A Pseudo-Dynamic Rupture Model Generator for Earthquakes on Geometrically Complex Faults

1. A Pseudo-Dynamic Rupture Model Generator for Earthquakes on Geometrically Complex Faults Daniel Trugman, July 2013

2. 2D Rough-Fault Dynamic Simulations Homogenous background stress + complex fault geometry  heterogeneity in tractions Eliminates important source of uncertainty: fault geometry is a direct observable

3. Rough Fault (not to scale)

4. “Pseudo-Dynamic” Source Model • Rough-fault simulations: high-frequency motions consistent with field observations • But: too computationally intensive to incorporate into probabilistic hazard analysis • Idea: use insight from rough-fault simulations to build a “pseudo-dynamic” source model • Source parameters consistent with dynamic models • Retain computational efficiency of kinematic models

5. Method:Building a Pseudo-Dynamic Model • Step 1: Study dynamic source parameters • Step 2: Represent pseudo-dynamic source parameters as spatial random fields that are consistent with dynamic simulations • Step 3: Compare source models and simulated ground motion for different fault profiles

6. Step 1: Analyze Dynamic Source Parameters • Δu, vrup, Vpeak • Mean, standard deviations • Autocorrelation: spatial coherence • Dependence on fault geometry • Shape of source-time function, V(t) • Restrict attention to: • subshear ruptures (background stress just high enough for self-sustaining ruptures) • region away from the hypocenter (nucleation zone)

7. Source parameters are strongly anti-correlated with fault slope m(x):

8. Source-time function of the form:

9. Step 2: Represent pseudo-dynamic source parameters as spatial random fields: • Assume Gaussian marginals • Use mean, standard deviations from dynamic simulations • Key step: anticorrelate with fault slope • Assume exponential ACF: • Correlation length β from dynamic sims • Vpeak, Δumore spatially coherent than vrup • Power spectrum ~ k-2

10. Basic rupture generating procedure:

11. Step 3: Model Comparison • Start with a direct comparison on a single (random) fractally-rough fault profile • Source parameters and seismic wave excitation • Also compare with flat-fault projection of pseudo-dynamic source parameters • Generalize to ensemble comparison • 30 different (random) fractally-rough fault profiles

12. Source Parameters final slip, Δu correlation coefficient: 0.80 rupture velocity, vrup correlation coefficient: 0.64 peak slip velocity, Vpeak correlation coefficient: 0.78

13. Seismograms fault-parallel velocity (vx) fault-normal velocity (vy)

14. Seismic Wavefield (fault-normal velocity) dynamic simulation pseudo-dynamic simulation

15. Seismic Wavefield (fault-normal velocity) rough fault pseudo-dynamic simulation flat fault pseudo-dynamic simulation

16. Ensemble Marginal Distributions:Δu

17. Ensemble Marginal Distributions:vrup

18. Fourier Amplitude Spectra(fault-normal acceleration)

19. Peak Ground Acceleration

20. Discussion: generalization to 3D • 2D autocorrelation structure • i.eβxand βz • Which slope to use? • Trace of the fault plane in the slip direction? • Component of rupture velocity in z direction? • No correlation with z-direction slope (given stress field)? • Need to taper source parameter distributions at source boundaries? • Thrust faults? • Which is the relevant slope? • Is this different for rupture velocity than for slip?

22. Extra Slides:

23. Conclusions • Fault geometry strongly influences rupture process and hence, the earthquake source parameters. • Our pseudo-dynamic model produces comparable ground motion to that seen in dynamic models, even at high frequencies. • Similar models could be implemented in programs like CyberShake to improve our understanding of seismic hazard.

24. Figure References • Dunham, E.M., Belanger, D., Cong, L., and J.E. Kozdon (2011). Earthquake ruptures with strongly rate-weakening friction and off-fault plasticity, Part 2: Nonplanar faults, BSSA, 101, no. 5, 2308-2322, doi: 10.1785/0120100076. • Graves, R. et al. (2011). CyberShake: A physics-based seismic hazard model for southern California, Pure Appl. Geophys., 168, no. 3-4, 367-381, doi: 10.1007/s00024-010-0161-6. • Sagy, A.,Brodsky, E. E., and G. J. Axen (2007). Evolution of fault-surface roughness with slip, Geology, 35, 283-286, doi: 10.1130/G23235A.1 • Shi, Z., and S. M. Day (2013). Rupture dynamics and ground motion from 3-D rough-fault simulations, J. Geophys. Res. (in press). • Song, S. G. and L. A. Dalguer (2013). Importance of 1-point statistics in earthquake source modelling for ground motion simulation, Geophys., J. Int., 192, no.3, 1255-1270, doi: 10.1093/gji/ggs089

25. Ensemble Marginal Distributions:Vpeak

26. Peak Ground Velocity

27. Fourier Amplitude Spectra

28. Basic Procedure: • Generate fault profile h(x) (filter Gaussian noise in Fourier domain to obtain correct PSD) • Correlate source parameter vectors with m(x) • Filter correlated vectors to achieve desired PSD • Rescale and shift: correct mean and std. dev. • Aggregate source parameters V(x,t)

29. Complex Fault Geometry Dixie Valley Fault, Nevada Sagy et al. Geology 2007; 35: 283-286 Most dynamic rupture simulations assume planar faults, model stress field as random field But faults are fractally rough: deviate from planarity at all length scales: