Order statistics of functionals of strong ground motion for a class of renewal processes

In this paper, probability distribution functions are derived for the order statistics of various functionals of strong ground motion at a site. These functionals can be: Modified Mercalli Intensity (MMI), peak ground acceleration (PGA), Fourier spectral amplitudes of acceleration, response spectrum amplitudes (spectral displacement, pseudo-spectral velocity and pseudo-spectral acceleration), and amplitudes of the peaks (local maxima and local minima) in the time historyof the response of SDOF and MDOF structures at the site. Three parameters of the response of a structure are considered: displacement, shear force and bending moment at each level (storey) of the structure. The earthquake sources contributing to the risk of ground motion at the site are a number of point, area or volume sources, each with defined frequency of occurence-magnitude relationship. The magnitudes of the possible events at these sources are discretized, and the occurrence of events of different magnitudes are assumed to be statistically independent. For each magnitude, it is assumed that the eartquakes occur in a Poissonian sequence or in a renewal process which is a generalization of the Poissonian. For these assumptions, the probability distribution functions are presented for the number of earthquakes, n, during which a given level of site or structural response is exceeded during the exposure time, and for the return period of the exceedances. For example, for single-degree- of-freedom: (SDOF) or multi-degree-of-freedom structures, (MDOF) n can be the number of earthquakes during which the response of a storey will exceed a given level at least m times(m = 1, 2, 3,…) during the exposure time. These probability distribution functions can be used to extend the concept of uniform probability functionals to more than one exceedance. A more important application is to generalize the uniform probability functionals method of site response (uniform probability Fourier or response spectra) to uniform probability envelopes of displacement, shears and bending moments of a given structure. The uniform probability envelopes can be for exceedance at least once during at least one earthquake, or, in general, for exceedance at least m times per earthquake (m = 1, 2,…) during at least n earthquakes. In other words, during at least n earthquakes at least m peaks in the response can be higher than the specified level. Such uniform probability envelopes can be used (1) to define new design guidelines for building codes based on cost-benefit analysis; (2) to construct more refined probability distribution functions for the damage and total economic losses caused by earthquakes; and (3) to develop planning and decision strategies on strengthening and retrofitting existing buildings.     

Earthquake Hazard Assessment for Dehradun, Uttarakhand, India, Including a Characteristic Earthquake Recurrence Model for the Himalaya Frontal Fault (HFF)

The seismic hazard has been computed for the city of Dehradun, Uttarakhand, India. The city lies in the Himalayan foothills between two faults: the Main Boundary Thrust (MBT) and the Himalayan Frontal Fault (HFF). The contributions from these two faults have been modelled differently in a probabilistic model. While the MBT has been modelled with a Poissonian earthquake distribution, the HFF has been modelled both with a characteristic earthquake recurrence model and a Poissonian model. The hazard scenarios reveal different patterns depending on the classical approaches and the characteristic models applied, and the obtained results indicate that Dehradun may experience PGA shaking around 2.2?m/s² for 225 years return period and around 4.6?m/s² for a 2,500?years return period.     

Tsunami Probability in the Caribbean Region

We calculated tsunami runup probability (in excess of 0.5 m) at coastal sites throughout the Caribbean region. We applied a Poissonian probability model because of the variety of uncorrelated tsunami sources in the region. Coastlines were discretized into 20 km by 20 km cells, and the mean tsunami runup rate was determined for each cell. The remarkable ~500-year empirical record compiled by O’Loughlin and Lander (2003) was used to calculate an empirical tsunami probability map, the first of three constructed for this study. However, it is unclear whether the 500-year record is complete, so we conducted a seismic moment-balance exercise using a finite-element model of the Caribbean-North American plate boundaries and the earthquake catalog, and found that moment could be balanced if the seismic coupling coefficient is c = 0.32. Modeled moment release was therefore used to generate synthetic earthquake sequences to calculate 50 tsunami runup scenarios for 500-year periods. We made a second probability map from numerically-calculated runup rates in each cell. Differences between the first two probability maps based on empirical and numerical-modeled rates suggest that each captured different aspects of tsunami generation; the empirical model may be deficient in primary plate-boundary events, whereas numerical model rates lack backarc fault and landslide sources. We thus prepared a third probability map using Bayesian likelihood functions derived from the empirical and numerical rate models and their attendant uncertainty to weight a range of rates at each 20 km by 20 km coastal cell. Our best-estimate map gives a range of 30-year runup probability from 0–30% regionally.     

An efficient method for estimating the collapse risk of structures in seismic regions

Assessing the probability of collapse is a computationally demanding component of performance‐based earthquake engineering. This paper examines various aspects involved in the computation of the mean annual frequency of collapse (λ_c) and proposes an efficient method for estimating the sidesway collapse risk of structures in seismic regions. By deaggregating the mean annual frequency of collapse, it is shown that the mean annual frequency of collapse is typically dominated by earthquake ground motion intensities corresponding to the lower half of the collapse fragility curve. Uncertainty in the collapse fragility curve and mean annual frequency of collapse as a function of the number of ground motions used in calculations is also quantified, and it is shown that using a small number of ground motions can lead to unreliable estimates of a structure's collapse risk. The proposed method is shown to significantly reduce the computational effort and uncertainty in the estimate. Copyright © 2012 John Wiley & Sons, Ltd.     

Error propagation in time-dependent probability of occurrence for characteristic earthquakes in Italy

Time-dependent models for seismic hazard and earthquake probabilities are at the leading edge of research nowadays. In the framework of a 2-year national Italian project (2005–2007), we have applied the Brownian passage time (BPT) renewal model to the recently released Database of Individual Seismogenic Sources (DISS) to compute earthquake probability in the period 2007–2036. Observed interevent times on faults in Italy are absolutely insufficient to characterize the recurrence time. We, therefore, derived mean recurrence intervals indirectly. To estimate the uncertainty of the results, we resorted to the theory of error propagation with respect to the main parameters: magnitude and slip rate. The main issue concerned the high variability of slip rate, which could hardly be reduced by exploiting geodetic constraints. We did some validation tests, and interesting considerations were derived from seismic moment budgeting on the historical earthquake catalog. In a time-dependent perspective, i.e., when the date of the last event is known, only 10–15% of the 115 sources exhibit a probability of a characteristic earthquake in the next 30 years higher than the equivalent Poissonian probabilities. If we accept the Japanese conventional choice of probability threshold greater than 3% in 30 years to define “highly probable sources,” mainly intermediate earthquake faults with characteristic M < 6, having an elapsed time of 0.7–1.2 times the recurrence interval are the most “prone” sources. The number of highly probable sources rises by increasing the aperiodicity coefficient (from 14 sources in the case of variable α ranging between 0.22 and 0.36 to 31 sources out of 115 in the case of an α value fixed at 0.7). On the other hand, in stationary time-independent approaches, more than two thirds of all sources are considered probabilistically prone to an impending earthquake. The performed tests show the influence of the variability of the aperiodicity factor in the BPT renewal model on the absolute probability values. However, the influence on the relative ranking of sources is small. Future developments should give priority to a more accurate determination of the date of the last seismic event for a few seismogenic sources of the DISS catalog and to a careful check on the applicability of a purely characteristic model.     

Probability of actuating a seismic shutoff device

Automatic seismic shutoff devices are used to reduce the risk to gas and liquid distribution systems from earthquakes. In the USA, the gas shutoff devices are tested and certified according to the American Society of Civil Engineers' Standard ASCE 25. During tests, devices are shaken by simple harmonic (sinusoidal) motions of different frequencies and checked for actuation. Because earthquake motions are not sinusoidal, the amplitude of earthquake motions that will actuate these devices is not clearly understood. This paper determines the probability of actuating devices by earthquake motions of different amplitudes. The probability of actuation increases with increase in the resultant peak horizontal ground acceleration (PGA). The probability of actuation is 50% for PGA = 0.23g and 90% for PGA = 0.31g, where g = 9.81 m/s² = acceleration due to gravity. On a ‘stiff soil’ site in San Francisco, CA, the mean recurrence interval of actuation is 51 years. On a similar site in Boston, MA, the mean recurrence interval of actuation is 3000 years. ASCE 25 compliant devices are actuated by high frequencies in ground motions. There is greater uncertainty in the actuation of these devices by ground motions that are damaging to very flexible systems. Copyright © 2016 John Wiley & Sons, Ltd.     

Hazard mapping of normalized peak strain in soils during earthquakes: microzonation of a metropolitan area

Seismic hazard maps of the Los Angeles metropolitan area are illustrated for normalized peak strain and for 50 years of exposure. The strain estimates are based on scaling in terms of peak ground velocity. The proportionality factor is the phase velocity with which the wave energy is propagating. A simplified seismicity model is used in which all earthquakes occur on faults represented by buried lines and in one zone of diffused seismicity. Poissonian model of earthquake occurrence is assumed. The same model was used in the 1980's to illustrate a method for microzoning of the same area for response spectral amplitudes. Maps of logarithms of normalized peak strain, cε_max, are presented for probabilities of at least one exceedance p = 0·99, 0·9, 0·5, 0·1 and 0·01. These can be used to construct site specific probability distribution functions of the normalized peak strain, cε_max. Such maps are useful for design of new and for retrofit of existing structures, sensitive to strain and differential ground motions (bridges, tunnels, pipelines, etc.).     

Pushover-based seismic risk assessment and loss estimation of masonry buildings

A pushover-based seismic risk assessment and loss estimation methodology for masonry buildings is introduced. It enables estimation of loss by various performance measures such as the probability of exceeding a designated economic loss, the expected annual loss, and the expected loss given a seismic intensity. The methodology enables the estimation of the economic loss directly from the results of structural analysis, which combines pushover analysis and incremental dynamic analysis of an equivalent SDOF model. The use of the methodology is demonstrated by means of two variants of a three-storey masonry building both of which have the same geometry, but they are built, respectively, from hollow clay masonry (model H) and solid brick masonry (model S). The probability of collapse given the selected design earthquake corresponding to a return period of 475 years was found to be negligible for model H, which indicates the proper behaviour of such a structure when designed according to the current building codes. However, the corresponding probability of collapse of model S was very high (46%). The expected total loss given the design earthquake was estimated to amount to 28 000 € and 290 000 €, respectively, for models H and S. The expected annual loss per 100 m² of gross floor area was estimated to amount to 75 € and 191 €, respectively, for models H and S. For the presented examples, it was also observed that nonstructural elements contributed more than 50% of the total loss.     

Integration and influence of paleoseismic and geologic data for the seismic hazard evaluation in the Catalan coastal ranges, Spain

In this study, the influence of paleoseismic and geologic data in the seismic hazard estimation for the Catalan coastal ranges is analysed. We computed the probabilistic seismic hazard using area seismic sources with a Poissonian assumption for the earthquake occurrence. For the computations, a previously published attenuation relationship based on European strong motion data was applied. The resulting hazard estimates show similarities to the previous assessments in the region. These results were then used as a reference for comparison with other new models. In order to analyse the influence of the paleoseismic data three different models were tested. Since the number of faults that are investigated in detail are few, the same area sources that were used in the Poissonian assumption were kept in all three new models. In addition, the new paleoseismic data with faults expressed as line sources were used. In this case, a cyclic earthquake occurrence was assumed. The three models were based on the paleoseismic data with different assumptions on the time elapsed since last event. The time elapsed was set to 0, 10 and 85% of the recurrence interval in each model. The results are presented as maps showing the difference between the three models and the reference model with the Poissonian assumption. The results are given in horizontal peak ground acceleration contour maps for different return periods, also taking into account large return periods as high as 25,000 years. This is done to demonstrate the effect of large recurrence intervals found for some of the active faults. In general, we observe that for short return periods (<1000 years), the Poissonian assumption of earthquake occurrence is probably sufficient and provides a robust estimate of the hazard. However, for longer return periods (>5000 years) the effects of the paleoseismic data become increasingly significant. In order to estimate the true seismic hazard potential of this apparently low seismicity area, long-term behaviour of the possible active faults in the region needs to be investigated systematically.     

Renewal models for earthquake predictability

The new Database of Italy’s Seismogenic Sources (Basili et al. 2008) identifies areas with a degree of homogeneity in earthquake generation mechanism judged sufficiently high. Nevertheless, their seismic sequences show rather long and regular interoccurrence times mixed with irregularly distributed short interoccurrence times. Accordingly, the following question could naturally arise: do sequences consist of nearly periodic events perturbed by a kind of noise; are they Poissonian; or short interoccurrence times predominate like in a cluster model? The relative reliability of these hypotheses is at present a matter of discussion (Faenza et al., Geophys J Int 155:521–531, 2003; Corral, Proc Geoph 12:89–100, 2005, Tectonophysics 424:177–193, 2006). In our regions, a statistical validation is not feasible because of the paucity of data. Moreover, the classical tests do not clearly suggest which one among different proposed models must be favoured. In this paper, we adopt a model of interoccurrence times able to interpret the three different hypotheses, ranging from exponential to Weibull distributions, in a scenario of increasing degree of predictability. In order to judge which one of these hypotheses is favoured, we adopt, instead of the classical tests, a more selective indicator measuring the error in respect to the chosen panorama of possible truths. The earthquake prediction is here simply defined and calculated through the conditional probability of occurrence depending on the elapsed time t₀ since the last earthquake. Short-term and medium-term predictions are performed for all the Italian seismic zones on the basis of datasets built in the context of the National Projects INGV-DPC 2004–2006, in the frame of which this research was developed. The mathematical model of interoccurrence times (mixture of exponential and Weibull distributions) is justified in its analytical structure. A dimensionless procedure is used in order to reduce the number of parameters and to make comparisons easier. Three different procedures are taken into consideration for the estimation of the parameter values; in most of the cases, they give comparable results. The degree of credibility of the proposed methods is evaluated. Their robustness as well as their sensitivity are discussed. The comparison of the probability of occurrence of a Maw >5.3 event in the next 5 and 30 years from January 1, 2003, conditional to the time elapsed since the last event, shows that the relative ranking of impending rupture in 5 years is roughly maintained in a 30-year perspective with higher probabilities and large fluctuations between sources belonging to the same macro region.     

Micro-zoning of the natural radioactivity levels and seismic velocities of potential residential areas in volcanic fields: The case of Isparta (Turkey)

This study involved the analysis of the locations with the lowest earthquake risk in the Isparta province of Turkey and the radiological properties of these locations. The most convenient residential areas in the region in terms of radiology and earthquake risk were identified. The radiological characteristics of soil are an important factor in the evaluation of residential areas. Gamma ray spectrometry and multi-source seismic refraction methods were used to conduct radioactive and seismic measurements. The measured ²³⁸U, ²³²Th and ⁴⁰K activity concentrations were used to calculate the absorbed gamma dose rate, the annual effective dose rate, the radium equivalent and the external hazard index of the environment to estimate the radiological risk of natural radioactivity. The compressional and shear wave velocities were calculated based on the results of multi-source seismic refraction. The calculated parameters were used to generate micro-zone maps. The shear wave velocity was used to analyze the stiffness of looseness of the soil. The radiological risks of the area were determined. Both the seismic and radiological hazards were considered in determining the appropriate areas for residential development. In the results of this study, the best location for residential development was demonstrated to be on limestone, and the worst location was determined to be on alluvium.     

A Bayesian Assessment of Seismic Semi-Periodicity Forecasts

Among the schemes for earthquake forecasting, the search for semi-periodicity during large earthquakes in a given seismogenic region plays an important role. When considering earthquake forecasts based on semi-periodic sequence identification, the Bayesian formalism is a useful tool for: (1) assessing how well a given earthquake satisfies a previously made forecast; (2) re-evaluating the semi-periodic sequence probability; and (3) testing other prior estimations of the sequence probability. A comparison of Bayesian estimates with updated estimates of semi-periodic sequences that incorporate new data not used in the original estimates shows extremely good agreement, indicating that: (1) the probability that a semi-periodic sequence is not due to chance is an appropriate estimate for the prior sequence probability estimate; and (2) the Bayesian formalism does a very good job of estimating corrected semi-periodicity probabilities, using slightly less data than that used for updated estimates. The Bayesian approach is exemplified explicitly by its application to the Parkfield semi-periodic forecast, and results are given for its application to other forecasts in Japan and Venezuela.     

A new <Emphasis Type="Italic">M</Emphasis><Subscript><Emphasis Type="Italic">w</Emphasis></Subscript> estimation parameter for use in earthquake early warning systems

We propose a method that employs the squared displacement integral (ID2) to estimate earthquake magnitudes in real time for use in earthquake early warning (EEW) systems. Moreover, using τ _c and P _d for comparison, we establish formulas for estimating the moment magnitudes of these three parameters based on the selected aftershocks (4.0 ≤ M _s  ≤ 6.5) of the 2008 Wenchuan earthquake. In this comparison, the proposed ID2 method displays the highest accuracy. Furthermore, we investigate the applicability of the initial parameters to large earthquakes by estimating the magnitude of the Wenchuan M _s 8.0 mainshock using a 3-s time window. Although these three parameters all display problems with saturation, the proposed ID2 parameter is relatively accurate. The evolutionary estimation of ID2 as a function of the time window shows that the estimation equation established with ID2 ^Ref determined from the first 8-s of P wave data can be directly applicable to predicate the magnitudes of 8.0. Therefore, the proposed ID2 parameter provides a robust estimator of earthquake moment magnitudes and can be used for EEW purposes.     

A Bayesian Approach to Seismic Hazard Estmation: Maximum Values of Magnitudes and Peak Ground Accelerations

Earthquake Researeh in Ch一na461 .METHODLet R be some value measured or estimated as a sequenee ina’‘Past”time interval(一丁,O)(I)万‘月,=(RI,…,R。),R,之R。,R=nlaX l二f匕11(RI,…,R,,) Values(l)eould have an arbitrary Physieal nature.BelowweshalleonsiderEq.(l)asearthquakemagnitudes in a given seismic aetive region or logarithms of seismie Peak ground aeeelerations at习given site.Ro isa而nimum eutoff value;it 15 defined by Possibilities of registration systems or wasehosen as the …     

An open-accessed inventory of landslides triggered by the MS 6.8 Luding earthquake,China on September 5, 2022

This study constructs a preliminary inventory of landslides triggered by the M_S 6.8 Luding earthquake based on field investigation and human-computer interaction visual interpretation on optical satellite images. The results show that this earthquake triggered at least 5 007 landslides, with a total landslide area of 17.36 ?km², of which the smallest landslide area is 65 ?m² and the largest landslide area reaches 120 747 ?m², with an average landslide area of about 3 500 ?m². The obtained landslides are concentrated in the IX intensity zone and the northeast side of the seismogenic fault, and the area density and point density of landslides are 13.8%, and 35.73 ?km^?2 peaks with 2 ?km as the search radius. It should be noted that the number of landslides obtained in this paper will be lower than the actual situation because some areas are covered by clouds and there are no available post-earthquake remote sensing images. Based on the available post-earthquake remote sensing images, the number of landslides triggered by this earthquake is roughly estimated to be up to 10 000. This study can be used to support further research on the distribution pattern and risk evaluation of the coseismic landslides in the region, and the prevention and control of landslide hazards in the seismic area.     

Earthquake hazard in Marmara Region, Turkey

Earthquake hazard in the Marmara Region, Turkey has been investigated using time-independent probabilistic (simple Poissonian) and time-dependent probabilistic (renewal) models. The study culminated in hazard maps of the Marmara Region depicting peak ground acceleration (PGA) and spectral accelerations (SA)'s at 0.2 and 1 s periods corresponding to 10 and 2% probabilities of exceedance in 50 yrs. The historical seismicity, the tectonic models and the known slip rates along the faults constitute the main data used in the assignment. Based on recent findings it has been possible to provide a fault segmentation model for the Marmara Sea. For the main Marmara Fault this model essentially identifies fault segments for different structural, tectonic and geometrical features and historical earthquake occurrences. The damage distribution and pattern of the historical earthquakes have been carefully correlated with this fault segmentation model. The inter-event time period between characteristic earthquakes in these segments is consistently estimated by dividing the seismic slip estimated from the earthquake catalog by the GPS-derived slip rate of 22±3 mm/yr. The remaining segments in the eastern and southern Marmara region are also identified using recent geological, geophysical studies and historical earthquakes. The model assumes that seismic energy along the segments is released by characteristic earthquakes. For the probabilistic studies characteristic earthquake based recurrence relationships are used. Assuming normal distribution of inter-arrival times of characteristic earthquakes, the ‘mean recurrence time’, ‘covariance’ and the ‘time since last earthquake’ are developed for each segment. For the renewal model, the conditional probability for each fault segment is calculated from the mean recurrence interval of the characteristic earthquake, the elapsed time since the last major earthquake and the exposure period. The probabilities are conditional since they change as a function of the time elapsed since the last earthquake. For the background earthquake activity, a spatially smoothed seismicity is determined for each cell of a grid composed of cells of size 0.005°×0.005°. The ground motions are determined for soft rock (NEHRP B/C boundary) conditions. Western US-based attenuation relationships are utilized, since they show a good correlation with the attenuation characteristics of ground motion in the Marmara region. The possibility, that an event ruptures several fault segments (i.e. cascading), is also taken into account and investigated by two possible models of cascading. Differences between Poissonian and renewal models, and also the effect of cascading have been discussed with the help of PGA ratio maps.     

基于泸定6.8级地震某二层混凝土框架结构损伤分析

2022年9月5日四川甘孜州泸定县发生6.8级地震,相关台站记录到水平向地震动峰值加速度达到891cm/s²,竖直向地震动峰值加速度为175cm/s²,地震造成严重人员伤亡和建筑物倒塌。为进一步了解本次地震对建筑物破坏作用,采用大型通用有限元软件SAUSG2022,对震中某二层钢筋混凝土框架结构进行弹塑性动力时程分析。结果表明,在泸定地震动作用下,该建筑物损伤严重,有倒塌风险,损伤部位与损伤程度与现场情况基本相符。而采用隔震技术后,分析结果表明在泸定地震动作用下建筑物损伤轻微。     

Probability forecast of earthquake magnitude in Chinese mainland before A．D． 2005

ＰｒｏｂａｂｉｌｉｔｙｆｏｒｅｃａｓｔｏｆｅａｒｔｈｑｕａｋｅｍａｇｎｉｔｕｄｅｉｎＣｈｉｎｅｓｅｍａｉｎｌａｎｄｂｅｆｏｒｅＡ．Ｄ．２００５ＸＩＡＯ－ＱＩＮＧＷＡＮＧ（王晓青），ＺＨＥＮＧ－ＸＩＡＮＧＦＵ（傅征祥）ａｎｄＭＩＮＧＪＩＡＮＧ（蒋铭）...     

Average spectral acceleration as an intensity measure for collapse risk assessment

This paper investigates the performance of spectral acceleration averaged over a period range (Sa_avg) as an intensity measure (IM) for estimating the collapse risk of structures subjected to earthquake loading. The performance of Sa_avg is evaluated using the following criteria: efficiency, sufficiency, the availability or ease of developing probabilistic seismic hazard information in terms of the IM and the variability of collapse risk estimates produced by the IM. Comparisons are also made between Sa_avg and the more traditional IM: spectral acceleration at the first‐mode period of the structure (Sa(T₁)). Though most previous studies have evaluated IMs using a relatively limited set of structures, this paper considers nearly 700 moment‐resisting frame and shear wall structures of various heights to compare the efficiency and sufficiency of the IMs. The collapse risk estimates produced by Sa_avg and Sa(T₁) are also compared, and the variability of the risk estimates is evaluated when different ground motion sets are used to assess the structural response. The results of this paper suggest that Sa_avg, when computed using an appropriate period range, is generally more efficient, more likely to be sufficient and provides more stable collapse risk estimates than Sa(T₁). Copyright © 2015 John Wiley & Sons, Ltd.     

基于ShakeMap_CNST的2014年云南鲁甸MS6.5地震震动图研究

分析了2014年8月3日云南鲁甸6.5级地震的发生背景及震害特征,介绍了ShakeMap_CNST震动图系统的设计思路和实现原理及地震动参数的校正方法,并将其应用于鲁甸6.5级地震的震动图预测中,进一步分析了震区场地条件对局部震害的影响。结果表明,震动图预测的地震动特征与现场宏观调查的结果总体上是相适应的,最后对震动图系统的优缺点及应用前景进行了探讨。