Stochastic Finite-fault Model Research Articles

Estimation of Strong Ground Motions for 2001 Bhuj (M w 7.6), India Earthquake

The strong ground motions for the 2001 Bhuj (Mw 7.6) India earthquake have been estimated on hard rock and B/C boundary (NEHRP) levels using a recently modified version of stochastic finite fault modeling based on dynamic corner frequency (Motazedian and Atkinson in Bull Seismol Soc Am 95, 995–1010 2005). Incorporation of dynamic corner frequency removes the limitations of earlier stochastic methods. Simulations were carried out at 13 sites in Gujarat where structural response recorder (SRR) recordings are available. In addition, accelerograms were simulated at the B/C boundary at a large number of points distributed on a grid. The corresponding response spectra have also been estimated. The values of peak ground accelerations and spectral accelerations at three periods (0.4, 0.75 and 1.25 s) are presented in the form of contour maps. The maximum value of peak ground acceleration (PGA) in the center of meizoseismal zone is 550 cm/s2. The response spectral acceleration in same zone is 900 cm/s2 (T = 0.4 s), 600 cm/s2 (T = 0.75 s) and 300 cm/s2 (T = 1.25 s). The innermost PGA contour is on the fault plane. A comparison of the PGA values obtained at 13 sites in this study with those obtained in earlier studies on the same sites, but employing different methods, show that the present PGA values are comparable at most of the sites. The rate of decay of PGA values is fast at short distances as compared to that at longer distances. The PGA values obtained here put some constraints on the expected values from a similar earthquake in the region. A synthetic intensity map has been prepared from the estimated values of PGA using an empirical relation. A comparison with the reported intensity map of the earthquake shows the synthetic MMI values, as expected, are lower by 1 unit compared to reported intensity map. The contour map of PGA along with the contour maps of spectral acceleration at various periods permit the assessment of damage potential to various categories of houses and other structures. Such information will be quite important in planning of mitigation and disaster management programs in the region.

Coseismic stress parameter of three California Earthquakes derived from the stochastic finite fault technique

Stochastic finite fault modeling is used to derive the coseismic stress parameter distribution on the fault surface of three well-recorded California earthquakes: M7.0, 1989, Loma Prieta; M7.3, 1992, Landers; and M6.7, 1994, Northridge. Classical waveform inversion techniques are inherently more powerful than stochastic modeling as a means of deriving detailed source parameters. However, the application of stochastic methods to the source modeling problem is useful to: (1) explore and calibrate the limitations and boundaries of stochastic modeling, (2) understand its relationship to more deterministically based techniques, and (3) provide a view of the source radiation not available from deterministic modeling. The stress parameter distribution for the M7.0 1989 Loma Prieta earthquake fault shows a concentration of stress in the lower part of the northwest side of the fault and another concentration in the upper southeast side of the fault, with an average stress parameter of 80 bars over the fault surface. The stress parameter distribution for the M7.3 1992 Landers earthquake fault shows a gradual increase of stress starting from the southeast side of the fault, close to the hypocenter, towards the center. The maximum stress occurs in the lower central part of the modeled fault surface. The average stress parameter is 70 bars for the Landers earthquake. The stress parameter distribution of the M6.7 1994 Northridge earthquake shows a concentration at the lower southeast end of the fault surface, extending toward the center of the fault surface and stretching to the northwest end. The average stress parameter is 80 bars for Northridge earthquake. The stress parameter distributions derived in this study by stochastic finite-fault modeling of high-frequency motions show considerable similarity to many of the slip distributions provided by different research groups for the same earthquakes, suggesting that the derivation of stress parameter distribution on a fault surface by the method applied in this study is reliable and closely tied to slip on the fault.

Predicted Ground Motions for Great Interface Earthquakes in the Cascadia Subduction Zone

Ground motions for earthquakes of moment magnitude ( M ) 7.5–9.0 on the Cascadia subduction zone interface are simulated based on a stochastic finite-fault model and used to estimate average response spectra for firm-site conditions in Vancouver, Victoria, and Seattle. We also express the response spectra as ground-motion prediction equations (GMPEs) for Cascadia events. The simulations are calibrated by modeling the wealth of ground-motion data from the M 8.1 Tokachi-Oki earthquake sequence of Japan. Adjustments to the calibrated model are made to consider average source, attenuation, and site parameters for the Cascadia region. We perform best estimate simulations for a preferred set of input parameters. Typical results suggest mean values of 5%-damped pseudoacceleration in the range from about 100 to 200 cm/sec2, at frequencies from 1 to 4 Hz, for firm-ground conditions in Vancouver, Victoria, and Seattle. Uncertainty in stress drop causes uncertainty in simulated response spectra of about ±50%. Uncertainties in the attenuation model produce even larger uncertainties in response spectral amplitudes—a factor of about 2 at 100 km, becoming even larger at greater distances. It is thus important to establish the regional attenuation model for ground-motion simulations. Furthermore, combining data from regions with different attenuation characteristics—in particular Japan and Mexico—into a global subduction zone database for development of global empirical GMPEs may not be a sound practice. Time histories of acceleration for the stochastically simulated motions are provided for reference sites in Vancouver, Victoria, and Seattle. An alternative set of motions, based on lightly modifying real recordings from the Tokachi-Oki earthquake to match expected conditions for Cascadia cities, are also provided. These alternative records have similar spectral content to the simulated motions but contain additional complexity and more realistic phasing. The provision of alternative record sets allows users to conduct studies to determine the importance of these effects for structural response.

Deterministic Seismic Scenarios for Imphal City

In this article, the spatial variation of ground motion in Imphal City has been estimated by the finite-fault seismological model coupled with site response analysis. The important seismic sources around Imphal City have been identified from the fault map and past seismicity data. The rock level acceleration time histories at Imphal City for the 1869 Cachar (Mw 7.5) earthquake and a hypothetical Mw 8.1 event in the Indo-Burma subduction zone have been estimated by a stochastic finite-fault model. Soil investigation data of 122 boreholes have been collected from several construction projects in Imphal City. Site response analysis has been carried out and the surface level ground motion has been determined for Imphal City for these two earthquake events. The results are presented in the form of peak ground acceleration (PGA) contour map. From the present study it has been ascertained that the maximum amplification for PGA over Imphal City is as high as 2.5. The obtained contour maps can serve as guidelines for identifying vulnerable areas and disaster mitigation in Imphal City.

Erratum to Stochastic Finite-Fault Modeling of Strong Ground Motions from the 26 December 2003 Bam, Iran, Earthquake

Equation (6) of Shoja-Taheri and Ghofrani (2007) was inadvertently deleted from page 1956. BSSA regrets the error. The equation is included here, along with surrounding text. Corrected text: To compare the attenuation of the synthetic ground motions with the attenuation relation for the region (Shoja-Taheri et al., 2005), we simulated accelerograms for nearly 5000 nodes in a mesh covering the area shaken by this earthquake. We assumed that all the stations in the area are located on rock. We fitted the simulated PGAs using

Earthquake ground-motion parameters at stiff sites in Addis Ababa, Ethiopia

Ground-motion relations are developed for peak ground acceleration (PGA) and response spectra (Pseudo-acceleration, 5% damped) for stiff sites in Addis Ababa (near-surface shear-wave velocity, β ≥ 760 m/s), as a function of moment magnitude (M) >5 and closest distance to the fault rupture (<100 km) considering uncertainties in seismological parameters. Because of the non availability of recorded ground motions in this magnitude-distance range, ground-motion relations are derived from a simulated ground-motion database. The simulated ground motions are developed from well established stochastic finite-fault model and source, path and site parameters of the region are adopted from published database of previous researchers. The simulations are performed with the computer code EXSIM. The ground motions acceleration response spectra for 5% damping obtained from simulations are compared with recently developed Campbell-Bozorgnia (NGA) empirical ground motion model as well as theoretical Brune's source based Random Vibration Theory (RVT) results. Statistical results show that there is a good agreement at selected periods and magnitude ranges of practical significance.

Earthquake ground-motion parameters at stiff sites in Addis Ababa, Ethiopia

Abstract Ground-motion relations are developed for peak ground acceleration (PGA) and response spectra (Pseudo-acceleration, 5% damped) for stiff sites in Addis Ababa (near-surface shear-wave velocity, β ≥ 760 m/s), as a function of moment magnitude (M) >5 and closest distance to the fault rupture (<100 km) considering uncertainties in seismological parameters. Because of the non availability of recorded ground motions in this magnitude-distance range, ground-motion relations are derived from a simulated ground-motion database. The simulated ground motions are developed from well established stochastic finite-fault model and source, path and site parameters of the region are adopted from published database of previous researchers. The simulations are performed with the computer code EXSIM. The ground motions acceleration response spectra for 5% damping obtained from simulations are compared with recently developed Campbell-Bozorgnia (NGA) empirical ground motion model as well as theoretical Brune's source...

Stochastic Finite-Fault Modeling of Strong Ground Motions from the 26 December 2003 Bam, Iran, Earthquake

Stochastic Finite-Fault Modeling of Strong Ground Motions from the 26 December 2003 Bam, Iran, Earthquake

Region-Specific Key Seismic Parameters for Earthquakes in Northern Iran

Strong-motion accelerograms recorded within northern Iran are used to examine the propagation characteristics of shear wave, including geometric spreading behavior, Q-value, j 0 , and horizontal-to-vertical (H/V) ratio. These region-specific key seismic parameters are estimated from 259 three-component records of 22 earth- quakes with magnitude ranging from M 4.9 to M 7.4 in northern Iran. The geometric spreading follows a trilinear behavior with a strong postcritical reflection from the Moho. The first and second hinges of the trilinear behavior are at 75 and 150 km, respectively. The associated Q-value, based on the vertical component is Q 87 f 1.46 . j0 value for vertical and horizontal components are 0.03 and 0.05, respec- tively. Because of lack of station-specific site information, the H/V ratio is considered to be a rough estimation of generic site amplification. The obtained region-specific parameters are used to estimate the average stress drop based on three stochastic modeling approaches. Stochastic point-source modeling suggests a Brune stress drop of 125 bars, whereas stochastic finite-fault modeling based on static and dynamic corner frequency approaches suggests a stress drop of 68 bars.

3D finite-difference simulations of strong ground motions in the Yanhuai area, Beijing, China during the 1720 Shacheng earthquake ( Ms 7.0) using a stochastic finite-fault model

Three-dimensional finite-difference (3D-FD) simulations of earthquake wave propagations in the Yanhuai area were performed for the 1720 Shacheng earthquake ( M s 7.0) using a stochastic finite-fault model, running on a parallel supercomputer Hitachi-SR8000 ( http://www.lrz-muenchen.de). A stochastic finite-fault model was implemented into the 3D-FD program. The basic idea of the stochastic finite-fault model is that the fault plane can be subdivided into several subfaults (or elements, sources). Radiation from a large earthquake is the sum of contributions from all subfaults with proper time delays, each of which acts as a small independent double-couple point source. Heterogeneity of the fault rupture process was modeled by randomizing the location of initial rupture (hypocenter), slip vectors (slip, rake), and rise-times of subfaults in this study. A 3D velocity model of the Yanhuai area was constructed based on studies that analyzed available geological and geophysical information. A grid increment of 75 m in three directions was used in the 3D-FD simulation, which made it possible to capture the short period information with a resolution as low as 0.5 s in sediment regions. The uncertainties of simulated results caused by the stochastic finite-fault model were studied with a homogeneous 3D model. We found that the effects of the randomness of source on simulated ground motions are only limited in near-fault-region including the surface exposure of the fault and its vicinities, which occupies about 5% of the whole study area. This article presents an integrated approach for simulating the strong ground motions for engineering purpose using the 3D-FD method. Such simulations would be useful for hazard mapping, land using planning, insurance rate assessment, particularly in planning, preparedness, and coordinating emergency response, which must be based on realistic situations induced by concrete (historic or scenario) earthquakes.

Hybrid stochastic finite fault modeling of 2003, M6.5, Bam earthquake (Iran)

Accelerographic time series of the M ∗ 6.5 Bam (Iran) earthquake of December 26, 2003, are used to calibrate the source and propagation path characteristics based on a hybrid stochastic approach, which includes stochastic finite fault and analytical modeling. Estimation of source characteristics is based on the calibration of finite-fault modeling to near-source observed time series, while propagation characteristics are estimated using far-field recorded ones. The distance-dependent Kappa factor is obtained from the slope of smoothed amplitude of acceleration Fourier spectrum at higher frequencies. The estimated zero-distance Kappa value is 0.06. Calibration based on near-source time series indicates a stress drop of 130 bars for the Bam earthquake. The strong impulsive long-period motion, recorded at the only near-source station, is modeled using analytical modeling of Mavroeidis and Papageorgiou (2003).

Earthquake Ground-Motion Prediction Equations for Eastern North America

New earthquake ground-motion relations for hard-rock and soil sites in eastern North America (ENA), including estimates of their aleatory uncertainty (vari- ability) have been developed based on a stochastic finite-fault model. The model incorporates new information obtained from ENA seismographic data gathered over the past 10 years, including three-component broadband data that provide new in- formation on ENA source and path effects. Our new prediction equations are similar to the previous ground-motion prediction equations of Atkinson and Boore (1995), which were based on a stochastic point-source model. The main difference is that high-frequency amplitudes (f 5 Hz) are less than previously predicted (by about a factor of 1.6 within 100 km), because of a slightly lower average stress parameter (140 bars versus 180 bars) and a steeper near-source attenuation. At frequencies less than 5 Hz, the predicted ground motions from the new equations are generally within 25% of those predicted by Atkinson and Boore (1995). The prediction equations agree well with available ENA ground-motion data as evidenced by near-zero average residuals (within a factor of 1.2) for all frequencies, and the lack of any significant residual trends with distance. However, there is a tendency to positive residuals for moderate events at high frequencies in the distance range from 30 to 100 km (by as much as a factor of 2). This indicates epistemic uncertainty in the prediction model. The positive residuals for moderate events at 100 km could be eliminated by an increased stress parameter, at the cost of producing negative residuals in other magnitude-distance ranges; adjustment factors to the equations are provided that may be used to model this effect.

Stochastic finite-fault modeling of ground motions from the June 27, 1998 Adana-Ceyhan earthquake

AbstractIn this study, acceleration time histories of the June 27, 1998 Adana-Ceyhan (Turkey) earthquake, are simulated using a stochastic modeling technique for finite faults proposed by Beresnev and Atkinson (1997). The fault length, width and the depth to the top of the fault for the earthquake are assumed 30 km, 21 km and 15 km, respectively, based on the aftershock distribution. Simulations are made for two common site classes: soil and rock. Their response characteristics are obtained from the site-specific amplification functions estimated for the weak motion seismograms at stations located in the region using spectral ratio methods. The results show that the overall agreement between simulated and observed waveforms and spectra is quite satisfying. However, significant discrepancies exist at certain stations, implying that site amplification functions play an important role in the simulation process. The effects of nonlinearity and basin edge generated surface waves do not clearly dominate on the results. The peak horizontal acceleration contours estimated using the calibrated model are consistent with the observed intensity values and the other evidences of strong ground motions.

Seismic ground motion relationship in southern China based on stochastic finite-fault model

The characteristics of seismic ground motions in southern China are difficult to determine statistically due to a lack of strong ground motion data. In this study, a stochastic finites-fault ground motion model was adopted to simulate the seismic ground motions at bedrock for southern China, based on parameters derived from small and medium earthquakes that have occurred in the region. From these, the response spectra was estimated. A set of ground motion attenuation relationships was then developed based on simulated peak ground motions and response spectral parameters through regression, which would be applicable for use in engineering practice. Through comparison, it was demonstrated that the proposed ground motion relationships are generally consistent with those obtained from other reported ground motion attenuation models for southern China.

Stochastic Finite-Fault Modeling of Ground Motions from the 1999 Chi-Chi, Taiwan, Earthquake: Application to Rock and Soil Sites with Implications for Nonlinear Site Response

The stochastic method for simulating strong ground motions from finite faults is applied to the records of the 1999 Chi-Chi, Taiwan, earthquake. The method involves discretization of the fault plane into smaller subfaults, each of which is assigned an x 2 spectrum. The contributions from all subfaults are empirically atten- uated to the observation site and summed to produce the synthetic acceleration time history. The method is initially calibrated against the data recorded at 24 rock sites, located within 7-120 km from the mainshock hypocenter and providing a broad azimuthal coverage of the fault plane. The accuracy of the simulations is quantified through the model bias, defined as the logarithm of the ratio of the observed to simulated spectrum, averaged over all stations. The calibrated model for the Chi-Chi event has a near-zero average bias in reproducing the ground motions at rock sites in the frequency range from 0.1 to 20 Hz. An unusually low value is found for the radiation- strength factor s, controlling the high-frequency radiation level and directly related to the maximum slip velocity on the fault, compared with the mean value found for North American earthquakes. This result reflects the observed low peak ground ac- celerations of the Chi-Chi mainshock and, physically, its lower-than-usual slip ve- locities. The calibrated model is then used to simulate soil-site (site class D) records using the linear-response assumption. The simulated soil-site input motions are amplified by the weak-motion amplification functions, estimated by the spectral-ratio technique from available aftershock records. This analysis reveals an average reduction in strong-motion amplification to about 0.5-0.6 of that in weak motions, with an ac- celeration threshold for detectable nonlinearity near 200-300 cm/sec 2 . However, the derivation of soil-site specific weak-motion amplification was limited by the amount of aftershock data available; further improvement in the quantification of nonlinear soil response during the Chi-Chi earthquake may be possible with the release of additional aftershock datasets.

Ground-Motion Attenuation Relationships for Cascadia Subduction Zone Megathrust Earthquakes Based on a Stochastic Finite-Fault Model

The number of strong ground motion recordings available for regression analysis in developing empirical attenuation relationships has rapidly grown in the last 10 years. However, the dearth of strong-motion data from the Cascadia subduc- tion zone has limited this development of relationships for the Cascadia subduction zone megathrust, which can be used in the calculation of design spectra for engi- neered structures. A stochastic finite-fault ground-motion model has been used to simulate ground motions for moment magnitude (M) 8.0, 8.5, and 9.0 megathrust earthquakes along the Cascadia subduction zone for both rock-and soil-site condi- tions. The stochastic finite-fault model was validated against the 1985 M 8.0 Mi- choacan, Mexico, and the 1985 M 8.0 Valpariso, Chile, earthquakes. These two subduction zone megathrust earthquakes were recorded at several rock sites located near the fault rupture. For the Cascadia megathrust earthquakes, three different rup- ture geometries were used to model the M 8.0, 8.5, and 9.0 events. The geometries only differ in their respective fault lengths. A fault dip of 9 to the east with a rupture width of 90 km was selected to represent average properties of the Cascadia sub- duction zone geometry. A regional crustal damping and velocity model was used with the stochastic finite-fault model simulations. Ground motions were computed for 16 site locations. The parametric uncertainties associated with the variation in source, path, and site effects were included in the development of the ground motions. A functional form was fit to the ground-motion model simulations to develop region- specific attenuation relationships for the Cascadia megathrust rupture zone for both rock and soil site conditions. The total uncertainty was based on a combination of the modeling and parametric uncertainties (sigmas). These newly developed atten- uation relationships for Cascadia subduction zone megathrust earthquakes can be used in both the probabilistic and deterministic seismic-hazard studies for engineer- ing design for the Pacific Northwest.

Stochastic finite-fault modeling of ground motions from the 1994 Northridge, California, earthquake. II. Widespread Nonlinear response at soil sites

AbstractOn average, soil sites behaved nonlinearly during the M 6.7 1994 Northridge, California, earthquake. This conclusion follows from an analysis that combines elements of two independent lines of investigation. First, we apply the stochastic finite-fault simulation method, calibrated with 28 rock-site recordings of the Northridge mainshock, to the simulation of the input motions to the soil sites that recorded this event. The calibrated model has a near-zero average bias in reproducing ground motions at rock sites in the frequency range from 0.1 to 12.5 Hz.The soil sites selected are those where there is colocation of strong-motion accelerographs and temporary instruments from the Northridge aftershock observation network. At these sites, weak-motion amplification functions based on numerous aftershock records have been empirically determined, in three separate investigations reported in the literature. These empirical weak-motion amplification factors can be applied to the simulated input rock motions, at each soil site, to determine the expected motions during the mainshock (i.e., neglecting nonlinearity). These expected motions can then be compared to the actual recordings during the mainshock.This analysis shows that the recorded strong-motion spectra are significantly over-estimated if weak-motion amplifications are used. The null hypothesis, stating that the inferred differences between weak- and strong-motion amplifications are statistically insignificant, is rejected with 95% confidence in the frequency range from approximately 2.2 to 10 Hz. On average, the difference between weak- and strong-motion amplifications is a factor of 2. Nonlinear response at those soil stations for which the input peak acceleration exceeded 150 to 200 cm/sec2 contributes most to this observed average difference. These findings suggest a significant nonlinear response at soil stations in the Los Angeles urban area during the Northridge mainshock. The effect is consistent with the increase in damping of shear waves at high levels of strain, which is well known from geotechnical studies of soil properties.

Stochastic finite-fault modeling of ground motions from the 1994 Northridge, California, earthquake. I. Validation on rock sites

AbstractThe stochastic method of simulating ground motions from finite faults is validated against strong-motion data from the M 6.7 1994 Northridge, California, earthquake. The finite-fault plane is subdivided into elements, each element is assigned a stochastic ω2 spectrum, and the delayed contributions from all subfaults are summed in the time domain. Simulated horizontal acceleration time histories and Fourier spectra at 28 rock sites are compared with observations. We first perform simulations using the slip distribution on the causative fault derived from strong-motion, teleseismic, GPS, and leveling data (Wald et al., 1996). We then test the performance of the method using quasi-random distributions of slip and alternative hypocenter locations; this is important because the rupture initiation point and slip distribution are in general not known for future earthquakes.The model bias is calculated as the ratio of the simulated to the observed spectrum in the frequency band of 0.1 to 12.5 Hz, averaged over a suite of rock sites. The mean bias is within the 95% confidence limits of unity, showing that the model provides an accurate prediction of the spectral content of ground motions on average. The maximum excursion of the model bias from the unity value, when averaged over all 28 rock stations, is a factor of approximately 1.6; at most frequencies, it is below a factor of 1.4.Interestingly, the spectral bias and the standard deviation of the stochastic simulations do not depend on whether the fault slip distribution and hypocenter location are based on data or are randomly generated. This suggests that these parameters do not affect the accuracy of predicting the average characteristics of ground motion, or they may have their predominant effect in the frequency range below about 0.1 Hz (below the range of this study). The implication is that deterministic slip models are not necessary to produce reasonably accurate simulations of the spectral content of strong ground motions. This is fortunate, because such models are not available for forecasting motions from future earthquakes. However, the directivity effects controlled by the hypocenter location are important in determining peak ground acceleration at individual sites.Although the method is unbiased when averaged over all rock sites, the simulations at individual sites can have significant errors (generally a factor of 2 to 3), which are also frequency dependent. Factors such as local geology, site topography, or basin-propagation effects can profoundly affect the recordings at individual stations. To generate more accurate site-specific predictions, empirical responses at each site could be established.

An empirical study of earthquake source spectra for California earthquakes

AbstractWe generalize source, path, and site effects for California earthquakes as functions of magnitude and distance, based on regression analysis of 1000 Fourier acceleration spectra from 43 California earthquakes in the moment magnitude range from 4.4 to 7.4, recorded at rupture distances from 1 to 200 km. Empirically derived source spectra for California earthquakes are generally inconsistent with the spectral shape implied by a Brune (“omega-squared”) point-source model. This is manifested by magnitude- and frequency-dependence of the Brune model parameters. For example, the Brune stress parameter that best matches the data at high frequencies decreases from a value of about 120 bars at M5.5 to a value near 50 bars at M7.5. At frequencies below 1 Hz, though, source spectra have much lower spectral amplitudes than predicted by the Brune point-source model for these values of stress; this discrepancy grows with increasing magnitude. Finite-fault simulations indicate that this is a consequence of the breakdown of the validity of the point-source approximation for large ruptures. A stochastic finite-fault model, in which the fault is discretized as a number of subfaults, each of which is represented by a Brune omegasquared point source, correctly matches the observed spectral shapes and amplitudes.The spectral decay parameter kappa, representing average near-surface attenuation of high-frequency motion at rock sites, increases with increasing magnitude, from values near 0.035 sec at M5.5 to 0.050 sec at M7.5. Magnitude dependence of kappa may be interpreted as evidence of nonlinearity for typical California sites subjected to strong ground motion.Comparisons of our empirical source spectra for California to corresponding spectra for eastern North America suggest that the spectral amplitudes are similar in the two regions for low-frequency motions (f &amp;lt; 2 Hz for M5.5, f &amp;lt; 0.5 Hz for M7.5), for equivalent crustal conditions. The eastern events appear to have enhanced high-frequency near-source amplitudes relative to the California events; this is particularly pronounced for large-magnitude earthquakes.