistest). These measurements were made in order to better constrain the geometry and velocity structure of the basin as the soil layers taper out close to rock outcrop, where geology is complex and we may expect significant changes of the subsoil structure over short distances. The data were analysed using the SPAC method and HVSR. The first interprets the measurements as Rayleigh waves (for the vertical component we analysed) and allows to invert a phase velocity dispersion curve from computed correlation coefficients. The second estimates a local transfer function directly, from ratios of Fourier amplitude spectra. A phase velocity dispersion curve could be derived for 12 of the 14 measurement sites, and at three of the sites no resonant frequency was observed in the HVSR. It is encouraging that we obtained good results at most of our sites, in spite of the lateral heterogeneity expected close to the edges of Euroseistest. Our results allow us to obtain shear wave velocity models at most of the measurement sites (12 out of 14). They are also useful to explore the relation between size of the array and wavelength range for which a dispersion curve may be estimated, which in our case has strong limitations. We identify the frequency of resonance of the sediments as a small loss of coherency in SPAC’s correlation coefficients. Finally, we also consider the applicability of the joint inversion of the resonance frequency determined using HVSR and the phase velocity dispersion curve obtained from SPAC.     

地震预警仪观测地脉动差异与评估场地条件的可行性研究

根据台站场地条件进行地震动参数校正,有助于提高地震预警的有效性和准确性。针对我国地震预警台网中部分台址场地条件信息不完整及观测仪器的多样性,通过采用不同灵敏度的力平衡式加速度仪、速度仪和MEMS烈度仪,同时进行大量不同类别场地的地脉动观测,多角度对比分析时、频差别,探讨基于地震预警仪观测地脉动评价场地条件的可行性。结果表明,加速度仪灵敏度越高,H/V谱比卓越频率越易识别;速度仪与力平衡式加速度仪观测的地脉动,三分向傅氏谱和H/V谱比的谱形与卓越频率均一致;与TAG-33M强震仪相比,TMA-53烈度仪观测的地脉动整体幅值略高,波形较差,但随着振幅增大趋于一致;在近80%的场地上,TAG-33M强震仪与TMA-53烈度仪观测的地脉动傅氏谱卓越频率相差＜0.5 Hz;当幅值均方根值＞0.05 Gal时,TAG-33M强震仪与TMA-53烈度仪观测的地脉动竖向和水平向傅氏谱均趋于一致;当幅值均方根值为0.02 Gal～0.05 Gal时,TAG-33M强震仪与TMA-53烈度仪观测的地脉动竖向和水平向傅氏谱谱形均有较高的相似性;当幅值均方根值＜0.02 Gal时,TAG-33M强震仪与TMA-53烈度仪观测的地脉动傅氏谱谱形相差较大,相似性低;依据TAG-33M强震仪观测地脉动H/V谱比的卓越频率判定场地类别,准确率达83.3%;TMA-53烈度仪观测地脉动的H/V谱比过于平坦,大多数场地上卓越频率识别困难。     

1976年8月松潘地震强震与脉动频谱特性的分析

地面脉动与地震地面运动之间有没有关系?是什么关系?众说不一。1976年松潘地震记录提供了探讨这一问题的条件。我们对台址进行了各种工作之后,得出的结论是:(1)地震地面运动加速度和富氏谱峰值随震级而增大;脉动幅值及谱幅值随测点高程及地表沉积层厚度而加大。(2)同一地区脉动和不同序列地震记录的幅值及谱幅值的最大值,均有一定方向性。(3)同一序列地震谱曲线特征极为相似。(4)一层穿斗木架房屋结构对地面脉动频谱特性没有影响;而后者在前者的谱曲线上有明显反应。结论:从1976年松潘地震文县台址的资料分析来看,地面脉动频谱特性在地震地面加速度谱形态或特征方面关系不明显。     

地震波动强度非平稳特征提取数学建模分析

地震对人类生活安全有很大的威胁,对建筑结构有明显的影响,研究地震波动强度非平稳特征可为地震的预防提供参考。研究地震波动强度非平稳特征提取模型,分别设定确定性参数和随机参数的取值。对地震波动强度非平稳特性进行傅里叶分析,根据分析结果选取数学模型,并对模型参数进行设定;将记录的地震波动强度所对应的数振幅谱进行分解,拆分成一组不同尺度的分量,并对其重组创建连续分量,提取地震波振幅谱;利用地震波的振幅谱和相位谱之间的关系对地震波动强度非平稳特征进行提取。经过仿真实验证明,本方法提取地震波动强度非平稳特征的准确度更高,对分析高分辨率地震资料具有重要意义。     

Response spectral ratios

At many sites on soft ground, spectral ratios (ratios of smoothed Fourier amplitude spectral ordinates at the site to those at a station on firm ground) for distant earthquakes are little sensitive to focal mechanism and coordinates and to magnitude. Spectral ratios furnish directly expected Fourier amplitude spectral ordinates at the site of interest. The corresponding response spectra can be estimated through the use of random vibration theory. This step is obviated by resorting directly to ratios of response spectral ordinates. Through comparisons for several sites on the Valley of Mexico we find that these ratios are as stable as those of Fourier amplitude spectral ordinates.     

线性SDOF体系共振动力响应的Hilbert谱分析

利用HHT方法分析了线性SDOF体系在共振状态下的强迫动力响应,系统地研究了线性SDOF体系在简谐波、线性调频波与正弦调频波输入下处于共振状态时结构动力响应的H ilbert谱与本征模态函数的特征,并且将H ilbert谱、Morlet小波谱及Fourier幅值谱所蕴含的物理意义及分辨率特性进行了比较。研究结果表明,与Fourier幅值谱相比,H ilbert谱在刻画非平稳时程的某些时变特征方面更加直观,其物理意义更加明确,而与Morlet小波谱相比H ilbert谱则具有较高的分辨率。     

基于保角变换的双谱域相位谱估计方法及其在地震子波估计中的应用(英文)

地震子波估计是地震资料处理与解释中的重要环节,它的准确与否直接关系到反褶积及反演等结果的好坏。高阶谱(双谱和三谱)地震子波估计方法是一类重要的、新兴的子波估计方法,然而基于高阶谱的地震子波估计往往因为高阶相位谱卷绕的原因,导致子波相位谱求解产生偏差,进而影响了混合相位子波估计的效果。针对这一问题,本文在双谱域提出了一种基于保角变换的相位谱求解方法。通过缩小傅里叶相位谱的取值范围,有效避免了双谱相位发生卷绕的情况,从而消除了原相位谱估计中双谱相位卷绕的影响。该方法与最小二乘法相位谱估计相结合,构成了基于保角变换的最小二乘地震子波相位谱估计方法,并与最小二乘地震子波振幅谱估计方法一起,应用到了地震资料混合相位子波估计中。理论模型和实际资料验证了该方法的有效性。同时本文将双谱域地震子波相位谱估计中保角变换的思想推广到三谱域地震子波相位谱估计中。     

特殊长周期地震动的参数特征研究

近断层脉冲型地震动和远场软土层场地类谐和地震动是两类特殊的长周期地震动,当前的规范均很少对这两类地震作用进行具体的规定。研究了近断层脉冲型和远场类谐和地震动的幅值、幅值比（V／A,D／V）、傅里叶幅值谱和反应谱的差别,分析了相位角和作用循环周期数对简单脉冲的影响,并用于解释两类特殊地震动的工程特征。以集集地震动为数据基础,分析了两类长周期地震动的傅里叶谱和反应谱特征;将平均加速度和位移规准反应谱分别与规范设计谱进行了比较。建议设计谱在长周期段考虑近断层作用和软土场地面波效应的影响。     

Enhancement of Signal-to-noise Ratio in Natural-source Transient Magnetotelluric Data with Wavelet Transform

—For audio-frequency magnetotelluric surveys where the signals are lightning-stroke transients, the conventional Fourier transform method often fails to produce a high quality impedance tensor. An alternative approach is to use the wavelet transform method which is capable of localizing target information simultaneously in both the temporal and frequency domains. Unlike Fourier analysis that yields an average amplitude and phase, the wavelet transform produces an instantaneous estimate of the amplitude and phase of a signal. In this paper a complex well-localized wavelet, the Morlet wavelet, has been used to transform and analyze audio-frequency magnetotelluric data. With the Morlet wavelet, the magnetotelluric impedance tensor can be computed directly in the wavelet transform domain. The lightning-stroke transients are easily identified on the dilation-translation plane. Choosing those wavelet transform values where the signals are located, a higher signal-to-noise ratio estimation of the impedance tensor can be obtained. ? In a test using real data, the wavelet transform showed a significant improvement in the signal-to-noise ratio over the conventional Fourier transform.     

基于双谱幅值和相位重构的地震子波提取

利用地震记录双谱中包含子波的幅值和相位信息，以及其超强的抗噪声干扰能力，采用一种基于双谱幅值和相位重构的地震子波提取方法，首先提取出子波幅值及相位信息，进而通过傅立叶反变换，使子波得以完全恢复.本文针对双谱相位重构递推公式，提出一种新的初值选取方法，使地震子波估计的稳定性得到了提高.仿真实验证实了该方法的可行性.     

Calculation of selected ordinates of fourier spectra

A method is presented for calculating single or, by repeated use, selected ordinates of Fourier spectra rapidly and efficiently. The approach differs from standard methods in that any frequency consistent with the interval of digitization may be chosen and records of arbitrary length may be analysed. The method is based on the relation between Fourier spectra of an accelerogram and the final response of an undamped oscillator to the same accelerogram. This relation is reviewed and extended to aid the development of the computing method and to assist in the interpretation of Fourier spectrum techniques in earthquake engineering. Because only the terminal values of the response of an undamped oscillator are required to define the Fourier spectra, repeated application of superposition is used to form equivalent excitations with durations of only one-quarter of the period of the oscillator.     

CALCULATION OF THE VERTICAL GRADIENT OF THE GRAVITY FIELD USING THE FOURIER TRANSFORM*

Fourier transform techniques have been used to calculate the theoretical filter (amplitude) response function of Nth order vertical derivative continuation operation. The amplitude response functions of the vertical gradient and its continuation follow from the same. These response functions are subsequently used to calculate the weighting coefficients suitable for two dimensional equispaced data. A shortening operator has been incorporated to limit the extent of the operator. For comparative study, some of the developed coefficient sets and the one presented in this paper are analysed in the frequency domain and their merits and demerits are discussed.     

Earthquake accelerogram simulation with statistical law of evolutionary power spectrum

By using the technique for evolutionary power spectrum proposed by Nakayama and with reference to the Kameda formula, an evolutionary spectrum prediction model for given earthquake magnitude and distance is established based on the 80 near-source acceleration records at rock surface with large magnitude from the ground motion database of western U.S.. Then a new iteration method is developed for generation of random accelerograms non-stationary both in amplitude and frequency which are compatible with target evolutionary spectrum. The phase spectra of those simulated accelerograms are also non-stationary in time and frequency domains since the interaction between amplitude and phase angle has been considered during the generation. Furthermore, the sign of the phase spectrum increment is identified to accelerate the iteration. With the proposed statistical model for predicting evolutionary power spectra and the new method for generating compatible time history, the artificial random earthquake accelerograms non-stationary both in amplitude and frequency for certain magnitude and distance can be provided.     

Empirical scaling of Fourier spectrum amplitudes of recorded strong earthquake accelerations in terms of Modified Mercalli Intensity, local soil conditions and depth of sediments

Empirical scaling equations of Fourier spectrum amplitudes in terms of the Modified Mercalli Intensity (MMI), local soil conditions (‘rock’, stiff soil, and deep soil), and local geologic conditions (depth of sediments) are presented. It is shown that both soil and geological site effects should be used together in estimation of the site specific Fourier amplitude spectra.     

根据渐进谱的统计规律生成地震加速度时程

基于美国西部80条基岩上的近场强震记录， 采用Nakayama方法生成记录的渐进谱， 并参照Kameda方式，用统计方法建立了根据震级、距离等地震参数预测渐进谱的统计模型. 提出一种以渐进谱为目标谱的生成幅值和频率非平稳地震加速度时程的迭代方法. 由于考虑了渐进谱幅值和相位的相互影响，所生成的时程的相位也是时频非平稳的，并在相位调整中识别了相位谱增量符号以加速迭代收敛进程. 最后根据统计回归的目标渐进谱模型和本文提出的拟合目标渐进谱的方法，可生成不同震级、距离条件下的幅值和频率均非平稳的地震加速度时程.