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Stochastic finitefault modeling based on a dynamic corner frequency
 Bulletin of the Seismological Society of America
, 2005
"... Abstract In finitefault modeling of earthquake ground motions, a large fault is divided into N subfaults, where each subfault is considered as a small point source. The ground motions contributed by each subfault can be calculated by the stochastic pointsource method and then summed at the observa ..."
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Cited by 33 (6 self)
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Abstract In finitefault modeling of earthquake ground motions, a large fault is divided into N subfaults, where each subfault is considered as a small point source. The ground motions contributed by each subfault can be calculated by the stochastic pointsource method and then summed at the observation point, with a proper time delay, to obtain the ground motion from the entire fault. A new variation of this approach is introduced based on a “dynamic corner frequency. ” In this model, the corner frequency is a function of time, and the rupture history controls the frequency content of the simulated time series of each subfault. The rupture begins with a high corner frequency and progresses to lower corner frequencies as the ruptured area grows. Limiting the number of active subfaults in the calculation of dynamic corner frequency can control the amplitude of lower frequencies. Our dynamic corner frequency approach has several advantages over previous formulations of the stochastic finitefault method, including conservation of radiated energy at high frequencies regardless of subfault size, application to a broader magnitude range, and control of the relative amplitude of higher versus lower frequencies.
Quantitative classification of nearfault ground motions using wavelet analysis
 Bulletin of the Seismological Society of America
"... Abstract A method is described for quantitatively identifying ground motions containing strong velocity pulses, such as those caused by nearfault directivity. The approach uses wavelet analysis to extract the largest velocity pulse from a given ground motion. The size of the extracted pulse relativ ..."
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Cited by 24 (5 self)
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Abstract A method is described for quantitatively identifying ground motions containing strong velocity pulses, such as those caused by nearfault directivity. The approach uses wavelet analysis to extract the largest velocity pulse from a given ground motion. The size of the extracted pulse relative to the original ground motion is used to develop a quantitative criterion for classifying a ground motion as “pulselike. ” The criterion is calibrated by using a training data set of manually classified ground motions. To identify the subset of these pulselike records of greatest engineering interest, two additional criteria are applied: the pulse arrives early in the ground motion and the absolute amplitude of the velocity pulse is large. The period of the velocity pulse (a quantity of interest to engineers) is easily determined as part of the procedure, using the pseudoperiods of the basis wavelets. This classification approach is useful for a variety of seismology and engineering topics where pulselike ground motions are of interest, such as probabilistic seismic hazard analysis, groundmotion prediction (“attenuation”) models, and nonlinear dynamic analysis of structures. The Next Generation Attenuation (NGA) project ground motion library was processed using this approach, and 91 largevelocity pulses were found in the faultnormal components of the approximately 3500 strong ground motion recordings considered. It is believed that many of the identified pulses are caused by nearfault directivity effects. The procedure can be used as a standalone classification criterion or as a filter to identify ground motions deserving more careful study.
Orientationindependent measures of ground The 14th World Conference on Earthquake Engineering October 1217
 Bulletin of the Seismological Society of America
, 2006
"... Abstract The geometric mean of the response spectra for two orthogonal horizontal components of motion, commonly used as the response variable in predictions of strong ground motion, depends on the orientation of the sensors as installed in the field. This means that the measure of groundmotion in ..."
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Cited by 20 (1 self)
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Abstract The geometric mean of the response spectra for two orthogonal horizontal components of motion, commonly used as the response variable in predictions of strong ground motion, depends on the orientation of the sensors as installed in the field. This means that the measure of groundmotion intensity could differ for the same actual ground motion. This dependence on sensor orientation is most pronounced for strongly correlated motion (the extreme example being linearly polarized motion), such as often occurs at periods of 1 sec or longer. We propose two new measures of the geometric mean, GMRotDpp, and GMRotIpp, that are independent of the sensor orientations. Both are based on a set of geometric means computed from the asrecorded orthogonal horizontal motions rotated through all possible nonredundant rotation angles. GMRotDpp is determined as the ppth percentile of the set of geometric means for a given oscillator period. For example, GMRotD00, GMRotD50, and GMRotD100 correspond to the minimum, median, and maximum values, respectively. The rotations that lead to GMRotDpp depend on period, whereas a singleperiodindependent rotation is used for GMRotIpp, the angle being chosen
Strong groundmotion prediction from stochasticdynamic source models
 Bull. seism. Soc. Am
, 2003
"... Abstract In the absence of sufficient data in the very near source, predictions of the intensity and variability of ground motions from future large earthquakes depend strongly on our ability to develop realistic models of the earthquake source. In this article we simulate nearfault strong ground m ..."
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Cited by 16 (2 self)
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Abstract In the absence of sufficient data in the very near source, predictions of the intensity and variability of ground motions from future large earthquakes depend strongly on our ability to develop realistic models of the earthquake source. In this article we simulate nearfault strong ground motion using dynamic source models. We use a boundary integral method to simulate dynamic rupture of earthquakes by specifying dynamic source parameters (fracture energy and stress drop) as spatial random fields. We choose these quantities such that they are consistent with the statistical properties of slip heterogeneity found in finitesource models of past earthquakes. From these rupture models we compute theoretical strongmotion seismograms up to a frequency of 2 Hz for several realizations of a scenario strikeslip Mw 7.0 earthquake and compare empirical response spectra, spectra obtained from our dynamic models, and spectra determined from corresponding kinematic simulations. We find that spatial and temporal variations in slip, slip rise time, and rupture propagation consistent with dynamic rupture models exert a strong influence on nearsource ground motion. Our results lead to a feasible approach to specify the variability in the rupture time distribution in kinematic models through a generalization of Andrews ’ (1976) result relating rupture speed to apparent fracture energy, stress drop, and crack length to 3D dynamic models. This suggests that a simplified representation of dynamic rupture may be obtained to approximate the effects of dynamic rupture without having to do full dynamic simulations.
Nearsource ground motions from simulations of sustained intersonic and supersonic fault ruptures
 Bull. Seis. Soc. Am
, 2004
"... Abstract We examine the longperiod nearsource ground motions from simulations of M 7.4 events on a strikeslip fault using kinematic ruptures with rupture speeds that range from subshear speeds through intersonic speeds to supersonic speeds. The strong alongstrike shearwave directivity present ..."
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Cited by 15 (3 self)
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Abstract We examine the longperiod nearsource ground motions from simulations of M 7.4 events on a strikeslip fault using kinematic ruptures with rupture speeds that range from subshear speeds through intersonic speeds to supersonic speeds. The strong alongstrike shearwave directivity present in scenarios with subshear rupture speeds disappears in the scenarios with ruptures propagating faster than the shearwave speed. Furthermore, the maximum horizontal displacements and velocities rotate from generally faultperpendicular orientations at subshear rupture speeds to generally faultparallel orientations at supersonic rupture speeds. For rupture speeds just above the shearwave speed, the orientations are spatially heterogeneous as a result of the random nature of our assumed slip model. At locations within a few kilometers of the rupture, the time histories of the polarization of the horizontal motion provide a better diagnostic with which to gauge the rupture speed than the orientation of the peak motion. Subshear ruptures are associated with significant faultperpendicular motion before faultparallel motion close to the fault; supershear ruptures are associated with faultperpendicular motion after significant faultparallel motion. Consistent with previous studies, we do not find evidence for prolonged supershear rupture in the longperiod (2 sec) ground motions from the 1979 Imperial Valley earthquake. However, we are unable to resolve the issue of whether a limited portion of the rupture (approximately 10 km in length) propagated faster than the shearwave speed. Additionally, a recording from the 2002 Denali fault earthquake does appear to be qualitatively consistent with locally supershear rupture. Stronger evidence for supershear rupture in earthquakes may require very dense station coverage in order to capture these potentially distinguishing traits.
Characterizing Near Fault Ground Motion for the Design and Evaluation of Bridges
 Third National Conference and Workshop on Bridges and
, 2002
"... Conference ABSTRACT: Nearfault ground motions are different from ordinary ground motions in that they often contain strong coherent dynamic long period pulses and permanent ground displacements, as expected from seismological theory. The dynamic motions are dominated by a large long period pulse of ..."
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Cited by 13 (0 self)
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Conference ABSTRACT: Nearfault ground motions are different from ordinary ground motions in that they often contain strong coherent dynamic long period pulses and permanent ground displacements, as expected from seismological theory. The dynamic motions are dominated by a large long period pulse of motion that occurs on the horizontal component perpendicular to the strike of the fault, caused by rupture directivity effects. Forward rupture directivity causes the horizontal strikenormal component of ground motion to be systematically larger than the strikeparallel component at periods longer than about 0.5 seconds. To accurately characterize near fault ground motions, it is therefore necessary to specify separate response spectra and time histories for the strikenormal and strike parallel components of ground motion. An empirical model for dynamic nearfault ground motions that assumes monotonically increasing spectral amplitude at all periods with increasing magnitude, representing directivity as a broadband effect at long periods, was developed by Somerville et al. (1997). However, near fault recordings from recent earthquakes indicate that the pulse is a narrow band pulse whose period increases with magnitude, causing the response spectrum to have a peak whose period increases with magnitude, such that the nearfault ground motions from moderate magnitude earthquakes may
An empirically calibrated framework for including the effects of nearfault directivity in probabilistic seismic hazard analysis
 Bulletin of the Seismological Society of America
, 2011
"... Abstract Forward directivity effects are known to cause pulselike ground motions at nearfault sites. We propose a comprehensive framework to incorporate the effects of nearfault pulselike ground motions in probabilistic seismic hazard analysis (PSHA) computations. Also proposed is a new method to ..."
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Cited by 10 (4 self)
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Abstract Forward directivity effects are known to cause pulselike ground motions at nearfault sites. We propose a comprehensive framework to incorporate the effects of nearfault pulselike ground motions in probabilistic seismic hazard analysis (PSHA) computations. Also proposed is a new method to classify ground motions as pulselike or nonpulselike by rotating the ground motion and identifying pulses in all orientations. We have used this method to identify 179 recordings in the Next Generation Attenuation (NGA) database (Chiou et al., 2008), where a pulselike ground motion is observed in at least one orientation. Information from these 179 recordings is used to fit several dataconstrained models for predicting the probability of a pulselike ground motion occurring at a site, the orientations in which they are expected relative to the strike of the fault, the period of the pulselike feature, and the response spectrum amplification due to the presence of a pulselike feature in the ground motion. An algorithm describing how to use these new models in a modified PSHA computation is provided. The proposed framework is modular, which will allow for modification of one or more models as more knowledge is obtained in the future without changing other models or the overall framework. Finally, the new framework is compared with existing methods to account for similar effects in PSHA computation. Example applications are included to illustrate the use of the proposed framework, and implications for selection of ground motions for analysis of structures at nearfault sites are discussed. Online Material: Groundmotion recordings identified as pulselike by the pulse classification algorithm.
Effects of fault dip and slip rake angles on nearsource ground motions: Why rupture directivity was minimal
 in the 1999
, 2004
"... Abstract We study how the fault dip and slip rake angles affect nearsource ground velocities and displacements as faulting transitions from strikeslip motion on a vertical fault to thrust motion on a shallowdipping fault. Ground motions are computed for five fault geometries with different combin ..."
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Cited by 10 (2 self)
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Abstract We study how the fault dip and slip rake angles affect nearsource ground velocities and displacements as faulting transitions from strikeslip motion on a vertical fault to thrust motion on a shallowdipping fault. Ground motions are computed for five fault geometries with different combinations of fault dip and rake angles and common values for the fault area and the average slip. The nature of the shearwave directivity is the key factor in determining the size and distribution of the peak velocities and displacements. Strong shearwave directivity requires that (1) the observer is located in the direction of rupture propagation and (2) the rupture propagates parallel to the direction of the fault slip vector. We show that predominantly alongstrike rupture of a thrust fault (geometry similar in the ChiChi earthquake) minimizes the area subjected to largeamplitude velocity pulses associated with rupture directivity, because the rupture propagates perpendicular to the slip vector; that is, the rupture propagates in the direction of a node in the shearwave radiation pattern. In our simulations with a shallow hypocenter, the maximum peaktopeak horizontal velocities exceed 1.5 m/sec over an area of only 200 km2 for the 30dipping fault (geometry similar to the ChiChi earthquake), whereas for the 60and 75dipping faults this velocity is exceeded over an area of 2700 km2. These simulations indicate that the area subjected to largeamplitude longperiod ground motions would be larger for events of the same size as ChiChi that have different styles of faulting or a deeper hypocenter.
Liquefaction limit during earthquakes and underground explosions: implications for groundmotion attenuation
 Bull. Seismol. Soc. Am
, 2006
"... Abstract Liquefaction of saturated soils and sediments documented during earthquakes shows an empirical relation log Rmax 2.05 (0.10) 0.45 M, where Rmax is the liquefaction limit in meters (i.e., the maximum distance from liquefaction site to the hypocenter) and M is the earthquake magnitude. Com ..."
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Cited by 7 (2 self)
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Abstract Liquefaction of saturated soils and sediments documented during earthquakes shows an empirical relation log Rmax 2.05 (0.10) 0.45 M, where Rmax is the liquefaction limit in meters (i.e., the maximum distance from liquefaction site to the hypocenter) and M is the earthquake magnitude. Combining this with an empirical relation between M and the seismic energy of an earthquake, we obtain a relation between the liquefaction limit and the seismic energy: E A Rbmax. The prefactor corresponds to a threshold energy for liquefaction ranging from 0.004 to 0.1 J/m3; the exponent, ranging from 3.2 to 3.3, implies that the energy density of ground motion attenuates with distance according to 1/r3.2–3.3, where r is the distance from the hypocenter. The value of the threshold energy suggests a preliquefaction degradation of the shear modulus of soils by more than 3 orders of magnitude. Liquefaction documented during underground explosions is characterized by a threshold energy several orders of magnitude greater than that for liquefaction during earthquakes but shows a similar functional relation between E and Rmax as that for liquefaction during earthquakes and implies a similar attenuation relation between groundmotion energy density and distance.
TRUNCATION OF THE DISTRIBUTION OF GROUNDMOTION RESIDUALS
 JOURNAL OF SEISMOLOGY, MANUSCRIPT JOSE 153 VERSION 10.4C
"... Recent studies to assess very longterm seismic hazard in the United States and in Europe have highlighted the importance of the upper tail of the groundmotion distribution at the very low annual frequencies of exceedance required by these projects. In particular, the use of an unbounded lognormal ..."
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Cited by 6 (1 self)
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Recent studies to assess very longterm seismic hazard in the United States and in Europe have highlighted the importance of the upper tail of the groundmotion distribution at the very low annual frequencies of exceedance required by these projects. In particular, the use of an unbounded lognormal distribution to represent the aleatory variability of ground motions leads to very high and potentially unphysical estimates of the expected level of shaking. Current practice in seismic hazard analysis consists of truncating the groundmotion distribution at a fixed number (εmax) of standard deviations (σ). However, there is a general lack of consensus regarding the truncation level to adopt. This paper investigates whether a physical basis for choosing εmax can be found, by examining records with large positive residuals from the dataset used to derive one of the groundmotion models of the Next Generation Attenuation (NGA) project. In particular, interpretations of the selected records in terms of causative physical mechanisms are reviewed. This leads to the conclusion that even in welldocumented cases, it is not possible to establish a robust correlation between specific physical mechanisms and large values of the residuals, and thus obtain direct physical constraints on εmax. Alternative approaches based on absolute levels of