Description of selected broadband ground motion simulation methods

Paul Somerville, URSYuehua Zeng, USGS Golden

Simulation Methods Described:

1. URS2. Zeng3. UCSB4. 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 (Mw

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.

• 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

Ti = r / Vr – t(D)

Vr = 80% local Vs depth > 8 km

= 56% local Vs depth < 5 km

linear transition between 5-8 km

t scales with local slip (D) to accelerate or decelerate rupture

t(Davg) = 0

Rise Time

= k · D1/2 depth > 8 km

= 2 · k · D1/2 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:

A = 1.6e-09 · Mo1/3 (WUS)

tA = 3.0e-09 · Mo1/3 (CEUS)

Rake

= o + -60o << 60o

Random perturbations of rake follow spatial distribution given by K-2 falloff.

• Corner frequency scales with local rupture speed (Vr):

fc = co · Vr / (dl) co = 2.1 (WUS), 1.15 (CEUS)

(empirically constrained)

Vr= 80% local Vs depth > 8 km= 56% local Vs depth < 5 kmlinear transition between 5-8 km

High Frequency Subfault Source Spectrum• Apply Frankel (1995) convolution operator:

S(f) = C · [ 1 + C · f 2 / fc2 ]-1

C = Mo / (Npdl3) N = number of subfaults

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

1994 Northridge EQ

Spectral Acceleration Goodness of Fit

Ri = ln(Oi /Si)

Bias = (1/N) Ri

= [(1/N) (Ri – Bias)2]1/2

2. Composite Source Model (Zeng et al., 1994)

A source composes of a superposition of smaller subevents. The distribution of subevents with radius R follows a power law distribution (Frankel, 1991)

DpRRd

dN )(ln

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. 2118-2130, doi: 10.1785/0120060036.

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:10.1029/2009JB006689.

Flowchart for Generating Broadband Strong Motion Synthetics

Flowchart for Generating Broadband Strong Motion Synthetics

Liu, Archuleta, Hartzell, BSSA

Correlated Source Parameters (LAH)

Correlated Source Parameters (LAH)

Slip

Average rupture velocity

Rise time

Spatial correlation 30%Spatial correlation 30%

Spatial correlation 60%

(Liu, Archuleta, Hartzell, 2006)(Liu, Archuleta, Hartzell, 2006)

New Kinematic Model (SAL)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:10.1029/2009JB006689.

Frequency dependent perturbation of strike, dip and rake (Pitarka et al, 2000)

With f1=1.0 Hz, f2=3.0 Hz

High FrequenciesHigh Frequencies

Randomness of the high frequencies is generated in the source description.

i 0 f f1

0 ( f f1) / f2 f1)((2ri 1) p , f1 f f2

0 (2* ri 1) * p f2 f

(

Ground Motion Computation: 3DGround 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:Combination of 1D and 3D:

1. Cross correlation at matching frequency fm to align seismograms.

2. Use 3D at frequencies

3. Use 1D at frequencies

4. For

Re(S( f )) r( f )Re(3D( f )) (1 r( f ))Re(1D( f ))

Im(S( f )) r( f )Im(3D( f )) (1 r( f ))Im(1D( f ))

r( f ) 1 f f low

fup f low

f low f fup

0 f f low

fup f fmax

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, 2124-2142.

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, 2143-2162.

4. 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 Combines low-frequency deterministic synthetics (f ~ 1 Hz) with high-frequency scattering operatorsscattering operators

SiteSite effects: effects: • Soil structureSoil structure• (De-)amplification of ground motions(De-)amplification of ground motions• Non-linear soil behaviorNon-linear soil behavior

ScatteringScattering effects: effects: • inhomogeneities in Earth structure at all scalesinhomogeneities in Earth structure at all scales• scattering model, based on site-kappa, Q, scattering and intrinsicscattering model, based on site-kappa, Q, scattering and intrinsic attenuation, attenuation, ssand and ii

Scattering Green’s functions computed for each component of motion based on Zeng et al. 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 (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 decaydynamically-consistent source-time function, generating 1/f spectral decay

Site-Scattering parameters (scattering and attenuation coefficient, site kappa, intrinsic 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 attenuation) are taken from the literature and are partly based on the site-specific velocity structure.structure.

Assuming scattering operators and moment release originate throughout the fault, but Assuming scattering operators and moment release originate throughout the fault, but starts at the hypocenterstarts at the hypocenter

Site-Specific Scattering Functions

Hybrid broadband seismograms are Hybrid broadband seismograms are calculated from low-frequency and high-calculated from low-frequency and high-frequency synthetics in the frequency frequency synthetics in the frequency domain using a simultaneous amplitude and domain using a simultaneous amplitude and phase matching algorithm (Mai and Beroza, phase matching algorithm (Mai and Beroza, 2003)2003)

Example BB calculation

BB

SC

LF

BB = broadbandLF = low frequencySC = scattering functions

1/f

Generation of hybrid broadband seismograms Generation of hybrid broadband seismograms

Method implemented on the SCEC Method implemented on the SCEC Broadband platform Broadband platform

Validations include Northridge, Landers Validations include Northridge, Landers and Loma Prieta, and NGA relations at and Loma Prieta, and NGA relations at selected sitesselected sites

Northridge Validation Northridge Validation (Mai et al., 2010)(Mai et al., 2010)

Verification and ValidationVerification and Validation

NGA validation at Precariously Balanced Rock NGA validation at Precariously Balanced Rock sites (Mena et al., 2010)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 parametersVariable rake, strike, …

In Zeng’s model: slip distribution is defined by subevent stress-drop withrandom distribution on subevent locations