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

Faults

Daniel Trugman, July 2013

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

Rough Fault (not to scale)

profile : y=h(x) slope : m=dhdx

“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

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

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)

Source parameters are strongly

anti-correlated with fault slope m(x):

Source-time function of the form:

V (t)=Δutp

t tp( )exp −t tp( )

Vpeak =Δuetp

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, Δu more spatially coherent than vrup

– Power spectrum ~ k-2

r(h)=exp(−h/ β )

Basic rupture generating procedure:

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

final slip, Δucorrelation coefficient: 0.80

rupture velocity, vrupcorrelation coefficient: 0.64

peak slip velocity, Vpeak

correlation coefficient: 0.78

Source Parameters

fault-parallel velocity (vx) fault-normal velocity (vy)

Seismograms

dynamic simulation pseudo-dynamic simulation

Seismic Wavefield (fault-normal velocity)

rough fault pseudo-dynamic simulation

flat faultpseudo-dynamic simulation

Seismic Wavefield (fault-normal velocity)

Ensemble Marginal Distributions:Δu

Ensemble Marginal Distributions:vrup

Fourier Amplitude Spectra (fault-normal acceleration)

Peak Ground Acceleration

Discussion: generalization to 3D• 2D autocorrelation structure– i.e βx and 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?

Extra Slides:

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.

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

Ensemble Marginal Distributions:Vpeak

Peak Ground Velocity

Fourier Amplitude Spectra

Basic Procedure:

1. Generate fault profile h(x) (filter Gaussian noise in Fourier domain to obtain correct PSD)

2. Correlate source parameter vectors with m(x)3. Filter correlated vectors to achieve desired

PSD4. Rescale and shift: correct mean and std. dev.5. Aggregate source parameters V(x,t)

Complex Fault Geometry• 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:

Sagy et al. Geology 2007; 35: 283-286

Dixie Valley Fault, Nevada