Simple generalization approach for intensity–duration–frequency relationships

Rainfall intensity–duration–frequency (IDF) relationships describe rainfall intensity as a function of duration and return period, and they are significant for water resources planning, as well as for the design of hydraulic constructions. In this study, the two‐parameter lognormal (LN2) and Gumbel distributions are used as parent distribution functions. Derivation of the IDF relationship by this approach is quite simple, because it only requires an appropriate function of the mean of annual maximum rainfall intensity as a function of rainfall duration. It is shown that the monotonic temporal trend in the mean rainfall intensity can successfully be described by this parametric function which comprises a combination of the parameters of the quantile function a(T) and completely the duration function b(d) of the separable IDF relationship. In the case study of Aegean Region (Turkey), the IDF relationships derived through this simple generalization procedure (SGP) may produce IDF relationships as successfully as does the well‐known robust estimation procedure (REP), which is based on minimization of the nonparametric Kruskal–Wallis test statistic with respect to the parameters θ and η of the duration function. Because the approach proposed herein is based on lower‐order sample statistics, risks and uncertainties arising from sampling errors in higher‐order sample statistics were significantly reduced. The authors recommend to establish the separable IDF relationships by the SGP for a statistically favorable two‐parameter parent distribution, because it uses the same assumptions as the REP does, it maintains the observed temporal trend in the mean additionally, it is easy to handle analytically and requires considerably less computational effort. Copyright © 2012 John Wiley & Sons, Ltd.     

福建地区中小地震加速度反应谱衰减规律

本文基于收集福建省地震监测台网7个基岩台站从1999年至2007年获得的94个地震(ML=2.8～4.9,△=13～462 km) 的1974条宽频带速度记录,利用实时仿真方法得到了相应的加速度记录,进而得到了福建地区基岩场地中小地震绝对加速度反应谱的衰减关系.对基岩反应谱有影响的因素主要有震源、传播途径,本文简要分析这两个因素对地震动的影响.此项工作对于福建省抗震设防具有重要的意义.     

Pooled frequency analysis for intensity–duration–frequency curve estimation

Rainfall intensity–duration–frequency (IDF) curves are used in the design of urban infrastructure. Their estimation is based on rainfall frequency analysis, usually performed on rainfall records from a single gauged station. However, available at‐site record length is often too short to provide accurate estimates for long return periods. In the present study, a general framework for pooled rainfall frequency analysis based on the index‐event model is proposed for IDF estimation at gauged stations. Pooling group formation is defined by the region of influence approach on the basis of the geographical distance similarity measure. Several pooled approaches are defined and evaluated by a procedure through which quantile estimation and uncertainty are assessed. Alternate approaches for the definition of a pooling group are based on different criteria regarding initial pooling group size (and the relationship between size and return period), approaches for assessing pooling group homogeneity, and the use of macroregions in pooling group formation. The proposed framework is applied to identify the preferred approach for pooled rainfall intensity frequency analysis in Canada. Pooled approaches are found to provide more precise estimates than the at‐site approach, especially for long return periods. Pooled parent distribution selection supported the use of the generalized extreme value distribution across the country. Recommendations for pooling group formation include increasing the pooling group size with increases in return period and identifying an appropriate trade‐off between pooling group homogeneity and size for long return periods.     

Reliability of rainfall kinetic power–intensity relationships

The rainfall erosivity plays a fundamental role in water soil erosion processes and it can be expressed by its kinetic power. At first in this paper, the raindrop‐size distributions measured, in the period June 2006–March 2014, by an optical disdrometer installed at the Department of Agricultural and Forestry Sciences of University of Palermo are aggregated into rainfall intensity classes, having different ranges, and the measured kinetic power values are determined. Measured kinetic power values are initially used for testing the applicability of the kinetic power‐rainfall intensity relationships proposed by Wischmeier and Smith ( 1978 ), used in Universal Soil Loss Equation (USLE), Brown and Foster ( 1987 ) (RUSLE), and McGregor et al. ( 1995 ) (RUSLE2). Then, the reliability of a theoretical relationship for estimating the kinetic power by rainfall intensity and median volume diameter is verified. Finally, using the literature available datasets, corresponding to measurements carried out by different techniques and in different geographical sites, the analysis demonstrated that the rainfall intensity is not sufficient to determine the rainfall kinetic power. On the contrary, the theoretically deduced relationship allows to reproduce adequately the kinetic power of all available datasets, demonstrating that the knowledge of both rainfall intensity and median volume diameter allows a reliable estimate of the rainfall erosivity.     

Response spectral attenuation relationships for Singapore and the Malay Peninsula due to distant Sumatran‐fault earthquakes

As part of the effort to assess the seismic hazards of Singapore and the Malay Peninsula, representative ground motion prediction models have to be established. Seven existing attenuation relationships developed for shallow crustal earthquakes in stable continent and active tectonic regions are examined, and they are found to consistently over‐predict the ground motions of Sumatran‐fault earthquakes recently recorded in Singapore. This may be attributed to the differences in the regional crustal structures and distance ranges considered. Since the number of recorded ground motions in the region is very limited, a new set of attenuation relationships is derived based on synthetic seismograms. The uncertainties in rupture parameters, such as stress drop, focal depth, dip and rake angles, are defined according to the regional geological and tectonic settings as well as the ruptures of previous earthquakes. Ground motions are simulated for earthquakes with Mw ranging from 4.0 to 8.0, within a distance range from 174 to 1379km. Besides magnitude and distance, source‐to‐station azimuth is found to influence the amplitudes of the ground motions simulated. Thus, the azimuth is taken as an independent variable in the derived ground motion attenuation relationships. The Sumatran‐fault segments that have the potential to generate a specified level of response spectral accelerations in Singapore and Kuala Lumpur are identified based on the newly derived ground motion models. Copyright © 2003 John Wiley & Sons, Ltd.     

四川地区地震动峰值衰减规律研究

基于四川省地震监测台网27个基岩台站,2008年5月12日——2008年6月10日105次地震（震级ML=4.0——6.4,震中距△=26——623km）的8505条宽频带速度记录,利用实时仿真方法得到了相应的加速度记录,进而对数据进行回归分析,获得了四川地区基岩场地中小地震峰值加速度和峰值速度的衰减关系,并用最近发生的一次4.8级地震对该规律进行了验证．通过四川台网的记录,提出了符合四川地质条件的衰减关系      

川滇地区中小震地震动衰减特征分析

利用2007年以来川滇地区24次中小型破坏性地震(Ms4.7～6.7)的基岩场地和土层场地的强震动记录,分别统计获得了川滇地区水平向基岩场地和土层场地的地震动峰值及加速度反应谱衰减关系.通过与俞言祥等2006年基于转换方法得到的我国西部基岩地震动衰减关系的对比,验证了本文衰减关系对利用中小地震进行地震动估计的可靠性.同时,根据强震动数据随震级以及震中距的分布,分析了本文结果的适用性和可靠性.     

A multiscaling‐based intensity–duration–frequency model for extreme precipitation

Rainfall intensity–duration–frequency (IDF) curves are a standard tool in urban water resources engineering and management. They express how return levels of extreme rainfall intensity vary with duration. The simple scaling property of extreme rainfall intensity, with respect to duration, determines the form of IDF relationships. It is supposed that the annual maximum intensity follows the generalized extreme value (GEV) distribution. As well known, for simple scaling processes, the location parameter and scale parameter of the GEV distribution obey a power law with the same exponent. Although, the simple scaling hypothesis is commonly used as a suitable working assumption, the multiscaling approach provides a more general framework. We present a new IDF relationship that has been formulated on the basis of the multiscaling property. It turns out that the GEV parameters (location and scale) have a different scaling exponent. Next, we apply a Bayesian framework to estimate the multiscaling GEV model and to choose the most appropriate model. It is shown that the model performance increases when using the multiscaling approach. The new model for IDF curves reproduces the data very well and has a reasonable degree of complexity without overfitting on the data.     

Ground motion attenuation relations of small and moderate earthquakes in Sichuan region

On the basis of 10 935 broadband velocity records of 135 earthquakes (ML3.0-6.4 and epicentral distance of 26-623 km) occurred from May 12 to June 10 in 2008, which are collected from 27 bedrock stations included in Sichuan Earthquake Monitoring Network, the corresponding acceleration records are obtained by a real-time simulation method. Then by regression analysis on the data, the relation between the peak ground acceleration and velocity attenuation of small and moderate bedrock earthquakes occurred in S...     

An attenuation model for distant earthquakes

Large magnitude earthquakes generated at source–site distances exceeding 100km are typified by low‐frequency (long‐period) seismic waves. Such induced ground shaking can be disproportionately destructive due to its high displacement, and possibly high velocity, shaking characteristics. Distant earthquakes represent a potentially significant safety hazard in certain low and moderate seismic regions where seismic activity is governed by major distant sources as opposed to nearby (regional) background sources. Examples are parts of the Indian sub‐continent, Eastern China and Indo‐China. The majority of ground motion attenuation relationships currently available for applications in active seismic regions may not be suitable for handling long‐distance attenuation, since the significance of distant earthquakes is mainly confined to certain low to moderate seismicity regions. Thus, the effects of distant earthquakes are often not accurately represented by conventional empirical models which were typically developed from curve‐fitting earthquake strong‐motion data from active seismic regions. Numerous well‐known existing attenuation relationships are evaluated in this paper, to highlight their limitations in long‐distance applications. In contrast, basic seismological parameters such as the Quality factor (Q‐factor) could provide a far more accurate representation for the distant attenuation behaviour of a region, but such information is seldom used by engineers in any direct manner. The aim of this paper is to develop a set of relationships that provide a convenient link between the seismological Q‐factor (amongst other factors) and response spectrum attenuation. The use of Q as an input parameter to the proposed model enables valuable local seismological information to be incorporated directly into response spectrum predictions. The application of this new modelling approach is demonstrated by examples based on the Chi‐Chi earthquake (Taiwan and South China), Gujarat earthquake (Northwest India), Nisqually earthquake (region surrounding Seattle) and Sumatran‐fault earthquake (recorded in Singapore). Field recordings have been obtained from these events for comparison with the proposed model. The accuracy of the stochastic simulations and the regression analysis have been confirmed by comparisons between the model calculations and the actual field observations. It is emphasized that obtaining representative estimates for Q for input into the model is equally important.Thus, this paper forms part of the long‐term objective of the authors to develop more effective communications across the engineering and seismological disciplines. Copyright © 2003 John Wiley & Sons, Ltd.     

Ground motion attenuation relation for small to moderate earthquakes in Fujian region, China

We collect 1974 broad-band velocity records of 94 earthquakes (ML=2.8~4.9, △=13~462 km) from seven stations of the Fujian Seismic Network from March 1999 to March 2007. Using real-time simulation, we obtain the corresponding acceleration and then adopt different models to analyze the seismic data. As a result, a new attenuation relationship between PGA and PGV of the small and moderate earthquakes on bedrock site in Fujian region is established. The Yongchun earthquake occurred recently verifies the attenuation relationship well. This paper provides a new approach for studying the ground motion attenuation relationship using velocity records.     

Response spectral attenuation relationships for Sumatran-subduction earthquakes and the seismic hazard implications to Singapore and Kuala Lumpur

Singapore and Kuala Lumpur, the capital of Malaysia, may well represent the classic examples of area with low seismic hazard but with high consequence. Both cities are located in a low-seismicity region of Southeast Asia, where active seismic sources are located more than 300 km away. Seismic designs have not been implemented in this seemingly low-hazard region though distant earthquakes in Sumatra had frequently shaken high-rise structures in the two cities. Several studies have been conducted to systematically assess the seismic hazards of Singapore and the Malay Peninsula. The present research particularly addresses issues in deriving a new set of attenuation relationships of peak ground acceleration (PGA), peak ground velocity (PGV) and response spectral acceleration (RSA) for the Sumatran-subduction earthquakes. To be relevant for the seismic hazard assessment of the remote metropolises, the derived attenuation relationships cover a long distance range from 150 to 1500 km. The attenuation relationships are derived using synthetic seismograms that account for source and path effects. The uncertainties in rupture parameters, such as stress drop, strike, dip and rake angles, have been defined according to the regional geological and tectonic settings as well as the ruptures of previous earthquakes. The seismic potential of the Sumatran subduction zone are high in the region from 2°N to 5°S as there has been no recurrence of great thrust events since 1861. A large event with M_w greater than 7.8 in this particular subduction zone may be capable of generating destructive ground motions in Singapore and Kuala Lumpur, even at a distance of 700 km.     

川滇地区水平向强地震动衰减关系研究

利用近几年在川滇地区破坏性地震及汶川地震强余震中获得的951条加速度记录,通过选取合适的衰减关系形式和距离参数,经统计获得了川滇地区水平向峰值加速度与35个周期点对应的加速度反应谱(阻尼比0.05)衰减关系.统计结果显示,震级越大,地震动随距离的衰减越慢;加速度反应谱的短周期部分随距离的衰减明显快于长周期部分;中强地震在近场也会产生较大的峰值加速度和较高的短周期加速度反应谱.由于统计资料的非完整性,本文统计结果尚不宜直接应用于相关工程场地的设计地震动参数确定中.但本文结果与目前由转换方法得到的我国西部地震动参数衰减规律的较大差异提示:进一步深入研究我国地震动参数衰减规律应是紧迫而重要的任务.     

川滇地区水平向强地震动衰减关系研究

利用近几年在川滇地区破坏性地震及汶川地震强余震中获得的951条加速度记录, 通过选取合适的衰减关系形式和距离参数, 经统计获得了川滇地区水平向峰值加速度与35个周期点对应的加速度反应谱(阻尼比0.05)衰减关系. 统计结果显示, 震级越大, 地震动随距离的衰减越慢; 加速度反应谱的短周期部分随距离的衰减明显快于长周期部分; 中强地震在近场也会产生较大的峰值加速度和较高的短周期加速度反应谱. 由于统计资料的非完整性, 本文统计结果尚不宜直接应用于相关工程场地的设计地震动参数确定中. 但本文结果与目前由转换方法得到的我国西部地震动参数衰减规律的较大差异提示： 进一步深入研究我国地震动参数衰减规律应是紧迫而重要的任务.     

不同仪器烈度算法在四川地区 历次地震中的比较应用

强震观测资料包括强震动时程记录资料和宏观震害调查资料两大类, 前者是定量的微观数据, 后者则是定性的宏观指标. 本文明晰给出了微观仪器烈度与宏观仪器烈度、 微观考察烈度与宏观考察烈度的概念, 并在此基础上提出了只有在宏观仪器烈度与宏观考察烈度之间进行比较才具有实质性的意义;同时对国内外常见的仪器烈度算法进行了比较性研究, 得出了袁一凡仪器烈度算法可靠性更高的结论;最后以四川地区历年来重要震例的强震动记录为依据, 对修正的袁一凡仪器烈度算法的可靠性进行了比较应用. 结果表明, 对袁一凡仪器烈度算法修正与扩展的应用是可行的, 同时也验证了将微观仪器烈度与宏观考察烈度直接进行比较会存在较大的差距.      

Ground‐motion attenuation relationship for the Sumatran megathrust earthquakes

A representative attenuation relationship is one of the key components required in seismic hazard assessment of a region of interest. Attenuation relationships for peak ground acceleration, peak ground velocity and response spectral accelerations for Sumatran megathrust earthquakes, covering M_w up to 9.0, are derived based on synthetic seismograms obtained from a finite‐fault kinematic model. The relationships derived are for very hard rock site condition and for a long‐distance range between 200 and 1500 km. They are then validated with recorded data from giant earthquakes on the Sumatran megathrust occurring since year 2000. A close examination of the recorded data also shows that spectral shapes predicted by most of the existing attenuation relationships and that specified in the IBC code are not particularly suitable for sites where potential seismic hazard is dominated by large‐magnitude, distant, earthquakes. Ground motions at a remote site are typically signified by the dominance of long‐period components with periods longer than 1 s, whereas the predominant periods from most of the existing attenuation relationships and the IBC code are shorter than 0.6 s. The shifting of response spectrum towards longer period range for distant earthquakes should be carefully taken into account in the formulation of future seismic codes for Southeast Asia, where many metropolises are located far from active seismic sources. The attenuation relationship derived in the present study can properly reproduce the spectral shape from distant subduction earthquakes, and could hopefully give insights into the formulation of future seismic codes. Copyright © 2009 John Wiley & Sons, Ltd.     

我国大陆地区常用浅壳地震的地震动参数衰减关系

对地震动参数衰减关系应用时涉及的地震动参数、地震参数、基本模型、回归方法等方面的要点进行了阐述。以华北地区为例,简要介绍了数十年我国工程抗震设防应用中常用的几组浅壳地震峰值加速度、加速度反应谱衰减关系的主要特点,并对其差异进行了比较分析。最后总结了我国现阶段衰减关系研究的不足,对其未来发展方向进行了展望。     

Calibration of the specific barrier model to Iranian plateau earthquakes and development of physically based attenuation relationships for Iran

Earthquake ground-motion relationships for soil and rock sites in Iran have been developed based on the specific barrier model (SBM) used within the context of the stochastic modeling and calibrated against up-to-date Iranian strong-motion data. A total of 171 strong-motion accelerograms recorded at distances of up to 200 km from 24 earthquakes with moment magnitudes ranging from Mw 5.2 to 7.4 are used to determine the region-specific source parameters of this model. Regression analysis was conducted using the “random effects” methodology that considers both earthquake-to-earthquake (inter-event) variability and within-earthquake (intra-event) variability to effectively handle the problem of weighting observations from different earthquakes. The minimization of the error function in each iteration of the “random effects” procedure was performed using the genetic algorithm method. The residuals are examined against available Iranian strong-motion data to confirm that the model predictions are unbiased and that there are no significant residual trends with distance and magnitude. No evidence of self-similarity breakdown is observed between the source radius and its seismic moment. To verify the robustness of the results, tests were performed to confirm that the results are unchanged if the number of observations is changed by removing different randomly selected datasets from the original database. Stochastic simulations, using the derived SBM, are then performed to predict peak ground-motion and response spectra parameters for a wide range of magnitudes and distances. The stochastic SBM predictions agree well with the new empirical regression equations proposed for Iran, Europe and Middle East in the magnitude–distance ranges well represented by the data. It has been shown that the SBM of this study provides unbiased ground-motion estimates over the entire frequency range of most engineering interests (1–10 Hz) for the Iranian earthquakes. Our results are also important for the assessment of hazards in other seismically active environments in the Middle East and Mediterranean regions.     

A macroseismic intensity prediction equation for intermediate depth earthquakes in the Vrancea region,Romania

The use of shake maps in terms of macroseismic intensity in earthquake early warning systems as well as intensity based seismic hazard assessments provides a valuable supplement to typical studies based on recorded ground motion parameters. A requirement for such applications is ground motion prediction equations (GMPE) in terms of macroseismic intensity, which have the advantages of good data availability and the direct relation of intensity to earthquake damage. In the current study, we derive intensity prediction equations for the Vrancea region in Romania, which is characterized by the frequent occurrence of large intermediate depth earthquakes giving rise to a peculiar anisotropic ground shaking distribution. The GMPE have a physical basis and take the anisotropic intensity distribution into account through an empirical regional correction function. Furthermore, the relations are easy to implement for the user. Relations are derived in terms of epicentral, rupture and Joyner–Boore distance and the obtained relations all provide a new intensity estimate with an uncertainty of ca. 0.6 intensity units.     

Intensity-attenuation and magnitude-intensity relationships for northwest european earthquakes

This study shows that, for Northwest Europe, an intraplate region of subdued seismicity, a comparatively simple attenuation model is adequate to predict quite accurately the fall-off of intensity with distance. The analysis shows that focal depths determined from macroseismic data are confined in the upper 25 km, and that shallow shocks attenuate far more rapidly than deeper events. There is no evidence for a regional variation of the absorption coefficient, which, together with the coefficient of geometric spreading, is a function of depth. Also, the intensity factor b, which is usually taken to be equal to 3, is a variable and a function of the energy absorption at the epicentre. It is shown that magnitudes can be predicted accurately by use of one or preferably by more isoseismal radii calibrated against re-assessed instrumental magnitudes.