Large-scale 3-D Simulations of Spontaneous Rupture and Wave Propagation in Complex, Nonlinear Media Roten, D. 1, Olsen, K.B. 2, Day, S.M. 2, Dalguer, L.A. 1 and Fäh, D. 1 1 Swiss Seismological Service / ETH Zürich 2 San Diego State University Annual Meeting of the Seismological Society of America April, Salt Lake City, UT

Annual Meeting of the Seismological Society of America, April , Salt Lake City, UT Introduction 2 Advances in computer codes and increases in computational resources enable numerical prediction of ground motions at increasingly higher frequencies, e.g.: - M8 up to 2 Hz (Cui et al., 2010) - Chino Hills EQ up to 5 Hz Nonlinear behavior of soft soils should be taken into account when predicting ground motions at frequencies above ~1 Hz Nonlinear material behavior may also occur in the damage zone around the fault (on- and off-fault plasticity; e.g. Andrews (2005), Ma (2008).

3 Annual Meeting of the Seismological Society of America, April , Salt Lake City, UT Implementation of damage rheology in AWP-ODC Non-associative Drucker-Prager plasticity with yielding in shear (based on guidelines from SCEC/USGS Spontaneous Rupture Code Verification Project):

4 Annual Meeting of the Seismological Society of America, April , Salt Lake City, UT Implementation of damage rheology in AWP-ODC Return map algorithm: Time-dependent relaxation (Andrews, 2005):

5 Annual Meeting of the Seismological Society of America, April , Salt Lake City, UT Staggering of grid requires interpolation of missing elements in stress tensor and initial stresses from adjacent nodes Optimization that reduces number of interpolations results in significantly reduced computational cost Material modelCPU time per iterationNormalized CPU time Elastic0.18 s100% Elastoplastic0.68 s378% Elastoplastic optimized0.29 s161% Computational aspects

6 Annual Meeting of the Seismological Society of America, April , Salt Lake City, UT Verification against SCEC/USGS TPV13 Spontaneous rupture on a planar, dipping fault (approximated by vertical fault in AWP-ODC) c = 5 Mpa tan(φ) = 0.85 T v = 0 s

7 Annual Meeting of the Seismological Society of America, April , Salt Lake City, UT Convergence test (vertical strike-slip fault)

8 Annual Meeting of the Seismological Society of America, April , Salt Lake City, UT ShakeOut Earthquake Scenario Based on kinematic source description (Graves et al., 2008) visco-elastic medium

9 Annual Meeting of the Seismological Society of America, April , Salt Lake City, UT ShakeOut Earthquake Scenario with Plasticity

10 Annual Meeting of the Seismological Society of America, April , Salt Lake City, UT

11 Annual Meeting of the Seismological Society of America, April , Salt Lake City, UT 11 ShakeOut Earthquake Scenario with Plasticity Visco-elasto-plasticVisco-elastic

12 Annual Meeting of the Seismological Society of America, April , Salt Lake City, UT ShakeOut Earthquake Scenario with Plasticity Final Principal Plastic Strain η at surface

13 Annual Meeting of the Seismological Society of America, April , Salt Lake City, UT ShakeOut Earthquake Scenario with Plasticity Final Principal Plastic Strain η at z = 600 m

14 Annual Meeting of the Seismological Society of America, April , Salt Lake City, UT Conclusions We have implemented damage rheology based on the Drucker-Prager yield condition into the highly scalable 3D finite difference code AWP-ODC The method has been validated against four finite element codes in the framework of the SCEC/USGS Spontaneous Rupture Code Verification Project Computational cost of modeling plasticity amounts to an additional ~60% of the CPU time required for an elastic simulation We simulate the ShakeOut-K earthquake scenario for a visco-elasto-plastic material, assuming that cohesions range from ~50 kPa in low-velocity sediments near the surface to several MPa at depth Our results suggest that long-period (< 2 s) ground motion in the Los Angles area, amplified by a wave guide of interconnected sedimentary basins, could be significantly reduced as compared to visco-elastic solutions Improved calibration of additional parameters (cohesion C and friction angle ϕ is required to reliably predict off-fault plasticity and nonlinear behavior of near-surface deposits