Geology Reports⌕ Search

Geology topics

A. Frankel

Publications and source records attributed to A. Frankel.

At least 19 recordsLinked to original sources
USGS2012

High-frequency spectral falloff of earthquakes, fractal dimension of complex rupture, b value, and the scaling of strength on faults

The high-frequency falloff ω −γ of earthquake displacement spectra and the b value of aftershock sequences are attributed to the character of spatially varying strength along fault zones. I assume that the high frequency energy of a main shock is produced by a self-similar distribution of subevents, where the number of subevents with radii greater than R is proportional to R −D , D being the fractal dimension. In this model, an earthquake is composed of a hierarchical set of smaller earthquakes. The static stress drop is parameterized to be proportional to R η , and strength is assumed to be proportional to static stress drop. I find that a distribution of subevents with D = 2 and stress drop independent of seismic moment (η = 0) produces a main shock with an ω −2 falloff, if the subevent areas fill the rupture area of the main shock. By equating subevents to “islands” of high stress of a random, self-similar stress field on a fault, I relate D to the scaling of strength on a fault, such that D = 2 − η. Thus D = 2 corresponds to constant stress drop scaling (η = 0) and scale-invariant fault strength. A self-similar model of aftershock rupture zones on a fault is used to determine the relationship between the b value, the size distribution of aftershock rupture zones, and the scaling of strength on a fault. The b value for aftershock sequences on a fault is found to equal (3 − 1.5η)/(3 + η). Therefore this model indicates that the typically observed spectral falloffs of ω −2 and b values of 1 can be entirely caused by scale-invariant strength (η = 0) along fault zones.

Journal of Geophysical Research↗
USGS2012

Frequency-dependent attenuation of the Hispaniola Island region of the Caribbean Sea

We determine frequency-dependent attenuation 1/Q( f ) for the Hispaniola region using direct S and Lg waves over five distinct passbands from 0.5 to 16 Hz. Data consist of 832 high-quality vertical and horizontal component waveforms recorded on short-period and broadband seismometers from the devastating 12 January 2010 M 7.0 Haiti earthquake and the rich sequence of aftershocks. For the distance range 250–700 km, we estimate an average frequency-dependent Q( f )=224(±27) f 0.64(±0.073) using horizontal components of motion and note that Q( f ) estimated with Lg at regional distances is very consistent across vertical and horizontal components. We also determine a Q( f )=142(±21) f 0.71(±0.11) for direct S waves at local distances, ≤100 km. The strong attenuation observed on both vertical and horizontal components of motion is consistent with expectations for a tectonically active region.

Bulletin of the Seismological Society of America↗
USGS2010

Effects of 3D random correlated velocity perturbations on predicted ground motions

Three-dimensional, finite-difference simulations of a realistic finite-fault rupture on the southern Hayward fault are used to evaluate the effects of random, correlated velocity perturbations on predicted ground motions. Velocity perturbations are added to a three-dimensional (3D) regional seismic velocity model of the San Francisco Bay Area using a 3D von Karman random medium. Velocity correlation lengths of 5 and 10 km and standard deviations in the velocity of 5% and 10% are considered. The results show that significant deviations in predicted ground velocities are seen in the calculated frequency range (≤1 Hz) for standard deviations in velocity of 5% to 10%. These results have implications for the practical limits on the accuracy of scenario ground-motion calculations and on retrieval of source parameters using higher-frequency, strong-motion data.

Bulletin of the Seismological Society of America↗
USGS2009

A constant stress-drop model for producing broadband synthetic seismograms: Comparison with the next generation attenuation relations

Broadband (0.1-20 Hz) synthetic seismograms for finite-fault sources were produced for a model where stress drop is constant with seismic moment to see if they can match the magnitude dependence and distance decay of response spectral amplitudes found in the Next Generation Attenuation (NGA) relations recently developed from strong-motion data of crustal earthquakes in tectonically active regions. The broadband synthetics were constructed for earthquakes of M 5.5, 6.5, and 7.5 by combining deterministic synthetics for plane-layered models at low frequencies with stochastic synthetics at high frequencies. The stochastic portion used a source model where the Brune stress drop of 100 bars is constant with seismic moment. The deterministic synthetics were calculated using an average slip velocity, and hence, dynamic stress drop, on the fault that is uniform with magnitude. One novel aspect of this procedure is that the transition frequency between the deterministic and stochastic portions varied with magnitude, so that the transition frequency is inversely related to the rise time of slip on the fault. The spectral accelerations at 0.2, 1.0, and 3.0 sec periods from the synthetics generally agreed with those from the set of NGA relations for M 5.5-7.5 for distances of 2-100 km. At distances of 100-200 km some of the NGA relations for 0.2 sec spectral acceleration were substantially larger than the values of the synthetics for M 7.5 and M 6.5 earthquakes because these relations do not have a term accounting for Q. At 3 and 5 sec periods, the synthetics for M 7.5 earthquakes generally had larger spectral accelerations than the NGA relations, although there was large scatter in the results from the synthetics. The synthetics showed a sag in response spectra at close-in distances for M 5.5 between 0.3 and 0.7 sec that is not predicted from the NGA relations.

Bulletin of the Seismological Society of America↗
USGS2006

Modeling and validation of a 3D velocity structure for the Santa Clara Valley, California, for seismic-wave simulations

A 3D seismic velocity and attenuation model is developed for Santa Clara Valley, California, and its surrounding uplands to predict ground motions from scenario earthquakes. The model is developed using a variety of geologic and geophysical data. Our starting point is a 3D geologic model developed primarily from geologic mapping and gravity and magnetic surveys. An initial velocity model is constructed by using seismic velocities from boreholes, reflection/refraction lines, and spatial autocorrelation microtremor surveys. This model is further refined and the seismic attenuation is estimated through waveform modeling of weak motions from small local events and strong-ground motion from the 1989 Loma Prieta earthquake. Waveforms are calculated to an upper frequency of 1 Hz using a parallelized finite-difference code that utilizes two regions with a factor of 3 difference in grid spacing to reduce memory requirements. Cenozoic basins trap and strongly amplify ground motions. This effect is particularly strong in the Evergreen Basin on the northeastern side of the Santa Clara Valley, where the steeply dipping Silver Creek fault forms the southwestern boundary of the basin. In comparison, the Cupertino Basin on the southwestern side of the valley has a more moderate response, which is attributed to a greater age and velocity of the Cenozoic fill. Surface waves play a major role in the ground motion of sedimentary basins, and they are seen to strongly develop along the western margins of the Santa Clara Valley for our simulation of the Loma Prieta earthquake.

California↗
USGS2004

Rupture process of the M 7.9 Denali fault, Alaska, earthquake: Subevents, directivity, and scaling of high-frequency ground motions

Displacement waveforms and high-frequency acceleration envelopes from stations at distances of 3-300 km were inverted to determine the source process of the M 7.9 Denali fault earthquake. Fitting the initial portion of the displacement waveforms indicates that the earthquake started with an oblique thrust subevent (subevent # 1) with an east-west-striking, north-dipping nodal plane consistent with the observed surface rupture on the Susitna Glacier fault. Inversion of the remainder of the waveforms (0.02-0.5 Hz) for moment release along the Denali and Totschunda faults shows that rupture proceeded eastward on the Denali fault, with two strike-slip subevents (numbers 2 and 3) centered about 90 and 210 km east of the hypocenter. Subevent 2 was located across from the station at PS 10 (Trans-Alaska Pipeline Pump Station #10) and was very localized in space and time. Subevent 3 extended from 160 to 230 km east of the hypocenter and had the largest moment of the subevents. Based on the timing between subevent 2 and the east end of subevent 3, an average rupture velocity of 3.5 km/sec, close to the shear wave velocity at the average rupture depth, was found. However, the portion of the rupture 130-220 km east of the epicenter appears to have an effective rupture velocity of about 5.0 km/ sec, which is supershear. These two subevents correspond approximately to areas of large surface offsets observed after the earthquake. Using waveforms of the M 6.7 Nenana Mountain earthquake as empirical Green's functions, the high-frequency (1-10 Hz) envelopes of the M 7.9 earthquake were inverted to determine the location of high-frequency energy release along the faults. The initial thrust subevent produced the largest high-frequency energy release per unit fault length. The high-frequency envelopes and acceleration spectra (>0.5 Hz) of the M 7.9 earthquake can be simulated by chaining together rupture zones of the M 6.7 earthquake over distances from 30 to 180 km east of the hypocenter. However, the inversion indicates that there was relatively little high-frequency energy generated along the 60-km portion of the Totschunda fault on the east end of the rupture.

Alaska↗
USGS2002

Simulation of broadband ground motion including nonlinear soil effects for a magnitude 6.5 earthquake on the Seattle fault, Seattle, Washington

The Seattle fault poses a significant seismic hazard to the city of Seattle, Washington. A hybrid, low-frequency, high-frequency method is used to calculate broadband (0-20 Hz) ground-motion time histories for a M 6.5 earthquake on the Seattle fault. Low frequencies (1 Hz) are calculated by a stochastic method that uses a fractal subevent size distribution to give an ω -2 displacement spectrum. Time histories are calculated for a grid of stations and then corrected for the local site response using a classification scheme based on the surficial geology. Average shear-wave velocity profiles are developed for six surficial geologic units: artificial fill, modified land, Esperance sand, Lawton clay, till, and Tertiary sandstone. These profiles together with other soil parameters are used to compare linear, equivalent-linear, and nonlinear predictions of ground motion in the frequency band 0-15 Hz. Linear site-response corrections are found to yield unreasonably large ground motions. Equivalent-linear and nonlinear calculations give peak values similar to the 1994 Northridge, California, earthquake and those predicted by regression relationships. Ground-motion variance is estimated for (1) randomization of the velocity profiles, (2) variation in source parameters, and (3) choice of nonlinear model. Within the limits of the models tested, the results are found to be most sensitive to the nonlinear model and soil parameters, notably the over consolidation ratio.

Washington↗
USGS2001

Geographic deaggregation of seismic hazard in the United States

The seismic hazard calculations for the 1996 national seismic hazard maps have been geographically deaggregated to assist in the understanding of the relative contributions of sources. These deaggregations are exhibited as maps with vertical bars whose heights are proportional to the contribution that each geographical cell makes to the ground-motion exceedance hazard. Bar colors correspond to average source magnitudes. We also extend the deaggregation analysis reported in Harmsen et al. (1999) to the western conterminous United States. In contrast to the central and eastern United States (CEUS); the influence of specific faults or characteristic events can be clearly identified. Geographic deaggregation for 0.2-sec and 1.0-sec pseudo spectral acceleration (SA) is performed for 10% probability of exceedance (PE) in 50 yr (475-yr mean return period) and 2% PE in 50 yr (2475-yr mean return period) for four western U.S. cities, Los Angeles, Salt Lake City, San Francisco, and Seattle, and for three central and eastern U.S. cities, Atlanta, Boston, and Saint Louis. In general, as the PE is lowered, the sources of hazard closer to the site dominate. Larger, more distant earthquakes contribute more significantly to hazard for 1.0-sec SA than for 0.2-sec SA. Additional maps of geographically deaggregated seismic hazard are available on the Internet for 120 cities in the conterminous United States (http://geohazards. cr.usgs.gov/eq/) for 1-sec SA and for 0.2-sec SA with a 2% PE in 50 yr. Examination of these maps of hazard contributions enables the investigator to determine the distance and azimuth to predominant sources, and their magnitudes. This information can be used to generate scenario earthquakes and corresponding time histories for seismic design and retrofit. Where fault density is lower than deaggregation cell dimensions, we can identify specific faults that contribute significantly to the seismic hazard at a given site. Detailed fault information enables investigators to include rupture information such as source directivity, radiation pattern, and basin-edge effects into their scenario earthquakes used in engineering analyses.

Bulletin of the Seismological Society of America↗
USGS2001

Observations of basin ground motions from a dense seismic array in San Jose, California

We installed a dense array of 41 digital seismographs in San Jose, California, to evaluate in detail the effects of a deep sedimentary basin and shallow sedimentary deposits on earthquake ground motions. This urban array is located near the eastern edge of the Santa Clara Valley and spans the Evergreen sedimentary basin identified by gravity data. Average station spacing is 1 km, with three stations initially spaced 110 m apart. Despite the high-noise urban environment, the stations of the array successfully triggered on and recorded small local earthquakes (M 2.5-2.8 at 10-25 km distance) and larger regional events such as the M 5.0 Bolinas earthquake (90 km distance), M 4.6-5.6 earthquakes near Mammoth Lakes (270 km distance), M 4.9-5.6 events in western Nevada (420 km distance) and the M 7.1 Hector Mine earthquake (590 km distance). Maps of spectral ratios across the array show that the highest amplitudes in all frequency bands studied (0.125-8 Hz) are generally observed at stations farther from the eastern edge of the Santa Clara Valley. Larger spectral amplitudes are often observed above the western edge of the Evergreen Basin. Snapshots of the recorded wavefield crossing the array for regional events to the east reveal that large, low-frequency (0.125-0.5 Hz) arrivals after the S-wave travel from south to north across the array. A moving-window, cross-correlation analysis finds that these later arrivals are surface waves traveling from the south. The timing and propagation direction of these arrivals indicates that they were likely produced by scattering of incident S waves at the border of the Santa Clara Valley to the south of the array. It is remarkable that the largest low-frequency phases at many of the valley sites for regional events to the east are basin surface waves coming from a direction about 70 degrees different from that of the epicenters. Basin surface waves emanating from the eastern edge of the valley are also identified by the cross-correlation analysis.

Bulletin of the Seismological Society of America↗
USGS2000

Three-dimensional simulations of ground motions in the Seattle region for earthquakes in the Seattle fault zone

We used the 3D finite-difference method to model observed seismograms of two earthquakes (ML 4.9 and 3.5) in the Seattle region and to simulate ground motions for hypothetical M 6.5 and M 5.0 earthquakes on the Seattle fault, for periods greater than 2 sec. A 3D velocity model of the Seattle Basin was constructed from studies that analyzed seismic-reflection surveys, borehole logs, and gravity and aeromagnetic data. The observations and the simulations highlight the importance of the Seattle Basin on long-period ground motions. For earthquakes occurring just south of the basin, the edge of the basin and the variation of the thickness of the Quaternary deposits in the basin produce much larger surface waves than expected from flat-layered models. The data consist of seismograms recorded by instruments deployed in Seattle by the USGS and the University of Washington (UW). The 3D simulation reproduces the peak amplitude and duration of most of the seismograms of the June 1997 Bremerton event (ML 4.9) recorded in Seattle. We found the focal mechanism for this event that best fits the observed seismograms in Seattle by combining Green's functions determined from the 3D simulations for the six fundamental moment couples. The February 1997 event (ML 3.5) to the south of the Seattle Basin exhibits a large surface-wave arrival at UW whose amplitude is matched by the synthetics in our 3D velocity model, for a source depth of 9 km. The M 6.5 simulations incorporated a fractal slip distribution on the fault plane. These simulations produced the largest ground motions in an area that includes downtown Seattle. This is mainly caused by rupture directed up dip toward downtown, radiation pattern of the source, and the turning of S waves by the velocity gradient in the Seattle basin. Another area of high ground motion is located about 13 km north of the fault and is caused by an increase in the amplitude of higher-mode Rayleigh waves caused by the thinning of the Quaternary deposits.

Bulletin of the Seismological Society of America↗
USGS2000

Variability of site response in Seattle, Washington

Ground motion from local earthquakes and the SHIPS (Seismic Hazards Investigation in Puget Sound) experiment is used to estimate site amplification factors in Seattle. Earthquake and SHIPS records are analyzed by two methods: (1) spectral ratios relative to a nearby site on Tertiary sandstone, and (2) a source/site spectral inversion technique. Our results show site amplifications between 3 and 4 below 5 Hz for West Seattle relative to Tertiary rock. These values are approximately 30% lower than amplification in the Duwamish Valley on artificial fill, but significantly higher than the calculated range of 2 to 2.5 below 5 Hz for the till-covered hills east of downtown Seattle. Although spectral amplitudes are only 30% higher in the Duwamish Valley compared to West Seattle, the duration of long-period ground motion is significantly greater on the artificial fill sites. Using a three-dimensional displacement response spectrum measure that includes the effects of ground-motion duration, values in the Duwamish Valley are 2 to 3 times greater than West Seattle. These calculations and estimates of site response as a function of receiver azimuth point out the importance of trapped surface-wave energy within the shallow, low-velocity, sedimentary layers of the Duwamish Valley. One-dimensional velocity models yield spectral amplification factors close to the observations for till sites east of downtown Seattle and the Duwamish Valley, but underpredict amplifications by a factor of 2 in West Seattle. A two-dimensional finite-difference model does equally well for the till sites and the Duwamish Valley and also yields duration estimates consistent with the observations for the Duwamish Valley. The two-dimensional model, however, still underpredicts amplification in West Seattle by up to a factor of 2. This discrepancy is attributed to 3D effects, including basin-edge-induced surface waves and basin-geometry-focusing effects, caused by the proximity of the Seattle thrust fault and the sediment-filled Seattle basin.

Washington↗
USGS2000

Geology in the 1996 USGS seismic-hazard maps, central and eastern United States

The current (1996) national probabilistic seismic-hazard maps utilize information about geologic structure and tectonics of the central and eastern U.S. to compensate for uncertainty that arises from the short seismicity record. Geology was incorporated into the maps mainly as seven source zones that are delineated in three distinct ways. The North American stable continental region is divided into two large zones, the sparsely seismic Precambrian craton and the more active Phanerozoic rim. Five other source zones are much smaller - the Wabash Valley source zone is within the craton, whereas the Reelfoot Rift, eastern Tennessee, Charleston, and Charlevoix source zones are in the Phanerozoic rim of the continent. We document these zones and explain and justify their use. The seven zones provide a foundation from which we suggest a criterion for including more geology in future maps.

Seismological Research Letters↗
USGS1999

Calculation of broadband time histories of ground motion: Comparison of methods and validation using strong-ground motion from the 1994 Northridge earthquake

This article compares techniques for calculating broadband time histories of ground motion in the near field of a finite fault by comparing synthetics with the strong-motion data set for the 1994 Northridge earthquake. Based on this comparison, a preferred methodology is presented. Ground-motion-simulation techniques are divided into two general methods: kinematic- and composite-fault models. Green's functions of three types are evaluated: stochastic, empirical, and theoretical. A hybrid scheme is found to give the best fit to the Northridge data. Low frequencies (< 1 Hz) are calculated using a kinematic-fault model and a 3D finite-difference code to propagate energy through a realistic 3D velocity structure. High frequencies (> 1 Hz) are calculated using a composite-fault model with a fractal subevent size distribution and stochastic, bandlimited, white-noise Green's functions. At frequencies below 1 Hz, theoretical elastic-wave-propagation synthetics introduce proper seismic-phase arrivals of body waves and surface waves. The 3D velocity structure more accurately reproduces record durations for the deep sedimentary basin structures found in the Los Angeles region. At frequencies above 1 Hz, scattering effects become important and wave propagation is more accurately represented by stochastic Green's functions. A fractal subevent size distribution for the composite fault model ensures an ω −2 spectral shape over the entire frequency band considered (0.1-20 Hz).

California↗
USGS1999

Site response for Seattle and source parameters of earthquakes in the Puget Sound Region

We analyzed seismograms from 21 earthquakes ( M L 2.0-4.9) recorded by digital seismographs we deployed in urban Seattle to determine site response and earthquake stress drops. The seismometers were situated on a wide variety of geologic units, including artificial fill (e.g., Kingdome, Harbor Island), Pleistocene age soils (glacial till and outwash deposits of Seattle's hills), modified land (downtown Seattle, Space Needle), and Tertiary sedimentary rock. Two mainshock-aftershock sequences were recorded: the June 1997 Bremerton sequence (mainshock M L 4.9) and the February 1997 South Seattle sequence (mainshock M L 3.5), along with other events in the Puget Sound region. We developed a new inversion procedure to estimate site response, source corner frequencies, and seismic moments from the S -wave spectra. This inversion uses corner frequencies determined from spectral ratios of mainshock-aftershock pairs as constraints. The site responses found from the inversion are not relative to the rock site but are relative to an idealized site with a flat frequency response. The response of the rock site is also found from the inversion. The inversion results show high response for the sites on artificial fill, more moderate amplification for most sites on stiff Pleistocene soils or modified land, and low response for the rock site. Some sites display resonances, such as a strong 2-Hz resonance at our site near the Kingdome, which is caused by the surficial layers of fill and younger alluvium. The sites in West Seattle exhibit high amplification, even though they are on relatively stiff soils of glacial outwash. This may be partly caused by basin surface waves produced by conversion of incident S waves. This high response in West Seattle is consistent with damage reports from the 1949 ( m b 7.1) and 1965 ( m b 6.5) earthquakes. Stress-drop estimates for the events we recorded were generally low, between 0.4 and 25 bars, although some of the events may have had higher stress drops that could not be resolved because of the limited passband. We calculated a stress drop of 24 bars for the Bremerton mainshock and 10 bars for the South Seattle mainshock.

Washington↗
USGS1999

Deaggregation of probabilistic ground motions in the central and eastern United States

Probabilistic seismic hazard analysis (PSHA) is a technique for estimating the annual rate of exceedance of a specified ground motion at a site due to known and suspected earthquake sources. The relative contributions of the various sources to the total seismic hazard are determined as a function of their occurrence rates and their ground-motion potential. The separation of the exceedance contributions into bins whose base dimensions are magnitude and distance is called deaggregation . We have deaggregated the hazard analyses for the new USGS national probabilistic ground-motion hazard maps (Frankel et al. , 1996). For points on a 0.2° grid in the central and eastern United States (CEUS) , we show color maps of the geographical variation of mean and modal magnitudes ( M , Mˇ ) and distances ( D , Dˇ ) for ground motions having a 2% chance of exceedance in 50 years. These maps are displayed for peak horizontal acceleration and for spectral response accelerations of 0.2, 0.3, and 1.0 sec. We tabulate M , D , Mˇ , and Dˇ for 49 CEUS cities for 0.2- and 1.0-sec response. Thus, these maps and tables are PSHA-derived estimates of the potential earthquakes that dominate seismic hazard at short and intermediate periods in the CEUS.

Bulletin of the Seismological Society of America↗
USGS1998

First-generation site-response maps for the Los Angeles region based on earthquake ground motions

Ground-motion records from aftershocks of the 1994 Northridge earthquake and mainshock records from the 1971 San Fernando, 1987 Whittier Narrows, 1991 Sierra Madre, and 1994 Northridge earthquakes are used to estimate site response relative to a rock site for the urban Los Angeles area. Site response is estimated at 232 mainshock and 201 aftershock sites relative to a low-amplitude site in the Santa Monica Mountains. Average amplification values are calculated for the frequency bands: 1 to 3, 3 to 5, and 5 to 7 Hz. These bands are chosen based on limitations in aftershock recording equipment at lower frequencies and reduced significance to the building inventory at higher frequencies. Site amplification factors determined at the instrumented locations are grouped by the surficial geology and contoured to produce a continuous spatial estimation of amplification. The maps in this article represent the first attempt to produce estimates of site amplification based on observations of ground motion for such a large areal extent of the Los Angeles region. These maps are expected to evolve as more data become available and more analysis is done.

California↗