Potential Ground Motion Research Articles

Physically adjusted ground motion prediction equations for induced seismicity at Preston New Road, UK

Predicting ground motions due to induced seismicity is a challenging task owing to the scarcity of data and heterogeneity of the uppermost crust. Dealing with this requires a thorough understanding of the underlying physics and consideration of inter-site variability. The most common ground motion model used in practice is the parametric ground motion prediction equation (GMPE), of which hundreds exist in the literature. However, relatively few are developed with a focus on induced seismicity. Developing GMPEs that are specific to an appropriate magnitude-distance range (R<30\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R < 30$$\\end{document} km; 2≤M≤6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2 \\le M \\le 6$$\\end{document}) is important for induced seismicity applications. This paper proposes a framework for the development of physically-based GMPEs to provide more accurate and reliable estimates of the potential induced-seismicity ground motion hazard, allowing for better risk assessment and management strategies. To demonstrate this approach, a new set of GMPEs for the 2018-2019 induced seismicity sequence at the Preston New Road (PNR) shale gas site near Blackpool, United Kingdom, is presented. The physically-based GMPE was developed based on a pseudo-finite-fault stochastic ground motion simulation, calibrated with parameters derived from the spectral analysis of weak-motion records from induced seismic events. An optimization-based calibration technique using the area metric (AM) was subsequently performed to calibrate optimal parameters for simulating ground motion at the PNR site. Finally, using a suite of forward simulations for events with 1≤M≤6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1 \\le M \\le 6$$\\end{document} recorded at distances up to 30 km, combined with empirical data, a location-specific GMPE was derived through adjustment of an existing model.

Assessing seismic hazard and uncertainty in Büyükçekmece using ground motion simulations

This study presents a comprehensive seismic hazard assessment for Büyükçekmece, a district in Istanbul, Turkey, situated near the seismically active North Anatolian Fault (NAF). The study utilizes stochastic ground motion simulations with the validated EXSIM algorithm to understand the potential impact of medium to large-magnitude earthquakes (ranging from MW 6.3 to 7.42) on this vulnerable community. The research employs a site-specific approach, considering unique amplification factors for each location. By conducting 50 scenario-based simulations, the study assesses the seismic hazard, highlighting the importance of comprehending variations in ground motion, even when they are small, for a more precise hazard assessment. Furthermore, this study addresses the critical issue of uncertainty, particularly concerning stress parameters and hypocenter locations. The researchers demonstrate that variability in these factors can introduce substantial uncertainty in ground motion predictions. The study provides insights into the range of potential ground motion outcomes through probabilistic assessments involving multiple scenarios and stress drop values. Notably, the results indicate that ground motion levels vary with earthquake magnitudes and underscore the significance of accounting for this variability. This research emphasizes the seismic vulnerability of Büyükçekmece and the importance of accurate ground motion simulations, offering valuable insights for earthquake preparedness and mitigation efforts in the region.

Evidence of Seattle Fault Earthquakes from Patterns in Deep-Seated Landslides

ABSTRACT Earthquake-induced landslides can record information about the seismic shaking that generated them. In this study, we present new mapping, Light Detection and Ranging-derived roughness dating, and analysis of over 1000 deep-seated landslides from the Puget Lowlands of Washington, U.S.A., to probe the landscape for past Seattle fault earthquake information. With this new landslide inventory, we observe spatial and temporal evidence of landsliding related to the last major earthquake on the Seattle fault ∼1100 yr before present. We find spatial clusters of landslides that correlate with ground motions from recent 3D kinematic models of Seattle fault earthquakes. We also find temporal patterns in the landslide inventory that suggest earthquake-driven increases in landsliding. We compare the spatial and temporal landslide data with scenario-based ground motion models and find stronger evidence of the last major Seattle fault earthquake from this combined analysis than from spatial or temporal patterns alone. We also compare the landslide inventory with ground motions from different Seattle fault earthquake scenarios to determine the ground motion distributions that are most consistent with the landslide record. We find that earthquake scenarios that best match the clustering of ∼1100-year-old landslides produce the strongest shaking within a band that stretches from west to east across central Seattle as well as along the bluffs bordering the broader Puget Sound. Finally, we identify other landslide clusters (at 4.6–4.2 ka, 4.0–3.8 ka, 2.8–2.6 ka, and 2.2–2.0 ka) in the inventory which let us infer potential ground motions that may correspond to older Seattle fault earthquakes. Our method, which combines hindcasting of the surface response to the last major Seattle fault earthquake, using a roughness-aged landslide inventory with forecasts of modeled ground shaking from 3D seismic scenarios, showcases a powerful new approach to gleaning paleoseismic information from landscapes.

Horizontal to Vertical Spectral Ratio (HVSR) Analysis of the Passive Seismic Data on Alluvial Lithology: An Example from Bandung Basin Rim

Bandung basin is surrounded by active volcanoes at the center of Western Java region. Soil type of this area consists mostly of volcanic alluvial, formed by the past volcanic activities. At this location, we performed passive seismic surveys to reveal the sedimentary characteristics using a triaxial seismometer, to study the properties which have potential implications on environmental aspects, such as natural disaster mitigation and the city planning. In this work we reported the analysis of three component vibration signals by means of the Horizontal to Vertical Spectral Ratio (HVSR) calculation to identify the sediment thickness through the dominant frequency of the earth vibration. The method signal processing successfully revealed the amplification factor of the area, which is very important to determine the potential ground motion induced disasters. The data was collected using a laboratory developed seismic logging device with sensitivity of 0.28 ± 5% V⋅s/cm. The signal preconditioning was carried out to shape the acquired signals with high noise level, prior to the HVSR calculation. From the measurements and computation, we obtained the thickness variation at the chosen survey area of around 32 to 64 meters, corresponding to the measured dominant frequency of around 2.5 to 5.0 Hz. The results agree very well with the reference sediment thickness measured by the microtremor surveys. The vibration frequencies are also consistent with the range suggested by the literature

A two-phase neuro-modal linear method for seismic analysis of structures

In this paper a two-phase neuro-modal solution for seismic analysis of skeletal structures was developed. Seismic analyses are required to design resisting structures against potential ground motions. Such analyses are, however, computationally intense because of coupled systems of differential equations, time-dependent analyses, uncertainty of seismic loads, and large number of degrees of freedom in high-rise structures. Here, through integration of modal analysis with Long Short-Term Memory neural networks, a method was developed to model and solve dynamic equations of motion more efficiently. Specifically, the method allowed us to convert a time-dependent problem to a recurrent neural network with fixed architecture, functions, and parameters so that the required CPU time for analysis of the problem reduced from order of 10−2 s to the order of 10−5 s for a single degree-of-freedom system under a seismic load. The model was validated through comparison between model predictions and ground truth values obtained from simulated and real data. The correlation between predictions and target values was between 0.98626 and 1 for different loading conditions. This level of accuracy was equivalent to error values ranging from ~ 0 to 1.7% for predicted displacements of the structures under the seismic loads. The developed model can be used to tackle iterative procedures such as design optimizations, risk analysis, Monte Carlo simulations, etc. for large systems such as high-rise skeletal buildings in more efficient time. Also, the proposed platform can be extended to perform vibration and dynamic analyses for continuous systems, plates and shells, bridges, and offshore structures, and under loading conditions such as tornadic wind loads, moving Loads, wave and sea loads, etc.

Integration of 3D large‐scale earthquake simulations into the assessment of the seismic risk of Bogota, Colombia

AbstractBogotá, the capital city of Colombia, is mostly located on a lacustrine soil deposit surrounded by hills in a central plateau of the eastern cordillera of the Colombian Andes. This highly populated urban area is exposed to a significant seismic hazard from local and regional fault systems. In addition, the potential ground motion amplification during earthquakes due to the presence of soft soil deposits, along with the effects of the surface and subsurface topography, can strongly influence the seismic hazard and consequently the seismic risk to the city. This study aims to develop a physics‐based framework to generate synthetic ground records that can help better understand the seismic response of the basin and other amplification effects during strong earthquake shaking in the region, and to incorporate these effects into the estimation of seismic risk. To this end, a set of simulations were first conducted on Hercules, the wave propagation octree‐based finite element simulator developed by the Quake Group at Carnegie Mellon University, to identify the impacts of hypothetical strong earthquakes scenarios. Then, the results from these simulations were integrated with the exposure and vulnerability information previously developed for the main building constructions in the city to assess the seismic risk in the region under different conditions of analysis. Results from this more detailed model are compared with previously published results from simplified models. Sensitivity analyses help identify critical aspects that should be considered in the future to improve the seismic risk assessment of infrastructure.

Seismic response evaluation of monuments based on ambient vibrations: the case studies of a Byzantine basilica and an Ottoman bath in Thessaloniki (Greece)

The present work focuses on the seismic response and damage distribution studies on two Thessaloniki monuments with different structural systems. The first one is the Acheiropoietos basilica—a Byzantine monument included in the World Heritage List of UNESCO—with a flexible structural system consisted of internal colonnades and perimeter walls. The second one is the Bey hamam, an Ottoman bath with a stiff structural system. Its successive square or rectangular functional spaces are organized in such a way as to obtain both spatial and structural (bearing structure) autonomy; thick internal and external walls in two directions bear the domes directly or through single or double arches. Both monuments were subjected to the June 20, 1978 Thessaloniki earthquake ground motion (EQ) (M6.5) with significant damage which were accurately recorded and demonstrated in the Ephorate of Antiquities of Thessaloniki (EFAPOTH) archives. Sets of ambient vibration measurements were performed before any intervention work at the basilica. For the present study, similar measurements were performed at both monuments. Their eigen-properties were then calculated based on this data. Both monuments were modeled in details by finite element method; the analytical models were calibrated for the optimum approach of the eigen-properties resulted by the measurements. The main calibration parameter was the modulus of elasticity of the masonry walls. These calibrated models were also analytically subjected to the recorded acceleration time history of the Thessaloniki 1978 EQ. The findings of this work are related to the appropriately documented material properties and factors of these monuments that are unique. The result of this procedure was the calibration of reliable finite element models for response evaluation of the structures to potential ground motions in future earthquakes. These models were capable to quantitatively explain the damage patterns observed in the monuments. The monument with higher stiffness (Ottoman bath) exhibited damage concentrated to fewer elements than the more flexible monument (Byzantine basilica) where the damages were distributed to many structural elements.

Forensic analysis reveals the causes of building damage in İzmir in the Oct. 30 Aegean Sea earthquake

Several buildings in İzmir collapsed during the Oct. 30 earthquake. Code compliance with better assessments of potential ground motion throughout the city would ensure the design of buildings to withstand strong ground shaking.

Safety factor analysis of landslides hazard as a result of rain condition infiltration on Buyan-Beratan Ancient Mountain

Disaster of soil movement from NDMA (National Disaster Management Authority) of Indonesia mention from 2003-2017 shows the increasing. Investigation of potential ground motion based on sampling data of boring test on slopes along the Denpasar-Singaraja road around Gitgit Village which provides the greatest threat to settlements and public facilities. This research is expected to show the influence of rainfall on slope stability. This research is expected to show the influence of rainfall on slope stability. Furthermore, safety factor analysis based on daily rainfall data and numerical analysis was assisted by SLOPE/W and SEEP/W software tools. The analysis was carried out using a normal, heavy, and very heavy rain model. Safety factor declined after the 3rd day of rain after that the safety factor dropped to the 6th day with a safety factor 1.141 indicating the condition to be critical. The result shows the effect of rainfall decreasing safety factor after the second day of rain and the fourth day of safety factor shows a value of 1.003 where the slope is in a critical condition leading to failure, these results can be used to make early warning system of landslide hazard.

Assessing Potential Ground-Motion Hazards from Induced Earthquakes

AbstractEarthquakes induced by the hydraulic fracturing and fluid injections pose hazards to communities in the United States, Canada, as well as other places in the world. Although several types o...

Lg-wave attenuation in the Australian crust

We estimate the Lg-wave quality factor (Q) across the Australian continent from vertical-component Lg waveforms. A tomographic inversion is performed to construct an Lg attenuation model for 58 frequencies between 0.05 and 10.0Hz. The available spatial resolution is approximately 1.5°×1.5° for the 0.5–2.0Hz band. At 1.0Hz, the Lg-wave Q over the whole island continent varies from 50 to 1250 with an average value of 850. Significant regional variations in the Lg-wave Q images tie well with many geological features and boundaries in Australia. The cratons in western, northern and southern parts of Australia usually have higher Q values (700–1250), while the volcanic regions, sedimentary basins and orogenic areas in eastern Australia are characterized by increased attenuation (lower Q values, 50–650). We determine the frequency-dependent Q of Lg waves for different blocks across Australia, and find the frequency dependence of Q is much more complex than the traditional single power law representation. When combined with the assumed geometrical spreading relation, the Lg Q maps provide a new way of assessing potential ground motion across the continent for any event location.

Physics-Based Hazard Assessment for Critical Structures Near Large Earthquake Sources

We argue that for critical structures near large earthquake sources: (1) the ergodic assumption, recent history, and simplified descriptions of the hazard are not appropriate to rely on for earthquake ground motion prediction and can lead to a mis-estimation of the hazard and risk to structures; (2) a physics-based approach can address these issues; (3) a physics-based source model must be provided to generate realistic phasing effects from finite rupture and model near-source ground motion correctly; (4) wave propagations and site response should be site specific; (5) a much wider search of possible sources of ground motion can be achieved computationally with a physics-based approach; (6) unless one utilizes a physics-based approach, the hazard and risk to structures has unknown uncertainties; (7) uncertainties can be reduced with a physics-based approach, but not with an ergodic approach; (8) computational power and computer codes have advanced to the point that risk to structures can be calculated directly from source and site-specific ground motions. Spanning the variability of potential ground motion in a predictive situation is especially difficult for near-source areas, but that is the distance at which the hazard is the greatest. The basis of a “physical-based” approach is ground-motion syntheses derived from physics and an understanding of the earthquake process. This is an overview paper and results from previous studies are used to make the case for these conclusions. Our premise is that 50 years of strong motion records is insufficient to capture all possible ranges of site and propagation path conditions, rupture processes, and spatial geometric relationships between source and site. Predicting future earthquake scenarios is necessary; models that have little or no physical basis but have been tested and adjusted to fit available observations can only “predict” what happened in the past, which should be considered description as opposed to prediction. We have developed a methodology for synthesizing physics-based broadband ground motion that incorporates the effects of realistic earthquake rupture along specific faults and the actual geology between the source and site.

Performance of response spectral models against New Zealand data

An important component of seismic hazard assessment is the prediction of the potential ground motion generated by a given earthquake source. In New Zealand seismic hazard studies, it is commonplace for analysts to only adopt one or two models for predicting the ground motion, which does not capture the epistemic uncertainty associated with the prediction. This study analyses a suite of New Zealand and international models against the New Zealand Strong Motion Database, both for New Zealand crustal earthquakes and earthquakes in the Hikurangi subduction zone. It is found that, in general, the foreign models perform similarly or better with respect to recorded New Zealand data than the models specifically derived for New Zealand application. Justification is given for using global models in future seismic hazard analysis in New Zealand. Although this article does not provide definitive model weights for future hazard analysis, some recommendations and guidance are provided.

An updated seismic hazard analysis of the Hong Kong region

This paper describes an updated probabilistic seismic hazard analysis which estimates potential seismic ground motions on rock sites in Hong Kong based on a new seismic source model. A detailed catalogue of historical and recent earthquakes within the South China region was reviewed and updated using data up to 2009. A new seismic source model was developed based on the consideration of seismicity, geological and tectonic information of the region, especially the source zone boundaries that were used to produce seismic hazard maps in the current Chinese code for seismic design of buildings, GB50011 [1].

Ground Motions from Three Recent Earthquakes in Western Alberta and Northeastern British Columbia and Their Implications for Induced-Seismicity Hazard in Eastern Regions

A key issue in the assessment of hazard due to induced seismicity from fluid injection activity is to determine the potential ground motions. Although wastewater disposal typically receives the most attention, hydraulic fracturing is increasingly recognized as a significant source of seismic hazard. We present an analysis of the ground motions from the three largest events of 2014 that occurred along the deformation front marking the western boundary of the stable Canadian craton: an M 4.0 and an M 4.2 near Fort St. John (FSJ), British Columbia, and an M 3.9 near Rocky Mountain House (RMH), Alberta. The two FSJ events were likely induced by hydraulic fracturing activities in the region. Although the cause of the RMH event remains unclear, it is of interest because it is of similar magnitude to the other events and had significant consequences to the public. The event triggered an automatic shutdown of a nearby gas plant and a subsequent precautionary flaring of gas, and several hundred people were without power for a prolonged period. We examine the ground motions and intensities for these events. We find that ground motions at frequencies up to about 2 Hz are in agreement with corresponding observations for similar‐sized events in California and with the predictions of applicable empirical ground‐motion prediction equations. However, high‐frequency ground motions appear to be lower than those predicted, suggesting that these events may be associated with a low stress drop; we believe that this is likely a focal depth effect, which may be a mitigating factor that limits high‐frequency ground motions from induced events. Our preliminary findings suggest that moderate‐induced events ( M 4–5) may be damaging to nearby infrastructure, because the shallow focal depth may result in localized strong ground motions to which some infrastructure may be vulnerable; this is a particular concern in low‐to‐moderate seismicity regions, because seismic design measures for structures in these regions may be minimal. Our results highlight the importance of seismic monitoring in the immediate vicinity of fluid injection sites (both wastewater disposal and hydraulic fracturing) to accurately characterize injection‐induced seismicity and ultimately mitigate the associated risk.

Assessment of seismic hazard in the Erzincan (Turkey) region: construction of local velocity models and evaluation of potential ground motions

Abstract: The fundamental step in estimation of seismic damage and losses in urban areas is identification of regional potential seismic hazard. The accuracy of seismic analyses depends on the reliability of the local input parameters used in the corresponding hazard and loss models. This paper presents detailed seismic hazard analyses for an earthquake-prone region using locally derived source and site parameters. Main components of this study are construction of local seismic velocity models, probabilistic and deterministic seismic hazard analyses, and estimation of corresponding potential ground motions. The study area is Erzincan, which is a city on the eastern part of the North Anatolian Fault Zone. Located at a triple junction of major fault systems within a basin structure, Erzincan experienced major events (Ms ~8.0) in 1939 and (Mw = 6.6) in 1992. This study presents the first discussion in the literature on site-specific probabilistic and deterministic hazard analyses for Erzincan. Using locally derived input parameters in site response modeling and hazard analyses, the earthquake potential of Erzincan is investigated in detail. Probabilistic seismic hazard analyses with a hybrid source model composed mainly of line sources show that for a return period of 475 years, the maximum peak ground acceleration value in the Erzincan city center is computed to be almost 1 g. On the other hand, probabilistic hazard analyses with only area sources yield ground motion amplitudes that are almost half of those obtained by the hybrid model. The deterministic hazard analyses also show that peak ground acceleration in the city center for a scenario event of Mw = 7.0 reaches 1.25 g at a soft soil site located at 2 km in distance from the fault plane. In summary, numerical results obtained with locally derived input parameters indicate that Erzincan has significant potential for hazard in terms of both local earthquake occurrence and site amplifications.

Ground motion simulations for İzmir, Turkey: parameter uncertainty

In ground motion simulation studies based on earthquake rupture scenarios, the absolute ground motion level, frequency content, signal duration and distribution of simulated ground motion is highly dependent on the input parameters used in the calculations. We conduct a predictive study assessing the potential ground motions for Izmir, Turkey based on earthquake scenarios. We calculate ground motions from a reference scenario (Mw6.8) and compare it to 25 test scenarios for the Izmir fault in order to investigate the effect of input parameter uncertainty on the simulated ground motion. In this study, we use a hybrid broadband frequency (0.1–10 Hz) ground motion simulation technique. We find average ground motion levels in the central area of Izmir of more than 600 cm/s2 and 60 cm/s for peak ground acceleration and velocity, respectively, while the standard deviation is found to exceed 200 cm/s2 and 20 cm/s, respectively. The tested parameters identified to have the largest influence on the absolute ground motion level are seismic moment, average stress-drop, rise time and rupture velocity. Parameters identified to have the least effect on ground motion level are rake and ratio of stress-drop on asperities to background stress-drop. The low-frequency ground motion, critical in terms of damage to the building stock in Izmir, is mostly affected by the location of nucleation point, seismic moment, depth of the rupture area, rise time and the velocity model. It is, therefore, highly recommended that future studies focus on reducing the uncertainties in these input parameters.

The seismic retrofit of UC Berkeley's California Memorial Stadium

SUMMARYThis paper addresses the seismic retrofit of the University of California at Berkeley's California Memorial Stadium (CMS) to accommodate surface fault rupture movements as well as intense seismic shaking from the Hayward fault. For the surface fault rupture aspect of the project, the project team took a multidisciplinary approach that involved structural engineers, geotechnical engineers, seismologists and geologists collaborating to establish design criteria and possible surface rupture scenarios. The mechanics of surface fault rupture are discussed relative to the structural design approach that mitigates the effects of surface deformations caused by the fault during an earthquake. The effects of the surface fault rupture were studied using small scale physical models and nonlinear finite element models of the building and rupturing ground surface. The retrofit scheme accommodates the concentrated ground deformations of an estimated 6 ft of horizontal movement and 2 ft of vertical offset caused by a surface fault rupture. Segments of the CMS that overlay the regions of possible surface fault rupture were decoupled from the main structure via movement gaps to accommodate relative displacements of the building segments, including tilting in the event of earthquake‐produced fault rupture. The results of the analyses are discussed along with the design decisions and challenges of retrofitting a historic structure that resides on an active fault. While a large portion of the engineering effort was devoted to solving the issue of accommodating surface rupture, another large engineering challenge also dominated the design of the CMS. One of the signature architectural features of the stadium is a two‐story, 375‐ft long press box that hovers above the new west side of the seating bowl. Although designing the press box on limited supports to give the appearance of ‘hovering’ was a challenge, the real challenge came in safely bracing this structure for large potential ground motions at this site. The interface between the flexible support of the press box and the rigid seating bowl became a challenge, solved by providing a separation between the bowl and press box structures allowing them to move independently while linking them only with fluid viscous dampers. Copyright © 2012 John Wiley &amp; Sons, Ltd.

Uncertainty treatment in earthquake modelling using Bayesian probabilistic networks

A probabilistic description of potential ground motion intensity is computed using a Bayesian probabilistic network (BPN) representing the standard probabilistic seismic hazard analysis (PSHA). Two earthquake ground motion intensity parameters are used: response spectral values for structural failures and peak ground acceleration for geotechnical failures. The correlation of these parameters is also considered within a BPN. It is further shown how deaggregation of the seismic hazard could be easily performed using BPNs. A systematic consideration of uncertainty in the values of the parameters of a particular seismic hazard model can be described by PSHA. But the correct choices for elements of the seismic hazard model are uncertain. Logic trees provide a convenient framework for the treatment of model uncertainty. The paper illustrates an alternative way of incorporating the model uncertainty by extending the developed BPN. Incorporation of time-dependent seismic hazard using a BPN is also illustrated. Finally, the uncertainty treatment in earthquake modelling using BPNs is illustrated on the region Adapazari, which is located close to the western part of the North Anatolian Fault in Turkey.

Statistics of Earthquake Stress Drops on a Heterogeneous Fault in an Elastic Half-Space

We investigate properties of earthquake stress drops in simulations of evolving seismicity and stress field on a heterogeneous fault. The model consists of an inherently discrete strike-slip fault surrounded by a 3D elastic half-space. We consider various spatial distributions of frictional properties and analyze results generated by 150–300 model years. In all cases, the self-organized heterogeneous initial stress distributions at the times of earthquake failure lead to stress drops that are systematically lower than those predicted for a homogeneous process. In particular, the large system-sized events have stress drops that are consistently ∼25% of predictions based on the average fault strength. The type and amount of assumed spatial heterogeneity on the fault affect the stress-drop statistics of small earthquakes ( M L <5) more than those of the larger events. This produces a decrease in the range of stress drops as the earthquake magnitudes increase. The results can resolve the discrepancy between traditional estimates of stress drops and seismological observations. The general tendency for low stress drops of large events provides a rationale for reducing the statistical estimates of potential ground motion associated with large earthquakes.