Geology topics

S. Hartzell

Publications and source records attributed to S. Hartzell.

At least 19 recordsLinked to original sources

USGS2013

Finite-fault source inversion using teleseismic P waves: Simple parameterization and rapid analysis

We examine the ability of teleseismic P waves to provide a timely image of the rupture history for large earthquakes using a simple, 2D finite‐fault source parameterization. We analyze the broadband displacement waveforms recorded for the 2010 M w &sim;7 Darfield (New Zealand) and El Mayor‐Cucapah (Baja California) earthquakes using a single planar fault with a fixed rake. Both of these earthquakes were observed to have complicated fault geometries following detailed source studies conducted by other investigators using various data types. Our kinematic, finite‐fault analysis of the events yields rupture models that similarly identify the principal areas of large coseismic slip along the fault. The results also indicate that the amount of stabilization required to spatially smooth the slip across the fault and minimize the seismic moment is related to the amplitudes of the observed P waveforms and can be estimated from the absolute values of the elements of the coefficient matrix. This empirical relationship persists for earthquakes of different magnitudes and is consistent with the stabilization constraint obtained from the L‐curve in Tikhonov regularization. We use the relation to estimate the smoothing parameters for the 2011 M w 7.1 East Turkey, 2012 M w 8.6 Northern Sumatra, and 2011 M w 9.0 Tohoku, Japan, earthquakes and invert the teleseismic P waves in a single step to recover timely, preliminary slip models that identify the principal source features observed in finite‐fault solutions obtained by the U.S. Geological Survey National Earthquake Information Center (USGS/NEIC) from the analysis of body‐ and surface‐wave data. These results indicate that smoothing constraints can be estimated a priori to derive a preliminary, first‐order image of the coseismic slip using teleseismic records.

Darfield, El Mayor-Cucapah↗

USGS2012

Comparison of seismic waveform inversion results for the rupture history of a finite fault: Application to the 1986 North Palm Springs, California, earthquake

The July 8, 1986, North Palm Springs earthquake is used as a basis for comparison of several different approaches to the solution for the rupture history of a finite fault. The inversion of different waveform data is considered; both teleseismic P waveforms and local strong ground motion records. Linear parametrizations for slip amplitude are compared with nonlinear parametrizations for both slip amplitude and rupture time. Inversions using both synthetic and empirical Green's functions are considered. In general, accurate Green's functions are more readily calculable for the teleseismic problem where simple ray theory and flat-layered velocity structures are usually sufficient. However, uncertainties in the variation in t * with frequency most limit the resolution of teleseismic inversions. A set of empirical Green's functions that are well recorded at teleseismic distances could avoid the uncertainties in attenuation. In the inversion of strong motion data, the accurate calculation of propagation path effects other than attenuation effects is the limiting factor in the resolution of source parameters. The assumption of a laterally homogeneous velocity structure is usually not a good one, and the use of empirical Green's functions is desirable. Considering the parametrization of the problem, any degree of fault rupture complexity can be described in terms of a linear parametrization for slip amplitudes. However, a nonlinear parametrization for rupture times and slip amplitudes can have a distinct advantage over a simple linear one by limiting the number of unknown parameters. Regardless of the choice of data or the type of parametrization, the model or solution will be affected by the choice of minimization norm and the type of stabilization used.

Journal of Geophysical Research Solid Earth↗

USGS2012

Source complexity of the 1987 Whittier Narrows, California, earthquake from the inversion of strong motion records

Strong motion records for the Whittier Narrows earthquake are inverted to obtain the history of slip. Both constant rupture velocity models and variable rupture velocity models are considered. The results show a complex rupture process within a relatively small source volume, with at least four separate concentrations of slip. Two sources are associated with the hypocenter, the larger having a slip of 55–90 cm, depending on the rupture model. These sources have a radius of approximately 2–3 km and are ringed by a region of reduced slip. The aftershocks fall within this low slip annulus. Other sources with slips from 40 to 70 cm each ring the central source region and the aftershock pattern. All the sources are predominantly thrust, although some minor right-lateral strike-slip motion is seen. The overall dimensions of the Whittier earthquake from the strong motion inversions is 10 km long (along the strike) and 6 km wide (down the dip). The preferred dip is 30° and the preferred average rupture velocity is 2.5 km/s. Moment estimates range from 7.4 to 10.0×10 24 dyn cm, depending on the rupture model.

Journal of Geophysical Research Solid Earth↗

USGS2011

Source and site response study of the 2008 Mount Carmel, Illinois, earthquake

Two separate inversions are performed using the ground-motion data from the 2008 Mount Carmel, Illinois, earthquake. One uses aftershocks as empirical Green’s functions to determine a finite-fault slip distribution. The second uses mainshock ground-motion spectra to calculate source, path, and site response parameters. The slip inversion reveals a prominent asperity at the hypocenter with an area of approximately 6 km 2 , moment of 7.0 x 10 23 dyn cm ( M w 5.20), and stress drop of about 100 bars. Considering all major and minor slip, the total moment is 1.7 x 10 24 dyn cm ( M w =5.45). The rupture velocity is not resolvable due to the small source area. After fixing the geometric spreading, the source, path, and site parameter inversion yields a similar moment of 8.8 x 10 23 dyn cm ( M w 5.26) and a corner frequency of 0.89 Hz, which also give a stress drop of approximately 100 bars. Our combined geometric and anelastic attenuation function, Q ( f ) r -b =1137 f 0.12 r -0.94 , fits the regional spectral amplitudes, where the data is more plentiful, as well as previously derived attenuation relationships. Site response spectra show prominent resonant frequencies that correlate with the thickness of Mississippi River sediments and Mississippi embayment deposits. In addition, higher frequency resonance peaks are observed that most likely represent higher mode resonances and resonances from shallower structure.

Illinois↗

USGS2010

Short baseline variations in site response and wave-propagation effects and their structural causes: Four examples in and around the santa clara valley, California

Ground motion records of local and regional events from a portable array are used to investigate the structural causes of variations in ground motion over distances of a few hundred meters to a few kilometers in the sedimentary basin environment of the Santa Clara Valley, California, and its margins. Arrays of portable seismic stations are used to target four study areas with different ground motion patterns: (1) an edge of the alluvial basin extending up onto a marginal ridge (Blossom Hill), (2) a Cenozoic basin with a nearly flat bottom (Cupertino Basin), (3) a long, narrow Cenozoic basin with a steep V profile (Evergreen Basin), and (4) a line perpendicular to the trace of the Hayward fault. Average peak velocities on Blossom Hill from local earthquakes are a factor of 2.5 times higher than nearby valley sites. Three-dimensional (3D) modeling is used to conclude that the majority of the amplification is due to lower shear-wave velocities along a local fault zone (Shannon–Berrocal). Site amplification over the Cupertino Basin in the frequency band 0.5–4 Hz is generally low (less than 2.0 relative to a Mesozoic rock site) and spatially uniform. This response is attributed to the shallow, flat-bottomed shape of the basin and the uniform, flat-laying sedimentary fill. In contrast, site amplification in the Evergreen Basin generally exceeds 3.0 and is attributed to the deep, V-shaped geometry of the basin and younger sedimentary fill. 3D waveform modeling shows the elongated shape of the Evergreen Basin causes more efficient trapping of long-period waves for sources along the long axis of the basin. A low-velocity zone is postulated along the Hayward fault with a width between 100 and 200 m, based on elevated site response along the fault trace and 4.5-Hz fault zone guided waves on the horizontal components of stations near the fault.

California↗

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

Source analysis using regional empirical Green's functions: The 2008 Wells, Nevada, earthquake

We invert three-component, regional broadband waveforms recorded for the 21 February 2008 Wells, Nevada, earthquake using a finite-fault methodology that prescribes subfault responses using eight M W &sim;4 aftershocks as empirical Green's functions (EGFs) distributed within a 20-km by 21.6-km fault area. The inversion identifies a seismic moment of 6.2 x 10 24 dyne-cm (5.8 M W ) with slip concentrated in a compact 6.5-km by 4-km region updip from the hypocenter. The peak slip within this localized area is 88 cm and the stress drop is 72 bars, which is higher than expected for Basin and Range normal faults in the western United States. The EGF approach yields excellent fits to the complex regional waveforms, accounting for strong variations in wave propagation and site effects. This suggests that the procedure is useful for studying moderate-size earthquakes with limited teleseismic or strong-motion data and for examining uncertainties in slip models obtained using theoretical Green's functions.

Nevada↗

USGS2009

Site characterization for urban seismic hazards in lower Manhattan, New York City, from microtremor array analysis

We characterize the shear-wave velocity (Vs) of soil deposits in lower Manhattan at six sites using the SPAC and HVSR microtremor methods. The soil Vs ranges from 140 m/s to 300 m/s over bedrock. We believe that bedrock depth is constrained to ±15% with these microtremor data, but an accurate quantification of bedrock Vs is unattainable because of low spectral coherency at frequencies below 3 Hz. HVSR data corroborate the SPAC microtremor results at sites based on good alignment of theoretical Rayleigh ellipticity peaks, 1D SH amplifications, and peak HVSR. Resonant frequencies vary between 1.4 and 5.5 Hz between the sites from both observed HVSR and predicted 1D SH amplification. Shear-wave velocities to 30 m classify the sites as C, D, or E. This study demonstrates that given relatively shallow bedrock depth the SPAC method can work in extremely urbanized areas.

New York↗

USGS2008

Ground-motion modeling of the 1906 San Francisco earthquake, part I: Validation using the 1989 Loma Prieta earthquake

We compute ground motions for the Beroza (1991) and Wald et al. (1991) source models of the 1989 magnitude 6.9 Loma Prieta earthquake using four different wave-propagation codes and recently developed 3D geologic and seismic velocity models. In preparation for modeling the 1906 San Francisco earthquake, we use this well-recorded earthquake to characterize how well our ground-motion simulations reproduce the observed shaking intensities and amplitude and durations of recorded motions throughout the San Francisco Bay Area. All of the simulations generate ground motions consistent with the large-scale spatial variations in shaking associated with rupture directivity and the geologic structure. We attribute the small variations among the synthetics to the minimum shear-wave speed permitted in the simulations and how they accommodate topography. Our long-period simulations, on average, under predict shaking intensities by about one-half modified Mercalli intensity (MMI) units (25%-35% in peak velocity), while our broadband simulations, on average, under predict the shaking intensities by one-fourth MMI units (16% in peak velocity). Discrepancies with observations arise due to errors in the source models and geologic structure. The consistency in the synthetic waveforms across the wave-propagation codes for a given source model suggests the uncertainty in the source parameters tends to exceed the uncertainty in the seismic velocity structure. In agreement with earlier studies, we find that a source model with slip more evenly distributed northwest and southeast of the hypocenter would be preferable to both the Beroza and Wald source models. Although the new 3D seismic velocity model improves upon previous velocity models, we identify two areas needing improvement. Nevertheless, we find that the seismic velocity model and the wave-propagation codes are suitable for modeling the 1906 earthquake and scenario events in the San Francisco Bay Area.

Bulletin of the Seismological Society of America↗

USGS2008

Ground-motion modeling of the 1906 San Francisco Earthquake, part II: Ground-motion estimates for the 1906 earthquake and scenario events

We estimate the ground motions produce by the 1906 San Francisco earthquake making use of the recently developed Song et al. (2008) source model that combines the available geodetic and seismic observations and recently constructed 3D geologic and seismic velocity models. Our estimates of the ground motions for the 1906 earthquake are consistent across five ground-motion modeling groups employing different wave propagation codes and simulation domains. The simulations successfully reproduce the main features of the Boatwright and Bundock (2005) ShakeMap, but tend to over predict the intensity of shaking by 0.1-0.5 modified Mercalli intensity (MMI) units. Velocity waveforms at sites throughout the San Francisco Bay Area exhibit characteristics consistent with rupture directivity, local geologic conditions (e.g., sedimentary basins), and the large size of the event (e.g., durations of strong shaking lasting tens of seconds). We also compute ground motions for seven hypothetical scenarios rupturing the same extent of the northern San Andreas fault, considering three additional hypocenters and an additional, random distribution of slip. Rupture directivity exerts the strongest influence on the variations in shaking, although sedimentary basins do consistently contribute to the response in some locations, such as Santa Rosa, Livermore, and San Jose. These scenarios suggest that future large earthquakes on the northern San Andreas fault may subject the current San Francisco Bay urban area to stronger shaking than a repeat of the 1906 earthquake. Ruptures propagating southward towards San Francisco appear to expose more of the urban area to a given intensity level than do ruptures propagating northward.

Bulletin of the Seismological Society of America↗

USGS2008

Finite-fault analysis of the 2004 Parkfield, California, earthquake using P nl waveforms

We apply a kinematic finite-fault inversion scheme to P nl displacement waveforms recorded at 14 regional stations (Δ<2°) to recover the distribution of coseismic slip for the 2004 Parkfield earthquake using both synthetic Green’s functions (SGFs) calculated for one-dimensional (1D) crustal-velocity models and empirical Green’s functions (EGFs) based on the recordings of a single M w 5.0 aftershock. Slip is modeled on a rectangular fault subdivided into 2×2 km subfaults assuming a constant rupture velocity and a 0.5 sec rise time. A passband filter of 0.1–0.5 Hz is applied to both data and subfault responses prior to waveform inversion. The SGF inversions are performed such that the final seismic moment is consistent with the known magnitude ( M w 6.0) of the earthquake. For these runs, it is difficult to reproduce the entire P nl waveform due to inaccuracies in the assumed crustal structure. Also, the misfit between observed and predicted vertical waveforms is similar in character for different rupture velocities, indicating that neither the rupture velocity nor the exact position of slip sources along the fault can be uniquely identified. The pattern of coseismic slip, however, compares well with independent source models derived using other data types, indicating that the SGF inversion procedure provides a general first-order estimate of the 2004 Parkfield rupture using the vertical P nl records. The best-constrained slip model is obtained using the single-aftershock EGF approach. In this case, the waveforms are very well reproduced for both vertical and horizontal components, suggesting that the method provides a powerful tool for estimating the distribution of coseismic slip using the regional P nl waveforms. The inferred slip model shows a localized patch of high slip (55 cm peak) near the hypocenter and a larger slip area (~50 cm peak) extending between 6 and 20 km to the northwest.

California↗

USGS2007

Basin structure beneath the Santa Rosa Plain, Northern California: Implications for damage caused by the 1969 Santa Rosa and 1906 San Francisco earthquakes

Regional gravity data in the northern San Francisco Bay region reflect a complex basin configuration beneath the Santa Rosa plain that likely contributed to the significant damage to the city of Santa Rosa caused by the 1969 M 5.6, 5.7 Santa Rosa earthquakes and the 1906 M 7.9 San Francisco earthquake. Inversion of these data indicates that the Santa Rosa plain is underlain by two sedimentary basins about 2 km deep separated by the Trenton Ridge, a shallow west-northwest-striking bedrock ridge west of Santa Rosa. The city of Santa Rosa is situated above the 2- km-wide protruding northeast corner of the southern basin where damage from both the 1969 and 1906 earthquakes was concentrated. Ground-motion simulations of the 1969 and 1906 earthquakes, two events with opposing azimuths, using the gravity- defined basin surface, show enhanced ground motions along the northeastern edge of this corner, suggesting that basin-edge effects contributed to the concentration of shaking damage in this area in the past and may also contribute to strong shaking during future earthquakes.

California↗

USGS2007

Stability and uncertainty of finite-fault slip inversions: Application to the 2004 Parkfield, California, earthquake

The 2004 Parkfield, California, earthquake is used to investigate stability and uncertainty aspects of the finite-fault slip inversion problem with different a priori model assumptions. We utilize records from 54 strong ground motion stations and 13 continuous, 1-Hz sampled, geodetic instruments. Two inversion procedures are compared: a linear least-squares subfault-based methodology and a nonlinear global search algorithm. These two methods encompass a wide range of the different approaches that have been used to solve the finite-fault slip inversion problem. For the Parkfield earthquake and the inversion of velocity or displacement waveforms, near-surface related site response (top 100 m, frequencies above 1 Hz) is shown to not significantly affect the solution. Results are also insensitive to selection of slip rate functions with similar duration and to subfault size if proper stabilizing constraints are used. The linear and nonlinear formulations yield consistent results when the same limitations in model parameters are in place and the same inversion norm is used. However, the solution is sensitive to the choice of inversion norm, the bounds on model parameters, such as rake and rupture velocity, and the size of the model fault plane. The geodetic data set for Parkfield gives a slip distribution different from that of the strong-motion data, which may be due to the spatial limitation of the geodetic stations and the bandlimited nature of the strong-motion data. Cross validation and the bootstrap method are used to set limits on the upper bound for rupture velocity and to derive mean slip models and standard deviations in model parameters. This analysis shows that slip on the northwestern half of the Parkfield rupture plane from the inversion of strong-motion data is model dependent and has a greater uncertainty than slip near the hypocenter.

California↗

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↗

USGS2005

An alternative approach to characterize nonlinear site effects

This paper examines the rationale of a method of nonstationary processing and analysis, referred to as the Hilbert-Huang transform (HHT), for its application to a recording-based approach in quantifying influences of soil nonlinearity in site response. In particular, this paper first summarizes symptoms of soil nonlinearity shown in earthquake recordings, reviews the Fourier-based approach to characterizing nonlinearity, and offers justifications for the HHT in addressing nonlinearity issues. This study then uses the HHT method to analyze synthetic data and recordings from the 1964 Niigata and 2001 Nisqually earthquakes. In doing so, the HHT-based site response is defined as the ratio of marginal Hilbert amplitude spectra, alternative to the Fourier-based response that is the ratio of Fourier amplitude spectra. With the Fourier-based approach in studies of site response as a reference, this study shows that the alternative HHT-based approach is effective in characterizing soil nonlinearity and nonlinear site response.

Earthquake Spectra↗

USGS2005

Calculation of broadband time histories of ground motion, Part II: Kinematic and dynamic modeling using theoretical Green's functions and comparison with the 1994 northridge earthquake

In the evolution of methods for calculating synthetic time histories of ground motion for postulated earthquakes, kinematic source models have dominated to date because of their ease of application. Dynamic models, however, which incorporate a physical relationship between important faulting parameters of stress drop, slip, rupture velocity, and rise time, are becoming more accessible. This article compares a class of kinematic models based on the summation of a fractal distribution of subevent sizes with a dynamic model based on the slip-weakening friction law. Kinematic modeling is done for the frequency band 0.2 to 10.0. Hz, dynamic models are calculated from 0.2 to 2.0. Hz. The strong motion data set for the 1994 Northridge earthquake is used to evaluate and compare the synthetic time histories. Source models are propagated to the far field by convolution with 1D and 3D theoretical Green’s functions. In addition, the kinematic model is used to evaluate the importance of propagation path effects: velocity structure, scattering, and nonlinearity. At present, the kinematic model gives a better broadband fit to the Northridge ground motion than the simple slip-weakening dynamic model. In general, the dynamic model overpredicts rise times and produces insufficient shorter-period energy. Within the context of the slip-weakening model, the Northridge ground motion requires a short slip-weakening distance, on the order of 0.15 m or less. A more complex dynamic model including rate weakening or one that allows shorter rise times near the hypocenter may fit the data better.

Bulletin of the Seismological Society of America↗

USGS2004

Probabilistic seismic hazard analysis for Sumatra, Indonesia and across the Southern Malaysian Peninsula

The ground motion hazard for Sumatra and the Malaysian peninsula is calculated in a probabilistic framework, using procedures developed for the US National Seismic Hazard Maps. We constructed regional earthquake source models and used standard published and modified attenuation equations to calculate peak ground acceleration at 2% and 10% probability of exceedance in 50 years for rock site conditions. We developed or modified earthquake catalogs and declustered these catalogs to include only independent earthquakes. The resulting catalogs were used to define four source zones that characterize earthquakes in four tectonic environments: subduction zone interface earthquakes, subduction zone deep intraslab earthquakes, strike-slip transform earthquakes, and intraplate earthquakes. The recurrence rates and sizes of historical earthquakes on known faults and across zones were also determined from this modified catalog. In addition to the source zones, our seismic source model considers two major faults that are known historically to generate large earthquakes: the Sumatran subduction zone and the Sumatran transform fault. Several published studies were used to describe earthquakes along these faults during historical and pre-historical time, as well as to identify segmentation models of faults. Peak horizontal ground accelerations were calculated using ground motion prediction relations that were developed from seismic data obtained from the crustal interplate environment, crustal intraplate environment, along the subduction zone interface, and from deep intraslab earthquakes. Most of these relations, however, have not been developed for large distances that are needed for calculating the hazard across the Malaysian peninsula, and none were developed for earthquake ground motions generated in an interplate tectonic environment that are propagated into an intraplate tectonic environment. For the interplate and intraplate crustal earthquakes, we have applied ground-motion prediction relations that are consistent with California (interplate) and India (intraplate) strong motion data that we collected for distances beyond 200 km. For the subduction zone equations, we recognized that the published relationships at large distances were not consistent with global earthquake data that we collected and modified the relations to be compatible with the global subduction zone ground motions. In this analysis, we have used alternative source and attenuation models and weighted them to account for our uncertainty in which model is most appropriate for Sumatra or for the Malaysian peninsula. The resulting peak horizontal ground accelerations for 2% probability of exceedance in 50 years range from over 100% g to about 10% g across Sumatra and generally less than 20% g across most of the Malaysian peninsula. The ground motions at 10% probability of exceedance in 50 years are typically about 60% of the ground motions derived for a hazard level at 2% probability of exceedance in 50 years. The largest contributors to hazard are from the Sumatran faults.

Tectonophysics↗

USGS2004

Prediction of nonlinear soil effects

Mathematical models of soil nonlinearity in common use and recently developed nonlinear codes compared to investigate the range of their predictions. We consider equivalent linear formulations with and without frequency-dependent moduli and damping ratios and nonlinear formulations for total and effective stress. Average velocity profiles to 150 m depth with midrange National Earthquake Hazards Reduction Program site classifications (B, BC, C, D, and E) in the top 30 m are used to compare the response of a wide range of site conditions from rock to soft soil. Nonlinear soil models are compared using the amplification spectrum, calculated as the ratio of surface ground motion to the input motion at the base of the velocity profile. Peak input motions from 0.1 g to 0.9 g are considered. For site class B, no significant differences exist between the models considered in this article. For site classes BC and C, differences are small at low input motions (0.1 g to 0.2 g ), but become significant at higher input levels. For site classes D and E the overdamping of frequencies above about 4 Hz by the equivalent linear solution with frequency-independent parameters is apparent for the entire range of input motions considered. The equivalent linear formulation with frequency-dependent moduli and damping ratios under damps relative to the nonlinear models considered for site class C with larger input motions and most input levels for site classes D and E. At larger input motions the underdamping for site classes D and E is not as severe as the overdamping with the frequency-independent formulation, but there are still significant differences in the time domain. A nonlinear formulation is recommended for site classes D and E and for site classes BC and C with input motions greater than a few tenths of the acceleration of gravity. The type of nonlinear formulation to use is driven by considerations of the importance of water content and the availability of laboratory soils data. Our average amplification curves from a nonlinear effective stress formulation compare favorably with observed spectral amplification at class D and E sites in the Seattle area for the 2001 Nisqually earthquake.

Bulletin of the Seismological Society of America↗