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: 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.