Stephen Hartzell

The 1994 Northridge, California, earthquake: Investigation of rupture velocity, risetime, and high‐frequency radiation

A hybrid global search algorithm is used to solve the nonlinear problem of calculating slip amplitude, rake, risetime, and rupture time on a finite fault. Thirty-five strong motion velocity records are inverted by this method over the frequency band from 0.1 to 1.0 Hz for the Northridge earthquake. Four regions of larger-amplitude slip are identified: one near the hypocenter at a depth of 17 km, a second west of the hypocenter at about the same depth, a third updip from the hypocenter at a depth of 10 km, and a fourth updip from the hypocenter and to the northwest. The results further show an initial fast rupture with a velocity of 2.8 to 3.0 km/s followed by a slow termination of the rupture with velocities of 2.0 to 2.5 km/s. The initial energetic rupture phase lasts for 3 s, extending out 10 km from the hypocenter. Slip near the hypocenter has a short risetime of 0.5 s, which increases to 1.5 s for the major slip areas removed from the hypocentral region. The energetic rupture phase is also shown to be the primary source of high-frequency radiation (1–15 Hz) by an inversion of acceleration envelopes. The same global search algorithm is used in the envelope inversion to calculate high-frequency radiation intensity on the fault and rupture time. The rupture timing from the low- and high-frequency inversions is similar, indicating that the high frequencies are produced primarily at the mainshock rupture front. Two major sources of high-frequency radiation are identified within the energetic rupture phase, one at the hypocenter and another deep source to the west of the hypocenter. The source at the hypocenter is associated with the initiation of rupture and the breaking of a high-stress-drop asperity and the second is associated with stopping of the rupture in a westerly direction.

Earthquake Hazards on the Cascadia Subduction Zone

Large subduction earthquakes on the Cascadia subduction zone pose a potential seismic hazard. Very young oceanic lithosphere (10 million years old) is being subducted beneath North America at a rate of approximately 4 centimeters per year. The Cascadia subduction zone shares many characteristics with subduction zones in southern Chile, southwestern Japan, and Colombia, where comparably young oceanic lithosphere is also subducting. Very large subduction earthquakes, ranging in energy magnitude (Mw) between 8 and 9.5, have occurred along these other subduction zones. If the Cascadia subduction zone is also storing elastic energy, a sequence of several great earthquakes (Mw 8) or a giant earthquake (Mw 9) would be necessary to fill this 1200-kilometer gap. The nature of strong ground motions recorded during subduction earthquakes of Mw less than 8.2 is discussed. Strong ground motions from even larger earthquakes (Mw up to 9.5) are estimated by simple simulations. If large subduction earthquakes occur in the Pacific Northwest, relatively strong shaking can be expected over a large region. Such earthquakes may also be accompanied by large local tsunamis.

Prediction of Broadband Ground-Motion Time Histories: Hybrid Low/High- Frequency Method with Correlated Random Source Parameters

We present a new method for calculating broadband time histories of ground motion based on a hybrid low-frequency/high-frequency approach with correlated source parameters. Using a finite-difference method we calculate low- frequency synthetics (< ∼1 Hz) in a 3D velocity structure. We also compute broadband synthetics in a 1D velocity model using a frequency-wavenumber method. The low frequencies from the 3D calculation are combined with the high frequencies from the 1D calculation by using matched filtering at a crossover frequency of 1 Hz. The source description, common to both the 1D and 3D synthetics, is based on correlated random distributions for the slip amplitude, rupture velocity, and rise time on the fault. This source description allows for the specification of source parameters independent of any a priori inversion results. In our broadband modeling we include correlation between slip amplitude, rupture velocity, and rise time, as suggested by dynamic fault modeling. The method of using correlated random source parameters is flexible and can be easily modified to adjust to our changing understanding of earthquake ruptures. A realistic attenuation model is common to both the 3D and 1D calculations that form the low- and high-frequency components of the broadband synthetics. The value of Q is a function of the local shear-wave velocity. To produce more accurate high-frequency amplitudes and durations, the 1D synthetics are corrected with a randomized, frequency-dependent radiation pattern. The 1D synthetics are further corrected for local site and nonlinear soil effects by using a 1D nonlinear propagation code and generic velocity structure appropriate for the site’s National Earthquake Hazards Reduction Program (nehrp) site classification. The entire procedure is validated by comparison with the 1994 Northridge, California, strong ground motion data set. The bias and error found here for response spectral acceleration are similar to the best results that have been published by others for the Northridge rupture.

Prediction of nonlinear soil effects

Mathematical models of soil nonlinearity in common use and recently developed nonlinear codes are 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. Manuscript received 18 June 2004.

IMPORTANCE OF MODEL PARAMETERIZATION IN FINITE FAULT INVERSIONS : APPLICATION TO THE 1974 MW 8.0 PERU EARTHQUAKE

The spatial and temporal slip distributions for the October 3, 1974 (Mw = 8.0), Peru subduction zone earthquake and its largest aftershock on November 9 (Ms = 7.1) are calculated and analyzed in terms of the inversion parameterization and tectonic significance. Teleseismic, long-period World-Wide Standard Seismograph Network, P and SH waveforms are inverted to obtain the rupture histories. We demonstrate that erroneous results are obtained if a parameterization is used that does not allow for a sufficiently complex source, involving spatial variation in slip amplitude, risetime, and rupture time. The inversion method utilizes a parameterization of the fault that allows for a discretized source risetime and rupture time. Well-located aftershocks recorded on a local network have the same general pattern as teleseismically determined hypocenters and help to constrain the geometry of the subduction zone. For the main shock a hinged fault is preferred having a shallow plane with a dip of 11° and a deeper, landward plane with a dip of 30°. The preferred nucleation depth lies between 11 and 15 km. A bilateral rupture is obtained with two major concentrations of slip, one 60 to 70 km to the northwest of the epicenter and a second 80 to 100 km to the south and southeast of the epicenter. For these source regions, risetimes vary from 6 to 18 s. Our estimates of risetimes are consistent with the time for the rupture to traverse the dominant local asperity. The slip distribution for the November 9 aftershock falls within a conspicuous hole in the main shock rupture pattern, near the hypocenter of the main shock. The November 9 event has a simple risetime function with a duration of 2 s. Aftershocks recorded by the local network are shown to cluster near the hypocenter of the impending November 9 event and downdip from the largest main shock source region. Slip during the main shock is concentrated at shallow depths above 15 km and extends updip from the hypocenter to near the plate boundary at the trench axis. The large amount of slip at shallow depths is attributed to the absence of any significant accretionary wedge of sediments, and the relatively young age and high convergence rate of the subducted plate, which results in good seismic coupling near the trench axis.

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 inten- sity (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 agree- ment 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. Online Material: Modified Mercalli intensities and velocity waveforms, and a movie of simulated wave propagation.

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.

Signatures of the Seismic Source in EMD-Based Characterization of the 1994 Northridge, California, Earthquake Recordings

In this article we use empirical mode decomposition (EMD) to charac- terize the 1994 Northridge, California, earthquake records and investigate the sig- natures carried over from the source rupture process. Comparison of the current study results with existing source inverse solutions that use traditional data processing suggests that the EMD-based characterization contains information that sheds light on aspects of the earthquake rupture process. We first summarize the fundamentals of the EMD and illustrate its features through the analysis of a hypothetical and a real record. Typically, the Northridge strong-motion records are decomposed into eight or nine intrinsic mode functions (IMFs), each of which emphasizes a different oscillation mode with different amplitude and frequency content. The first IMF has the highest-frequency content; frequency content decreases with an increase in IMF component. With the aid of a finite-fault inversion method, we then examine aspects of the source of the 1994 Northridge earthquake that are reflected in the second to fifth IMF components. This study shows that the second IMF is predominantly wave motion generated near the hypocenter, with high-frequency content that might be related to a large stress drop associated with the initiation of the earthquake. As one progresses from the second to the fifth IMF component, there is a general migration of the source region away from the hypocenter with associated longer-period signals as the rupture propagates. This study suggests that the different IMF components carry information on the earthquake rupture process that is expressed in their different frequency bands.

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 overconsolidation ratio.

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.