Rotation of vertically oriented objects during earthquakes

Vertically oriented objects, such as tombstones, monuments, columns, and stone lanterns, are often observed to shift and rotate during earthquake ground motion. Such observations are usually limited to the mesoseismal zone. Whether near-field rotational ground motion components are necessary in addition to pure translational movements to explain the observed rotations is an open question. We summarize rotation data from seven earthquakes between 1925 and 2009 and perform analog and numeric rotation testing with vertically oriented objects. The free-rocking motion of a marble block on a sliding table is disturbed by a pulse in the direction orthogonal to the rocking motion. When the impulse is sufficiently strong and occurs at the ‘right’ moment, it induces significant rotation of the block. Numeric experiments of a free-rocking block show that the initiation of vertical block rotation by a cycloidal acceleration pulse applied orthogonal to the rocking axis depends on the amplitude of the pulse and its phase relation to the rocking cycle. Rotation occurs when the pulse acceleration exceeds the threshold necessary to provoke rocking of a resting block, and the rocking block approaches its equilibrium position. Experiments with blocks subjected to full 3D strong motion signals measured during the 2009 L’Aquila earthquake confirm the observations from the tests with analytic ground motions. Significant differences in the rotational behavior of a monolithic block and two stacked blocks exist.     

Investigation of ground rotational motions caused by direct and scattered P-waves from the 4 March 2008 TAIGER explosion experiment

High-frequency rotational motions of P-waves and coda waves were analysed using rotation rate sensors and strong motion array data from the 4 March 2008 TAiwan Integrated GEodynamics Research (TAIGER) explosion experiment in northeastern Taiwan. Theoretical and observational investigations focussed on the effects of this experiment on the free surface. The main goal of this study was to explore possible applications of combined measurements of artificial explosion-derived translational and rotational motions. Also investigated was the consistent ground rotation observed directly by rotation rate sensors and derived using translational seismic arrays. Common near-source high-frequency rotational motion observations and array-recorded translational motions from one shallow borehole explosion are analysed in this study. Using a half-space assumption of plane P-wave propagation across the recording site, we conclude that: (1) rotational motions induced by direct P-waves interacting with a free surface in theory can be used to estimate wave radial direction, velocity and anisotropic properties; (2) rotational motions derived from scattering are predominant among the observed rotations during the TAIGER explosion experiments and allow us to image the heterogeneous structure of the medium at the investigated site; and (3) rotation sensor measurements undertaken during TAIGER explosion experiments may be affected by cross-axis sensitivities, which need to be considered when using the data obtained during these experiments.     

Free‐field rotations during earthquakes: Relevance on buildings

Soil rotations around horizontal axes, during an earthquake, are studied through records collected by closely spaced arrays of strong motion accelerometers. The cross power spectrum of accelerations at nearby stations has been generally utilized to describe the spatial distribution of the motion. A number of cross spectra have been obtained during the training of these arrays. To take profit of these elaborations, a mathematical relation is established between the cross power spectrum and the power spectrum of the rotation. Rotation data presented by Liu et al, concerning 52 earthquake records collected at a single station in Taiwan, are compared with rotation data computed according to our procedure. The two series of data are suitably normalized to the peak horizontal acceleration. The data are shown in function of the distance from epicentre. The same ratio, computed according to our procedure, is in good agreement with the average value of these data. Direct measurements and the present approach have lead to evaluations of rotation higher than those predicted by mathematical investigations on the basis of the wave propagation theory, for comparable circumstances. The relevance of this input motion for relatively tall structures is examined, with reference to the structural effects that the horizontal motion concurrently provides. Meaningful will be ranked those effects of the order of magnitude of 20% or higher than those implied by the horizontal excitation. For understanding the relevance on building structures, the procedure has two areas of concern: 1) the coherence implicit in the cross power spectra, which depends on the interpolation process of the original records, collected in the arrays of instruments, and 2) the relative importance of the vertical to the horizontal input motion. As to the second item, the relevance of the rotation component on structures largely depends on the relative importance of the vertical to the horizontal input motion. When the records in an area a few km from the epicenter are considered, the response spectrum of vertical motion is comparable and in some records even higher, than that of horizontal motion, over the entire range of frequencies. This has been observed as well for the 2009 earthquake event of L'Aquila, Italy, and that at the Christchurch (New Zealand) 2011. When the response spectrum of vertical motion is comparable to that of horizontal motion, the effects of rotational motions on most engineering structures can be meaningful. Copyright © 2011 John Wiley & Sons, Ltd.     

Estimation of Strong Ground Motion from a Great Earthquake Mw 8.5 in Central Seismic Gap Region, Himalaya (India) Using Empirical Green’s Function Technique

In the present study ground motions for a Mw 8.5 scenario earthquake are estimated at 13 sites in Kumaun-Garhwal region using the empirical Green’s function technique. The recordings of 1991 Uttarkashi earthquake of Mw 6.8 at these sites are used as an element earthquake. A heterogeneous source model consisting of two asperities is considered for simulating the ground motions. The entire central seismic gap (CSG) can expect acceleration in excess of 100 cm/s² with NW portion in excess of 400 cm/s² and SE between 100 and 200 cm/s². The central portion can expect peak ground acceleration (PGA) between 200 and 400 cm/s². It has been observed from simulation of strong ground motion that sites located near the rupture initiation point can expect accelerations in excess of 1g. In the present analysis, Bhatwari and Uttarkashi can expect ground accelerations in excess of 1g. The estimates of the PGA are compared with earlier studies in the same region using different methodologies and it was found that the results are comparable. This has put constrains on the expected PGAs in this region. The obtained PGA values can be used in identifying the vulnerable areas in the central Himalaya, thereby facilitating the planning, design and construction of new structures and strengthening of the existing structures in the region.     

汶川地震强余震场地非线性反应

采用汶川地震强余震26个强震动台站记录,基于H/V谱比法,计算台站场地的强、弱震作用下场地卓越频率之比R_(fp)和体现强、弱震作用下场地H/V谱比曲线差异程度的DNL,进而识别并分析场地非线性反应特征。结果显示,R_(fp)、DNL与PGA之间存在显著相关性;其中10个台站出现明显的场地非线性反应特征;大部分台站发生场地非线性反应的PGA阈值为100 cm/s~2,部分为50 cm/s~2;实例证明,因某些台站不易通过H/V谱比法识别场地卓越频率,因此采用R_(fp)识别场地非线性反应具有一定局限性。     

Strong ground motion simulation of the 2003 Bam, Iran, earthquake using the empirical Green’s function method

The 2003 Bam, Iran, earthquake caused catastrophic damage to the city of Bam and neighboring villages. Given its magnitude (M _w ) of 6.5, the damage was remarkably large. Large-amplitude ground motions were recorded at the Bam accelerograph station in the center of Bam city by the Building and Housing Research Center (BHRC) of Iran. We simulated the Bam earthquake acceleration records at three BHRC strong-motion stations—Bam, Abaraq, and Mohammad-Abad—by the empirical Green’s function method. Three aftershocks were used as empirical Green’s functions. The frequency range of the empirical Green’s function simulations was 0.5–10 Hz. The size of the strong motion generation area of the mainshock was estimated to be 11 km in length by 7 km in width. To estimate the parameters of the strong motion generation area, we used 1D and 2D velocity structures across the fault and a combined source model. The empirical Green’s function method using a combination of aftershocks produced a source model that reproduced ground motions with the best fit to the observed waveforms. This may be attributed to the existence of two distinct rupture mechanisms in the strong motion generation area. We found that the rupture starting point for which the simulated waveforms best fit the observed ones was near the center of the strong motion generation area, which reproduced near-source ground motions in a broadband frequency range. The estimated strong motion generation area could explain the observed damaging ground motion at the Bam station. This suggests that estimating the source characteristics of the Bam earthquake is very important in understanding the causes of the earthquake damage.     

Peak ground accelerations from large (<Emphasis Type="Bold">M</Emphasis> ≥ 7.2) shallow crustal earthquakes: a comparison with predictions from eight recent ground-motion models

Strong-motion data from large (M ≥ 7.2) shallow crustal earthquakes invariably make up a small proportion of the records used to develop empirical ground motion prediction equations (GMPEs). Consequently GMPEs are more poorly constrained for large earthquakes than for small events. In this article peak ground accelerations (PGAs) observed in 38 earthquakes worldwide with M ≥ 7.2 are compared with those predicted by eight recent GMPEs. Well over half of the 38 earthquakes were not considered when deriving these GMPEs but the data were identified by a thorough literature review of strong-motion reports from the past 60 years. These data are provided in an electronic supplement for future investigations on ground motions from large earthquakes. The addition of these data provides better constraint of the between-event ground-motion variability in large earthquakes. It is found that the eight models generally provide good predictions for PGAs from these earthquakes, although there is evidence for slight under- or over-prediction of motions by some models (particularly for M > 7.6). The between-event variabilities predicted by most models match the observed variability, if data from two events (2001 Bhuj and 2005 Crescent City) that are likely atypical of earthquakes in active regions are excluded. For some GMPEs there is evidence that they are over-predicting PGAs in the near-source region of large earthquakes as well as over-predicting motions on hard rock. Overall, however, all the considered models, despite having been derived using limited data, provide reliable predictions of PGAs in the largest crustal earthquakes.     

Near-field horizontal and vertical earthquake ground motions

Strong-motion attenuation relationships are presented for peak ground acceleration, spectral acceleration, energy density, maximum absolute input energy for horizontal and vertical directions and for the ratio of vertical to horizontal of these ground motion parameters. These equations were derived using a worldwide dataset of 186 strong-motion records recorded with 15 km of the surface projection of earthquakes between M_s=5.8 and 7.8. The effect of local site conditions and focal mechanism is included in some of these equations.     

Strong motion characteristics of the M_w 6.6 Lushan earthquake,Sichuan,China——an insight into the spatial difference of a typical thrust fault earthquake

Near-field strong ground motions are useful for engineering seismology studies and seismic design, but dense observation networks of damaging earthquakes are still rare. In this study, based on the strong-motion data from the M w 6.6 Lushan earthquake, the ground motion parameters in different spatial regions are systematically analyzed, and the contributions from different effects, like the hanging-wall effect, directivity effect, and attenuation effect are separated to the extent possible. Different engineering parameters from the observed ground motions are compared with the local design response spectra and a new attenuation relation of Western China. General results indicate that the high frequency ground motion, like the peak ground acceleration, on two sides of the fault plane is sensitive to the hanging-wall effect, whereas the low frequency ground motion, like the long period spectral acceleration, in the rupture propagation direction is affected by the directivity effect. Moreover, although the M w 6.6 Lushan earthquake is not a large magnitude event, the spatial difference of ground motion is still obvious; thus, for a thrust faulting earthquake, in addition to the hanging effect, the directivity effect should also be considered.     

Pan-European ground-motion prediction equations for the average horizontal component of PGA,PGV, and 5 %-damped PSA at spectral periods up to 3.0 s using the RESORCE dataset

This article presents a set of Ground-Motion Prediction Equations (GMPEs) for Europe and the Middle East, derived from the RESORCE strong motion data bank, following a standard regression approach. The parametric GMPEs are derived for the peak ground acceleration, peak ground velocity, and 5 %-damped pseudo-absolute acceleration response spectra computed over 23 periods between 0.02 and 3 s, considering the average horizontal-component ground-motions. The GMPEs are valid for distances less than 300 km, hypocentral depth up to 35 km and over the magnitude range 4–7.6. Two metrics for the source-to-station distance (i.e. Joyner-Boore and hypocentral) are considered. The selected dataset is composed by 2,126 recordings (at a period of 0.1 s) related to 365 earthquakes, that includes strong-motion data from 697 stations.The EC8 soil classification (four classes from A to D) discriminates recording sites and four classes (normal, reverse, strike-slip, and unspecified) describe the style of faulting. A subset which contains only stations with measured Vs30 and earthquakes with specified focal mechanism (1,224 records from 345 stations and 255 earthquakes) is used to test of the accuracy of the median prediction and the variability associated to the broader data set. A random effect regression scheme is applied and bootstrap analyses are performed to estimate the 95 % confidence levels for the parameters. The total standard deviation sigma is decomposed into between-events and within-event components, and the site-to-site component is evaluated as well. The results show that the largest contribution to the total sigma is coming from the within-event component. When analyzing the residual distributions, no significant trends are observed that can be ascribed to the earthquake type (mainshock-aftershock classification) or to the non-linear site effects. The proposed GMPEs have lower median values than global models at short periods and large distances, while are consistent with global models at long periods $(\hbox {T} > 1)$  s. Consistency is found with two regional models developed for Turkey and Italy, as the considered dataset is dominated by waveforms recorded in these regions.     

Comparison of point and array-computed rotations for the TAIGER explosions of 4 March 2008

Two large explosions were recorded by a dense array of strong-motion accelerometers and rotational seismometers in northeastern Taiwan associated with a Taiwan Integrated Geodynamics Research long-range refraction experiment. The objective of this experiment was to test the response of the experimental eentec rotational seismometers against calculated array rotations. Computed array rotation rates are seen to have little variation across the array, but point rotation rate measurements obtained from individual rotational seismometers show significant deviations with each other and with the array rotation rates in the ranges of 3?C5?Hz and, especially, 3?C50?Hz. A cross-correlation method was used to compare array-computed rotation rates and point rotation rate measurements in the frequency band of 3?C5?Hz with the result that the absolute value of the normalized maximum correlation coefficient for each station set varied from 0.45 to 0.97 with an average of 0.84. Amplitude differences of the point rotation rate measurements are seen to be factors of 0.2 to 1.8 times the array rotations as well. It is not likely that the differences seen in the point and array-computed rotation rates are due to nonlinear or heterogeneous site conditions under each array element since these effects should also be seen in the acceleration data used to determine rotation rate. A rigorous method for accurately calibrating rotation rate instruments is needed to understand their response in the field.     

唐山响堂三维场地影响观测台阵

１９９４年７月中国地震局工程力学研究所在唐山余震区响堂镇建成了我国第一个三维场地影响观测台阵。该台阵目前有四个测点,分别布设在基岩地表、土层地表、地下１７ｍ和地下３２ｍ处。它安装了分辨率为１６位的井下数字观测系统,主机和从机同步运行,系统时钟采用Ｏｍｅｇａ导航信号自动校对（精度１ｍｓ）,地震数据采用固态方式（ＣＭＯＳ）存储,每个测点均布设一组 量力平衡式加速度计。该台阵自投入运行至１９９７年１２月     

旋转运动在地震学中的应用概述

旋转地震学是研究由天然地震、爆破和周围环境振动引起的地面旋转运动的新兴学科。对于它的研究不仅有助于对质点运动(平移运动、旋转运动和形变)进行完整的描述,而且对广义地球物理学,如强地面运动地震学、地震工程学、地震物理学、地震仪器等的研究也有重要指导意义。本文系统介绍了旋转运动在地震学中4个方面的应用。首先,介绍基于平移运动和旋转运动的共同测量,得出了计算远震瑞利波和勒夫波相速度的理论公式,并以西伯利亚地震为例,得出台站附近的相速度结构;其次,利用环形激光仪仅对地震SH波敏感的特性,分离P波和S波,分辨海洋噪声和面波,确定海洋噪声的反方位角;然后,介绍利用旋转传感器对自由振荡的长周期环形模式的观测;最后,对包含旋转观测量的多参数反演问题的重要性和实用性进行了阐述,并分析了旋转地震学研究现存的问题。     

A κ Model for Mainland France

An important parameter for the characterization of strong ground motion at high-frequencies (>1 Hz) is kappa, κ, which models a linear decay of the acceleration spectrum, a(f), in log-linear space (i.e. a(f) = A ₀ exp(? π κ f) for f > f _E where f is frequency, f _E is a low frequency limit and A ₀ controls the amplitude of the spectrum). κ is a key input parameter in the stochastic method for the simulation of strong ground motion, which is particularly useful for areas with insufficient strong-motion data to enable the derivation of robust empirical ground motion prediction equations, such as mainland France. Numerous studies using strong-motion data from western North America (WNA) (an active tectonic region where surface rock is predominantly soft) and eastern North America (ENA) (a stable continental region where surface rock is predominantly very hard) have demonstrated that κ varies with region and surface geology, with WNA rock sites having a κ of about 0.04 s and ENA rock sites having a κ of about 0.006 s. Lower κs are one reason why high-frequency strong ground motions in stable regions are generally higher than in active regions for the same magnitude and distance. Few, if any, estimates of κs for French sites have been published. Therefore, the purpose of this study is to estimate κ using data recorded by the French national strong-motion network (RAP) for various sites in different regions of mainland France. For each record, a value of κ is estimated by following the procedure developed by Anderson and Hough (Bull Seismol Soc Am 74:1969–1993, 1984): this method is based on the analysis of the S-wave spectrum, which has to be performed manually, thus leading to some uncertainties. For the three French regions where most records are available (the Pyrenees, the Alps and the Côtes-d’Azur), a regional κ model is developed using weighted regression on the local geology (soil or rock) and source-to-site distance. It is found that the studied regions have a mean κ between the values found for WNA and ENA. For example, for the Alps region a κ value of 0.0254 s is found for rock sites, an estimate reasonably consistent with previous studies.     

Canyon topography effects on ground motion at Feitsui damsite

The free-field accelerograms along Feitsui Canyon are analyzed and modeled by a numerical scheme to study the effect of canyon topography. Since six strong-motion accelerometers (SC1–SC6) were deployed along the Feitsui Canyon in 1991; there are 14 earthquakes (4.9≤M_L≤6.6) recorded by these stations until June 1996, but only five triggered all six stations. The maximum PGA value is 68.6 cm s⁻² recorded at station SC1. According to the present data, the effect of the dam on the ground motions at canyon stations can be negligible. The amplitude of ground motion on the slopes of the canyon is bigger than that at its trough. The integral equation method is applied to a two dimensional model of Feitsui Canyon to study the effects of the canyon topography. We choose the ground motion of SC3 or SC4 station at the trough of the canyon as the input motion for the model, which is then used to predict the ground motion at the other five stations. Apart from the earthquake close to the damsite, the simple model can reproduce the observed accelerations at all frequencies below 4 Hz. Overall, the numerical method can well predict the ground motion along the canyon, although the high-frequency simulation is underestimated.     

On the characteristics of ground motion rotational components using Chiba dense array data

An effort is made to examine the properties of rotational (torsional and rocking) ground motions using Chiba dense array data. The Chiba array system, located 30 km east of Tokyo, Japan, is composed of 15 boreholes with separation distances varying from 5 to 320 m. This provides a unique opportunity to examine the characteristics of rotational components. For this purpose, 17 events are considered and rotational ground motions are evaluated using spatial derivatives of translational ones. The effects of seismological parameters and separation distances between stations on properties of rotational motions are examined, showing a sudden increase in rotational motions for the earthquakes with large magnitude or PGA and decrease of these motions with increasing separation distance. While the duration of torsional motion is found to be larger than translational ones, there is no significant difference between durations of rocking and vertical motions. The effects of separation distance and earthquake magnitude on rotational response spectra are also investigated. The normalized rotational response spectra are found to be strongly affected by separation distance. The spectral ratios of rotational and translational motions are not linearly proportional to period as suggested by the previous studies. Finally, the torsional motion is predicted from translation ones for different separation distances at the site. The comparison of the predicted and the calculated torsional motions reveals a weak estimation in close separation distances (<30m) and satisfactory predictions in other cases. Copyright © 2007 John Wiley & Sons, Ltd.     

Strong motion characteristics of the <Emphasis Type="Italic">M</Emphasis><Subscript>w</Subscript> 6.6 Lushan earthquake,Sichuan, China — an insight into the spatial difference of a typical thrust fault earthquake

Near-field strong ground motions are useful for engineering seismology studies and seismic design, but dense observation networks of damaging earthquakes are still rare. In this study, based on the strong-motion data from the M w 6.6 Lushan earthquake, the ground motion parameters in different spatial regions are systematically analyzed, and the contributions from different effects, like the hanging-wall effect, directivity effect, and attenuation effect are separated to the extent possible. Different engineering parameters from the observed ground motions are compared with the local design response spectra and a new attenuation relation of Western China. General results indicate that the high frequency ground motion, like the peak ground acceleration, on two sides of the fault plane is sensitive to the hanging-wall effect, whereas the low frequency ground motion, like the long period spectral acceleration, in the rupture propagation direction is affected by the directivity effect. Moreover, although the M w 6.6 Lushan earthquake is not a large magnitude event, the spatial difference of ground motion is still obvious; thus, for a thrust faulting earthquake, in addition to the hanging effect, the directivity effect should also be considered.