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This study assesses existing intensity prediction equations (IPEs) for small unspecified magnitude (M ≤3.5) earthquakes at short hypocentral distances (Dh) and explores such earthquakes’ contribution to the felt shaking hazard. In particular, we consider IPEs by Atkinson and Wald (2007) and Atkinson et al. (2014), and evaluate their performance based on “Did You Feel It” (DYFI) reports and recorded peak ground velocities (PGVs) in the central United States. Both IPEs were developed based on DYFI reports in the central and eastern United States with moment magnitudes above Mw 3.0. DYFI reports are often used as the ground truth when evaluating and developing IPEs, but they could be less reliable when there are limited responses for small-magnitude earthquakes. We first compare the DYFI reports with intensities interpolated from recorded PGVs. Results suggest a minimal discrepancy between the two when the intensity is large enough to be felt (i.e., M >2 and Dh

Large earthquakes, such as Wenchuan in 2008, Mw 7.9, Sichuan, China, provide an opportunity for earthquake early warning (EEW), as many heavily shaken areas are far (∼50 km) from the epicenter and warning times could be sufficient (≥5 s) to take preventive action. On the other hand, earthquakes with magnitudes larger than ∼M 6.5 are challenging for EEW because source dimensions need to be defined to adequately estimate shaking. Finite-fault rupture detector (FinDer) is an approach to identify fault rupture extents from real-time seismic records. In this study, we playback local and regional onscale strong-motion waveforms of the 2008 Mw 7.9 Wenchuan, 2013 Mw 6.6 Lushan, and 2017 Mw 6.5 Jiuzhaigou earthquakes to study the performance of FinDer for the current layout of the China Strong Motion Network. Overall, the FinDer line-source models agree well with the observed spatial distribution of aftershocks and models determined from waveform inversion. However, because FinDer models are constructed to characterize seismic ground motions (as needed for EEW) instead of source parameters, the rupture length can be overestimated for events radiating high levels of high-frequency motions. If the strong-motion data used had been available in real time, 50%–80% of sites experiencing intensity modified Mercalli intensity IV–VII (light to very strong) and 30% experiencing VIII–IX (severe to violent) could have been issued a warning with 10 and 5 s, respectively, before the arrival of the S wave. We also show that loss estimates based on the FinDer line source are more accurate compared to point-source models. For the Wenchuan earthquake, for example, they predict a four to six times larger number of fatalities and injured, which is consistent with official reports. These losses could be provided 1/2∼3 hr faster than if they were based on more complex inversion rupture models.

Human behavioral response to earthquake ground motion has long been a subject of multidisciplinary interest and research. In most versions of seismic intensity scales, human perceptions and behavior are one component of the assignment of intensity. Public health research has shown that actions taken during earthquakes have a significant impact on the incidence of injury or the maintenance of safety. Based on this research, emergency managers and organizations promoting emergency preparedness have advocated strategies such as drop, cover, and hold on (DCHO) and promoted this safety measure through public education and annual drills. The “Did You Feel It?” (DYFI) mapping system (see Data and Resources) based on an online questionnaire developed and maintained by the U.S. Geological Survey has provided opportunities for those who have experienced an earthquake to report this experience worldwide since 2004. The DYFI questionnaire, although designed to assign intensity, also contains questions regarding the behavior in which one has engaged during the earthquake. The questionnaire includes other important information that may elucidate behavioral response to earthquakes, including assigned intensity, emotional reaction, and whether damage occurred at the location where the earthquake was experienced. The very large number of people who completed DYFI questionnaires following the July 2019 Ridgecrest, California, earthquakes provides a robust dataset for analysis and suggests that as intensity and levels of fear increase, behavior becomes more active in terms of physical movement to locations of presumed safety. Among active responses including DCHO, going to a doorway, and running outside, DCHO was the least likely to be implemented. The study provides possible explanations for low participation in DCHO despite active campaigns to promote this strategy.

Methods that account for site response range in complexity from simple linear categorical adjustment factors to sophisticated nonlinear constitutive models. Seismic‐hazard analysis usually relies on ground‐motion prediction equations (GMPEs); within this framework site response is modeled statistically with simplified site parameters that include the time‐averaged shear‐wave velocity to 30 m ( V S 30 ) and basin depth parameters. Because V S 30 is not known in most locations, it must be interpolated or inferred through secondary information such as geology or topography. In this article, we analyze a subset of stations for which V S 30 has been measured to address effects of V S 30 proxies on the uncertainty in the ground motions as modeled by GMPEs. The stations we analyze also include multiple recordings, which allow us to compute the repeatable site effects (or empirical amplification factors [EAFs]) from the ground motions. Although all methods exhibit similar bias, the proxy methods only reduce the ground‐motion standard deviations at long periods when compared to GMPEs without a site term, whereas measured V S 30 values reduce the standard deviations at all periods. The standard deviation of the ground motions are much lower when the EAFs are used, indicating that future refinements of the site term in GMPEs have the potential to substantially reduce the overall uncertainty in the prediction of ground motions by GMPEs.

We analyzed the regional dependence of ground motion to intensity conversion equations and derived a new global relationship to improve ground motion and intensity estimates for earthquake hazard applications, including those related to the ShakeMap system. For this purpose, we merged several databases collected by other authors in different geographical regions to highlight any systematic regional effects in the relationship between macroseismic intensities and both peak ground velocity and peak ground acceleration. Our database contains macroseismic intensities derived from expert assignments or from the “Did You Feel It?” database, paired with peak ground motions (PGM) from seismic stations. We constrain our intensity–ground‐motion pairs to those with a maximum 2 km separation. For each region, we derived invertible relationships between intensities and ground motion using an orthogonal regression. We also derived a global relationship to quantify the regional differences. We investigated the dependence of intensity on predictor variables such as PGM, magnitude, and hypocentral distance. Our analyses indicate that PGM is the most robust predictor variable of intensity. Within one standard deviation, our regional and global results are in agreement with the relations of Worden et al. (2012) for California, Faenza and Michelini (2010) for Italy, Tselentis and Danciu (2008) for Greece, and Atkinson and Kaka (2007) for central–eastern United States. The earthquakes in the study ranged in magnitude from 2.5 to 7.3, and the distances ranged from less than a kilometer to about 200 km from the epicenter. Online Material: Table summarizing published relationships and figures showing the relationship between peak ground acceleration and intensity.

Equations that predict intensity as a function of magnitude and distance are useful tools for hazard and risk assessment, and in interpretation of both contemporary and historical earthquake information. The intensity prediction equations of Atkinson and Wald (2007; hereafter AW07) have been remarkably successful in describing the level and intensity of motions reported under the “Did You Feel It?” (DYFI) program over the last several years. Examination of the performance of AW07 for North American earthquakes, evaluated using an extensive compiled database of DYFI observations from 2000 to 2013, suggests that there is little statistical basis for revising these equations. However, a problem with the AW07 equations is that they predict unrealistically large median intensities for large events ( M >6) at close distances. In this study, we revise AW07 to improve the intensity scaling at large magnitudes and close distances, by reconciling intensity equations with ground‐motion prediction equations.

For many earthquake engineering applications, site response is estimated through empirical correlations with the time‐averaged shear‐wave velocity to 30 m depth ( V S 30 ). These applications therefore depend on the availability of either site‐specific V S 30 measurements or V S 30 maps at local, regional, and global scales. Because V S 30 measurements are sparse, a proxy frequently is needed to estimate V S 30 at unsampled locations. We present a new V S 30 map for California, which accounts for observational constraints from multiple sources and spatial scales, such as geology, topography, and site‐specific V S 30 measurements. We apply the geostatistical approach of regression kriging (RK) to combine these constraints for predicting V S 30 . For the V S 30 trend, we start with geology‐based V S 30 values and identify two distinct trends between topographic gradient and the residuals from the geology V S 30 model. One trend applies to deep and fine Quaternary alluvium, whereas the second trend is slightly stronger and applies to Pleistocene sedimentary units. The RK framework ensures that the resulting map of California is locally refined to reflect the rapidly expanding database of V S 30 measurements throughout California. We compare the accuracy of the new mapping method to a previously developed map of V S 30 for California. We also illustrate the sensitivity of ground motions to the new V S 30 map by comparing real and scenario ShakeMaps with V S 30 values from our new map to those for existing V S 30 maps. Online Material: California statewide V S 30 and ShakeMaps for Loma Prieta.

Rapid evaluation of strong ground‐shaking maps after moderate‐to‐large earthquakes is crucial to recognizing those areas where the largest damage and losses are expected. These maps play a fundamental role for emergency management. This is particularly important for areas having high seismic risk potential and covered by dense seismic networks. In near‐real‐time applications, ground‐shaking maps are produced by integrating recorded data and estimates obtained by using ground‐motion predictive equations, which assume point‐source models. However, particularly for large earthquakes, improvements in the predictions of the peak ground motion can be obtained when fault extension and orientation are available. In fact, detailed source information allows one to use a more robust source‐to‐site distance metric compared with hypocentral distance. In this paper, a technique for estimating both fault extent (in terms of its surface projection) and dominant rupture direction is presented. This technique can be used in near‐real‐time ground‐motion map calculation codes with the aim of improving ground‐motion estimates with respect to a point‐source model. The model parameters are estimated by maximizing a probability density function based on the residuals between observed and predicted peak‐ground‐motion quantities, the latter obtained by using predictive equations. The model space to be investigated is defined through a Bayesian approach, and it is explored by a grid‐searching technique. The effectiveness of the proposed technique is demonstrated by offline numerical tests using data from three earthquakes occurring in different seismotectonic environments. The selected earthquakes are the 17 August 1999 M w 7.5 Kocaeli (Turkey) earthquake, the 6 April 2009 M w 6.3 L’Aquila (Italy) earthquake, and the 17 January 1994 M w 6.7 Northridge (California) earthquake. The obtained results show that the proposed technique allows for fast and first order estimates of the fault extent and dominant rupture direction, which could be used to improve ground‐shaking map calculations.

We develop globally applicable macroseismic intensity prediction equations (IPEs) for earthquakes of moment magnitude M W 5.0–7.9 and intensities of degree II and greater for distances less than 300 km for active crustal regions. The IPEs are developed for two distance metrics: closest distance to rupture (R rup) and hypocentral distance (R hyp). The key objective for developing the model based on hypocentral distance—in addition to more rigorous and standard measure R rup—is to provide an IPE which can be used in near real-time earthquake response systems for earthquakes anywhere in the world, where information regarding the rupture dimensions of a fault may not be known in the immediate aftermath of the event. We observe that our models, particularly the model for the R rup distance metric, generally have low median residuals with magnitude and distance. In particular, we address whether the direct use of IPEs leads to a reduction in overall uncertainties when compared with methods which use a combination of ground-motion prediction equations and ground motion to intensity conversion equations. Finally, using topographic gradient as a proxy and median model predictions, we derive intensity-based site amplification factors. These factors lead to a small reduction of residuals at shallow gradients at strong shaking levels. However, the overall effect on total median residuals is relatively small. This is in part due to the observation that the median site condition for intensity observations used to develop these IPEs is approximately near the National Earthquake Hazard Reduction Program CD site-class boundary.

We present a new automatic earthquake discrimination procedure to determine in near-real time the tectonic regime and seismotectonic domain of an earth- quake, its most likely source type, and the corresponding ground-motion prediction equation (GMPE) class to be used in the U.S. Geological Survey (USGS) Global ShakeMap system. This method makes use of the Flinn-Engdahl regionalization scheme, seismotectonic information (plate boundaries, global geology, seismicity cat- alogs, and regional and local studies), and the source parameters available from the USGS National Earthquake Information Center in the minutes following an earthquake to give the best estimation of the setting and mechanism of the event. Depending on the tectonic setting, additional criteria based on hypocentral depth, style of faulting, and regional seismicity may be applied. For subduction zones, these criteria include the use of focal mechanism information and detailed interface models to discriminate among outer-rise, upper-plate, interface, and intraslab seismicity. The scheme is validated against a large database of recent historical earthquakes. Though developed to assess GMPE selection in Global ShakeMap operations, we anticipate a variety of uses for this strategy, from real-time processing systems to any analysis involving tectonic classification of sources from seismic catalogs.

We use a database of approximately 200,000 modified Mercalli intensity (MMI) observations of California earthquakes collected from USGS “Did You Feel It?” (DYFI) reports, along with a comparable number of peak ground‐motion amplitudes from California seismic networks, to develop probabilistic relationships between MMI and peak ground velocity (PGV), peak ground acceleration (PGA), and 0.3‐s, 1‐s, and 3‐s 5% damped pseudospectral acceleration (PSA). After associating each ground‐motion observation with an MMI computed from all the DYFI responses within 2 km of the observation, we derived a joint probability distribution between MMI and ground motion. We then derived reversible relationships between MMI and each ground‐motion parameter by using a total least squares regression to fit a bilinear function to the median of the stacked probability distributions. Among the relationships, the fit to peak ground velocity has the smallest errors, though linear combinations of PGA and PGV give nominally better results. We also find that magnitude and distance terms reduce the overall residuals and are justifiable on an information theoretic basis. For intensities MMI≥5, our results are in close agreement with the relations of Wald, Quitoriano, Heaton, and Kanamori (1999); for lower intensities, our results fall midway between Wald, Quitoriano, Heaton, and Kanamori (1999) and those of Atkinson and Kaka (2007). The earthquakes in the study ranged in magnitude from 3.0 to 7.3, and the distances ranged from less than a kilometer to about 400 km from the source. Online Material: Figures showing the relationship between 0.3 s, 1.0 s, and 3.0 s pseudospectral acceleration and MMI.

Wedescribe aweighted-average approach for incorporating varioustypes of data (observed peak ground motions and intensities and estimates from ground- motion prediction equations) into theShakeMap ground motion and intensity mapping framework.ThisapproachrepresentsafundamentalrevisionofourexistingShakeMap methodology. In addition, the increased availability of near-real-time macroseismic intensitydata,thedevelopmentofnewrelationshipsbetweenintensityandpeakground motions, and new relationships to directly predict intensity from earthquake source information have facilitated the inclusion of intensity measurements directly into ShakeMap computations. Our approach allows for the combination of (1) direct observations (ground-motion measurements or reported intensities), (2) observations converted from intensity to ground motion (or vice versa), and (3) estimated ground motionsandintensities frompredictionequationsornumerical models.Critically,each oftheaforementioneddatatypesmustincludeanestimateofitsuncertainties,including those caused by scaling the influence of observations to surrounding grid points and those associated with estimates given an unknown fault geometry. The ShakeMap ground-motion and intensity estimates are an uncertainty-weighted combination of these various data and estimates. A natural by-product of this interpolation process is an estimate of total uncertainty at each point on the map, which can be vital for comprehensive inventory loss calculations. We perform a number of tests to validate this new methodology and find that it produces a substantial improvement in the accuracy of ground-motion predictions over empirical prediction equations alone.

An alternative method has recently been proposed for evaluating global seismic site conditions, or the average shear velocity to 30 m depth ( V S 30), from the Shuttle Radar Topography Mission (SRTM) 30 arcsec digital elevation models (DEMs). The basic premise of the method is that the topographic slope can be used as a reliable proxy for V S 30 in the absence of geologically and geotechnically based site-condition maps through correlations between V S 30 measurements and topographic gradient. Here we evaluate the use of higher-resolution (3 and 9 arcsec) DEMs to examine whether we are able to resolve V S 30 in more detail than can be achieved using the lower-resolution SRTM data. High-quality DEMs at resolutions greater than 30 arcsec are not uniformly available at the global scale. However, in many regions where such data exist, they may be employed to resolve finer-scale variations in topographic gradient, and consequently, V S 30. We use the U.S. Geological Survey Earth Resources Observation and Science (EROS) Data Center’s National Elevation Dataset (NED) to investigate the use of high-resolution DEMs for estimating V S 30 in several regions across the United States, including the San Francisco Bay area in California, Los Angeles, California, and St. Louis, Missouri. We compare these results with an example from Taipei, Taiwan, that uses 9 arcsec SRTM data, which are globally available. The use of higher-resolution NED data recovers finer-scale variations in topographic gradient, which better correlate to geological and geomorphic features, in particular, at the transition between hills and basins, warranting their use over 30 arcsec SRTM data where available. However, statistical analyses indicate little to no improvement over lower-resolution topography when compared to V S 30 measurements, suggesting that some topographic smoothing may provide more stable V S 30 estimates. Furthermore, we find that elevation variability in canopy-based SRTM measurements at resolutions greater than 30 arcsec are too large to resolve reliable slopes, particularly in low-gradient sedimentary basins.

SUMMARY A key step in many earthquake source inversions requires knowledge of the geometry of the fault surface on which the earthquake occurred. Our knowledge of this surface is often uncertain, however, and as a result fault geometry misinterpretation can map into significant error in the final temporal and spatial slip patterns of these inversions. Relying solely on an initial hypocentre and CMT mechanism can be problematic when establishing rupture characteristics needed for rapid tsunami and ground shaking estimates. Here, we attempt to improve the quality of fast finite-fault inversion results by combining several independent and complementary data sets to more accurately constrain the geometry of the seismic rupture plane of subducting slabs. Unlike previous analyses aimed at defining the general form of the plate interface, we require mechanisms and locations of the seismicity considered in our inversions to be consistent with their occurrence on the plate interface, by limiting events to those with well-constrained depths and with CMT solutions indicative of shallow-dip thrust faulting. We construct probability density functions about each location based on formal assumptions of their depth uncertainty and use these constraints to solve for the ‘most-likely’ fault plane. Examples are shown for the trench in the source region of the Mw 8.6 Southern Sumatra earthquake of March 2005, and for the Northern Chile Trench in the source region of the November 2007 Antofagasta earthquake. We also show examples using only the historic catalogues in regions without recent great earthquakes, such as the Japan and Kamchatka Trenches. In most cases, this method produces a fault plane that is more consistent with all of the data available than is the plane implied by the initial hypocentre and CMT mechanism. Using the aggregated data sets, we have developed an algorithm to rapidly determine more accurate initial fault plane geometries for source inversions of future earthquakes.

We describe a technique to derive first-order site condition maps directly from topographic data. For calibration, we use global 30 arc sec topographic data and V S 30 measurements (here V S 30 , refers to the average shear-velocity down to 30 m) aggregated from several studies in the U.S., as well as in Taiwan, Italy, and Australia. V S 30 values are correlated against topographic slope to develop two sets of parameters for deriving V S 30 : one for active tectonic regions where topographic relief is high, and one for stable shields where topography is more subdued. By taking the gradient of the topography and choosing ranges of slope that maximize the correlation with shallow shear-velocity observations, we can recover, to first order, many of the spatially varying features of sitecondition maps developed for California. Our site-condition map for the low-relief Mississippi Embayment also predicts the bulk of the V S 30 observations in that region despite rather low slope ranges. We find that maps derived from the slope of the topography is often well correlated with other independently-derived, regional-scale site-condition maps, but the latter maps vary in quality and continuity, and subsequently, also in their ability to match observed V S 30 measurements contained therein. Alternatively, the slope-based method provides a simple approach to uniform site condition mapping.

During the M w 7.1 Hector Mine earthquake, peak ground velocities recorded at sites in the central San Bernardino basin region were up to 2 times larger and had significantly longer durations of strong shaking than sites just outside the basin. To better understand the effects of 3D structure on the long-period ground-motion response in this region, we have performed finite-difference simulations for this earthquake. The simulations are numerically accurate for periods of 2 sec and longer and incorporate the detailed spatial and temporal heterogeneity of source rupture, as well as complex 3D basin structure. Here, we analyze three models of the San Bernardino basin: model A (with structural constraints from gravity and seismic reflection data), model F (water well and seismic refraction data), and the Southern California Earthquake Center version 3 model (hydrologic and seismic refraction data). Models A and F are characterized by a gradual increase in sediment thickness toward the south with an abrupt step-up in the basement surface across the San Jacinto fault. The basin structure in the SCEC version 3 model has a nearly uniform sediment thickness of 1 km with little basement topography along the San Jacinto fault. In models A and F, we impose a layered velocity structure within the sediments based on the seismic refraction data and an assumed depth-dependent V p / V s ratio. Sediment velocities within the SCEC version 3 model are given by a smoothly varying rule-based function that is calibrated to the seismic refraction measurements. Due to computational limitations, the minimum shear-wave velocity is fixed at 600 m/sec in all of the models. Ground-motion simulations for both models A and F provide a reasonably good match to the amplitude and waveform characteristics of the recorded motions. In these models, surface waves are generated as energy enters the basin through the gradually sloping northern margin. Due to the basement step along the San Jacinto fault, the surface wave energy is confined to the region north of this structure, consistent with the observations. The SCEC version 3 model, lacking the basin geometry complexity present in the other two models, fails to provide a satisfactory match to the characteristics of the observed motions. Our study demonstrates the importance of using detailed and accurate basin geometry for predicting ground motions and also highlights the utility of integrating geological, geophysical, and seismological observations in the development and validation of 3D velocity models.

The San Andreas fault is the longest fault in California and one of the longest strike-slip faults in the world, yet little is known about the aftershocks following the most recent great event on the San Andreas, the M_W 7.8 San Francisco earthquake on 18 April 1906. We conducted a study to locate and to estimate magnitudes for the largest aftershocks and triggered events of this earthquake. We examined existing catalogs and historical documents for the period April 1906 to December 1907, compiling data on the first 20 months of the aftershock sequence. We grouped felt reports temporally and assigned modified Mercalli intensities for the larger events based on the descriptions judged to be the most reliable. For onshore and near-shore events, a grid-search algorithm (derived from empirical analysis of modern earthquakes) was used to find the epicentral location and magnitude most consistent with the assigned intensities. For one event identified as far offshore, the event's intensity distribution was compared with those of modern events, in order to constrain the event's location and magnitude. The largest aftershock within the study period, an M ∼6.7 event, occurred ∼100 km west of Eureka on 23 April 1906. Although not within our study period, another M ∼6.7 aftershock occurred near Cape Mendocino on 28 October 1909. Other significant aftershocks included an M ∼5.6 event near San Juan Bautista on 17 May 1906 and an M ∼6.3 event near Shelter Cove on 11 August 1907. An M ∼4.9 aftershock occurred on the creeping segment of the San Andreas fault (southeast of the mainshock rupture) on 6 July 1906. The 1906 San Francisco earthquake also triggered events in southern California (including separate events in or near the Imperial Valley, the Pomona Valley, and Santa Monica Bay), in western Nevada, in southern central Oregon, and in western Arizona, all within 2 days of the mainshock. Of these triggered events, the largest were an M ∼6.1 earthquake near Brawley and an M ∼5.0 event under or near Santa Monica Bay, 11.3 and 31.3 hr after the San Francisco mainshock, respectively. The western Arizona event is inferred to have been triggered dynamically. In general, the largest aftershocks occurred at the ends of the 1906 rupture or away from the rupture entirely; very few significant aftershocks occurred along the mainshock rupture itself. The total number of large aftershocks was less than predicted by a generic model based on typical California mainshock–aftershock statistics, and the 1906 sequence appears to have decayed more slowly than average California sequences. Similarities can be drawn between the 1906 aftershock sequence and that of the 1857 (M_W 7.9) San Andreas fault earthquake.

We compare two methods of seismic-intensity estimation from ground-motion records for the two recent strong earthquakes: the 1999 ( M 7.1) Hector Mine, California, and the 1999 ( M 7.6) Chi-Chi, Taiwan. The first technique utilizes the peak ground acceleration (PGA) and velocity (PGV), and it is used for rapid generation of the instrumental intensity map in California. The other method is based on the revised relationships between intensity and Fourier amplitude spectrum (FAS). The results of using the methods are compared with independently observed data and between the estimations from the records. For the case of the Hector Mine earthquake, the calculated intensities in general agree with the observed values. For the case of the Chi-Chi earthquake, the areas of maximum calculated intensity correspond to the areas of the greatest damage and highest number of fatalities. However, the FAS method producees higher-intensity values than those of the peak amplitude method. The specific features of ground-motion excitation during the large, shallow, thrust earthquake may be considered a reason for the discrepancy. The use of PGA and PGV is simple; however, the use of FAS provides a natural consideration of site amplification by means of generalized or site-specific spectral ratios. Because the calculation of seismic-intensity maps requires rapid processing of data from a large network, it is very practical to generate a “first-order” map from the recorded peak motions. Then, a “second-order” map may be compiled using an amplitude–spectra method on the basis of available records and numerical modeling of the site-dependent spectra for the regions of sparse station spacing.

We develop a methodology to perform finite fault source inversions from strong motion data using Green's functions (GFs) calculated for a three-dimensional (3-D) velocity structure. The 3-D GFs are calculated numerically by inserting body forces at each of the strong motion sites and then recording the resulting strains along the target fault surface. Using reciprocity, these GFs can be recombined to represent the ground motion at each site for any (heterogeneous) slip distribution on the fault. The reciprocal formulation significantly reduces the required number of 3-D finite difference computations to at most 3NS, where NS is the number of strong motion sites used in the inversion. Using controlled numerical resolution tests, we have examined the relative importance of accurate GFs for finite fault source inversions which rely on near-source ground motions. These experiments use both 1-D and 3-D GFs in inversions for hypothetical rupture models in order (1) to analyze the ability of the 3-D methodology to resolve trade-offs between complex source phenomena and 3-D path effects, (2) to address the sensitivity of the inversion results to uncertainties in the 3-D velocity structure, and (3) to test the adequacy of the 1-D GF method when propagation effects are known to be three-dimensional. We find that given “data” from a prescribed 3-D Earth structure, the use of well-calibrated 3-D GFs in the inversion provides very good resolution of the assumed slip distribution, thus adequately separating source and 3-D propagation effects. In contrast, using a set of inexact 3-D GFs or a set of hybrid 1-D GFs allows only partial recovery of the slip distribution. These findings suggest that in regions of complex geology the use of well-calibrated 3-D GFs has the potential for increased resolution of the rupture process relative to 1-D GFs. However, realizing this full potential requires that the 3-D velocity model and associated GFs should be carefully validated against the true 3-D Earth structure before performing the inverse problem with actual data.

We assess two competing dynamic interpretations that have been proposed for the short slip durations characteristic of kinematic earthquake models derived by inversion of earthquake waveform and geodetic data. The first interpretation would require a fault constitutive relationship in which rapid dynamic restrengthening of the fault surface occurs after passage of the rupture front, a hypothesized mechanical behavior that has been referred to as “self-healing.” The second interpretation would require sufficient spatial heterogeneity of stress drop to permit rapid equilibration of elastic stresses with the residual dynamic friction level, a condition we refer to as “geometrical constraint.” These interpretations imply contrasting predictions for the time dependence of the fault-plane shear stresses. We compare these predictions with dynamic shear stress changes for the 1992 Landers (M 7.3), 1994 Northridge (M 6.7), and 1995 Kobe (M 6.9) earthquakes. Stress changes are computed from kinematic slip models of these earthquakes, using a finite-difference method. For each event, static stress drop is highly variable spatially, with high stress-drop patches embedded in a background of low, and largely negative, stress drop. The time histories of stress change show predominantly monotonic stress change after passage of the rupture front, settling to a residual level, without significant evidence for dynamic restrengthening. The stress change at the rupture front is usually gradual rather than abrupt, probably reflecting the limited resolution inherent in the underlying kinematic inversions. On the basis of this analysis, as well as recent similar results obtained independently for the Kobe and Morgan Hill earthquakes, we conclude that, at the present time, the self-healing hypothesis is unnecessary to explain earthquake kinematics.

Using strong-motion data recorded in the Los Angeles region from the 1992 (Mw 7.3) Landers earthquake, we have tested the accuracy of existing three-dimensional (3D) velocity models on the simulation of long-period (≧2 sec) ground motions in the Los Angeles basin and surrounding San Fernando and San Gabriel Valleys. First, the overall pattern and degree of long-period excitation of the basins were identified in the observations. Within the Los Angeles basin, the recorded amplitudes are about three to four times larger than at sites outside the basins; amplitudes within the San Fernando and San Gabriel Valleys are nearly a factor of 3 greater than surrounding bedrock sites. Then, using a 3D finite-difference numerical modeling approach, we analyzed how variations in 3D earth structure affect simulated waveforms, amplitudes, and the fit to the observed patterns of amplification. Significant differences exist in the 3D velocity models of southern California that we tested (Magistrale et al., 1996; Graves, 1996a; Hauksson and Haase, 1997). Major differences in the models include the velocity of the assumed background models; the depth of the Los Angeles basin; and the depth, location, and geometry of smaller basins. The largest disparities in the response of the models are seen for the San Fernando Valley and the deepest portion of the Los Angeles basin. These arise in large part from variations in the structure of the basins, particularly the effective depth extent, which is mainly due to alternative assumptions about the nature of the basin sediment fill. The general ground-motion characteristics are matched by the 3D model simulations, validating the use of 3D modeling with geologically based velocity-structure models. However, significant shortcomings exist in the overall patterns of amplification and the duration of the long-period response. The successes and limitations of the models for reproducing the recorded ground motions as discussed provide the basis and direction for necessary improvements to earth structure models, whether geologically or tomographically derived. The differences in the response of the earth models tested also translate to variable success in the ability to successfully model the data and add uncertainty to estimates of the basin response given input “scenario” earthquake source models.

We present a rupture model of the Northridge earthquake, determined from the joint inversion of near-source strong ground motion recordings, P and SH teleseismic body waves, Global Positioning System (GPS) displacement vectors, and permanent uplift measured along leveling lines. The fault is defined to strike 122° and dip 40° to the south-southwest. The average rake vector is determined to be 101°, and average slip is 1.3 m; the peak slip reaches about 3 m. Our estimate of the seismic moment is 1.3 ± 0.2 × 1026 dyne-cm (potency of 0.4 km3). The rupture area is small relative to the overall aftershock dimensions and is approximately 15 km along strike, nearly 20 km in the dip direction, and there is no indication of slip shallower than about 5 to 6 km. The up-dip, strong-motion velocity waveforms are dominated by large S-wave pulses attributed to source directivity and are comprised of at least 2 to 3 distinct arrivals (a few seconds apart). Stations at southern azimuths indicate two main S-wave arrivals separated longer in time (about 4 to 5 sec). These observations are best modeled with a complex distribution of subevents: The initial S-wave arrival comes from an asperity that begins at the hypocenter and extends up-dip and to the north where a second, larger subevent is centered (about 12 km away). The secondary S arrivals at southern azimuths are best fit with additional energy radiation from another high slip region at a depth of 19 km, 8 km west of the hypocenter. The resolving power of the individual data sets is examined by predicting the geodetic (GPS and leveling) displacements with the dislocation model determined from the waveform data, and vice versa, and also by analyzing how well the teleseismic solution predicts the recorded strong motions. The general features of the geodetic displacements are not well predicted from the model determined independently from the strong-motion data; likewise, the slip model determined from geodetic data does not adequately reproduce the strong-motion characteristics. Whereas a particularly smooth slip pattern is sufficient to satisfy the geodetic data, the strong-motion and teleseismic data require a more heterogeneous slip distribution in order to reproduce the velocity amplitudes and frequency content. Although the teleseismic model can adequately reproduce the overall amplitude and frequency content of the strong-motion velocity recordings, it does a poor job of predicting the geodetic data. Consequently, a robust representation of the slip history and heterogeneity requires a combined analysis of these data sets.

[1] We describe and present a new model of global subduction zone geometries, called Slab1.0. An extension of previous efforts to constrain the two-dimensional non-planar geometry of subduction zones around the focus of large earthquakes, Slab1.0 describes the detailed, non-planar, three-dimensional geometry of approximately 85% of subduction zones worldwide. While the model focuses on the detailed form of each slab from their trenches through the seismogenic zone, where it combines data sets from active source and passive seismology, it also continues to the limits of their seismic extent in the upper-mid mantle, providing a uniform approach to the definition of the entire seismically active slab geometry. Examples are shown for two well-constrained global locations; models for many other regions are available and can be freely downloaded in several formats from our new Slab1.0 website, http://on.doi.gov/d9ARbS. We describe improvements in our two-dimensional geometry constraint inversion, including the use of ‘average’ active source seismic data profiles in the shallow trench regions where data are otherwise lacking, derived from the interpolation between other active source seismic data along-strike in the same subduction zone. We include several analyses of the uncertainty and robustness of our three-dimensional interpolation methods. In addition, we use the filtered, subduction-related earthquake data sets compiled to build Slab1.0 in a reassessment of previous analyses of the deep limit of the thrust interface seismogenic zone for all subduction zones included in our global model thus far, concluding that the width of these seismogenic zones is on average 30% larger than previous studies have suggested.

We have determined a source rupture model for the 1992 Landers earthquake (MW 7.2) compatible with multiple data sets, spanning a frequency range from zero to 0.5 Hz. Geodetic survey displacements, near-field and regional strong motions, broadband teleseismic waveforms, and surface offset measurements have been used explicitly to constrain both the spatial and temporal slip variations along the model fault surface. Our fault parameterization involves a variable-slip, multiple-segment, finite-fault model which treats the diverse data sets in a self-consistent manner, allowing them to be inverted both independently and in unison. The high-quality data available for the Landers earthquake provide an unprecedented opportunity for direct comparison of rupture models determined from independent data sets that sample both a wide frequency range and a diverse spatial station orientation with respect to the earthquake slip and radiation pattern. In all models, consistent features include the following: (1) similar overall dislocation patterns and amplitudes with seismic moments of 7 to 8 × 1026 dyne-cm (seismic potency of 2.3 to 2.7 km3); (2) very heterogeneous, unilateral strike slip distributed over a fault length of 65 km and over a width of at least 15 km, though slip is limited to shallower regions in some areas; (3) a total rupture duration of 24 sec and an average rupture velocity of 2.7 km/sec; and (4) substantial variations of slip with depth relative to measured surface offsets. The extended rupture length and duration of the Landers earthquake also allowed imaging of the propagating rupture front with better resolution than for those of prior shorter-duration, strike-slip events. Our imaging allows visualization of the rupture evolution, including local differences in slip durations and variations in rupture velocity. Rupture velocity decreases markedly at shallow depths, as well as near regions of slip transfer from one fault segment to the next, as rupture propagates northwestward along the multiply segmented fault length. The rupture front slows as it reaches the northern limit of the Johnson Valley/Landers faults where slip is transferred to the southern Homestead Valley fault; an abrupt acceleration is apparent following the transfer. This process is repeated, and is more pronounced, as slip is again passed from the northern Homestead Valley fault to the Emerson fault. Although the largest surface offsets were observed at the northern end of the rupture, our modeling indicates that substantial rupture was also relatively shallow (less than 10 km) in this region.

All quality teleseismic recordings of the great 1906 San Francisco earthquake archived in the 1908 Carnegie Report by the State Earthquake Investigation Commission were scanned and digitized. First order results were obtained by comparing complexity and amplitudes of teleseismic waveforms from the 1906 earthquake with well calibrated, similarly located, more recent earthquakes (1979 Coyote Lake, 1984 Morgan Hill, and 1989 Loma Prieta earthquakes) at nearly co-located modern stations. Peak amplitude ratios for calibration events indicated that a localized moment release of about 1 to 1.5 × 1027 dyne-cm was responsible for producing the peak the teleseismic body wave arrivals. At longer periods (50 to 80 sec), we found spectral amplitude ratios of the surface waves require a total moment release between 4 and 6 × 1027 dyne-cm for the 1906 earthquake, comparable to previous geodetic and surface wave estimates (Thatcher, 1975). We then made a more detailed source analysis using Morgan Hill S body waves as empirical Green's Functions in a finite fault subevent summation. The Morgan Hill earthquake was deemed most appropriate for this purpose as its mechanism is that of the 1906 earthquake in the central portion of the rupture. From forward and inverse empirical summations of Morgan Hill Green's functions, we obtained a good fit to the best quality teleseismic waveforms with a relatively simple source model having two regions of localized strong radiation separated spatially by about 110 km. Assuming the 1906 epicenter determined by Bolt (1968), this corresponds with a large asperity (on the order of the Loma Prieta earthquake) in the Golden Gate/San Francisco region and one about three times larger located northwest along strike between Point Reyes and Fort Ross. This model implies that much of the 1906 rupture zone may have occurred with relatively little 10 to 20 sec radiation. Consideration of the amplitude and frequency content of the 1906 teleseismic data allowed us to estimate the scale length of the largest asperity to be less than about 40 km. With rough constraints on the largest asperity (size and magnitude) we produced a suite of estimated synthetic ground velocities assuming a slip distribution similar to that of the Loma Prieta earthquake but with three times as much slip. For purposes of comparison with the recent, abundant Loma Prieta strong motion data set, we “moved” the largest 1906 asperity into Loma Prieta region. Peak ground velocity amplitudes are substantially greater than those recorded during the Loma Prieta earthquake, and are comparable to those predicted by the attenuation relationship of Joyner and Boore (1988) for a magnitude MW = 7.7 earthquake.

We thank Art Frankel for his continuing interest in unraveling the details of the complicated source process of the 1987 Superstition Hills earthquake. His insightful comments and subsequent modeling on our part has helped to resolve some of the differences between the rupture model presented in Wald et al. (1990), hereafter referred to as WEA, and that published by Frankel and Wennerberg (1989), hereafter F&W.

[1] Ongoing developments in earthquake source inversions incorporate nonplanar fault geometries as inputs to the inversion process, improving previous approaches that relied solely on planar fault surfaces. This evolution motivates advancing the existing framework for constraining fault geometry, particularly in subduction zones where plate boundary surfaces that host highly hazardous earthquakes are clearly nonplanar. Here, we improve upon the existing framework for the constraint of the seismic rupture plane of subduction interfaces by incorporating active seismic and seafloor sediment thickness data with existing independent data sets and inverting for the most probable nonplanar subduction geometry. Constraining the rupture interface a priori with independent geological and seismological information reduces the uncertainty in the derived earthquake source inversion parameters over models that rely on simpler assumptions, such as the moment tensor inferred fault plane. Examples are shown for a number of wellconstrained global locations. We expand the coverage of previous analyses to a more uniform global data set and show that even in areas of sparse data this approach is able to accurately constrain the approximate subduction geometry, particularly when aided with the addition of data from local active seismic surveys. In addition, we show an example of the integration of many two-dimensional profiles into a threedimensional surface for the Sunda subduction zone and introduce the development of a new global threedimensional subduction interface model: Slab1.0. Components: 8122 words, 8 figures, 1 table.

A pair of significant earthquakes occurred on conjugate faults in the western Imperial Valley involving the through-going Superstition Hills fault and the Elmore Ranch cross fault. The first event was located on the Elmore Ranch fault, Ms = 6.2, and the larger event on the Superstition Hills fault, Ms = 6.6. The latter event is seen as a doublet teleseismically with the amplitudes in the ratio of 1:2 and delayed by about 8 sec. This 8-sec delay is also seen in about a dozen strong-motion records. These strong-motion records are used in a constrained least-squares inversion scheme to determine the distribution of slip on a 2-D fault. Upon closer examination, the first of the doublets was found to be itself complex requiring two episodes of slip. Thus, the rupture model was allowed to have three separate subevents, treated as separate ruptures, with independent locations and start times. The best fits were obtained when all three events initiated at the northwestern end of the fault near the intersection of the cross-fault. Their respective delays are 2.1 and 8.6 sec relative to the first subevent, and their moments are 0.4, 0.9, and 3.5 × 1025 dyne-cm, which is about half of that seen teleseismically. This slip distribution suggests multi-rupturing of a single asperity with stress drops of 60, 200, and 15 bars, respectively. The first two subevents were confined to a small area around the epicenter while the third propagated 18 km southwestward, compatible with the teleseismic and afterslip observations.

We investigate the rupture process of the 1999 Chi-Chi, Taiwan, earthquake using extensive near-source observations, including three-component velocity waveforms at 36 strong motion stations and 119 GPS measurements. A three-plane fault geometry derived from our previous inversion using only static data [ Ji et al., 2001 ] is applied. The slip amplitude, rake angle, rupture initiation time, and risetime function are inverted simultaneously with a recently developed finite fault inverse method that combines a wavelet transform approach with a simulated annealing algorithm [ Ji et al., 2002b ]. The inversion results are validated by the forward prediction of an independent data set, the teleseismic P and SH ground velocities, with notable agreement. The results show that the total seismic moment release of this earthquake is 2.7 × 10^20 N m and that most of the slip occurred in a triangular-shaped asperity involving two fault segments, which is consistent with our previous static inversion. The rupture front propagates with an average rupture velocity of ∼2.0 km s^(−1), and the average slip duration (risetime) is 7.2 s. Several interesting observations related to the temporal evolution of the Chi-Chi earthquake are also investigated, including (1) the strong effect of the sinuous fault plane of the Chelungpu fault on spatial and temporal variations in slip history, (2) the intersection of fault 1 and fault 2 not being a strong impediment to the rupture propagation, and (3) the observation that the peak slip velocity near the surface is, in general, higher than on the deeper portion of the fault plane, as predicted by dynamic modeling.

We present a new procedure for the determination of rupture complexity from a joint inversion of static and seismic data. Our fault parameterization involves multiple fault segments, variable local slip, rake angle, rise time, and rupture velocity. To separate the spatial and temporal slip history, we introduce a wavelet transform that proves effective at studying the time and frequency characteristics of the seismic waveforms. Both data and synthetic seismograms are transformed into wavelets, which are then separated into several groups based on their frequency content. For each group, we use error functions to compare the wavelet amplitude variation with time between data and synthetic seismograms. The function can be an L1 + L2 norm or a correlative function based on the amplitude and scale of wavelet functions. The objective function is defined as the weighted sum of these functions. Subsequently, we developed a finite-fault inversion routine in the wavelet domain. A simulated annealing algorithm is used to determine the finite-fault model that minimizes the objective function described in terms of wavelet coefficients. With this approach, we can simultaneously invert for the slip amplitude, slip direction, rise time, and rupture velocity efficiently. Extensive experiments conducted on synthetic data are used to assess the ability to recover rupture slip details. We, also explore slip-model stability for different choices of layered Earth models assuming the geometry encountered in the 1999 Hector Mine, California, earthquake.

We present a rupture model of the Hector Mine earthquake (M 7.1), determined from the joint inversion of strong-motion records, P and SH teleseismic body waves, Global Positioning System (GPS) displacement vectors, and measured surface offset. We solve for variable local slip, rake angle, rise time, and rupture velocity of a finite-fault model involving multiple segments. The inversion methodology developed in a companion article (Ji et al., 2002) combines a wavelet transform approach with a nonlinear (simulated annealing) algorithm. The final model is checked by forward simulating the Interferometric Synthetic Aperture Radar (InSar) data. Our estimation to the seismic moment is 6.28 × 10^(19) N m, which is distributed along three segments from north to south, releasing 37%, 41%, and 22% of the total moment, respectively. The average slip is 1.5 m, with peak amplitudes as high as 7 m. The fault rupture has an average rise time of 3.5 sec and a relatively slow average rupture velocity (1.9 km/sec) resulting in a 14-sec rupture propagation history. Our approach permits large variation in rupture velocity and rise time, and indicates that rise time appears to be roughly proportional to slip and shorter rise times are associated with the initiation of asperity rupture. We also find evidence for nearly simultaneous rupture of the two northern branches.

We introduce a technique for using broadband seismograms recorded from earthquakes at local and regional distances to refine basin structure. For the region outside the basin, we assume a one-dimensional (1D) crustal model and analytical techniques (GRT) to propagate the energy from sources to the basin edge where the motions are then interfaced with a (2D) finite-difference algorithm (Wen and Helmberger, 1996). We parameterize the basin section by isovelocity layers with linear dipping segments between control points. The control point depths are allowed to vary to improve the modeling of waveform data of stations inside the basin. The comparison between data and synthetics is qualified by a fitness function defined by two factors; the timing shift required for best alignment and the correlation coefficient. The procedure was applied to a strong-motion waveform profile across the extended Los Angeles Basin produced by the 1992 Landers, California earthquake to refine the velocity structure using sensitivity testing and forward modeling. Only the correlation coefficient and amplitude were used because absolute timing was unknown. The procedure was extended to a direct waveform inversion by employing a conjugate gradient approach, which uses numerical derivatives. Numerical tests using the new inversion process with synthetic data demonstrate that it is possible to recover a detailed basin structure, if a sufficient amount of high-quality data exists.

The San Andreas fault is the longest fault in California and one of the longest strike-slip faults anywhere in the world, yet we know little about many aspects of its behavior before, during, and after large earthquakes. We conducted a study to locate and to estimate magnitudes for the largest foreshocks and aftershocks of the 1857 M 7.9 Fort Tejon earthquake on the central and southern segments of the fault. We began by searching archived first-hand accounts from 1857 through 1862, by grouping felt reports temporally, and by assigning modified Mercalli intensities to each site. We then used a modified form of the grid-search algorithm of Bakun and Wentworth, derived from empirical analysis of modern earthquakes, to find the location and magnitude most consistent with the assigned intensities for each of the largest events. The result confirms a conclusion of Sieh that at least two foreshocks (“dawn” and “sunrise”) located on or near the Parkfield segment of the San Andreas fault preceded the mainshock. We estimate their magnitudes to be M ≈ 6.1 and M ≈ 5.6, respectively. The aftershock rate was below average but within one standard deviation of the number of aftershocks expected based on statistics of modern southern California mainshock-aftershock sequences. The aftershocks included two significant events during the first eight days of the sequence, with magnitudes M ≈ 6.25 and M ≈ 6.7, near the southern half of the rupture; later aftershocks included a M ≈ 6 event near San Bernardino in December 1858 and a M ≈ 6.3 event near the Parkfield segment in April 1860. From earthquake logs at Fort Tejon, we conclude that the aftershock sequence lasted a minimum of 3.75 years.

Short period and broadband teleseismic waveform data and three-component strong motion records were analyzed to obtain the source parameters of the 1991 Sierra Madre earthquake. Close-in strong motion velocity records (analyzed from 5 s to 5 Hz) show two distinct pulses about 0.35 s apart, requiring some rupture complexity. The near-field shear wave displacement pulse from this event has a relatively short duration (about 1 s) for the magnitude of the event, requiring a particularly high average stress drop. To further constrain the rupture process, the data were used in a finite fault source inversion to determine the temporal and spatial distribution of slip. We chose a fault plane orientation striking S 62°W and dipping 50° toward the northwest as required by the distribution of aftershocks, the first motion mechanism and the teleseismic bodywave point source inversion. In addition to the aftershock locations, depth constraints are provided by teleseismic short period and broadband recordings which require a centroid depth of 10–11 km. Our inverse modeling results indicate that both the teleseismic and strong motion data sets can be fit with a compact rupture area, about 12 km2, southwest and up-dip from the hypocenter. The average slip is approximately 50 cm, and the maximum slip is 120 cm. The seismic moment obtained from either of the separate data sets or both sets combined is about 2.8 ± 0.3 × 1024 dyn cm and the potency is 0.01 km3. Using the area of significant slip estimated from the finite fault inversion, the resulting stress drop is on the order of 150–200 bars.