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At least 757 records · Page 42Linked to original sources

Near-fault amplification and ground motion variability during the 2019 Ridgecrest, California sequence

We estimate ground-motion variability near the 2019 M 7.1 Ridgecrest earthquake sequence. Accurate seismic hazard estimation requires understanding ground-motion spatial correlations, yet many studies lack the dense station coverage needed to resolve small-scale variability. The 2019 M 7.1 Ridgecrest earthquake sequence presents a unique opportunity to examine ground motions and their spatial correlations at a range of interstation distances. The permanent seismic network was augmented with hundreds of temporary stations including several fault-crossing nodal arrays. We compute the event ( δE i ) and within-event ( δW ij ) residuals from the observed peak ground velocity and peak ground acceleration data to isolate potential sources of ground-motion variability. We then compare δW ij between station pairs that record an event to understand the semivariance of the ground motion versus interstation distance. By fitting an exponential model to the semivariances, we determine a correlation range of 25 km for the Ridgecrest region. Although the exponential model fits the broad-scale increase of semivariance with interstation distance, we also observe smaller-scale trends. We find that ground motions are less correlated for station pairs that are near or across faults that ruptured during the 2019 Ridgecrest sequence. We also find large, positive median δW ij with relative values 2–3 times larger than nearby stations for individual stations’ near-fault traces. Near-fault amplification and greater ground-motion variability can delineate fault zones and may locally increase the seismic hazard.

California↗

Constraining source and path effects of large magnitude earthquakes using ground motion simulations

The purpose of this study is to use ground‐motion simulations to investigate ways in which source and path effects for large‐magnitude earthquakes can be represented in nonergodic ground‐motion models (GMMs). To achieve this, we designed a ground‐motion study in the San Francisco Bay Area that includes earthquakes with a broad range of magnitudes distributed uniformly on a fault plane, and sites covering a large range of rupture distances and azimuths. After running a large suite of kinematic simulations (magnitude 4–7), we then develop a nonergodic GMM with the simulated data. We find that trends in the within‐site residuals are affected significantly by the earthquake radiation pattern, rupture directivity, and slip patterns. Next, we modify an existing rupture directivity model to fit and remove the observed radiation pattern and rupture directivity from the residuals. We also minimize the contributions of slip patterns by averaging the within‐site residuals among multiple source realizations. Finally, after removing the source effects from the within‐site residuals, we compare the path effects computed with different magnitude groups using two approaches. The first approach only considers the small events that have the same shortest path to a site as the large events, whereas the second approach considers all small events on the fault plane. The results indicate that it is difficult to satisfactorily approximate the path effects of large events with those of small events using either approach, at least in the case of simulations.

California↗

Use of precariously balanced rocks to constrain postglacial earthquake magnitudes in New England, United States

We use the age and fragility of 13 precariously balanced rocks (PBRs) in Massachusetts, New Hampshire, and southwestern Maine to evaluate the estimated probabilistic seismic hazard (PSH) from the U.S. Geological Survey’s National Seismic Hazard Model (NSHM), and also develop a map of maximum postglacial earthquake magnitudes in the region. The PBRs are erratic boulders left behind by the retreat of the Laurentide ice sheet between 13 and 18 ka, and published ice retreat maps are used to estimate their fragility ages. The fragilities and ages of the rocks appear to be consistent with the NSHM, in that the estimated earthquake magnitudes and resulting ground motions that would topple them are only expected on timescales longer than their fragility ages. This result, on the North American passive margin, contrasts with PBR studies at active plate boundaries, where the PBR constraints imply large reductions to estimated PSH. It may be that the PBRs are not old enough in the eastern United States to reveal the same PSH modeling issues as those revealed in the plate boundary settings. The study provides constraints on maximum magnitudes of postglacial earthquakes across much of Massachusetts, New Hampshire, and southwestern Maine, with the constraints limited to the ages of the PBRs.

Maine. Massachusetts, New Hampshire↗

Stress states on the eve of past earthquakes inform earthquake rupture through fault complexity along the San Andreas and San Jacinto faults

Estimating the evolving state of stress along active fault systems can provide insight into the conditions that generated past ground‐rupturing earthquakes and influenced their ability to propagate through areas of geometric complexity, such as fault branches and stepovers. We use quasi‐static forward numerical models that incorporate the 3D complex configuration of active faults in southern California to estimate shear tractions on the geometrically complex southern San Andreas and San Jacinto faults from 1000 to 1900 C.E. These tractions include interseismic accumulation of traction due to tectonic loading, viscoelastic relaxation of shear stress within the upper crust between earthquakes, and effects of other earthquakes on the fault network. We simulate ground‐rupturing earthquakes based on the along‐strike earthquake extents modeled by Scharer and Yule (2020) , assuming that stress drop is complete in each earthquake. We use Monte Carlo simulations to estimate uncertainty in evolving shear tractions due to uncertainties in earthquake timing and in upper‐crustal viscosity. Pre‐earthquake shear tractions typically do not exceed ∼2 MPa. Although ruptures with length <200 km have pre‐earthquake shear tractions that range from near zero to ∼1.75 MPa, these tractions are not less than ∼0.4 MPa for earthquakes with rupture length >200 km. Earthquakes with long (>200 km) ruptures occur only in the single‐stranded part of the system, whereas those with short (<125 km) rupture length and high pre‐earthquake shear traction occur near fault stepovers and branches. This suggests that high accumulated shear traction encourages longer rupture propagation, but may not be sufficient to overcome geometric complexities. This modeling approach informs our understanding of rupture propagation and provides estimates of fault shear tractions that are unavailable from direct measurements.

Callifornia↗

Ground motions from finite faults with unknown geometry

Earthquake emergency response and loss modeling require accurate models of ground‐motion intensity metrics (IMs), such as those produced by ShakeMap. In the critical minutes and hours after an earthquake, however, knowledge of the earthquake source geometry limits the accuracy of these models, especially in areas where seismic instrumentation is insufficient to constrain the shaking intensity pattern. Previous attempts to overcome this limitation have centered on computing the mean distance metrics from a suite of assumed source geometries. That approach is inadequate with modern ground‐motion models (GMMs) because they typically include terms for the hanging wall effect, depth to top of rupture, and other nonlinear terms. Such approaches also propagate the distance uncertainty through the GMMs and may not properly allocate the additional uncertainty into the between‐ and within‐event components. Here we present Finite‐Fault SIMulation with Mixed Effects Regression (FFSIMMER), a method to address these limitations by computing IM distributions from a suite of rupture realizations that fully accounts for all geometry‐related GMM terms and allows for the separation of the between‐ and within‐event components of the total uncertainty. The accuracy of this method is limited by the available constraints on the source parameters. To address this, FFSIMMER can incorporate constraints based on knowledge of the source, such as the approximate strike and dip based on knowledge of the plate tectonics and focal mechanism of the earthquake. We demonstrate the improvement in accuracy that can be achieved with the 2025 M 7.7 Mandalay, Burma (Myanmar), earthquake by incorporating constraints on the range of plausible source parameters.

Bulletin of the Seismological Society of America↗

Orientation dependence of probabilistic seismic hazard estimates from CyberShake physics-based simulations

Earthquake ground‐motion intensities, such as pseudospectral accelerations (SAs), can vary significantly with horizontal orientation. However, conducting probabilistic seismic hazard analysis (PSHA) for each horizontal orientation is challenging because current ground‐motion models used in PSHA consider only a single horizontal intensity value, usually the median across all orientations, known as RotD50. To address this limitation, we employ physics‐based simulations for PSHA, which contain full waveforms from which ground‐motion intensities can be computed for all horizontal orientations to study directional seismic hazard. We apply our approach to the latest CyberShake study of the Greater Los Angeles metropolitan area, developed by the Statewide California Earthquake Center, finding that seismic hazard at a 2475‐yr return period, a common value used for earthquake‐resistant design, varies significantly with horizontal orientation. For instance, for SAs at 3 s, the maximum seismic hazard across all horizontal orientations is, on average, 15% higher than the median RotD50 hazard, with these differences becoming more pronounced at longer periods. These observed variations can generally be attributed to physical mechanisms that polarize seismic waves, such as the radiation pattern of the earthquake source and the influence of the subsurface structure. These results may have important implications for earthquake engineering applications, particularly for long‐period structures in areas with substantial horizontal variations in seismic hazard.

California↗

Detecting earthquakes in noisy real-time GNSS data with deep learning for improved PGD magnitude estimation

To disseminate accurate and useful warnings, earthquake early warning (EEW) systems must quickly determine the size and location of an earthquake to estimate expected shaking. Traditional seismic‐based algorithms tend to underestimate the true magnitudes of large earthquakes, a phenomenon known as magnitude saturation. This limitation motivated the recent inclusion of Global Navigation Satellite Systems (GNSS) data into the U.S. Geological Survey’s ShakeAlert EEW system with the Geodetic First Approximation of Size and Time (GFAST) algorithm because GNSS data do not saturate with large ground motions. However, the noise levels of GNSS data are very high compared with traditional seismic data, which obscures P ‐wave arrivals and can result in less accurate magnitude estimations if displacement amplitudes are low, such as for lower magnitude earthquakes or large source–station distances. In this study, we develop a deep‐learning model that detects earthquakes in GNSS data and use the Ridgecrest, California, earthquake sequence as a case study to demonstrate how the model could act as a filter to reduce the amount of low‐quality data that enters an algorithm like GFAST. To preserve our limited real earthquake data for model inference, we generated a training dataset composed of >700,000 synthetic displacement waveforms. We combined the synthetic waveforms with real‐time GNSS noise to produce realistically noisy training waveforms and then tested our model on additional synthetic data and performed inference using the real data that were held back. We discuss the performance of our trained model on both the unseen synthetic data and real inference data. Our model can be used to selectively filter only high‐quality data where an earthquake signal is observed for input into an algorithm like GFAST (outperforming a simple signal‐to‐noise ratio–based filter) to reduce the error in GFAST’s real‐time earthquake magnitude estimations.

California↗

How to determine an earthquake rate budget? A comparison of geodetic, geologic, and seismologic moment rates

How much tectonic geodetic strain is accommodated as earthquakes? Can estimates of tectonic geodetic strain be used in probabilistic seismic hazard analyses? Understanding the balance of moment accumulation (i.e., geodetic moment) and accommodation (i.e., geologic and seismologic moment) is a necessary step toward leveraging corrected geodetic strain rates to quantify earthquake budgets. We investigate these questions using updated geodetic, geologic, and seismologic datasets compiled for the western United States (WUS) portion of the 2023 U.S. National Seismic Hazard Model (NSHM23‐WUS) to provide new views of moment rates across the WUS. We compare moment rates using a floating footprint approach across the extent of the NSHM23‐WUS fault sections database. We make these comparisons using “moment rate deviation (MRD),” which is defined as a surplus or deficit of geodetic moment rate relative to the sum of geologic and seismologic moment rates. We find that, in general, higher strain rate areas of the WUS (i.e., plate boundary) have smaller values of MRD, meaning that geodetic moment rates approximate the earthquake record preserved by geologic and seismologic moment rates well. In contrast, the lower strain rate, eastern portions of our analysis domain (i.e., intraplate) have very high values of MRD, with geodetic moment rates exceeding measured geologic and seismologic moment rates. We find that geodetic moment rates appear to be representative of the earthquake budget in relatively well‐characterized, interplate regions, and geodetic estimates of off‐fault deformation could be considered in seismic hazard analyses where MRD is minimized.

western United States↗

ShakeAlert Earthquake Early Warning System performance during the Mw 7.0 offshore Cape Mendocino earthquake

The 5 December 2024 M w 7.0 Offshore Cape Mendocino earthquake was a challenging test of the U.S. West Coast ShakeAlert earthquake early warning system due to its offshore epicenter and limited near‐source station coverage. We analyzed real‐time performance of all components of the ShakeAlert system, including the seismic algorithms (earthquake point‐source integrated code [EPIC] and Finite‐fault rupture Detector [FinDer]), the geodetic algorithm (Geodetic First Approximation of Size and Time–peak ground displacement [GFAST‐PGD]), and network telemetry during the event. EPIC created the first solution for this earthquake 15 s after origin time with an initial magnitude estimate of M 5.6 and location error of 10 km from the Advanced National Seismic System epicenter. An early spurious trigger from station CE.89101 fortuitously maintained location accuracy and, correspondingly, magnitude accuracy. FinDer contributed its first solution at 18 s with a location estimate closer to the seismic network and produced two distinct rupture geometries, leading to minor fluctuations in estimated intensity contours. GFAST‐PGD did not meet alerting thresholds but otherwise performed as expected. Network latencies were <2 s for most stations, supporting the rapid detection of this earthquake by the system. Roughly five million alerts were delivered to cell phone devices in California and Oregon during this event. This was also the first instance of a school district‐wide ShakeAlert‐powered system being activated. Comparisons to recorded seismograms demonstrate that the maximum warning times before potentially damaging shaking (intensity 6+) were in the range of 5–55 s. Although the ShakeAlert system provided accurate solutions and useful alert delivery, this earthquake raised awareness of potential issues within the system, including the need for improved offshore location estimates, a combination of solutions from ShakeAlert servers, and handling of spurious triggers.

California↗

The potential impact of three-dimensional distributed slip models derived from real-time GNSS data on the performance of the ShakeAlert earthquake early warning system for slab interface earthquakes

The ShakeAlert® earthquake early warning (EEW) system is designed to warn users of imminent strong ground motion with sufficient time to take protective actions. ShakeAlert currently uses three algorithms to characterize the earthquake source. One estimates the location and magnitude using the first few seconds of the P wave and, while fast, tends to underestimate magnitude for M w 7.0+ earthquakes. A second estimates the location, orientation, length, and corresponding magnitude of a line source using observed peak ground acceleration and contributes primarily to M w 5.5+ earthquakes. The third infers earthquake magnitude from peak ground displacement measured using Global Navigation Satellite System (GNSS) data and offers nonsaturating magnitudes for M w 7.0+ earthquakes. Other EEW algorithms exist that infer temporally evolving spatially variable slip on a 3D fault surface from real‐time GNSS data, information that might enable more accurate and timely alerts in the event of large‐magnitude subduction interface earthquakes. Here, we evaluate the potential contribution of one such algorithm, BEFORES ( Minson et al. , 2014 ), to improve ShakeAlert performance through a simulated real‐time implementation of Bayesian evidence‐based fault orientation and real‐time earthquake slip (BEFORES) and other ShakeAlert algorithms using data for eight M w 7.6+ earthquakes. The test results demonstrate that BEFORES can produce well‐constrained and accurate magnitude estimates as soon as or sooner than other EEW algorithms, in turn enabling it to increase the amount of warning time users receive in many cases. However, with a modified Mercalli intensity (MMI) threshold of 3.5, which is commonly used for issuing alerts, BEFORES would tend to alert large geographic regions that did not feel strong shaking (MMI 6+). This effect can be mitigated using a higher alert threshold of MMI 4.5 without negative impact on the amount of warning time obtainable with BEFORES.

Bulletin of the Seismological Society of America↗

Temporal and spatial changes in seismic attenuation associated with inferred fluid migration in the 2016 central Apennines earthquake sequence

Prior work suggests that high‐frequency seismic attenuation acts as a highly sensitive proxy for crustal permeability and fluid mobility in fractured media. We test the hypothesis that the fault system responsible for the 2016–2017 Amatrice–Visso–Norcia–Capitignano sequence acted as an impermeable seal, compartmentalizing pressurized fluids until dynamic rupture triggered widespread fluid diffusion. By tracking across the sequence the spatiotemporal evolution of the S ‐wave anelastic attenuation parameter, we identify large, positive low‐frequency attenuation anomalies emerging within the hanging wall following the Amatrice mainshock and strictly preceding subsequent large ruptures. Conversely, we observe weaker, negative anomalies in the footwall, anticorrelated in time with those of the hanging wall, revealing a massive asymmetry in fluid redistribution and permeability evolution across the fault system. Furthermore, aftershock migration rates reveal distinct linear alignments in a distance‐reduced time space, allowing us to explicitly track and quantify episodes of lateral and upward fluid migration. These physically consistent patterns suggest that stress‐driven fluid diffusion directly weakens adjacent fault patches, dictating the spatiotemporal migration of seismicity. We conclude that near‐real‐time monitoring of seismic attenuation may help detect fluid redistribution in active fault systems and may provide useful information for time‐dependent seismic hazard assessment.

central Apennines↗

Simulation-based scenario ShakeMaps for large magnitude (MW6.5+) crustal earthquakes on the Seattle, Tacoma, and southern Whidbey Island faults, Washington, USA

Scenario ground‐motion maps based on empirical ground‐motion models (GMMs) provide a rapid and generally reliable means of estimating the amplitude and distribution of earthquake shaking. However, because GMMs are designed for broad applicability, they often rely on simplified representations of Earth structure, which can limit their accuracy in regions with complex source, path, and site effects. This can substantially impact the accuracy of predicted shaking in areas like western Washington State, where deep, interconnected basin structure exerts a strong influence on seismic‐wave propagation. In this study, we present a new suite of simulation‐based scenario ShakeMaps that characterize ground shaking from large‐magnitude ( ⁠ M W 6.5–7.5) earthquakes on the Seattle, Tacoma, and southern Whidbey Island faults. These maps are developed using results from recent 3D wave propagation simulations ( Stone et al. , 2022 , 2023 , 2025 ) that incorporate realistic rupture geometries, variable slip distributions, and a regional 3D seismic velocity model with shallow soils. Broadband ground motions are estimated by combining the low‐frequency (<1 Hz) deterministic seismograms from these studies with high‐frequency (1–10 Hz) stochastic seismograms. Simulated ground motions are corrected to account for the enforced minimum shear‐wave velocity and nonlinear site response. The resulting ShakeMaps represent median ground‐shaking estimates derived from multiple rupture scenarios with varying slip distributions and hypocenter locations for each fault. To extend ShakeMap coverage beyond the simulation domain (i.e., into eastern Washington, northern Oregon, and southwestern British Columbia), we scale GMM‐based ground‐motion estimates using amplification patterns observed in the simulations. These new ShakeMaps reveal the substantial influence of deep basin structure on shaking intensity, underscoring the importance of considering crustal structure complexity in regional hazard assessments for the Pacific Northwest.

Washington↗

Efficient physics‐informed ground‐motion simulations with reduced‐order models: CyberShake implications and high‐resolution site terms for southern San Andreas fault earthquakes

Recent advances in Probabilistic Seismic Hazard Analysis (PSHA) leverage physics‐based ground‐motion simulations to estimate seismic hazard, such as the CyberShake project. However, computational costs quickly escalate when performing PSHA for numerous faults or sites and can become prohibitively expensive. To reduce computational demands, CyberShake uses reciprocity and interpolates physics‐informed corrections from simulations conducted at fewer locations, but the accuracy of these interpolations remains poorly quantified. To quantify the interpolation accuracy, we derive high‐resolution, frequency‐dependent site terms for southern California and compare them with interpolated site terms using the CyberShake approach. We accomplish this by performing a set of earthquake point‐source simulations distributed along the nonplanar fault geometry for the southern San Andreas fault (SSAF) extending from Bombay Beach to Lake Hughes. Using SeisSol, we simulate three minutes of viscoelastic seismic wave propagation for these sources and store the horizontal‐component Green’s functions for 480,000 sites. We then use a scientific machine learning approach based on interpolated proper orthogonal decomposition to construct an accurate reduced‐order model of the Green’s functions to efficiently predict effective amplitude spectra (EAS) for finite‐source rupture models of SSAF earthquakes. Using minimum curvature interpolation with tension, as used in CyberShake, we compare the interpolated site terms against our high‐resolution site terms. We identify local discrepancies with EAS differing by up to a factor of approximately three. Furthermore, we identify locations where unexpectedly high or low ground motions are missed when using the interpolated dataset for these earthquakes. We estimate that our approach may be used within CyberShake to reduce the time‐to‐solution by a factor of 336 for the entire earthquake rupture forecast. Our analysis of physics‐based site terms provides more insight into the seismic hazard due to SSAF ruptures and guides future developments by combining high‐performance computing and reduced‐order modeling techniques for PSHA.

California↗

High‐resolution surface deformation and slip distribution observations for the 2023 Kahramanmaraş, Türkiye, earthquake sequence help constrain the rupture process

Splay, or branch, faults are a common geometric feature of earthquake surface ruptures and may provide constraints on the rupture behavior of an earthquake. The 2023 M w 7.8 Pazarcık and M w 7.5 Elbistan, Türkiye, earthquakes are examples of ruptures with multiple small splays, and the Pazarcık earthquake nucleated on a splay fault, the Narlı fault, before rupturing bilaterally on the East Anatolian fault (EAF). Here, we present 3‐m‐resolution surface displacement from subpixel correlation of Planet Dove optical images for the entirety of both ruptures with corresponding surface slip distributions. For a 30‐km‐long study region spanning the Narlı‐EAF intersection, we compare surface slip derived from five data sets with different resolutions (on‐the‐ground, WorldView, Planet Dove, Sentinel‐2, and Sentinel‐1) to elucidate complementary information. In addition, we integrate information from the surface expression of faulting with published dynamic rupture simulations and rupture process studies to constrain a rupture evolution for the Pazarcık earthquake that is consistent across data sets. This work highlights the complementary nature of disparate surface slip data sets and the role that high‐resolution surface displacement information, including from fault splays, can play in constraining nonunique rupture models and refining understanding of the earthquake rupture process.

Bulletin of the Seismological Society of America↗

Testing characteristic magnitude distributions in modern PSHA models

The characteristic magnitude distribution hypothesis predicts a higher rate of large earthquakes than a Gutenberg–Richter extrapolation of the small‐earthquake rate would imply. Characteristic magnitude distributions have been commonly applied to faults in probabilistic seismic hazard analysis (PSHA), and in modern models they can emerge from the way short‐term seismicity constraints are combined with long‐term geologic and geodetic constraints. We test the characteristic magnitude distribution hypothesis by comparing the fault‐based magnitude distributions from the 2023 update to the National Seismic Hazard Model (NSHM23) in the Western United States with observed seismicity over the past 93 yr. We find that observed magnitude distributions fall outside the model‐predicted confidence bounds in regions where NSHM23 produces characteristic magnitude distributions: in these regions, the model predicts higher rates of large earthquakes than are observed. An analysis of the earlier California model (Uniform California Earthquake Rupture Forecast, version 3) also reveals discrepancies between the modeled and observed magnitude distributions. In addition, we find that observed magnitude distributions near modeled faults are not significantly different from those in background regions. These results challenge the prevalence of characteristic magnitude distributions in fault‐based seismic hazard models and call for a reassessment of how disparate data sets are integrated in PSHA.

western United States↗

DevelNet: Earthquake detection on Develocorder films with deep learning: Application to the rangely earthquake control experiment

There exists over a century of instrumental seismic data; however, most seismograms recorded before the 1980s are only available in analog form. Although analog seismograms are of great value, they are underutilized due to the difficulties of making quantitative measurements on the original media and in converting them to digital time series. In this study, we present an alternative workflow, based on deep learning, to reconstruct an earthquake catalog from images of analog data without conversion to vector time series. We trained a convolutional neural network—DevelNet, using synthetic analog data to detect earthquakes on scanned multichannel Develocorder film images. We then developed an image‐based processing workflow to measure arrival times, locate, and determine the magnitudes of earthquakes in the data. We demonstrate the performance of this approach on two years of continuous Develocorder film recordings from the Rangely earthquake control experiment in the mid‐1970s. Our approach detects twice the number of events reported in the original catalog ( Raleigh et al. , 1976 ). This demonstrates that DevelNet efficiently detects earthquakes from Develocorder film scans, performs consistently over time, and is robust to changes in network geometry. Our locations generally agree with the original study, although the automatically measured arrival times are less precise than manual reading, leading to increased location scatter. Our automatic workflow of Develocorder films rivals the performance of skilled analysts in earthquake detection, but with minimal human intervention. This image‐based processing offers a new approach for effectively and efficiently extracting earthquake information from analog seismic data.

Bulletin of the Seismological Society of America↗

Earthquake of August 19, 1966, Varto Area, eastern Turkey

The earthquake of August 19, 1966, centered near Varto in eastern Turkey. It occurred at 12:22:09.6 G. M. T. and had a Richter magnitude of about 7. Intensities reached IX. Reportedly, 2,529 people were killed, 1,500 injured, and 19,013 buildings were demolished or heavily damaged. Surface fractures in three parallel fracture zones trending N65-70°W display both right-lateral strike slip and extension normal to the fractures. The trend and sense of displacement relate the fracturing to the North Anatolia fault system. Examples of geologic factors influencing damage include: (1) degree of saturation of the alluvium, (2) proximity to landslides, and (3) relation to surface faulting.

Near Varto in eastern Turkey↗

A method for estimating the uncertainty of seismic velocities measured by refraction techniques

Time residuals from 7 5-km segments of 18 crustal seismic-refraction profiles in the Basin and Range province are used to investigate the validity of the linear-regression model and to make large sample estimates of the variance in the travel time distributions. A formula for unbiased estimates of velocity uncertainty is derived, assuming a linear trend with distance for the variances of the travel-time distributions. If the recording units are symmetric about the center of the recording interval, this formula is equivalent to the one derived assuming the variances are equal. At the 95-per cent confidence level the chi-squared test implied 84 per cent of the time-residual samples were inconsistent with the hypothesis that their parent populations had Gaussian distributions. If the number of recording locations expceeds 8, confidence limits computed without the Gaussian assumption suggest the departures from normality are not significant for velocity uncertainty estimates. The large sample estimates of the time-residual populations may be applicable to other areas. This evidence motivated the development of a method, requiring very little numerical calculation, for estimating uncertainties in velocities. The method requires, in addition to the large sample estimates of the travel time variances, information on the quality of the data, the location of the recording interval, and the number of recording units. The method is useful for the design of new experiments and independent estimates of uncertainty reported in the literature.

Arizona, California, Idaho, Nevada, Oregon, Utah↗