ALBERT

Description: We numerically model broadband ground motion (up to 5–7.5  Hz) from blind‐thrust scenario earthquakes matching the fault geometry of the 1994 Mw 6.7 Northridge earthquake. Several realizations are modeled (by varying the hypocenter location in the dynamic rupture simulation) in a 1D‐layered velocity profile. In addition, we include Q(f ), nonlinear effects from Drucker–Prager plasticity, and superimpose small‐scale medium complexity in both a 1D‐layered and 3D velocity model within the subsequent wave propagation. We investigate characteristics of the ground motion and its variability up to 50 km from the fault by comparing them with ground‐motion prediction equations (GMPEs), simple proxy metrics, as well as strong ground motion records from the Northridge event. We find that median ground motion closely follows the trend predicted by GMPEs and that the intraevent standard deviation, although varying with hypocenter location, lies near that of GMPE models. Plasticity affects ground‐motion amplitudes in regions near the source, reducing intraevent variability above ∼0.5  Hz. Heterogeneity in the velocity structure on both the regional and small scales is needed for the simulated data to match two proxy metrics: the period‐to‐period correlation of spectral acceleration (SA) and the ratio of maximum‐to‐median SA. Although small‐scale heterogeneity has a negligible effect on median SA for this style of rupture, it serves to significantly increase the cumulative absolute velocity, better agreeing with observations. When compared with strong‐motion data, we find that long‐wavelength velocity structure within our deterministic simulations reduces bias at both short and long periods. Finally, synthetic ground motion at both footwall and hanging‐wall sites has no clear dependence on the distance to rupture (at both short and long periods); directivity is likely overpowering any hanging‐wall effect.

Description: We model deterministic broadband (0–7.5 Hz) ground motion from an Mw 7.1 bilateral strike‐slip earthquake scenario with dynamic rupture propagation along a rough‐fault topography embedded in a medium including small‐scale velocity and density perturbations. Spectral accelerations (SAs) at periods 0.2–3 s and Arias intensity durations show a similar distance decay (at the level of 1–2 interevent standard deviations above the median) when compared to Next Generation Attenuation‐West2 (NGA)‐West2 ground‐motion prediction equations (GMPEs) using a Q(f ) power‐law exponent of 0.6–0.8 above 1 Hz in models with a minimum VS of 750  m/s. With a trade‐off from Q(f ), the median ground motion is slightly increased by scattering from statistical models of small‐scale heterogeneity with standard deviation (σ) of the perturbations at the lower end of the observed range (5%) but reduced by scattering attenuation at the upper end (10%) when using a realistic 3D background velocity model. The ground‐motion variability is strongly affected by the addition of small‐scale media heterogeneity, reducing otherwise large values of intraevent standard deviation closer to those of empirical observations. These simulations generally have intraevent standard deviations for SAs lower than the GMPEs for the modeled bandwidth, with an increasing trend with distance (most pronounced in low‐to‐moderate scattering media) near the level of observations at distances greater than 35 km from the fault. Durations for the models follow the same increasing trend with distance, in which σ ∼ 5% produces the best match to GMPE values. We find that a 3D background‐velocity model reduces the pulse period into the expected range by breaking up coherent waves from directivity, generating a lognormal distribution of ground‐motion residuals. These results indicate that a strongly heterogeneous medium is needed to produce realistic deterministic broadband ground motions. Finally, the addition of a thin surficial layer with low, frequency‐independent Q in the model (with a minimum VS of 750  m/s) controls the high‐frequency decay in energy, as measured by the parameter κ, that may be necessary to include as simulations continue to extend to higher frequencies.

Description: We performed a suite of numerical simulations based on the 1811–1812 New Madrid seismic zone (NMSZ) earthquakes, which demonstrate the importance of 3D geologic structure and rupture directivity on the ground‐motion response throughout a broad region of the central United States (CUS) for these events. Our simulation set consists of 20 hypothetical earthquakes located along two faults associated with the current seismicity trends in the NMSZ. The hypothetical scenarios range in magnitude from M 7.0 to 7.7 and consider various epicenters, slip distributions, and rupture characterization approaches. The low‐frequency component of our simulations was computed deterministically up to a frequency of 1 Hz using a regional 3D seismic velocity model and was combined with higher‐frequency motions calculated for a 1D medium to generate broadband synthetics (0–40 Hz in some cases). For strike‐slip earthquakes located on the southwest–northeast‐striking NMSZ axial arm of seismicity, our simulations show 2–10 s period energy channeling along the trend of the Reelfoot rift and focusing strong shaking northeast toward Paducah, Kentucky, and Evansville, Indiana, and southwest toward Little Rock, Arkansas. These waveguide effects are further accentuated by rupture directivity such that an event with a western epicenter creates strong amplification toward the northeast, whereas an eastern epicenter creates strong amplification toward the southwest. These effects are not as prevalent for simulations on the reverse‐mechanism Reelfoot fault, and large peak ground velocities (〉40  cm/s) are typically confined to the near‐source region along the up‐dip projection of the fault. Nonetheless, these basin response and rupture directivity effects have a significant impact on the pattern and level of the estimated intensities, which leads to additional uncertainty not previously considered in magnitude estimates of the 1811–1812 sequence based only on historical reports.The region covered by our simulation domain encompasses a large portion of the CUS centered on the NMSZ, including several major metropolitan areas. Based on our simulations, more than eight million people living and working near the NMSZ would experience potentially damaging ground motion and modified Mercalli intensities ranging from VI to VIII if a repeat of the 1811–1812 earthquakes occurred today. Moreover, the duration of strong ground shaking in the greater Memphis metropolitan area could last from 30 to more than 60 s, depending on the magnitude and epicenter.Online Material: Tables of 1D velocity models used to generate the high‐frequency synthetics, and figures of source models and peak ground motion synthetics.

Description: The Southern California San Jacinto fault is geometrically complex, consisting of several major strands with smaller scale complexity within each strand. The two northernmost strands, the Claremont and the Casa Loma–Clark, are separated by a 25‐km‐long extensional stepover with an average of 4 km separation between the strands. We use a combined modeling method to assess probable rupture and ground‐motion behaviors for this stepover. First, dynamic rupture modeling on geometrically complex fault strands embedded in a state‐of‐the‐art 3D crustal velocity model is used to generate a series of scenario earthquakes. We then use the resulting near‐fault low‐frequency (〈1  Hz) ground‐motion time histories to generate broadband synthetic seismograms with a hybrid approach. These synthetics are then compared with a distribution of precariously balanced rocks (PBRs) near the fault to constrain our results and assess shaking hazard for the region surrounding the fault. Our dynamic models produce sources between Mw 5.4 and 6.9, with rupture limits imposed by sharp contrasts in fault stress or by geometrical barriers. The main stepover serves as a primary barrier to rupture in our model, producing event sizes that are consistent with the historical behavior of the San Jacinto fault. The largest broadband synthetics are a good match to leading ground‐motion prediction equations and are generally consistent with the distribution of PBRs, none of which experience accelerations that produce toppling probabilities significantly higher than zero. Thus, although the PBRs do not rule out any of our model scenarios, they confirm that our models produce realistic rupture extents and shaking.Online Material: Figures of total slip for additional rupture models, low‐frequency intensity plots, synthetic seismograms, and comparison with ground‐motion prediction equations.

Description: Ground‐motion simulations can be viable alternatives to empirical relations for seismic hazard analysis when data are sparse. Interfrequency correlation is revealed in recorded seismic data, which has implications for seismic risk (Bayless and Abrahamson, 2018a). However, in many cases, simulated ground‐motion time series, in particular those originating from stochastic methods, lack interfrequency correlation. Here, we develop a postprocessing method to rectify simulation techniques that otherwise produce synthetic time histories deficient in an interfrequency correlation structure. An empirical correlation matrix is used in our approach to generate correlated random variables that are multiplied in the frequency domain with the Fourier amplitudes of the synthetic ground‐motion time series. The method is tested using the San Diego State University broadband ground‐motion generation module, which is a broadband ground‐motion generator that combines deterministic low‐frequency and stochastic high‐frequency signals, validated for the median of the spectral acceleration. Using our method, the results for seven western U.S. earthquakes with magnitude between 5.0 and 7.2 show that empirical interfrequency correlations are well simulated for a large number of realizations without biasing the fit of the median of the spectral accelerations to data. The best fit of the interfrequency correlation to data is obtained assuming that the horizontal components are correlated with a correlation coefficient of about 0.7.

Description: Field studies of historic rupture traces show that fault stepovers commonly serve as endpoints to earthquake ruptures. This is an effect that is corroborated by past dynamic modeling studies. However, field studies also show a great deal of complexity in fault‐zone structure within a stepover, which is often simplified out of modeling studies. In the present study, we use the 3D finite‐element method to investigate the effect of one type of smaller‐scale complexity on the rupture process: a smaller fault segment positioned between the two primary strands of a strike‐slip fault stepover. We find that such small faults can have a controlling effect on whether or not a rupture is able to jump the stepover and on the resulting ground motions from these ruptures. However, this effect is neither straightforward nor linear: the length of the intermediate segment and its basal depth, as well as whether the stepover is extensional or compressional, all contribute to the rupture behavior and ground‐motion distribution. These results have important implications for assessing the probability of a rupture propagating through small‐ and large‐scale discontinuities in faults, as well as for evaluating ground‐motion intensities near fault stepovers. Because of the sensitivity of results to so many parameters, these results also suggest that modeling studies on idealized fault geometries may not be sufficient to describe the rupture behaviors of specific complex fault systems. Site‐specific modeling studies, where possible, will provide better inputs and constraints for probabilistic rupture length assessments as well as for ground‐motion estimates.

Description: Memory-variable methods have been widely applied to approximate frequency-independent quality factor Q in numerical simulation of wave propagation. The frequency-independent model is often appropriate for frequencies up to about 1 Hz but at higher frequencies is inconsistent with some regional studies of seismic attenuation. We apply the memory-variable approach to frequency-dependent Q models that are constant below, and follow a power-law above, a chosen transition frequency. We present numerical results for the corresponding memory-variable relaxation times and weights, obtained by nonnegative least-squares fitting of the Q(f ) function, for a range of exponent values; these times and weights can be scaled to an arbitrary transition frequency and a power-law prefactor, respectively. The resulting memory-variable formulation can be used with numerical wave-propagation solvers based on methods such as finite differences (FDs) or spectral elements and may be implemented in either conventional or coarse-grained form. In the coarse-grained approach, we fit effective Q for low-Q values (〈200) using a nonlinear inversion technique and use an interpolation formula to find the corresponding weighting coefficients for arbitrary Q. A 3D staggered-grid FD implementation closely approximates the frequency–wavenumber solution to both a half-space and a layered model with a shallow dislocation source for Q as low as 20 over a bandwidth of two decades. We compare the effects of different power-law exponents using a finite-fault source model of the 2008 Mw 5.4 Chino Hills, California, earthquake and find that Q(f ) models generally better fit the strong-motion data than the constant Q models for frequencies above 1 Hz.Online Material: Figures comparing finite difference and frequency–wavenumber seismograms for an elastic layered-model point source simulation. Median spectral acceleration centered at 1 s and Fourier amplitude centered at 0.25 and 2.25 Hz for strong ground motion recordings and synthetics from the Chino Hills earthquake.