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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↗
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

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↗
USGS1997

Variability of site response in the Los Angeles urban area

This article addresses the variability of site response in the Los Angeles area and possible structural causes for the observations. Aftershock records from 231 sites in the San Fernando and Los Angeles basins and the surrounding mountains are used in this study. Spectral ratios, taken with respect to a low-amplitude reference site, are used to document the variation in site amplification in the frequency range 2 to 6 Hz, both spatially and with backazimuth to the source. At higher frequencies (6 to 10 Hz), spectral ratios are shown to have greater spatial variability. Interstation spectral ratios are used to measure the standard deviation among source as a function of station separation. An increase in the variation in ground motion is shown to take place at a station separation of 1 km. Relative site-response estimates between nearby stations are used to demonstrate that preferred directions of motion can exist even in areas with no surface topographic effects.

California↗
USGS1997

Regional Lg attenuation for the continental United States

Measurements of the Fourier amplitude spectra of Lg phases recorded at high frequency (0.5 to 14.0 Hz) by broadband seismic stations are used to determine regional attenuation relationships for southern California, the Basin and Range Province, the central United States, and the northeastern United States and southeastern Canada. Fourier spectral amplitudes were measured every quarter octave from Lg phases windowed between 3.0 and 3.7 km sec −1 and recorded in the distance range of 150 to 1000 km. Attenuation at each frequency is determined by assuming a geometrical spreading exponent of 0.5 and inverting for Q and source and receiver terms. Both southern California and the Basin and Range Province are well described by low Lg Q and frequency-dependent attenuation. Lg spectral amplitudes in southern California are fit at low frequencies (0.625 to 0.875 Hz) by a constant Lg Q of 224 and by a frequency-dependent Lg Q function Q = 187 −7 +7 f 0.55(±0.03) in the frequency band 1.0 to 7.0 Hz. The Basin and Range Province is characterized by a constant Lg Q of 192 for frequencies of 0.5 to 0.875 Hz and by the frequency-dependent Lg Q function Q = 235 −11 +11 f 0.56(±0.04) in the frequency band 1.0 to 5.0 Hz. A change in frequency dependence above 5.0 Hz is possible due to contamination of the Lg window by Pn and Sn phases. Lg spectral amplitudes in the central United States are fit by a mean frequency-independent Lg Q of 1291 for frequencies of 1.5 to 7.0 Hz, while a frequency-dependent Lg Q of Q = 1052 −83 +91 ( f /1.5) 0.22(±0.06) fits the Lg spectral amplitudes for the northeastern United States and southeastern Canada over the passband 1.5 to 14.0 Hz. Attenuation measurements for these areas were restricted to frequencies >1.5 Hz due to larger microseismic noise levels at the lower frequencies.

Bulletin of the Seismological Society of America↗
USGS1996

Urban seismology - Northridge aftershocks recorded by multi-scale arrays of portable digital seismographs

We deployed portable digital seismographs in the San Fernando Valley (SFV), the Los Angeles basin (LAB), and surrounding hills to record aftershocks of the 17 January 1994 Northridge California earthquake. The purpose of the deployment was to investigate factors relevant to seismic zonation in urban areas, such as site amplification, sedimentary basin effects, and the variability of ground motion over short baselines. We placed seismographs at 47 sites (not all concurrently) and recorded about 290 earthquakes with magnitudes up to 5.1 at five stations or more. We deployed widely spaced stations for profiles across the San Fernando Valley, as well as five dense arrays (apertures of 200 to 500 m) in areas of high damage, such as the collapsed Interstate 10 overpass, Sherman Oaks, and the collapsed parking garage at CalState Northridge. Aftershock data analysis indicates a correlation of site amplification with mainshock damage. We found several cases where the site amplification depended on the azimuth of the aftershock, possibly indicating focusing from basin structures. For the parking garage array, we found large ground-motion variabilities (a factor of 2) over 200-m distances for sites on the same mapped soil unit. Array analysis of the aftershock seismograms demonstrates that sizable arrivals after the direct S waves consist of surface waves traveling from the same azimuth as that of the epicenter. These surface waves increase the duration of motions and can have frequencies as high as about 4 Hz. For the events studied here, we do not observe large arrivals reflected from the southern edge of the San Fernando Valley.

California↗
USGS1996

Site response for urban Los Angeles using aftershocks of the Northridge earthquake

Ground-motion records from aftershocks of the 1994 Northridge earthquake are used to estimate site response in the urban Los Angeles area. Over 1300 shear-wave records from 61 sources and 90 sites are used in a linear inversion for source and site-response spectra. The methodology makes no assumptions about the shape of the source spectrum. To obtain a stable unique inverse, a Q model and geometrical spreading factor are assumed. In addition, the site response at a hard-rock site is constrained to be approximately 1.0 with a kappa of 0.02. The site-response spectra compare favorably with the results of previous and on-going investigations in Los Angeles. A couple of first-order effects are lower site response in the surrounding mountains, dominated by Mesozoic and Tertiary rocks, and higher values in the San Fernando and Los Angeles Basins, containing surficial Pleistocene and Holocene alluvial deposits. Results show good correlation of high site-response spectral values with localized areas of severe damage (Interstate 10 collapse, Sherman Oaks, Northridge, Interstate 5/14 collapse). However, widespread trends in site response across the sedimentary basins are not obvious. The data suggest that site responses are lower near the southern margin of the San Fernando Valley for sources to the north, due to north-dipping sedimentary structures. But the general pattern of site response is characterized by high variability on length scales less than a kilometer. Variations of a factor of 2 in site response are observed over the length scale of 200 m and for the same surficial geologic unit. For some of the alluvial basin sites, surface-wave generation is a significant contributor to elevated site response at lower frequencies, below 2 Hz. The total damage pattern for the Northridge earthquake is influenced by strong source directivity to the north and strong local site effects. The correlation of weak-motion site-response estimates with areas of significant damage demonstrates the value of these field measurements in future urban planning and in the reduction of seismic risk in urban areas.

California↗
USGS1996

New USGS seismic hazard maps for the United States

The US Geological Survey (USGS) is preparing new seismic national maps for release in April 1996. The new maps plot probabilistic ground motions for return times of about 500, 1000, and 2500 years. Deterministic (scenario) ground-motion maps are being prepared for selected faults in the western US. Due to the diversity of tectonic settings in the US, mapping methodologies for different regions had to be modified. A four-model approach is used to eliminate the need for drawing seismic source zones to determine seismic activity levels. A logic tree approach is used to incorporate alternative models of seismic hazard and alternative relations of seismic attenuation.

Conference Paper↗