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Deterministic high-frequency ground motions from simulations of dynamic rupture along rough faults

Kyle B. Withers, Kim B. Olsen, Zheqiang Shi, Steven M. Day, & Rumi Takedatsu

Published 2013, SCEC Contribution #1867

The accuracy of earthquake source descriptions is a major limitation in high-frequency (~>1 Hz) deterministic ground motion prediction, which is critical for performance-based design by building engineers. We address this issue by an attempt to quantify the contributions to high-frequency ground motion from both small-scale fault geometry and media complexity and perform validation against recent Next Generation Attenuation (NGA) relations. Specifically, we use ground motion synthetics using dynamic rupture propagation along a rough fault imbedded in a velocity structure with small-scale heterogeneities described by a statistical model (Shi and Day, 2013). Here, the assumed fault roughness follows a self-similar fractal distribution with wavelength scales spanning three orders of magnitude from ~10^2 m to ~10^5 m. The rupture irregularity caused by fault roughness generates high-frequency accelerations with near-flat power spectra up to almost 10 Hz. We then use the moment-rate time histories from the dynamic rupture simulation as a kinematic source to extend the ground motions out to farther distances (35 km+) from the fault with a highly scalable fourth-order staggered-grid finite difference method (AWP-ODC). The latter wave propagation simulations use a characteristic 1D rock model with and without small-scale heterogeneities. We find that our simulations are within one inter-event standard deviation of the median up to 10 Hz as given by recent NGA relations. Furthermore, small-scale heterogeneities tend to increase the elastic spectral accelerations at the higher frequencies. To address the effects of small-scale fault and media complexity it is important to model anelastic attenuation as accurately as possible. In the bandwidth below about 1 Hz, observations show that a frequency-independent Q relationship is appropriate. This has been modeled in many simulations with good accuracy using the coarse-grained approach of Day (1998) for a 3D anelastic medium, and was used in our simulations described above. At higher frequencies, however, ground motion data indicates that anelastic attenuation falls off as frequency increases. Here, we implement frequency-dependent Q in AWP via a power-law function, Q=Q0*f^n, where Q is the quality factor and f is frequency, and Q0 and n are constants that may vary with the region of interest. We modify the coarse-grained approach, using least squares to optimize the weighting of the anelastic functions to fit a target Q(f) function. To validate our method, we compare the finite difference synthetics seismograms computed with AWP with those from a frequency-wavenumber code to account for dispersion.

Withers, K. B., Olsen, K. B., Shi, Z., Day, S. M., & Takedatsu, R. (2013). Deterministic high-frequency ground motions from simulations of dynamic rupture along rough faults. Seismological Research Letters, 84(2), 335. doi: 10.1785/0220130011.