WAVELET ESTIMATION USING THE MULTITAPER METHOD1

An accurate estimate of the seismic wavelet on a seismic section is extremely important for interpretation of fine details on the section and for estimation of acoustic impedance. In the absence of well-control, the recognized best approach to wavelet estimation is to use the technique of multiple coherence analysis to estimate the coherent signal and its amplitude spectrum, and thence construct the seismic wavelet under the minimum-phase assumption. The construction of the minimum-phase wavelet is critically dependent on the decay of the spectrum at the low-frequency end. Traditional methods of cross-spectral estimation, such as frequency smoothing using a Papoulis window, suffer from substantial side-lobe leakage in the areas of the spectrum where there is a large change of power over a relatively small frequency range. The low-frequency end of the seismic spectrum (less than 4 Hz) decays rapidly to zero. Side-lobe leakage causes poor estimates of the low-frequency decay, resulting in degraded wavelet estimates. Thomson's multitaper method of cross-spectral estimation which suffers little from side-lobe leakage is applied here, and compared with the result of using frequency smoothing with the Papoulis window. The multitaper method seems much less prone to estimating spuriously high coherences at very low frequencies. The wavelet estimated by the multitaper approach from the data used here is equivalent to imposing a low-frequency roll-off of some 48 dB/oct (below 3.91 Hz) on the amplitude spectrum. Using Papoulis smoothing the equivalent roll-off is only about 36 dB/oct. Thus the multitaper method gives a low-frequency decay rate of the amplitude spectrum which is some 4 times greater than for Papoulis smoothing. It also gives more consistent results across the section. Furthermore, the wavelet obtained using the multi-taper method and seismic data only (with no reference to well data) has more attractive physical characteristics when compared with a wavelet extracted using well data, than does an estimate using traditional smoothing.     

接收函数提取的多正弦窗方法

接收函数方法是研究地壳、上地幔速度结构的重要方法之一.稳定、可靠的提取接收函数的方法是实现的基础.频率域反褶积是一种常用的提取接收函数的方法,在加窗截断数据时,单一窗函数会降低信号的饱和度并造成频率泄露.为解决这一问题,引入了正交数据窗函数,对信号多次采样实现互补,保证了数据信息饱和度并有效抑制频谱泄露.多正弦窗是一种最小偏差正交窗函数,具有解析表达式,应用方便.在此文中,我们用多正弦窗来提取接收函数,且把震前噪声作为计算接收函数的一部分,增强了接收函数的稳定性.对观测数据的试验效果显示,多正弦窗频率相关估计方法提取的接收函数稳定性好,精度高,是一种提取高质量接收函数的方法.     

多窗谱分析在Q值估算中的应用

正弦窗谱分析和Slepian窗谱分析是两种常用的多窗谱分析方法.本文利用两种窗函数分别对含噪声的衰减模型进行谱分析对比,并根据谱比法估算了Q值.研究结果表明：正弦窗函数谱分析应用的效果优于Slepian窗谱分析应用的效果,而且多正弦窗谱估计更接近真实的谱.对于深部地层,噪声的影响更加严重,利用多正弦窗谱估计估算的Q值更接近理论的Q值.     

Low-frequency scaling applied to stochastic finite-fault modeling

Stochastic finite-fault modeling is an important tool for simulating moderate to large earthquakes. It has proven to be useful in applications that require a reliable estimation of ground motions, mostly in the spectral frequency range of 1 to 10 Hz, which is the range of most interest to engineers. However, since there can be little resemblance between the low-frequency spectra of large and small earthquakes, this portion can be difficult to simulate using stochastic finite-fault techniques. This paper introduces two different methods to scale low-frequency spectra for stochastic finite-fault modeling. One method multiplies the subfault source spectrum by an empirical function. This function has three parameters to scale the low-frequency spectra: the level of scaling and the start and end frequencies of the taper. This empirical function adjusts the earthquake spectra only between the desired frequencies, conserving seismic moment in the simulated spectra. The other method is an empirical low-frequency coefficient that is added to the subfault corner frequency. This new parameter changes the ratio between high and low frequencies. For each simulation, the entire earthquake spectra is adjusted, which may result in the seismic moment not being conserved for a simulated earthquake. These low-frequency scaling methods were used to reproduce recorded earthquake spectra from several earthquakes recorded in the Pacific Earthquake Engineering Research Center (PEER) Next Generation Attenuation Models (NGA) database. There were two methods of determining the stochastic parameters of best fit for each earthquake: a general residual analysis and an earthquake-specific residual analysis. Both methods resulted in comparable values for stress drop and the low-frequency scaling parameters; however, the earthquake-specific residual analysis obtained a more accurate distribution of the averaged residuals.     

Local Site Effects in the Town of Benevento (Italy) from Noise Measurements

— The study of ground motion amplification produced by surface geology is extremely interesting in the Benevento area, Southern Italy, as it is characterized by high seismic hazard. The present moderate-to-low seismicity makes the noise method appropriate to estimate the seismic site response in the area. The three components of seismic noise have been recorded in five sites in the Benevento metropolitan area characterized by different surface geology, in order to estimate the seismic site response. In evaluating site amplification effects we used the direct interpretation of amplitude spectra and standard spectral ratio techniques, evaluating sediment-to-bedrock, sediment-to-average and H/V spectral ratios. The temporal evolution of the noise spectra is analysed within one day, in order to assess the stationarity of the noise signal. The noise wavefield properties have been studied through polarization analyses in selected bands of frequency, where spectral peaks are observed to dominate, to better understand the real nature of those peaks. Results give evidence of low amplification levels, missing any correlation between spectral amplitudes and sediment thickness over the basement. We interpret this result as due to the poor impedance contrast between sediments and basement, which is characterized by low values of shear waves velocity. Moreover, sharp amplitude peaks are observed in the raw spectra of the sediment-sites, in the 2–4 Hz frequency band; a numerical simulation interprets this effect as possibly associated with a wide-scale structure, invoking the presence of a sharper impedance contrast at greater depth. At high frequencies the action of ambient noise sources, mainly active on horizontal components of motion, is retained dominant to generate the prominent peaks observed in the H/V spectral ratios; in some cases the presence of a near-surface low-velocity layer can contribute to amplify the seismic motion generated at these frequencies.     

A note on autoregressive spectral estimates for frequency-wavenumber analysis of strong-motion array data

Frequency-wavenumber (f-k) spectra of seismic strong-motion array data are useful in estimating back-azimuth and apparent propagation velocity of seismic waves arriving at the array. Such estimates are required to model wave passage effects while studying spatial variability of strong ground motion. Although periodogram-based spectral estimates are commonly used, practical applications based on them encounter limitations, such as, lack of objective criteria for selecting a proper smoothing window and its associated bandwidth, and relatively large variance of the estimated spectral quantities. We present an alternative spectral estimate based on parametric time series modelling approach. The well-known autoregressive (AR) time series model is used in a system-based approach to estimate the spectral matrix of auto- and cross-spectral densities. Such spectral estimates are found to be smoother than the windowed periodogram estimates, and can directly be used in f-k spectral analysis. We present an example application of the proposed technique using strong-motion data recorded by the SMART-1 array in Taiwan during the January 29 1981 $M_{L}$ 6.3 earthquake. Our results, in terms of back azimuth and apparent propagation velocity, are found to be in excellent agreement with those reported in the literature.     

基于易损性的基础隔震结构地震动选取方法研究

对基础隔震结构进行动力弹塑性时程分析时,地震记录的选择是关键.提出基于基础隔震结构弹塑性动力放大系数谱进行地震记录选取的方法:首先采用动力弹塑性时程分析方法对基础隔震结构的两自由度简化模型进行分析,得到结构的动力放大系数谱;然后采用谱匹配的方法选取地震记录,对一8层混凝土框架结构的基础隔震结构进行增量动力分析、地震易损...     

Static and dynamic stiffness measurements with Opalinus Clay

In this work, an experimental study was carried out with the aim of reconciling static and dynamic stiffness of Opalinus Clay. The static and dynamic stiffness of core plugs from a shaly and a sandy facies of Opalinus Clay were characterized at two different stress states. The measurements included undrained quasi-static loading–unloading cycles from which the static stiffness was derived, dynamic stiffness measurement at seismic frequencies (0.5–150 Hz) and ultrasonic velocity measurements (500 kHz) probing the dynamic stiffness at ultrasonic frequencies. The experiments were carried out in a special triaxial low-frequency cell. The obtained results demonstrate that the difference between static and dynamic stiffness is due to both dispersion and non-elastic effects: Both sandy and shaly facies of Opalinus Clay exhibit large dispersion, that is, a large frequency dependence of dynamic stiffness and acoustic velocities. Especially dynamic Young's moduli exhibit very high dispersion; between seismic and ultrasonic frequencies they may change by more than a factor 2. P-wave velocities perpendicular to bedding are by more than 200 m/s higher at ultrasonic frequencies than at seismic frequencies. The static undrained stiffness of both sandy and shaly facies is strongly influenced by non-elastic effects, resulting in significant softening during both loading and unloading with increasing stress amplitude. The zero-stress extrapolated static undrained stiffness, however, reflects the purely elastic response and agrees well with the dynamic stiffness at seismic frequency.     

The Effects of Attenuation and Site on the Spectra of Microearthquakes in the Shillong Region of Northeast India

Microearthquake spectra from the Shillong region are analyzed to observe the effect of attenuation and site on these spectra. The spectral ratio method is utilized to estimate the Q values for both P- and S-waves in the subsurface layer, wherein the ratio of spectral amplitudes at lower and higher frequencies are taken into consideration for three stations at varying epicentral distances. Average estimates of Q _P and Q _S are 178 and 195. The ratio of Q _S to Q _P is estimated to be greater than 1 in major parts of the Shillong area, which can be related to the dry crust prevailing in the Shillong region. Typically, the variation in corner frequencies for these spectra is inferred to be characteristic of the site. Simultaneously, observations from spectral content of local earthquakes recorded at two different stations with respect to the reference site yield greater amplification of incoming seismic signals in the frequency range of 2–5 Hz, which is found to be well supported by the existing local lithology pertinent to that region.     

Assessment of seismic hazard of the Japanese islands based on fractal analysis of GPS time series

Based on the fractal analysis of the time series of the Earth’s surface vertical displacements in the region of the Japanese Archipelago, the maps of the estimates of seismic activity in the region over 2015 are constructed. The analysis of the maps revealed several segments of the territory which are prone to the emergence of significant earthquakes. The characteristic peculiarity is noted in the change of the behavior of the geophysical dynamic system—the Earth’s crust—before the occurrence of seismic events: the mechanism of transition to the critical state demonstrates the energy preservation of the low frequencies with the simultaneous energy decay of the middle and high frequencies, which differs from the behavior of the other dynamical systems.     

Soil and structure damping from single station measurements

In seismology and seismic engineering soils and structures are modeled as oscillators characterized by modal (resonance) frequencies, shapes and damping. In 1973 Cole proposed the RandomDec technique to estimate both the damping and the fundamental mode of structures from the recorded time series at a single point, with no need for spectral analyses. Here we propose a number of modifications to the original RandomDec approach, that we group under the name DECÓ, which allow to determine the damping as a function of the frequency and therefore the damping of all the vibration modes. However, the motion of structures is so amplified at the resonance frequencies that detecting the characteristic parameters by recording ambient vibrations is relatively easy. More interesting is to apply the DECÓ approach to the soil in the attempt to estimate the mode damping from single station measurements. On soils, the resonance frequencies are normally identified as peaks in the horizontal to vertical spectral ratios of microtremors. However, at these frequencies what is observed is a local minimum in the vertical spectral component, sometimes associated to local maxima in the horizontal components, whose visibility depend on the specific amount of SH and Love waves at the site. The determination of soil damping is therefore a much less trivial task on soils than on structures. By using microtremor and earthquake recordings we estimate the soil damping as a function of shear strain and observe that this is one order of magnitude larger than what is measured in the laboratory on small scale samples, at least at low-intermediate strain levels. This has severe consequences on the numerical seismic site response analyses and on soil dynamic modeling.     

Seismic analysis of the fatih sultan mehmet (second Bosporus) suspension bridge

Theoretical dynamic characteristics of the Fatih Bridge in terms of natural frequencies and mode shapes of free vibration were obtained using a range of finite element models. Based on this free-vibration data, separate analyses of the asynchronous response of the bridge to earthquake excitation in three orthogonal axes with different speeds of wave propagation, and of stochastic response to vertical excitation were used to estimate levels of dynamic response due to seismic loading. Fatih is the third of three modern European long-span box-girder suspension bridges that have been investigated and the relationship of the different design features and the dynamic responses of this type of bridge is reviewed. The main conclusion is that where seismic response is an important consideration, the effects of asynchronous excitation can be significant and must be considered.     

Probabilistic estimation of maximum inelastic displacement demands for performance‐based design

A probabilistic approach to estimate maximum inelastic displacement demands of single‐degree‐of‐freedom (SDOF) systems is presented. By making use of the probability of exceedance of maximum inelastic displacement demands for given maximum elastic spectral displacement and the mean annual frequency of exceedance of elastic spectral ordinates, a simplified procedure is proposed to estimate mean annual frequencies of exceedance of maximum inelastic displacement demands. Simplifying assumptions are thoroughly examined and discussed. Using readily available elastic seismic hazard curves the procedure can be used to compute maximum inelastic displacement seismic hazard curves and uniform hazard spectra of maximum inelastic displacement demands. The resulting maximum inelastic displacement demand spectra provide a more rational way of establishing seismic demands for new and existing structures when performance‐based approaches are used. The proposed procedure is illustrated for elastoplastic SDOF systems having known‐lateral strength located in a region of high seismicity in California. Copyright © 2007 John Wiley & Sons, Ltd.     

High-frequency filtering of strong-motion records

The influence of noise in strong-motion records is most problematic at low and high frequencies where the signal to noise ratio is commonly low compared to that in the mid-spectrum. The impact of low-frequency noise (<1 Hz) on strong-motion intensity parameters such as ground velocities, displacements and response spectral ordinates can be dramatic and consequentially it has become standard practice to low-cut (high-pass) filter strong-motion data with corner frequencies often chosen based on the shape of Fourier amplitude spectra and the signal-to-noise ratio. It has been shown that response spectral ordinates should not be used beyond some fraction of the corner period (reciprocal of the corner frequency) of the low-cut filter. This article examines the effect of high-frequency noise (>5 Hz) on computed pseudo-absolute response spectral accelerations (PSAs). In contrast to the case of low-frequency noise our analysis shows that filtering to remove high-frequency noise is only necessary in certain situations and that PSAs can often be used up to 100 Hz even if much lower high-cut corner frequencies are required to remove the noise. This apparent contradiction can be explained by the fact that PSAs are often controlled by ground accelerations associated with much lower frequencies than the natural frequency of the oscillator because path and site attenuation (often modelled by Q and κ, respectively) have removed the highest frequencies. We demonstrate that if high-cut filters are to be used, then their corner frequencies should be selected on an individual basis, as has been done in a few recent studies.     

The contribution of scattering to near-surface attenuation

The rapid decrease of the acceleration spectral amplitude at high frequencies has widely been modeled by the spectral decay factor kappa (κ). Usually, the path-corrected component of κ, often called κ₀, is believed to be a local and frequency-independent site characteristic, in turn representing attenuation related to waves propagating vertically through the very shallow layers beneath the study site. Despite the known relevance of κ₀ in a wide range of seismological applications, most methods for its calculation do not fully consider the influence of the scattering component. To account for the scattering component, we present a summary of statistical observations of the seismic wavefield at sites of the Swiss seismic networks. The intrinsic properties of the wavefield show a clear dependency on the local shallow subsoil conditions with differences in the structural heterogeneity of the shallow subsoil layers producing different scattering regimes. Such deviations from the ballistic behavior (i.e., direct waves that sample only distinct directions) are indicative for local structural heterogeneities and the associated level of scatter. Albeit the attenuation term related to scattering depends nonlinearly on the intrinsic term, the results indicate that the commonly used explanation for the high-frequency decay spectrum might not be appropriate but involving the amount of scattering might allow better constrained estimates of κ₀.     

The reference spectral noise ratio method to evaluate the seismic response of a site

The seismic response of several sites in the Durban area of South Africa has been investigated using a refined version of the spectral ratio (H/V) generated by cultural seismic noise. Two samples of noise separated by an interval of several minutes for the vertical and the two orthogonal horizontal components were taken at each site. Though the two samples differed noticeably in the time as well as in the frequency domain, when the components are considered separately, the ratios of the horizontal to the vertical spectra were very similar for most of the pairs. This similitude was obvious not only in the frequencies of the peaks, but also in the range of amplifications involved. These observations have been used to introduce a refinement to the Nakamura Method. This refinement consists in using as a reference the H/V spectral ratio of a well-known, hard rock site. All the other soft sites of interest are then compared with this standard reference site. This comparison provides valuable information on the frequencies and amplification factors introduced by the critical soft sediments. This refined method will be referred here as the ‘Reference spectral noise ratio’.This method, is compared to a similar one devised to investigate the response of horizontal layers to longitudinal seismic waves, using the ratio of the spectra generated by long- period waves.     

Separation of source and site effects by generalized inversion technique using the aftershock recordings of the 2009 L��Aquila earthquake

We exploit S-wave spectral amplitudes from 112 aftershocks (3.0 ≤ M_L ≤ 5.3) of the L’Aquila 2009 seismic sequence recorded at 23 temporary stations in the epicentral area to estimate the source parameters of these events, the seismic attenuation characteristics and the site amplification effects at the recording sites. The spectral attenuation curves exhibit a very fast decay in the first few kilometers that could be attributed to the large attenuation of waves traveling trough the highly heterogeneous and fractured crust in the fault zone of the L’Aquila mainshock. The S-waves total attenuation in the first 30 km can be parameterized by a quality factor Q_S(f) = 23f ^0.58 obtained by fixing the geometrical spreading to 1/R. The source spectra can be satisfactorily modeled using the omega-square model that provides stress drops between 0.3 and 60 MPa with a mean value of 3.3±2.8 MPa. The site responses show a large variability over the study area and significant amplification peaks are visible in the frequency range from 1 to more than 10 Hz. Finally, the vertical component of the motion is amplified at a number of sites where, as a consequence, the horizontal-to-vertical spectral ratios (HVSR) method fails in detecting the amplitude levels and in few cases the resonance frequencies.     

Maximum entropy spectral analysis of volcanic tremor using data from Etna (Sicily) and Merapi (central Java)

The maximum entropy spectral analysis (MESA) method is applied to synthetic and observed tremor time series using autoregressive processes and recordings from the volcanoes Etna (Sicily) and Merapi (central Java). The MESA analysis can be used to estimate power spectra with sharp peaks from short data records. If the tremor source process can be modelled by an autoregressive process, the MESA method is well-suited for determining the coefficients of the underlying difference equations. As in the standard periodogram method of power spectrum estimation, a mesagram estimate using record segmentation and MESA spectrum averaging reduces the variance of the spectral estimator. In combination with periodogram estimates, mesagram estimates confirm that the tremor source may be modelled as an ensemble of randomly excited resonators. Used together, these estimates provide a valuable method for short-term monitoring of volcanic activity. In addition, they can be applied to the determination of new source parameters such as resonator frequencies, damping coefficients, excitation probabilities, correlation of exciting forces, and resonator coupling and in the pattern recognition of source types.     

汶川与昆仑山强烈地震激发的地球自由振荡频谱的对比分析

强烈地震激发的地震波信息非常丰富,高频信息能量部分会在小范围短时间内迅速衰减,而低频信息特别是较低频信息能量部分则衰减较慢,会绕地球很多圈后才会消耗殆尽,从而激发地球的自由振荡.虽然地球自由振荡的固有频率不变,但不同震源机制的地震激发的地球自由振荡频率成分会随着震级、震源机制、方位等的不同而有显著差别.本文利用2008年5月12日汶川(M_w7.9)地震与2001年11月14日昆仑山(M_w7.8)地震这两个能量震级相当但震源机制不同的地震,基于地震波传播理论,考虑横向各向同性PREM地球模型并融合Crust2.0地壳模型、S20RTS地幔模型及PREM径向衰减模型,利用谱元法结合高性能并行计算,对这两次强烈地震激发的全球地震波传播进行了数值模拟,计算它们激发的地球自由振荡频谱特征差异.计算结果显示了汶川地震的逆冲-走滑特性及昆仑山地震的水平左旋走滑特征.利用理论计算得到的地震波动记录进行功率谱密度估计对比分析,研究结果显示这两次强烈地震释放的低频信息能量大小相当,但总体上看昆仑山地震释放的能量略小于汶川地震的.对比分析表明,不同地震激发的地球自由振荡模式在同一台站处的发育程度不同;同一地震激发的地球自由振荡在不同台站处记录到的振型频率成分也有很大差异.对于不同地震激发的地球自由振荡,有一些频率成分共同出现,表现为地球自由振荡功率谱能量均较大;也有一些振型由于相长干涉,仅在某些地震中被激发而得以良好发育,表现为功率谱能量明显较大;而一些振型由于相消干涉,在一些地震激发方式下被压制,表现为功率谱能量明显很小,甚至接近于0.计算结果清楚地显示了不同地震激发方式下地球振荡模式丰富而复杂的特性,需要对不同地震激发的地球振荡信息进行综合深入的分析,才能对地球内部结构尤其横向不均匀特性给予全面的科学解释.     

Empirical estimate of fundamental frequencies and damping for Italian buildings

The aim of this work is to estimate the fundamental translational frequencies and relative damping of a large number of existing buildings, performing ambient vibration measurements. The first part of the work is devoted to the comparison of the results obtained with microtremor measurements with those obtained from earthquake recordings using four different techniques: horizontal‐to‐vertical spectral ratio, standard spectral ratio, non‐parametric damping analysis (NonPaDAn) and half bandwidth method. We recorded local earthquakes on a five floors reinforced concrete building with a pair of accelerometers located on the ground and on top floor, and then collected microtremors at the same location of the accelerometers. The agreement between the results obtained with microtremors and earthquakes has encouraged extending ambient noise measurements to a large number of buildings. We analysed the data with the above‐mentioned methods to obtain the two main translational frequencies in orthogonal directions and their relative damping for 80 buildings in the urban areas of Potenza and Senigallia (Italy). The frequencies determined with different techniques are in good agreement. We do not have the same satisfactory results for the estimates of damping: the NonPaDAn provides estimates that are less dispersed and grouped around values that appear to be more realistic. Finally, we have compared the measured frequencies with other experimental results and theoretical models. Our results confirm, as reported by previous authors, that the theoretical period–height relationships overestimate the experimental data. Copyright © 2008 John Wiley & Sons, Ltd.