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At least 793 records · Page 44Linked to original sources

USGS2006

Quantifying the uncertainty in site amplification modeling and its effects on site-specific seismic-hazard estimation in the upper Mississippi embayment and adjacent areas

The Mississippi embayment, located in the central United States, and its thick deposits of sediments (over 1 km in places) have a large effect on earthquake ground motions. Several previous studies have addressed how these thick sediments might modify probabilistic seismic-hazard maps. The high seismic hazard associated with the New Madrid seismic zone makes it particularly important to quantify the uncertainty in modeling site amplification to better represent earthquake hazard in seismic-hazard maps. The methodology of the Memphis urban seismic-hazard-mapping project (Cramer et al., 2004) is combined with the reference profile approach of Toro and Silva (2001) to better estimate seismic hazard in the Mississippi embayment. Improvements over previous approaches include using the 2002 national seismic-hazard model, fully probabilistic hazard calculations, calibration of site amplification with improved nonlinear soil-response estimates, and estimates of uncertainty. Comparisons are made with the results of several previous studies, and estimates of uncertainty inherent in site-amplification modeling for the upper Mississippi embayment are developed. I present new seismic-hazard maps for the upper Mississippi embayment with the effects of site geology incorporating these uncertainties.

Bulletin of the Seismological Society of America↗

USGS1990

Seismic site effects and the spatial interpolation of earthquake seismograms: Results using aftershocks of the 1986 North Palm Springs, California, earthquake

We address the following two questions. Can a microearthquake's ground motions be modeled by incident P and S waves that excite a site transfer-function that is a smooth function of incidence angle? Given recorded ground motions from a set of earthquakes having known locations and mechanisms, can we derive such a site transfer-function and use it to obtain the ground motions that would result from an earthquake source occurring somewhere in the same volume but having a location and mechanism that are different from the recorded events? Although many factors will cause two distinct microearthquake sources to have different seismograms at a common station, in this paper we concentrate only upon the differences caused by source mechanisms, P- and S-wave travel-time variations and by variations in the site transfer-function. We specifically exclude the effects of waves scattered from heterogeneities in the geologic structure away from the seismic site. We express the site transfer-function as a sum of several terms having simple dependences upon incidence angle and azimuth. Each term is an independent function of time. Given a set of seismograms observed at the site, we solve a linear system of equations for the time dependences of each term. These time series may be used to calculate the seismograms that would have resulted from an earthquake having arbitrary mechanism and location. This step is an interpolation. We have applied this technique to seismograms after aftershocks of the 1986 North Palm Springs earthquake. Our interpolation technique works fairly well within the volume occupied by the recorded events, but the method is not very successful at providing accurate seismograms for sources located outside the aftershock volume. The primary causes of the inaccuracy are the inadequacy of our chosen angular functions to model the site response fully and the likely scattering of seismic waves by geological heterogeneities (in this case, the Banning and Mission Creek faults) near the seismic stations. Our methods could be used to determine the effects of single scattering from lateral heterogeneities in geologic structure.

California↗

USGS1998

Use of fault striations and dislocation models to infer tectonic shear stress during the 1995 Hyogo-Ken Nanbu (Kobe) earthquake

Dislocation models of the 1995 Hyogo-ken Nanbu (Kobe) earthquake derived by Yoshida et al. (1996) show substantial changes in direction of slip with time at specific points on the Nojima and Rokko fault systems, as do striations we observed on exposures of the Nojima fault surface on Awaji Island. Spudich (1992) showed that the initial stress, that is, the shear traction on the fault before the earthquake origin time, can be derived at points on the fault where the slip rake rotates with time if slip velocity and stress change are known at these points. From Yoshida's slip model, we calculated dynamic stress changes on the ruptured fault surfaces. To estimate errors, we compared the slip velocities and dynamic stress changes of several published models of the earthquake. The differences between these models had an exponential distribution, not gaussian. We developed a Bayesian method to estimate the probability density function (PDF) of initial stress from the striations and from Yoshida's slip model. Striations near Toshima and Hirabayashi give initial stresses of about 13 and 7 MPa, respectively. We obtained initial stresses of about 7 to 17 MPa at depths of 2 to 10 km on a subset of points on the Nojima and Rokko fault systems. Our initial stresses and coseismic stress changes agree well with postearthquake stresses measured by hydrofracturing in deep boreholes near Hirabayashi and Ogura on Awaji Island. Our results indicate that the Nojima fault slipped at very low shear stress, and fractional stress drop was complete near the surface and about 32% below depths of 2 km. Our results at depth depend on the accuracy of the rake rotations in Yoshida's model, which are probably correct on the Nojima fault but debatable on the Rokko fault. Our results imply that curved or cross-cutting fault striations can be formed in a single earthquake, contradicting a common assumption of structural geology.

Bulletin of the Seismological Society of America↗

USGS2019

Combining dynamic rupture simulations with ground motion data to characterize seismic hazard from Mw 3-5.8 earthquakes in Oklahoma and Kansas

Many seismically active areas suffer from a lack of near‐source ground‐motion recordings, making ground‐motion prediction difficult at distances within ∼ 40    km "> ∼ 40 km ∼40 km from an earthquake. We aim to aid the development of near‐source ground‐motion prediction equations (GMPEs) by generating synthetic ground‐motion data via simulation. Building on previous work using point‐source moment tensor sources to simulate small ( ⁠ M w "> M w Mw 3–4) earthquakes for a target region encompassing north central Oklahoma and south central Kansas, we perform dynamic rupture simulations of earthquakes up to M w "> M w Mw 5.8. We introduce complexity into the rupture process by adding stochastically generated heterogeneity to initial stress conditions. Our simulated ground‐motion data are added to a catalog of recorded ground‐motion data to construct a composite recorded‐simulated ground‐motion catalog that we use to develop a GMPE for the target region. This procedure can be generalized and used for GMPE development in other regions with near‐source ground‐motion data scarcity, which could directly benefit critical applications such as the National Seismic Hazard Maps produced by the U.S. Geological Survey (USGS).

Kansas, Oklahoma↗

USGS1988

Elastic-wave propagation and site amplification in the Salt Lake Valley, Utah, from simulated normal faulting earthquakes

The two-dimensional seismic response of the Salt Lake valley to near- and far-field earthquakes has been investigated from simulations of vertically incident plane waves and from normal-faulting earthquakes generated on the basin-bounding Wasatch fault. The response to normal faulting earthquakes was simulated using a two-dimensional finite-element method and the plane-wave response was calculated from two-dimensional finite-difference simulations. The plane-wave simulations were then compared with observed site amplifications in the Salt Lake valley, based on seismic recordings from nuclear explosions in southern Nevada, that show 10 times greater amplification within the basin than measured values on hard-rock sites. While previous studies attribute this increased site amplification to the near-surface unconsolidated/consolidated alluvial fill contact, our synthetic seismograms suggest that in the frequency band 0.3 to 1.5 Hz at least one-half the site amplification can be attributed to the impedance contrast between the basin sediments and higher velocity basement rocks. Synthetic seismograms from vertically incident plane-wave sources and buried double-couple sources predict large amplitude Rayleigh-wave propagation from the edges of the basin and, in general, uniform site amplification. In contrast, near-field simulations of basin-bounding, normal-faulting earthquakes predict large-amplitude Rayleigh waves propagating westward from the fault across the basin. Spectra of synthetic accelerograms computed from the normal-faulting earthquakes shows that spectral amplification within the basin is primarily due to source directivity with a maxima near the surface projection of the fault that decays rapidly away from the fault. Importantly, the synthetic modeling of near-field earthquake sources show that near-field directivity effects are important and should be considered in an earthquake hazard assessment of the Salt Lake valley and similar geologic settings along the Wasatch Front.

Utah↗

USGS1994

Some observations of landslides triggered by the 29 April 1991 Racha earthquake, Republic of Georgia

On 29 April 1991 an M s 7.0 earthquake occurred in the Racha region of the Great Caucasus Mountains in north-central Republic of Georgia. The earthquake occurred on a thrust fault striking roughly east-west and dipping about 20° to 45° northward; focal depth was 17 ± 2 km. We observed no surface fault rupture, but the earthquake caused extensive structural damage to the many unreinforced stone buildings in the area, and at least 114 people were killed. Many landslides were triggered in a 2500-km 2 epicentral area, and they caused much of the structural damage and at least half the fatalities. We observed the following six types of landslides (in order of decreasing abundance): rock falls, debris slides, slumps, earth slides, rock block slides, and rock avalanches. The types of landslides triggered by the earthquake are controlled primarily by lithology and geologic structure. Enigmatic landslide processes associated with this earthquake include (1) delays of several days between earthquake shaking and significant landslide movement, probably caused by changes in groundwater conditions; (2) small co-seismic displacement of landslides active at the time of the earthquake, a possible result of viscoplastic damping of the seismic shaking; and (3) somewhat unusual failure geometries related to local topography and geologic structure.

Bulletin of the Seismological Society of America↗

USGS1978

Clarence Allen talks about the responsibilities in earthquake prediction

Dr. Clarence R. Allen is professor of geology and geophysics at the California Institute of Technology. He has been a member of advisory panels to the Executive Office of the President, National Academy of Sciences, National Science Foundation, U.S Geological Survey, UNESCO, California State Mining and Geology Board, and the California Department of Water Resources. Dr. Allen has been President of both the Geological Society of America and the Seismological Society of America (SSA). The title of this interview is based on his presidential address to the SSA in 1976.

Earthquake Information Bulletin (USGS)↗

USGS2020

Spectral inversion for seismic site response in central Oklahoma: Low-frequency resonances from the Great Unconformity

We investigate seismic site response by inverting seismic ground‐motion spectra for site and source spectral properties, in a region of central Oklahoma, where previous ground‐motion studies have indicated discrepancies between observations and ground‐motion models (GMMs). The inversion is constrained by a source spectral model, which we computed from regional seismic records, using aftershocks as empirical Green’s functions to deconvolve site and path effects. Site spectra across the region exhibit multiple, strong, low‐frequency ( ⁠ f <2 Hz ⁠ ) resonances. Modeling of vertically propagating SH waves reproduces the mean amplitudes and frequencies of the site spectra and requires a deep ( ⁠ ∼1–2 km ⁠ ) impedance contrast. Comparison of regional seismic velocity models and geologic profiles indicates that the seismic impedance contrast is, or is in proximity to, the Great Unconformity, which marks the interface between Precambrian basement rocks and overlying Paleozoic sedimentary rocks. Depth to Precambrian basement increases to the southwest across the study region ( ⁠ ∼1500–4500 m ⁠ ), and the fundamental frequencies of the site spectra are anticorrelated with basement depth. The first higher‐mode resonance also exhibits dependence on basement depth; although modeling suggests that the second higher mode should depend on basement depth, site spectra do not support this. The low‐frequency resonances in central Oklahoma are not represented in the GMMs used in current seismic hazard analyses for tectonic earthquakes, though approaches to account for such features are under consideration in other regions of the central and eastern United States. Given the broad spatial extent of the Great Unconformity underlying eastern North America, it is likely that similar effects on seismic site response also occur in other areas. This study highlights the impact of regional geologic structure on earthquake ground motions and reiterates the need for modeling regional effects to improve ground‐motion predictions and seismic hazard assessments.

Oklahoma↗

USGS2005

Empirical relations between elastic wavespeeds and density in the Earth's crust

A compilation of compressional-wave (Vp) and shear-wave (Vs) velocities and densities for a wide variety of common lithologies is used to define new nonlinear, multivalued, and quantitative relations between these properties for the Earth's crust. Wireline borehole logs, vertical seismic profiles, laboratory measurements, and seismic tomography models provide a diverse dataset for deriving empirical relations between crustal Vp and Vs. The proposed Vs as a function of Vp relations fit Vs and Vp borehole logs in Quaternary alluvium and Salinian granites as well as laboratory measurements over a 7-km/sec-wide range in Vp. The relations derived here are very close to those used to develop a regional 3D velocity model for southern California, based on pre-1970 data, and thus provide support for that model. These data, and these relations, show a rapid increase in Vs as Vp increases to 3.5 km/sec leading to higher shear-wave velocities in young sedimentary deposits than commonly assumed. These relations, appropriate for active continental margins where earthquakes are prone to occur, suggests that amplification of strong ground motions by shallow geologic deposits may not be as large as predicted by some earlier models.

Bulletin of the Seismological Society of America↗

USGS2022

Shallow faulting and folding in the epicentral area of the 1886 Charleston, South Carolina, earthquake

The moment magnitude ( ⁠ M w "> M w �w ⁠ ) ∼7 earthquake that struck Charleston, South Carolina, on 31 August 1886 is the largest historical earthquake in the United States east of the Appalachian Mountains. The fault(s) that ruptured during this earthquake has never been conclusively identified, and conflicting fault models have been proposed. Here we interpret reprocessed seismic reflection profiles, reprocessed legacy aeromagnetic data, and newly collected ground penetrating radar (GPR) profiles to delineate faults deforming the Cretaceous and younger Atlantic Coastal Plain (ACP) strata in the epicentral area of the 1886 earthquake. The data show evidence for faults folding or vertically displacing ACP strata, including apparent displacements of near‐surface strata (upper ∼20 m). Aeromagnetic data show several northeast (NE)‐trending lineaments, two of which correlate with faults and folds with vertical displacements as great as 55 m on the seismic reflection and radar profiles. ACP strata show only minor thickness changes across these structures, indicating that much of the displacement postdates the shallowest well‐imaged ACP strata of Eocene age. Faults imaged on the seismic reflection profiles appear on GPR profiles to displace the erosional surface at the top of the upper Eocene to Oligocene Cooper Group, including where railroad tracks were bent during the 1886 earthquake. Some faults coincide with changes in river trends, bifurcations of river channels, and unusual river meanders that could be related to recent fault motion. In contrast to our interpreted NE fault trends, earthquake locations and some focal mechanisms in the modern seismic zone have been interpreted as defining a nearly north‐striking, west‐dipping zone of aftershocks from the 1886 earthquake. The relationship between the modern seismicity and the faults we image is therefore enigmatic. However, multiple faults in the area clearly have been active since the Eocene and deform strata in the upper 20 m, providing potential targets for field‐based geologic investigations.

South Carolina↗

USGS2009

Effect of time dependence on probabilistic seismic-hazard maps and deaggregation for the central Apennines, Italy

We produce probabilistic seismic-hazard assessments for the central Apennines, Italy, using time-dependent models that are characterized using a Brownian passage time recurrence model. Using aperiodicity parameters, ?? of 0.3, 0.5, and 0.7, we examine the sensitivity of the probabilistic ground motion and its deaggregation to these parameters. For the seismic source model we incorporate both smoothed historical seismicity over the area and geological information on faults. We use the maximum magnitude model for the fault sources together with a uniform probability of rupture along the fault (floating fault model) to model fictitious faults to account for earthquakes that cannot be correlated with known geologic structural segmentation.

Bulletin of the Seismological Society of America↗

USGS2004

Observed and simulated ground motions in the San Bernardino basin region for the Hector Mine, California, earthquake

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

California↗

USGS2005

Coal-mining seismicity and ground-shaking hazard: A case study in the Trail Mountain area, Emery County, Utah

We describe a multipart study to quantify the potential ground-shaking hazard to Joes Valley Dam, a 58-m-high earthfill dam, posed by mining-induced seismicity (MIS) from future underground coal mining, which could approach as close as ???1 km to the dam. To characterize future MIS close to the dam, we studied MIS located ???3-7 km from the dam at the Trail Mountain coal mine. A 12-station local seismic network (11 stations above ground, one below, combining eight triaxial accelerometers and varied velocity sensors) was operated in the Trail Mountain area from late 2000 through mid-2001 for the dual purpose of (1) continuously monitoring and locating MIS associated with longwall mining at a depth of 0.5-0.6 km and (2) recording high-quality data to develop ground-motion prediction equations for the shallow MIS. (Ground-motion attenuation relationships and moment-tensor results are reported in companion articles.) Utilizing a data set of 1913 earthquakes (M ??? 2.2), we describe space-time-magnitude distributions of the observed MIS and source-mechanism information. The MIS was highly correlated with mining activity both in space and time. Most of the better-located events have depths constrained within ??0.6 km of mine level. For the preponderance (98%) of the 1913 located events, only dilatational P-wave first motions were observed, consistent with other evidence for implosive or collapse-type mechanisms associated with coal mining in this region. We assess a probable maximum magnitude of M 3.9 (84th percentile of a cumulative distribution) for potential MIS close to Joes Valley Dam based on both the worldwide and regional record of coal-mining-related MIS and the local geology and future mining scenarios.

Bulletin of the Seismological Society of America↗

USGS2021

Evaluating spectral ratio methods for characterizing fundamental resonance peaks on flat sediments: An example from the Atlantic Coastal Plain, Eastern United States

Damaging ground motions from the 2011 M w "> M w 5.8 Virginia earthquake were likely increased due to site amplification from the unconsolidated sediments of the Atlantic Coastal Plain (ACP), highlighting the need to understand site response on these widespread strata along the coastal regions of the eastern United States. The horizontal‐to‐vertical spectral ratio (HVSR) method, using either earthquake signals or ambient noise as input, offers an appealing method for measuring site response on laterally extensive sediments, because it requires a single seismometer rather than requiring a nearby bedrock site to compute a horizontal sediment‐to‐bedrock spectral ratio (SBSR). Although previous studies show mixed results when comparing the two methods, the majority of these studies investigated site responses in confined sedimentary basins that can generate substantial 3D effects or have relatively small reflection coefficients at their base. In contrast, the flat‐lying ACP strata and the underlying bedrock reflector should cause 1D resonance effects to dominate site response, with amplification of the fundamental resonance peaks controlled by the strong impedance contrast between the base of the sediments and the underlying bedrock. We compare site‐response estimates on the ACP strata derived using the HVSR and SBSR methods from teleseismic signals recorded by regional arrays and observe a close match in the frequencies of the fundamental resonance peak ( ⁠ f 0 "> f 0 ⁠ ) determined by both methods. We find that correcting the HVSR amplitude using source term information from a bedrock site and multiplying the peak by a factor of 1.2 results in amplitude peaks that, on average, match SBSR results within a factor of 2. We therefore conclude that the HVSR method may successfully estimate regional linear weak‐motion site‐response amplifications from the ACP, or similar geologic environments, when appropriate region‐specific corrections to the amplitude ratios are used.

Atlantic Coastal Plain↗

USGS2005

Liquefaction at Oceano, California, during the 2003 San Simeon earthquake

The 2003 M 6.5 San Simeon, California, earthquake caused liquefaction-induced lateral spreading at Oceano at an unexpectedly large distance from the seismogenic rupture. We conclude that the liquefaction was caused by ground motion that was enhanced by both rupture directivity in the mainshock and local site amplification by unconsolidated fine-grained deposits. Liquefaction occurred in sandy artificial fill and undisturbed eolian sand and fluvial deposits. The largest and most damaging lateral spread was caused by liquefaction of artificial fill; the head of this lateral spread coincided with the boundary between the artificial fill and undisturbed eolian sand deposits. Values of the liquefaction potential index, in general, were greater than 5 at liquefaction sites, the threshold value that has been proposed for liquefaction hazard mapping. Although the mainshock ground motion at Oceano was not recorded, peak ground acceleration was estimated to range from 0.25 and 0.28g on the basis of the liquefaction potential index and aftershock recordings. The estimates fall within the range of peak ground acceleration values associated with the modified Mercalli intensity = VII reported at the U.S. Geological Survey (USGS) "Did You Feel It?" web site.

Bulletin of the Seismological Society of America↗

USGS2012

Estimating pole/zero errors in GSN-IRIS/USGS network calibration metadata

Mapping the digital record of a seismograph into true ground motion requires the correction of the data by some description of the instrument's response. For the Global Seismographic Network (Butler et al., 2004), as well as many other networks, this instrument response is represented as a Laplace domain pole–zero model and published in the Standard for the Exchange of Earthquake Data (SEED) format. This Laplace representation assumes that the seismometer behaves as a linear system, with any abrupt changes described adequately via multiple time-invariant epochs. The SEED format allows for published instrument response errors as well, but these typically have not been estimated or provided to users. We present an iterative three-step method to estimate the instrument response parameters (poles and zeros) and their associated errors using random calibration signals. First, we solve a coarse nonlinear inverse problem using a least-squares grid search to yield a first approximation to the solution. This approach reduces the likelihood of poorly estimated parameters (a local-minimum solution) caused by noise in the calibration records and enhances algorithm convergence. Second, we iteratively solve a nonlinear parameter estimation problem to obtain the least-squares best-fit Laplace pole–zero–gain model. Third, by applying the central limit theorem, we estimate the errors in this pole–zero model by solving the inverse problem at each frequency in a two-thirds octave band centered at each best-fit pole–zero frequency. This procedure yields error estimates of the 99% confidence interval. We demonstrate the method by applying it to a number of recent Incorporated Research Institutions in Seismology/United States Geological Survey (IRIS/USGS) network calibrations (network code IU).

Bulletin of the Seismological Society of America↗

USGS2009

Earthquake stress drops and inferred fault strength on the Hayward Fault, east San Francisco Bay, California

We study variations in earthquake stress drop with respect to depth, faulting regime, creeping versus locked fault behavior, and wall-rock geology. We use the P-wave displacement spectra from borehole seismic recordings of M 1.0-4.2 earthquakes in the east San Francisco Bay to estimate stress drop using a stack-and-invert empirical Green's function method. The median stress drop is 8.7 MPa, and most stress drops are in the range between 0.4 and 130 MPa. An apparent correlation between stress drop and magnitude is entirely an artifact of the limited frequency band of 4-55 Hz. There is a trend of increasing stress drop with depth, with a median stress drop of ~5 MPa for 1-7 km depth, ~10 MPa for 7-13 km depth, and ~50 MPa deeper than 13 km. We use S=P amplitude ratios measured from the borehole records to better constrain the first-motion focal mechanisms. High stress drops are observed for a deep cluster of thrust-faulting earthquakes. The correlation of stress drops with depth and faulting regime implies that stress drop is related to the applied shear stress. We compare the spatial distribution of stress drops on the Hayward fault to a model of creeping versus locked behavior of the fault and find that high stress drops are concentrated around the major locked patch near Oakland. This also suggests a connection between stress drop and applied shear stress, as the locked patch may experience higher applied shear stress as a result of the difference in cumulative slip or the presence of higher-strength material. The stress drops do not directly correlate with the strength of the proposed wall-rock geology at depth, suggesting that the relationship between fault strength and the strength of the wall rock is complex.

Bulletin of the Seismological Society of America↗

USGS2013

Conditional spectrum computation incorporating multiple causal earthquakes and ground-motion prediction models

The conditional spectrum (CS) is a target spectrum (with conditional mean and conditional standard deviation) that links seismic hazard information with ground-motion selection for nonlinear dynamic analysis. Probabilistic seismic hazard analysis (PSHA) estimates the ground-motion hazard by incorporating the aleatory uncertainties in all earthquake scenarios and resulting ground motions, as well as the epistemic uncertainties in ground-motion prediction models (GMPMs) and seismic source models. Typical CS calculations to date are produced for a single earthquake scenario using a single GMPM, but more precise use requires consideration of at least multiple causal earthquakes and multiple GMPMs that are often considered in a PSHA computation. This paper presents the mathematics underlying these more precise CS calculations. Despite requiring more effort to compute than approximate calculations using a single causal earthquake and GMPM, the proposed approach produces an exact output that has a theoretical basis. To demonstrate the results of this approach and compare the exact and approximate calculations, several example calculations are performed for real sites in the western United States. The results also provide some insights regarding the circumstances under which approximate results are likely to closely match more exact results. To facilitate these more precise calculations for real applications, the exact CS calculations can now be performed for real sites in the United States using new deaggregation features in the U.S. Geological Survey hazard mapping tools. Details regarding this implementation are discussed in this paper.

Bulletin of the Seismological Society of America↗