An Equivalent Point‐Source Model for Stochastic Simulation of Earthquake Ground Motions in California

Abstract

Response spectra for California earthquakes of 3:0 ≤ M < 7:5 are well described by a simple stochastic ground-motion model using an equivalent point-source concept. We determine the best-fit stress parameter of each California earthquake in the Next Generation Attenuation-West 2 database based on matching simulated to observed response spectral shapes over a wide frequency range, and we derive an expression for the mean stress as a function of magnitude and focal depth. A calibration factor is calculated for each event; this constant is the required amplitude adjustment in order that the simulations match the observed response spectral amplitudes with zero bias. The best-fit simulation model suggests that the attenuation in California can be modeled as R −1:3 at distances < 50 km and R −0:5 at further distances; this does a better job at matching attenuation trends than the traditional model 1=R model at distances < 50 km, particularly for M < 5:5 events. The model requires an overall multiplicative calibration factor of C sim 3:16 in order for the simulations to match the observed response spectral amplitudes, for all magnitudes and distances. The calibration constant could be attributed to simplifications inherent in the modeling of source, attenuation, and site processes, and the lack of consideration of multiple phases in stochastic simulations. We conclude that the equivalent point-source simulation method with the proposed modeling parameters can predict average ground motions in California, generally within a 25% error band, for magnitudes up to M 7.5, distances < 400 km, and frequencies > 0:2 Hz. We finish the paper by providing a recipe for developing a simulation-based generic ground-motion prediction equation that can be adjusted for source and attenuation attributes in different regions by simple modifications to its key source and attenuation modeling parameters.

Interfrequency Correlations among Fourier Spectral Ordinates and Implications for Stochastic Ground‐Motion Simulation

“…The first option is to define the model for the expected Fourier amplitudes using a seismologically informed functional form for the spectrum of far-field shear waves. In the present work, the recently proposed model of Yenier and Atkinson (2015; hereafter, YA15) is adapted for this purpose. The adaptation that is made is to define a new model of the form:…”

“…The between-site correlation model ρ S f i ; f j is therefore developed using the random effects from the empirical approach. An additional reason for this decision was that when using the FAS-based approach, site impedance effects are often modeled using the quarter-wavelength approach (Boore, 2003;Yenier and Atkinson, 2015). However, in a sitespecific application for which a site transfer function was available, these impedance effects could include resonant peaks associated with the various contrasts within layered sites.…”

Regionally Adjustable Generic Ground‐Motion Prediction Equation Based on Equivalent Point‐Source Simulations: Application to Central and Eastern North America

“…It is defined for the reference stress (Δσ), κ 0 parameter, and site condition. We choose Δσ 100 bar and κ 0 0:025 s as the reference modeling parameters based on the findings of Yenier and Atkinson (2015) for California earthquakes. In equation (2), F Δσ represents the stress adjustment factor that is needed when Δσ is different than 100 bars.…”

“…The generic GMPE can be adjusted for use in any region by modifying a few key modeling parameters, and calibrated to match the empirical data in the target region. The basic idea is that we first develop a simulation-based GMPE using synthetic motions generated based on parameters that were calibrated to observed motions in California by Yenier and Atkinson (2015). We parameterize this GMPE so as to isolate the effects of the basic source and attenuation parameters on peak ground motions and response spectra.…”

“…Finally, the formulation facilitates the efficient exploration of the effects on the GMPE in terms of epistemic uncertainty in key seismological parameters-stress drop and attenuation. Importantly, sound overall scaling behavior of the GMPE in terms of near-distance saturation effects and magnitude-saturation effects is ensured by the calibration of the model form to an extensive empirical data in California obtained from the (Next Generation Attenuation-West 2) NGA-West 2 database (Yenier and Atkinson, 2015).…”