Description of selected broadband ground motion simulation methods Paul Somerville, URS Yuehua Zeng, USGS Golden

Simulation Methods Described: 1. URS 2. Zeng 3. UCSB 4. SDSU

1.URS Hybrid Approach to Broadband Ground Motion Simulations (Graves and Pitarka, 2004)

For f < 1 Hz: Kinematic representation of heterogeneous rupture on a finite fault –Slip amplitude and rake, rupture time, slip function 1D FK or 3D FDM approach for Green’s function For f > 1 Hz: Extension of Boore (1983) with limited kinematic representation of heterogeneous fault rupture –Slip amplitude, rupture time, conic averaged radiation pattern, Stochastic phase Simplified Green’s functions for 1D velocity structure –Geometrical spreading, impedance effects Both frequency ranges have the nonlinear site amplification based on Vs30 (Campbell and Bozorgnia, 2008)

Scenario Earthquake Begin with uniform slip having mild taper at edges. Use Mai and Beroza (2002) spatial correlation functions (M w dependent, K -2 falloff) with random phasing to specify entire wavenumber spectrum. Kinematic Rupture Generator –Unified scaling rules for rise time, rupture speed and corner frequency –Depth scaling for shallow (< 5 km) moment release: rise time (increase) and rupture speed (decrease)

Validation Earthquake Validation events begin with coarse representation from slip inversion. e.g., Loma Prieta, Wald et al (1991)

Validation Earthquake Validation events begin with coarse representation from slip inversion. e.g., Loma Prieta, Wald et al (1991) Low-pass filter to retain only long wavelength features. Preserves gross asperity locations.

Validation Earthquake Validation events begin with coarse representation from slip inversion. e.g., Loma Prieta, Wald et al (1991) Extend to fine grid using Mai and Beroza (2002) spatial correlation functions with random phasing for shorter wavelengths.

Rupture Initiation Time T i = r / V r – d t(D) V r = 80% local V s depth > 8 km = 56% local V s depth < 5 km linear transition between 5-8 km d tscales with local slip (D) to accelerate or decelerate rupture d t(D avg ) = 0

Rise Time t = k · D 1/2 depth > 8 km = 2 · k · D 1/2 depth < 5 km linear transition between 5-8 km Scales with square root of local slip (D) with constant (k) set so average rise time is given by the Somerville et al (1999, 2009) relations: t A = 1.6e-09 · M o 1/3 (WUS) t A = 3.0e-09 · M o 1/3 (CEUS)

Rake l = l o + e -60 o < e < 60 o Random perturbations of rake follow spatial distribution given by K -2 falloff.

Corner frequency scales with local rupture speed (V r ): f c = c o · V r / ( p dl) c o = 2.1 (WUS), 1.15 (CEUS) (empirically constrained) V r = 80% local V s depth > 8 km = 56% local V s depth < 5 km linear transition between 5-8 km High Frequency Subfault Source Spectrum Apply Frankel (1995) convolution operator: S(f) = C · [ 1 + C · f 2 / f c 2 ] -1 C = M o / (Ns p dl 3 ) N = number of subfaults s p = stress parameter (50 - WUS), (125 – CEUS) dl = subfault dimension –scales to target mainshock moment –scales to mainshock rise time –results generally insensitive to subfault size

1994 Northridge EQ

Spectral Acceleration Goodness of Fit R i = ln(O i /S i ) Bias = (1/N) S R i s = [(1/N) S (R i – Bias) 2 ] 1/2

S-velocity P-velocity

3. UCSB Broadband Strong Motion Synthetics Method Archuleta, Hartzell, Lavallée, Liu, Schmedes 3. UCSB Broadband Strong Motion Synthetics Method Archuleta, Hartzell, Lavallée, Liu, Schmedes Liu, P., R. J. Archuleta and S. H. Hartzell (2006). Prediction of broadband ground-motion time histories: Hybrid low/high-frequency method with correlated random source parameters, Bull. Seismol. Soc. Am. vol. 96, No. 6, pp , doi: / Schmedes, J., R. J. Archuleta, and D. Lavallée (2010). Correlation of earthquake source parameters inferred from dynamic rupture simulations, J. Geophys. Res., 115, B03304, doi: /2009JB

Flowchart for Generating Broadband Strong Motion Synthetics Flowchart for Generating Broadband Strong Motion Synthetics Liu, Archuleta, Hartzell, BSSA

Correlated Source Parameters (LAH) Slip Average rupture velocity Rise time Spatial correlation 30% Spatial correlation 60% (Liu, Archuleta, Hartzell, 2006)

New Kinematic Model (SAL) Schmedes, J., R. J. Archuleta, and D. Lavallée (2010), Correlation of earthquake source parameters inferred from dynamic rupture simulations, J. Geophys. Res., 115, B03304, doi: /2009JB

Frequency dependent perturbation of strike, dip and rake (Pitarka et al, 2000) With f 1 =1.0 Hz, f 2 =3.0 Hz High Frequencies Randomness of the high frequencies is generated in the source description. (

Ground Motion Computation: 3D Fourth-order viscoelastic FD code: Perfectly matched layers Coarse grained method Allows for two regions of different grid spacing

Combination of 1D and 3D: 1.Cross correlation at matching frequency f m to align seismograms. 2.Use 3D at frequencies 3.Use 1D at frequencies 4.For

Martin Mai, Walter Imperatori, and Kim Olsen Mai, P.M., W. Imperatori, and K.B. Olsen (2010). Hybrid broadband ground-motion simulations: combining long-period deterministic synthetics with high-frequency multiple S-to-S back- scattering, Bull. Seis. Soc. Am. 100, 5A, Mena, B., P.M. Mai, K.B. Olsen, M.D. Purvance, and J.N. Brune (2010). Hybrid broadband ground motion simulation using scattering Green's functions: application to large magnitude events, Bull. Seis. Soc. Am. 100, 5A, Hybrid Broadband Ground-Motion Simulations: Combining Long-Period Deterministic Synthetics with High-Frequency Multiple S-to-S Backscattering

Combines low-frequency deterministic synthetics (f ~ 1 Hz) with high-frequency scattering operators Site effects: Soil structure Soil structure (De-)amplification of ground motions (De-)amplification of ground motions Non-linear soil behavior Non-linear soil behavior Scattering effects: inhomogeneities in Earth structure at all scales inhomogeneities in Earth structure at all scales scattering model, based on site-kappa, Q, scattering and intrinsic attenuation,  s  and  i scattering model, based on site-kappa, Q, scattering and intrinsic attenuation,  s  and  i

 Scattering Green’s functions computed for each component of motion based on Zeng et al. (1991, 1993) and and P and S arrivals from 3D ray tracing (Hole, 1992) convolved with a dynamically-consistent source-time function, generating 1/f spectral decay  Site-Scattering parameters (scattering and attenuation coefficient, site kappa, intrinsic attenuation) are taken from the literature and are partly based on the site-specific velocity structure.  Assuming scattering operators and moment release originate throughout the fault, but starts at the hypocenter Site-Specific Scattering Functions

 Hybrid broadband seismograms are calculated from low-frequency and high- frequency synthetics in the frequency domain using a simultaneous amplitude and phase matching algorithm (Mai and Beroza, 2003) Example BB calculation BB SC LF BB = broadband LF = low frequency SC = scattering functions 1/f Generation of hybrid broadband seismograms

 Method implemented on the SCEC Broadband platform  Validations include Northridge, Landers and Loma Prieta, and NGA relations at selected sites Northridge Validation (Mai et al., 2010) Verification and Validation NGA validation at Precariously Balanced Rock sites (Mena et al., 2010)

URS and Zeng’s models have considered scaling of rise-time/stress-drop and rupture speed for the upper 5 km depth. URS, UCSB, Zeng, and SDSU have variable rupture velocities, subevent rakes, rise-time ~ local slip, K -2 fall off in slip distribution UCSB considered dynamic rupture characteristics for slip time function, correlations between rupture speed, rise time, local slip, … Matched filter for the hybrid approaches: - amplitude match - phase match - wavelet match Comments and issues: 1 Hz

URS, UCSB, and SDSU use Green’s functions from 1D/3D wave propagation. Zeng uses 1D Green’s function. They all naturally include body waves and surface waves, Lg and Rg phases for regional wave propagation Zeng and SDSU use scattering functions for high frequency coda waves URS, UCSB, Zeng, and SDSU explicitly consider nonlinear soil responses. URS, UCSB, and SDSU are included in the SCEC computation platform. Zeng is planning to included his. Comments and issues:

Input: For all the models: Fault geometry, hypocenter, P- and S-wave velocities, Qp and Qs, fmax, seismic moment, site condition based on Vs30 (nonlinearity), site kappa For URS, UCSB, Olsen, Zeng (except slip): Slip, rise-time, and rupture-time distribution; correlation between these source parameters Variable rake, strike, … In Zeng’s model: slip distribution is defined by subevent stress-drop with random distribution on subevent locations