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At least 649 records · Page 36Linked to original sources
USGS2024

The impact of source time function complexity on stress drop estimates

Earthquake stress drop—a key parameter for describing the energetics of earthquake rupture—can be estimated in several different, but theoretically equivalent, ways. However, independent estimates for the same earthquakes sometimes differ significantly. We find that earthquake source complexity plays a significant role in why theoretically (for simple rupture models) equivalent methods produce different estimates. We apply time‐ and frequency‐domain methods to estimate stress drops for real earthquakes in the SCARDEC (Seismic source ChAracteristics Retrieved from DEConvolving teleseismic body waves, Vallée and Douet, 2016 ) source time function (STF) database and analyze how rupture complexity drives stress‐drop estimate discrepancies. Specifically, we identify two complexity metrics—Brune relative energy (BRE) and spectral decay—that parameterize an earthquake’s complexity relative to the standard Brune model and strongly correlate with the estimate discrepancies. We find that the observed systematic magnitude–stress‐drop trends may reflect underlying changes in STF complexity, not necessarily trends in actual stress drop. Both the decay and BRE parameters vary systematically with magnitude, but whether this magnitude–complexity relationship is real remains unresolved.

Bulletin of the Seismological Society of America↗
USGS2024

Static and dynamic strain in the 1886 Charleston, South Carolina, earthquake

During the 1886 Mw 7.3 Charleston, South Carolina, earthquake, three railroads emanating from the city were exposed to severe shaking. Expansion joints in segmented railroad tracks are designed to allow railroad infrastructure to withstand a few parts in 10,000 of thermoelastic strain. We show that, in 1886, transient contractions exceeding this limiting value buckled rails, and transient extensions pulled rails apart. Calculated values for dynamic strain in the meizoseismal region are in reasonable agreement with those anticipated from the relation between strain and moment magnitude proposed by Barbour et al. (2021) and exceed estimated tectonic strain released by the earthquake by an order of magnitude. Almost all of the documented disturbances of railroad lines, including evidence for shortening of the rails, can thus be ascribed to the effects of dynamic strain changes, not static strain. Little or no damage to railroads was reported outside the estimated 10 −4 dynamic strain contour. The correspondence between 10 −3 and 2×10 −4 contours of dynamic strain and Mercalli intensity 9 and 8, anticipated from the dependence of each quantity on peak ground velocity, suggests it may be possible to use railroad damage to quantitatively estimate shaking intensity. At one location, near Rantowles, ≈20 km west of Charleston, a photograph of buckled track taken one day after the earthquake has been cited as evidence for shallow dextral slip and has long focused a search for a causal fault in this region. Photogrammetric analysis reveals that the buckle was caused by transient contraction of <10 cm with no dextral offset. Our results further weaken the evidence for faulting in the swamps and forests south of the Ashley River in 1886, hitherto motivated by the photograph and limited macroseismic evidence for high‐intensity shaking.

South Carolina↗
USGS2024

Are the horizontal-to-vertical spectral ratios of earthquakes and microtremors the same?

We consider the similarities and differences between earthquake and microtremor horizontal‐to‐vertical spectral ratios (eHVSR and mHVSR, respectively) using a dataset of 161 sites in southern California. Quantitative comparisons are made in terms of the eHVSR and mHVSR lognormal median curves, as well as the frequencies and amplitudes associated with the fundamental‐ and higher‐mode resonances where present. The results show only 58% of the eHVSR–mHVSR pairs agree in terms of their median curve and only 25% of the eHVSR–mHVSR pairs agree in terms of shared resonances, which increases to 68% if flat HVSRs are considered equivalent. Furthermore, while the shared resonances match very well in terms of frequency (root mean square error, RMSE, <0.11 Hz), the amplitudes of those resonances do not agree (RMSE >1.6). These findings demonstrate that while eHVSR and mHVSR agree at some sites, they are not equivalent at all sites. To investigate if the agreement between eHVSR and mHVSR could be related to features of the microtremor data, earthquake recordings, and/or the site conditions, three machine learning (ML) models at varying levels of interpretability are presented. The ML models—which include multivariate logistic regression, gradient‐boosted trees, and support vector machines—show only partial success at using site‐specific data to predict whether eHVSR and mHVSR will likely agree in terms of their median curve (accuracy of 78%) and number of resonances (accuracy of 84%). Therefore, we conclude that while eHVSR and mHVSR can be quite similar in terms of resonant frequencies at some sites, they are not identical at all sites. Furthermore, preliminary evidence shows that the agreement of eHVSR and mHVSR can be predicted a priori given features of the microtremor measurements, earthquake recordings, and site conditions, although a larger dataset will be necessary for developing a robust predictive model.

California↗
USGS2025

Generalized Bancroft algorithm for locating earthquakes with P- and S-wave arrival times

Because of similarities between locating an earthquake with seismic stations and locating a Global Positioning System (GPS) receiver from satellites, the Bancroft algorithm developed for GPS processing can be used to locate earthquakes. Such an approach to earthquake location differs from the conventional method of choosing an initial or trial solution and then iteratively improving the solution until convergence. The Bancroft algorithm has the advantage of being a direct, noniterative solution but with the disadvantage of only being able to accommodate a homogeneous velocity model. An additional limitation of the standard Bancroft algorithm is that it considers arrival times in a medium with a single propagation velocity. This poses no problem for GPS processing because electromagnetic waves travel at the speed of light; however, for seismic waves it means the algorithm can be applied to collections of either P ‐ or S ‐wave arrival times. Here, I show how the Bancroft algorithm can be generalized to handle both P ‐ and S ‐wave arrival‐time measurements simultaneously. I also show how to accommodate depth‐varying P ‐ and S ‐wave velocity models. I apply the generalized Bancroft algorithm to microearthquakes beneath Tanaga Volcano in Alaska and compare standard locations from the widely used HYPOINVERSE location code to Bancroft locations and to the output of HYPOINVERSE when setting the trial location to the Bancroft location. I find the Bancroft locations outperform the results from the other methods for shallow earthquakes near sea level, where a quantity known as the geometric dilution of precision is large and linearized approaches such as HYPOINVERSE are expected to struggle.

Alaska↗
USGS2024

Precariously balanced rocks in northern New York and Vermont, U.S.A.: Ground-motion constraints and implications for fault sources

Precariously balanced rocks (PBRs) and other fragile geologic features have the potential to constrain the maximum intensity of earthquake ground shaking over millennia. Such constraints may be particularly useful in the eastern United States (U.S.), where few earthquake‐source faults are reliably identified, and moderate earthquakes can be felt at great distances due to low seismic attenuation. We describe five PBRs in northern New York and Vermont—a region of elevated seismic hazard associated with historical seismicity. These boulders appear to be among the most fragile PBRs in the region, based on reports from hobbyists. The PBRs are glacial erratics, best evidenced by glacial striations on bedrock pedestals. The pedestals themselves are locally high knobs, often situated on regionally high topography; this setting limits soil development and indicates that any outwash deposits were likely ephemeral. As a result, PBR ages can be reliably established by the retreat of the last continental ice sheet, ∼15–13 ka. To quantify the fragility of the PBRs, we surveyed them with ground‐based light detection and ranging and calculated geometric parameters from the point clouds, field observations, and seismic responses. Preliminary validation of the 2023 time‐independent U.S. National Seismic Hazard Model (NSHM) shows that the existence of PBRs is generally consistent with the median site‐specific hazard curves. Only the Blue Ridge Road site suggests a modest reduction in hazard. To visualize the ensemble of data, we mapped the minimum permissible distance to potential source faults around each PBR site as a function of source magnitude by using the ground‐motion models from the 2023 NSHM. Viewed in this manner, our data are consistent with potential M ∼6.5 earthquake‐source faults in many parts of the Lake Champlain Valley and northern Adirondack Mountains. Our work illustrates a potential pathway for better constraining earthquake‐source faults in regions of cryptic faults.

Bulletin of the Seismological Society of America↗
USGS2025

Examining the role of elevated and sustained strain in dynamically triggering earthquakes on the Anza section of the San Jacinto fault

Microearthquakes can be dynamically triggered in southern California by remote earthquakes. However, directly connecting dynamic triggering mechanisms with observational data remains challenging. One proposed failure mechanism suggests that both the amplitude and duration of cyclic fatigue caused by the passing seismic wave contribute to triggering occurrence. Here, we measure dynamic strains recorded by borehole strainmeters in the Anza section of the San Jacinto fault zone from 710 earthquakes that occurred over 300 km away between 2008 and 2017 to systematically investigate the role of elevated and sustained strain in controlling dynamic triggering. We design a suite of tests to evaluate whether specific amplitude thresholds and durations of strain can predict dynamic triggering cases. We further test whether the peak dynamic strain (PDS) can predict triggering occurrence in combination with the strain amplitude and duration. Based on these tests, there is no strain amplitude–duration threshold that can distinguish triggering occurrence in Anza. Dynamic triggering is more likely to occur if a remote earthquake causes a PDS above 100 nanostrain, though many cases were triggered at smaller PDSs. The lack of clear correlation between triggering and characteristics of the dynamic strain field suggests that the tested features of the incoming waves do not determine triggering occurrence and local fault conditions and slip processes are more important in controlling dynamic triggering in Anza.

California↗
USGS2024

Extending the Boore and Abrahamson (2023) modified square-root-impedance method for the development of site amplifications consistent with the full-resonance approach to a range of VS30 values

The square-root-impedance (SRI) method is commonly used to approximate the seismic site amplifications computed using the full-resonance (FR) method for gradient shear-wave velocity ( V S ) profiles that are smoothly varying with depth. The SRI site amplifications have been observed to systematically underpredict the FR site amplifications by a ratio of FR/SRI amplifications around 1.05 to 1.3 across a wide frequency range (Boore, 2013). Recently, Boore and Abrahamson (2023; hereafter, BA23) related this difference in the SRI and FR methods to differences in the exponent η of the ratio of seismic impedances between the two methods. They proposed the implementation of a modified frequency-dependent η in the SRI method to improve its match to the FR site amplifications. This modified η was derived using only five V S profiles. We investigate the performance of the BA23 η for a wide range of realistic gradient V S profiles with V S30 ranging from 180 to 1500 m/s. These gradient V S profiles are constructed using two power-law functions of depth and are constrained by the assigned VS30 value, the depth and velocity of the half-space, and depths to shear-wave velocity horizons of 1.0 and 2.5 km/s ( Z 1.0 and Z 2.5 ) based on western United States sites. Despite observing a V S30 dependence of η, we find that the BA23 η generally works reasonably well for the range of V S profiles analyzed. Using the VS30 -dependent η derived in this study results in improvements in matching the FR site amplification compared to using the BA23 η. These improvements are more pronounced for the soft-site conditions and become modest to negligible for the stiff site conditions

Bulletin of the Seismological Society of America↗
USGS2025

Earthquake stress drop, source spectra from laboratory experiments, and the apparent unsteadiness of frictional slip

Over a range of co-seismic total energy release, high sample rate slip, stress, and slip velocity measurements were made during frictional failure to determine seismic source properties. The near-field measurements were used to estimate stress drops using spectral approaches that are analogous to the standard seismological moment-corner determined Δσ and acceleration amplitude Δσ arms stress drops. Rapid frictional sliding produces slip velocity amplitude spectra that vary with frequency -1 so long as the energy dissipated by friction approaches the total energy release. Under these conditions Δσ and Δσ arms are similar in size. Since these are nearly direct measurements of fault slip velocity and because they produce flat acceleration spectra between the corner and an apparent fmax, friction in these experiments seems to produce dynamic acceleration and deceleration at all resolved frequencies. The physical origin of this unsteady motion is not known exactly but likely reflects rapid dynamic variations in fault strength or applied stress. On the other hand, when the total energy stored prior to failure is artificially made somewhat larger relative to that which can be dissipated by friction the velocity spectra vary with frequency -2 immediately below the corner. At these conditions Δσ and Δσ arms diverge. The excess stored energy is preferentially partitioned into radiated energy upon failure. Collectively the experiments imply that to produce unsteady, white noise accelerations that are observed for natural earthquakes, requires that at least 95% of the energy released does not escape the source region to be radiated to the far-field.

Bulletin of the Seismological Society of America↗
USGS2024

SCEC/USGS Community Stress Drop Validation Study: How spectral fitting approaches influence measured source parameters

Spectral source parameters used to estimate an earthquake’s stress drop (Δσ) can vary significantly across measurement approaches. The Statewide California Earthquake Center/U.S. Geological Survey Community Stress-Drop Validation Study was initiated to compare source parameter estimates, focusing initially on a dataset from the 2019 Ridgecrest earthquake sequence. As part of that validation effort, here we focus on one potential source of uncertainty: whether spectral fitting approaches alone, applied to a common set of spectra from the 2019 Ridgecrest sequence result in different source parameter estimates. By using a common set of benchmark spectra analyzed across a consistent frequency band of 1–40 Hz, we eliminate many sources of variability. A subgroup of validation study participants volunteered to estimate the low-frequency displacement (Ω0) and corner frequency ( f c ) by fitting a smooth function to benchmark displacement spectra. Participants used linear- or log-sampled spectra, assumed a Brune or Boatwright spectral model, and applied different misfit criteria. We compare 17 approaches used to estimate Ω0, f c , and Δσ for 54 earthquake spectra. Our results reveal that 35% of events have Δσ estimates within a factor of two, whereas others exhibit variations exceeding an order of magnitude. The variability in Ω0 and f c can largely be attributed to whether a spectrum is consistent with the smooth function of an idealized simple crack model. The trade-off between Ω0 and f c may be more pronounced when using linearly sampled spectra, as higher frequency spectral bumps control the fits. As expected, methods that assumed a Boatwright model tended to have lower Ω0 and somewhat higher f c compared to those assuming a Brune model, although resulting Δσ estimates are similar. When compared to the overall validation study results, the fitting approach alone may account for between 5% and 90% (25% on average) of the total variability in spectral Δσ.

California↗
USGS2024

Characterizing directivity in small (M 2.4-5) aftershocks of the Ridgecrest sequence

Directivity, or the focusing of energy along the direction of an earthquake rupture, is a common property of earthquakes of all sizes and can cause increased hazard due to azimuthally dependent ground‐motion amplification. For small earthquakes, the effects of directivity are generally less pronounced due to reduced rupture size, yet the directivity in small events can bias source property estimates and provide important insights into general regional faulting patterns. However, due to observational limitations, directivity is usually only measured and modeled for large events. As such, many studies of small earthquakes either ignore directivity altogether or assume a constant rupture direction for all events in a cluster. In our study, we apply a refined directivity fitting method constrained with two separate methods of source deconvolution to the dataset of aftershocks of the 2019 Ridgecrest earthquakes, which contain a large number of well‐recorded small‐to‐mid sized earthquakes occurring in close proximity to each other. The revealed directivity of 100+ small (M 2.4–5) earthquakes is highly heterogeneous and primarily oblique to and away from the main fault strike, suggesting a complex postseismic stress redistribution. In addition, the energy focusing effect of directivity appears to bias the selection of high‐quality data from stations in the direction of rupture, leading to average stress‐drop increases of 50% if directivity is not accounted for.

California↗
USGS2025

Overview of The SCEC/USGS Community Stress Drop Validation Study using the 2019 Ridgecrest earthquake sequence

We present initial findings from the ongoing Community Stress Drop Validation Study to compare spectral stress‐drop estimates for earthquakes in the 2019 Ridgecrest, California, sequence. This study uses a unified dataset to independently estimate earthquake source parameters through various methods. Stress drop, which denotes the change in average shear stress along a fault during earthquake rupture, is a critical parameter in earthquake science, impacting ground motion, rupture simulation, and source physics. Spectral stress drop is commonly derived by fitting the amplitude‐spectrum shape, but estimates can vary substantially across studies for individual earthquakes. Sponsored jointly by the U.S. Geological Survey and the Statewide (previously, Southern) California Earthquake Center our community study aims to elucidate sources of variability and uncertainty in earthquake spectral stress‐drop estimates through quantitative comparison of submitted results from independent analyses. The dataset includes nearly 13,000 earthquakes ranging from M 1 to 7 during a two‐week period of the 2019 Ridgecrest sequence, recorded within a 1° radius. In this article, we report on 56 unique submissions received from 20 different groups, detailing spectral corner frequencies (or source durations), moment magnitudes, and estimated spectral stress drops. Methods employed encompass spectral ratio analysis, spectral decomposition and inversion, finite‐fault modeling, ground‐motion‐based approaches, and combined methods. Initial analysis reveals significant scatter across submitted spectral stress drops spanning over six orders of magnitude. However, we can identify between‐method trends and offsets within the data to mitigate this variability. Averaging submissions for a prioritized subset of 56 events shows reduced variability of spectral stress drop, indicating overall consistency in recovered spectral stress‐drop values.

California↗
USGS2025

Seismic moment and local magnitude scales in Ridgecrest, CA from the SCEC/USGS Community Stress Drop Validation Study

We illustrate the systematic difference between moment magnitude and local magnitude caused by underlying earthquake source physics, using seismic moments submitted to the Statewide California Earthquake Center/United States Geological Survey Community Stress Drop Validation Study 2019 Ridgecrest data set. While the relationship between seismic moment and moment magnitude ( M or M w ) of log 10 ( M 0 ) ~ 1.5* M is uniformly valid for all earthquake sizes by definition (Hanks and Kanamori, 1979), the relationship between local magnitude M L and moment is itself magnitude dependent. For moderate events, ~3< M < ~6, M and M L are coincident; for earthquakes smaller than ~3, M L ~ 1.0 log 10 M 0 (Hanks and Boore, 1984). This is a physical consequence of the corner frequency fc becoming larger than the upper frequency of observation and implies that M L and M differ systematically by a factor of 1.5 for these small events. While this idea is not new, we propose a new, continuous relationship between local magnitude and moment, for magnitudes 2 to 6 which extrapolates to smaller and larger magnitudes, applicable to southern California specific to the Ridgecrest region. We make use of the plethora of seismic moments as submitted by many participants of the Community Stress Drop study, compared to the Southern California Seismic Network (SCSN) catalog magnitudes. Overall, the seismic moments in the Community Study recover moment magnitude well, so we use our new M L - M 0 to convert M L to M , refining the SCSN operational M Lr scale. This systematic difference of 50% in slope between local and moment magnitude at small magnitudes has implications for spectral stress drop estimates, earthquake ground motion modeling, as well as other magnitude scales and earthquake occurrence statistics.

California↗
USGS2025

ShakeAlert® version 3: Expected performance in large earthquakes

The ShakeAlert earthquake early warning (EEW) system partners along with U.S. Geological Survey (USGS) licensed operators deliver EEW alerts to the public and trigger automated systems when a significant earthquake is expected to impact California, Oregon, or Washington. ShakeAlert’s primary goal is to provide usable warning times before the arrival of damaging shaking. EEW is most likely to achieve this goal in large‐magnitude earthquakes. In recent years, ShakeAlert has gone through a series of upgrades to its underlying scientific algorithms aimed at improved performance during large earthquakes. Version 3 of this software recently went live in the production system and includes improvements to all algorithms. The main seismic algorithms that detect an earthquake and characterize its location, magnitude, and fault rupture orientation are faster than older versions. Other key changes include: using real‐time geodetic data to characterize the magnitude growth in large earthquakes; the introduction of an alert pause procedure to compromise between speed near the epicenter and improved accuracy at larger distances; and the inclusion of a nonergodic site‐response model in the ground‐motion predictions. ShakeAlert has achieved its primary goal of usable warning times before strong shaking at some locations in real‐time operations in recent M 6 earthquakes. Using offline tests, we demonstrate usable warning times are possible for many sites with peak shaking values of modified Mercalli intensity (MMI) 7–8 in M 7+ earthquakes and also for many MMI 8–9 sites in M 8+ earthquakes. ShakeAlert partners use a variety of MMI and magnitude thresholds in deciding when to alert their users within bounds set by the USGS. Our study shows that there is room to raise the magnitude thresholds up to about M 5.5 without adversely affecting performance in large earthquakes. The ground‐motion criteria are more complex owing to a significant drop‐off in warning times between the MMI 4 and 5 levels of predicted shaking. However, widely used ShakeAlert products, such as the MMI 3 and 4 contour products, can provide sufficiently long warning times before strong shaking in moderate‐to‐great earthquakes to enable a range of protective actions.

Bulletin of the Seismological Society of America↗
USGS2025

A scientific vision and roadmap for earthquake rupture forecast developments, a USGS perspective

We articulate a scientific vision and roadmap for the development of improved Earthquake Rupture Forecast models, which are one of the two main modeling components used in modern seismic hazard and risk analysis. One primary future objective is to provide fully time-dependent models that include both elastic rebound and spatiotemporal clustering nationwide, which is particularly important for shorter-term hazard and risk considerations (e.g., earthquake insurance products). We also discuss the importance and perennial challenges associated with quantifying epistemic uncertainties, including those associated with deformation-model slip rates, un-quantified sampling errors with respect to off-fault seismicity, and any spatial covariances. The need for more physics-based approaches is also emphasized, as is the benefit of adding model valuation (quantifying usefulness) to our verification and validation protocols. Given the multidisciplinary and system-level nature of this activity, modular design is critical. Future updates will also draw from best-available science by both the United States Geological Survey and the external community. The primary goal of this paper is to highlight plans that guide research and facilitate community engagement with model development, especially with respect to lowering the entry barrier for early career scientists and engineers. The paper is written so readers can focus on the sections that interest them most (see table of contents), with the Introduction and Discussion providing a stand-alone overview and summary.

Bulletin of the Seismological Society of America↗
USGS2025

Combining multisite tsunami and deformation modeling to constrain slip distributions for the 1700 C.E. Cascadia earthquake

A major earthquake ruptured the Cascadia subduction zone (CSZ) on 26 January 1700. Key paleoseismic evidence associated with this event include tsunami deposits, stratigraphic evidence of coastal coseismic subsidence, written Japanese records of a tsunami unaccompanied by earthquake shaking, and margin‐wide turbidites found offshore and in lacustrine environments. Despite this wealth of independent clues, important details about this event remain unresolved. Dating uncertainties do not conclusively establish whether the proxies are from one earthquake or a sequence of them, and we have limited knowledge of the likely slip distributions of the event or events. Here, we use a catalog of 37,500 candidate synthetic ruptures between M w 7.8 and 9.2 and simulate their resulting coseismic deformation and tsunami inundation. Each model is then compared against estimated Japan tsunami arrivals, regional coastal subsidence records, and local paleotsunami deposits mapped at six different coastal marshes and one coastal lake along the CSZ. We find that seven full‐margin ruptures with a median magnitude of M w 9.1 satisfy all three constraints. We favor one M w 9.11 model that best matches all site paleoseismic observations and suggests that the Cascadia megathrust slipped up to ∼30 m and must have shallow geodetic coupling. We also find that some sequences composed of three or four ruptures can still satisfy the observations, yet no sequences of two ruptures can. Sequences are differentiated into three groups based on whether they contain a mainshock rupture located in the south (>44° N) or further north. All sequences contain unruptured portions of the megathrust and most contain mainshocks with peak slip above 40 m. The fit of the geologic evidence from sequences is poor in comparison to single‐event models. Therefore, sequences are generally less favored compared to full‐margin events.

British Columbia, California, Oregon, Washington↗
USGS2026

Rupture into slow-slip fault regime during the 2018 Mw 6.9 Island of Hawaiʻi earthquake is followed by modest postseismic slip

On 4 May 2018, a M w 6.9 earthquake occurred on the south flank of Kīlauea, in the midst of an historic event that included a voluminous eruption from Kīlauea’s lower East Rift zone and caldera collapse at its summit. The earthquake was a consequence of both short‐ and long‐term stress buildup due to magmatic activity associated with the eruption and steady flank motion, respectively, and it revealed features of Kīlauea’s décollement fault that can inform understanding of future earthquake activity. We used geodetic data to determine the distributions of slip during the coseismic and postseismic periods and compared these with areas of known fault slip during past earthquakes and slow‐slip events (SSEs). The 2018 earthquake ruptured into an area of the décollement fault that was active during quasi‐regular SSEs that occurred in the two decades prior to 2018 but that have not been observed since. The coseismic slip model indicates that the amount of motion on the décollement fault was several times greater than what typically occurred during SSEs, suggesting that it may take decades for the fault to rebuild stress to the point at which SSEs will occur again. Postseismic afterslip also occurred in an area of the fault known to experience slow slip; however, unlike at other creeping faults, postseismic afterslip was rapid, being largely over within 2–3 days. The rapid nature and small magnitude of the postseismic afterslip may be due to the lack of a viscoelastic relaxation component, which is possibly a result of the shallow dip of the décollement fault not transferring stress efficiently into the lower crust.

Hawaii↗
USGS2025

Capturing the uncertainty of seismicity observations in earthquake rate estimates: Implications for probabilistic seismic hazard analysis and the USGS National Seismic Hazard Model

The rate of earthquakes in a region is a fundamental input to Probabilistic Seismic Hazard Analysis. We present a Monte Carlo method for computing that rate from seismicity catalogs while including a range of data and analysis uncertainties. This method is applied to regions for which the b value is assumed to be spatially invariant. Each region is broken down into epochs for which each epoch is estimated to have a uniform magnitude of completeness ( ⁠⁠ M c ). The distribution of earthquake rates for M ≥ M c is determined for each epoch by considering the Poisson likelihood of rates given the number of observed earthquakes with M ≥ M c ⁠ . We use a Monte Carlo process to include the uncertainty in b , ⁠ M c , and individual event magnitudes. The result for each epoch is the joint distribution of the Poisson rate of earthquakes with magnitudes larger than the minimum value used to calculate hazard ( ⁠⁠ M 1 ) and the Gutenberg–Richter b values, which control the extrapolation to other magnitudes. The rate for each region is either the duration‐weighted average over the epochs or, to better capture temporal variations, we also consider mixture models. The mixture models also provide an avenue to allow temporal variations in b values. To implement this joint distribution in a logic tree, we use the mean and 95% confidence branches, each of which is parameterized with an M ≥ M 1 rate and b value. We explore different ways of defining those branches, as well as non‐Gutenberg–Richter branches, and their impact on hazard estimates. The mean hazard, but not the fractiles, is robust with respect to these choices. To illustrate these new methods, we use synthetic data and catalogs from recent U.S. Geological Survey National Seismic Hazard Models for the Central and Eastern United States and for Puerto Rico and the U.S. Virgin Islands.

central and eastern United States, Puerto Rico, U.↗
USGS2025

Relationship between peak and cumulative ground motions from 49 Mw 3-6 earthquakes in the San Francisco Bay Area

We examine the relationship between peak ground velocity (PGV) and cumulative absolute displacement (CAD) for 49 M w 3 – 6 earthquakes in the San Francisco Bay Area (SFBA) and gain insight into the spatiotemporal partitioning of seismic energy in ground motion records with respect to source, path, and site effects. PGV and CAD are positively correlated, but there can be large deviations from the average trend. For example, ground motion records with either very long duration resonance or short pulse-like motions will have higher or lower CAD, respectively, but could have very similar PGV. We perform principal component analysis (PCA) on PGV-CAD for >7000 records in the SFBA with the goal of investigating what influences positive or negative anomalies in cumulative motions. PCA rotates the PGV-CAD datapoints into two principal components, where the one with the larger variance, which we call the “primary intensity” represents mostly the distance-dependence of ground motion amplitudes. The other principal component, which we call the “excess motion”, represents the deviation from cumulative motions that would be typical for a ground motion record with a given PGV. The excess motion will be positive in the case of records with long duration ringing and will be negative for short duration pulse-like ground motions. We find that excess motion is generally positive at sites in sedimentary basins and in soft sediments around the SF Bay. Excess motion is generally negative in the very near field, as well as at sites on hard bedrock. We discuss the findings here in terms of implications for seismic hazard applications and other wave propagation phenomena.

California↗