Rotation-invariant measures of earthquake response spectra

A new procedure for combining the response spectra of two horizontal components of recorded ground motion is presented. The presented formulation accounts for different orientations of accelerometer sensors and derives the maximum and the expected (mean) horizontal response spectra at a site, both of which are invariant to rotation of sensor axes. The maximum response spectrum is derived as the peak resultant response of single degree of freedom oscillators subjected to the as-recorded ground acceleration. The expected spectrum is derived by projecting the displacement response (due to as-recorded motion) along two orthogonal axes to a principal axes in which the displacement responses are uncorrelated. This property is used to formulate an approximation for the expected response spectrum over all possible sensor orientations. A large set of accelerometric data from Europe and the Middle East is used to demonstrate the applicability of the proposed response spectral measures.     

盆地对三分量地震动持时的影响初探

利用关东盆地及其周边KiK-net台网井上台站记录的2004—2017年15次中强地震（矩震级为5.1～6.9级）构建三分量记录显著持时Ds_5-95数据库。针对该数据库,基于残差分析方法和3种水平向地震动持时参数预测方程,计算并给出事件间残差和事件内残差及其随不同类别参数的变化。在此基础上,初步探讨了水平向地震动持时预测方程应用于预测竖向地震动持时的可行性及盆地对三分量地震动持时的影响。研究结果表明,对于震源距和场地V_S30相当的情况,盆地内台站持时普遍大于盆地外台站持时,盆地内、外台站竖向地震动持时均大于水平向地震动持时;3种预测方程均可实现对盆地外台站水平向地震动Ds_5-95的合理估计,但在一定程度上低估了盆地内台站的水平向地震动Ds_5-95;3种预测方程均无法直接应用于竖向地震动持时预测。     

Characteristics of strong ground motion data recorded in the Gubbio sedimentary basin (Central Italy)

Various authors, analysing the set of accelerograms recorded at Gubbio Piana (GBP) (central Italy), have demonstrated that strong amplification occurs at this accelerometric station, which is installed within an alluvial basin. In particular, Ambraseys et al. [(2005a), Bull Earthq Eng 3:1–53; (2005b), Bull Earth Eng 3:55–73] observed that the strong motion peaks at GBP greatly exceed the median values predicted by the attenuation relationships they derived for Europe. In this work, we analyse and discuss some characteristics of the ground motion recorded at the GBP station. We show that the ground motion parameters, such as peak-ground acceleration and peak-ground velocity, are strongly influenced by the presence of locally induced surface waves that produce both a lengthening of the significant shaking duration and an increase in the peak values with respect to a nearby bedrock site. The basin-induced surface waves are observed in the three components of motion and their effects on the peak values are particularly evident in the vertical component. In the frequency domain, the energy of the surface waves is mostly restricted to the frequency band 0.4–0.8 Hz for both the horizontal and vertical components. The horizontal and vertical Fourier amplitudes are also very similar, and this indicates that the H/V spectral ratio technique is not applicable to describing the site response due to the propagation of seismic wave in a complex 2D/3D geological structure. Finally, a preliminary polarization analysis shows that the directions of polarization, as well as the degree of elliptical polarization, exhibit a strong variability with time, that may be related to a complex propagation of Love and Rayleigh waves within the basin.     

同一测点不同地震动分量空间相干性分析

利用SMART-1台阵的3次地震记录计算了同一测点三平动地震动分量问的相干值,并提出了相干函数模型。分析表明,同一测点各地震动分量间是低相干的,随频率衰减不明显;两水平分量问的相干性比水平分量与垂直分量间的相干性大。因此在工程计算中不计相干函数随频率的变化不会带来太大的误差。     

Robust dual‐sensor data sea‐surface ghost attenuation for quality control purposes

Three‐dimensional receiver ghost attenuation (deghosting) of dual‐sensor towed‐streamer data is straightforward, in principle. In its simplest form, it requires applying a three‐dimensional frequency–wavenumber filter to the vertical component of the particle motion data to correct for the amplitude reduction on the vertical component of non‐normal incidence plane waves before combining with the pressure data. More elaborate techniques use three‐dimensional filters to both components before summation, for example, for ghost wavelet dephasing and mitigation of noise of different strengths on the individual components in optimum deghosting. The problem with all these techniques is, of course, that it is usually impossible to transform the data into the crossline wavenumber domain because of aliasing. Hence, usually, a two‐dimensional version of deghosting is applied to the data in the frequency–inline wavenumber domain. We investigate going down the “dimensionality ladder” one more step to a one‐dimensional weighted summation of the records of the collocated sensors to create an approximate deghosting procedure. We specifically consider amplitude‐balancing weights computed via a standard automatic gain control before summation, reminiscent of a diversity stack of the dual‐sensor recordings. This technique is independent of the actual streamer depth and insensitive to variations in the sea‐surface reflection coefficient. The automatic gain control weights serve two purposes: (i) to approximately correct for the geometric amplitude loss of the Z data and (ii) to mitigate noise strength variations on the two components. Here, Z denotes the vertical component of the velocity of particle motion scaled by the seismic impedance of the near‐sensor water volume. The weights are time‐varying and can also be made frequency‐band dependent, adapting better to frequency variations of the noise. The investigated process is a very robust, almost fully hands‐off, approximate three‐dimensional deghosting step for dual‐sensor data, requiring no spatial filtering and no explicit estimates of noise power. We argue that this technique performs well in terms of ghost attenuation (albeit, not exact ghost removal) and balancing the signal‐to‐noise ratio in the output data. For instances where full three‐dimensional receiver deghosting is the final product, the proposed technique is appropriate for efficient quality control of the data acquired and in aiding the parameterisation of the subsequent deghosting processing.     

Statistical analysis of peaks and directivity of earthquake ground motion

Conversion factors are useful for attenuation and damage estimation relationships. These factors among different definitions of peaks (i.e. larger, average and resultant) for peak ground motion indices and acceleration response spectrum were investigated. A large number of horizontal acceleration records recorded at 76 free-field sites of the Japan Meteorological Agency were used in this study. Two orthogonal horizontal components were combined in the time domain to get the maximum resultant peak ground motion indices and acceleration response spectrum in the horizontal plane. From the analysis, the means of the larger/resultant ratio were found to be 0·934 for acceleration, 0·926 for velocity, and 0·913 for displacement. A similar decreasing trend was observed for the means of the average/resultant ratio of the ground motion indices and acceleration response spectrum. The directivity of peak ground motion indices was also examined. It was found that the peak ground motion is more likely to occur in the transverse direction than in other directions. This trend is more prominent in the long-period contents of ground motion.     

A note on the useable dynamic range of accelerographs recording translation

Since the late 1970s, the dynamic range and resolution of strong motion digital recorders have leaped from 65 to 135 dB, opening new possibilities for advanced data processing and interpretation. One of these new possibilities is the calculation of permanent displacement of the ground or of structures, associated with faulting or with non-linear response. Proposals on how permanent displacements could be recovered from recorded strong motion have been published since 1976. The analysis in this paper concludes that permanent displacements of the ground and of structures in the near-field can be calculated provided all six components of strong motion (three translations and three rotations) have been recorded, and the records are corrected for transducer rotation, misalignment and cross-axis sensitivity.     

Stochastic model for simulation of near‐fault ground motions

A parameterized stochastic model of near‐fault ground motion in two orthogonal horizontal directions is developed. The major characteristics of recorded near‐fault ground motions are represented. These include near‐fault effects of directivity and fling step; temporal and spectral non‐stationarity; intensity, duration, and frequency content characteristics; directionality of components; and the natural variability of ground motions. Not all near‐fault ground motions contain a forward directivity pulse, even when the conditions for such a pulse are favorable. The proposed model accounts for both pulse‐like and non‐pulse‐like cases. The model is fitted to recorded near‐fault ground motions by matching important characteristics, thus generating an ‘observed’ set of model parameters for different earthquake source and site characteristics. A method to generate and post‐process synthetic motions for specified model parameters is also presented. Synthetic ground motion time series are generated using fitted parameter values. They are compared with corresponding recorded motions to validate the proposed model and simulation procedure. The use of synthetic motions in addition to or in place of recorded motions is desirable in performance‐based earthquake engineering applications, particularly when recorded motions are scarce or when they are unavailable for a specified design scenario. Copyright © 2016 John Wiley & Sons, Ltd.     

Analysis of three-dimensional strong ground motions along principal axes,San Fernando earthquake

An orthogonal set of principal axes is defined for earthquake ground motions. These principal axes are obtained such that the corresponding variances of motion have maximum, minimum and intermediate values and the covariances equal zero. This indicates that the corresponding components of motion along the principal axes are uncorrelated with respect to each other. Since real earthquake accelerograms are assumed to be reasonably well represented by Gaussian random processes, the three components of motion along the principal axes are statistically independent of each other. Using these principal axes and applying the moving-window technique to the ground accelerograms recorded during the San Fernando earthquake of 9 February 1971, time-dependent characteristics of three-dimensional ground motions along principal axes are determined. Results of the analysis indicate significant correlation between directions of principal axes and directions from the recording stations to the fault slip zone. It is concluded that three components of ground motion can be generated stochastically with statistical independence being maintained, provided they are assumed to be directed along principal axes.     

Strong motion records and synthetic isoseismals of the Pyrgos,Peloponnisos, Southern Greece,Earthquake Sequence of March 26, 1993

In this work, several seismological observations are presented in order to explain characteristic features of the earthquake sequence which occurred in March 1993 in southwestern Greece, very close to the city of Pyrgos.Fault plane solutions of the largest fore- and aftershocks and the main shock, as well as the directions at which the maximum ground accelerations were recorded suggest that this earthquake sequence has been developed by rupturing three distinct focal planes with different focal mechanisms. The first focal plane, located in the off-shore area, strikes NW-SE, dips SE and includes most of the foreshock activity. The foreshock activity migrated to the northeastern part of the city of Pyrgos and took place on planes with a predominant direction NE-SW. The main shock ofM _x =5.5 occurred in a focal plane located between the two above-mentioned areas. Strong motion records of significant shocks of the sequence show peak acceleration values on components consistent with the relevant fault plane solutions.Furthermore, the observed macroseismic field has been compared with synthetic isoseismals computed by using a certain velocity model and the focal mechanism parameters of the main shock.     

地震危险性分析与抗震设防标准的确定

确定抗震设防标准是地震安全性评价工作的主要目的，目前通常的做法是以５０年超越概率６３％的地震动作为第一阶段设计的强度验算标准，而以５０年２－３％的地震动作为第二阶段设计的弹塑性变形验算标准，并认为此种做法可以体现“小震不坏，中震可修，大震不倒”的原则，本文从危险性分析不确定性的角度指出上述做法存在较大的问题，以引起讨论和进一步的研究。     

Wavelet‐based simulation of spectrum‐compatible aftershock accelerograms

In damage‐based seismic design it is desirable to account for the ability of aftershocks to cause further damage to an already damaged structure due to the main shock. Availability of recorded or simulated aftershock accelerograms is a critical component in the non‐linear time‐history analyses required for this purpose, and simulation of realistic accelerograms is therefore going to be the need of the profession for a long time to come. This paper attempts wavelet‐based simulation of aftershock accelerograms for two scenarios. In the first scenario, recorded main shock and aftershock accelerograms are available along with the pseudo‐spectral acceleration (PSA) spectrum of the anticipated main shock motion, and an accelerogram has been simulated for the anticipated aftershock motion such that it incorporates temporal features of the recorded aftershock accelerogram. In the second scenario, a recorded main shock accelerogram is available along with the PSA spectrum of the anticipated main shock motion and PSA spectrum and strong motion duration of the anticipated aftershock motion. Here, the accelerogram for the anticipated aftershock motion has been simulated assuming that temporal features of the main shock accelerogram are replicated in the aftershock accelerograms at the same site. The proposed algorithms have been illustrated with the help of the main shock and aftershock accelerograms recorded for the 1999 Chi–Chi earthquake. It has been shown that the proposed algorithm for the second scenario leads to useful results even when the main shock and aftershock accelerograms do not share the same temporal features, as long as strong motion duration of the anticipated aftershock motion is properly estimated. Copyright © 2008 John Wiley & Sons, Ltd.     

GROUND MOTION CHARACTERISTICS OF GAOYOU-BAOYING M4.9 EARTHQUAKE

An M4.9 earthquake occurred at the junction of Gaoyou and Baoying on July 20, 2012. In this paper, 43 sets of strong motion records of the main shock are analyzed. With these data, we analyzed the characteristics of the peak ground motion value, attenuation relation, duration and acceleration response spectrum. We draw the peak acceleration contour map of the region near the epicenter. The contour line is smooth and the trend of long axis is northwest-southeast. Distribution of peak acceleration of the observed records is basically consistent with the real intensity distribution. Compared with the predicted result based on the seismic attenuation relation proposed by Yu Yanxiang and Wang Suyunon for eastern China and the Fifth-generation ground motion zonation map, the horizontal PGA and PGV of Gaoyou-Baoying earthquake are higher than the predicted results that are based on the model of Fifth-generation ground motion zonation map, while the PGV is similar with the predicted results which are based on Yu Yanxiang and Wang Suyun's model. We regressively analyzed the spatial-temporal change curves of the two types of relative ground motion durations. Compared with the predicted results proposed by Bommer et al. (2009) based on the NGA strong motion records, the durations of all the three components of this earthquake are higher. 10 typical recordings' acceleration response spectra with 5% damping are calculated, their peak periods are around 0.1~0.3s. The acceleration response spectrum of the station 32BYT, which has the largest amplitude, is considerably larger than the Chinese code design spectra, while it becomes notably smaller when the period is larger than 0.4s. Compared with the horizontal bedrock acceleration response spectrum predicted by the attenuation relationship for the eastern part of China, the observed response spectrum shape is similar with the predicted ones, while almost all the observed response spectrum values (except station 32YCT)are smaller than the predicted bedrock acceleration response spectrum. These phenomena suggest that this earthquake has a weak impact on the seismic fortification standards in this area. Using H/V single-station spectral ratio method, amplitude and site amplification effect of the two typical stations are calculated, and the results show the H/V values are obviously larger than that of ground microtremor. This suggests that the site of the station has obvious amplification effect on ground motion.     

Semi‐empirical model for site effects on acceleration time histories at soft‐soil sites. Part 2: calibration

A previously developed simplified model of ground motion amplification is applied to the simulation of acceleration time histories at several soft‐soil sites in the Valley of Mexico, on the basis of the corresponding records on firm ground. The main objective is to assess the ability of the model to reproduce characteristics such as effective duration, frequency content and instantaneous intensity. The model is based on the identification of a number of parameters that characterize the complex firm‐ground to soft‐soil transfer function, and on the adjustment of these parameters in order to account for non‐linear soil behavior. Once the adjusted model parameters are introduced, the statistical properties of the simulated and the recorded ground motions agree reasonably well. For the sites and for the seismic events considered in this study, it is concluded that non‐linear soil behavior may have a significant effect on the amplification of ground motion. The non‐linear soil behavior significantly affects the effective ground motion duration for the components with the higher intensities, but it does not have any noticeable influence on the lengthening of the dominant ground period. Copyright © 2004 John Wiley & Sons, Ltd.     

Simulation of orthogonal horizontal ground motion components for specified earthquake and site characteristics

A method for generating an ensemble of orthogonal horizontal ground motion components with correlated parameters for specified earthquake and site characteristics is presented. The method employs a parameterized stochastic model that is based on a time‐modulated filtered white‐noise process with the filter having time‐varying characteristics. Whereas the input white‐noise excitation describes the stochastic nature of the ground motion, the forms of the modulating function and the filter and their parameters characterize the evolutionary intensity and nonstationary frequency content of the ground motion. The stochastic model is fitted to a database of recorded horizontal ground motion component pairs that are rotated into their principal axes, a set of orthogonal axes along which the components are statistically uncorrelated. Model parameters are identified for each ground motion component in the database. Using these data, predictive equations are developed for the model parameters in terms of earthquake and site characteristics and correlation coefficients between parameters of the two components are estimated. Given a design scenario specified in terms of earthquake and site characteristics, the results of this study allow one to generate realizations of correlated model parameters and use them along with simulated white‐noise processes to generate synthetic pairs of horizontal ground motion components along the principal axes. The proposed simulation method does not require any seed recorded ground motion and is ideal for use in performance‐based earthquake engineering. Copyright © 2011 John Wiley & Sons, Ltd.     

Site effect evaluation at Mexico City: Dominant period and relative amplification from strong motion and microtremor records

Site effects in Mexico City are discussed in terms of simple 1D, one-layer, linear models. The analysis is focussed on two parameters: dominant period and maximum amplification relative to a firm site within the city. The data used is a compilation of strong motion data and microtremor measurements. Strong motion data consist of digital acceleration records for nine events recorded by the Accelerographic Network of Mexico City. The authors analyzed spectral ratios of horizontal components of soft soil sites relative to an average of firm site observations for this data set. Dominant period, maximum relative amplification and an estimate of material damping were computed from the empirical transfer functions thus obtained. Microtremor data were compiled from measurement of different groups during the period 1985–1992. In all, 409 measurement points were analyzed. Values of dominant period obtained from microtremor measurements are in excellent agreement with those obtained from empirical transfer functions for strong motion data. The synthesis of results allows us to draw a detailed and robust map of dominant period for Mexico City. Based on this map, the authors propose some modifications to the current microzonation of Mexico City and evaluate a proposed model to account for site effects in this city.     

Filtered incremental velocity: A novel approach in intensity measures for seismic collapse estimation

This study evaluates the performance of a new intensity measure, referred to as filtered incremental velocity FIV3, which is computed using time-domain features extracted from an acceleration time series and is aimed at the evaluation of structural collapse. This novel approach focuses on the area under a small number of acceleration pulses in the ground motion instead of focusing on the peak response of linear elastic oscillators as in many recently proposed measures of ground motion intensity. FIV3 is developed based on previous research that has highlighted the close relation between the incremental velocity of a ground motion and its potential to induce large inelastic incursions on structures. However, unlike the original definition of incremental velocity which provides a single level of intensity for a ground motion, this new intensity measure is period-dependent and computed as the sum of the three largest incremental velocities obtained from a low-pass filtered ground acceleration time series. Efficiency and sufficiency with respect to several ground motion parameters such as magnitude, source-to-site-distance, spectral shape, scale factor, and duration are carefully evaluated and compared against those computed with some traditional and recently proposed intensity measures using collapse results from a four-story reinforced concrete frame. Results indicate that FIV3 leads to lower variability of collapse estimates and therefore higher efficiency as well as high sufficiency compared with those of other ground motion intensity parameters indicating that this new intensity measure is a promising parameter for structural collapse risk assessment.     

The effects of torsion and motion coupling in site response estimation

Soil amplification characteristics are investigated using data from the Chibaken‐Toho‐Oki earthquake and its aftershocks recorded at Chiba dense array in Japan. The frequency‐dependent amplification function of soil is calculated using uphole‐to‐downhole spectral ratio analysis, considering the horizontal components of shear wave. The identified spectral ratios consistently demonstrate the splitting of peaks in their resonance frequencies and low amplification values in comparison with a 1D model. The torsional behaviour and horizontal ground motion coupling are clarified as the reasons for these phenomena at the site. To prove the hypothesis, the torsional motion is directly evaluated using the data of the horizontal dense array in different depths at the site. The comparison between Fourier spectra of torsional motion and identified transfer functions reveals the peaks at the same frequencies. The wave equation including torsion and horizontal motion coupling is introduced and solved for the layered media by applying wave propagation theory. Using the developed model, the effects of torsional motion with horizontal motion coupling on soil transfer function are numerically examined. Splitting and low amplification at resonance frequencies are confirmed by the results of numerical analysis. Furthermore, the ground motion in two horizontal directions at the site is simulated using site geotechnical specification and optimizing the model parameters. The simulated and recorded motions demonstrate good agreement that is used to validate the hypothesis. In addition, the spectral density of torsional ground motions are compared with the calculated one and found to be well predicted by the model. Finally, the results are used to explain the overestimation of damping in back‐calculation of dynamic soil properties using vertical array data in small strain level. Copyright © 2003 John Wiley & Sons, Ltd.     

Damping coefficients for near-fault ground motion response spectra

Damping coefficients are frequently used in earthquake engineering as a simple way to adjust the pseudo-acceleration or displacement response spectra associated with a viscous damping ratio of 5% to the higher values of viscous damping needed for design of structures equipped with base isolation and/or supplemental energy dissipation devices. In this study, damping coefficients for the single-degree-of-freedom system subjected to near-fault ground motions are calculated for a large range of periods and damping levels. The results indicate that damping coefficients proposed in design codes and previous studies, based primarily on far-field ground motion records, tend to not be conservative for near-fault seismic excitations. A new approach is recommended for the derivation of damping coefficients appropriate for engineering analysis and design in the immediate vicinity of the earthquake fault. This includes the normalization of the period axis with respect to the duration of the ground velocity pulses recorded in the near-fault region. The pulse duration is controlled by the rise time on the fault plane and scales directly with earthquake magnitude.     

Extracting rotational components of earthquake ground motion using data recorded at multiple stations

Rotational components of earthquake ground motion have not been considered for seismic analysis, design and performance assessment because recordings of these components are unavailable. A number of procedures have been proposed to extract rotational components of ground motion from translational time series recorded at multiple, closely spaced recording stations. In this paper, a new procedure that is capable of capturing higher frequency content in rotational time‐series is presented. The frequencies at which numerical errors are introduced in the solution, which are a function of apparent wave velocity and array dimension, are identified. Results are presented for the proposed procedure, the widely accepted geodetic method, and a single‐station procedure developed by the authors, all using data recorded at the Lotung array in Taiwan. Copyright © 2012 John Wiley & Sons, Ltd.