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Summary of Ground Mo.on Simula.ons Methods: Finite-‐Source and Point-‐Source

July 15, 2014 NGA-‐East SSHAC Workshop 2

Douglas Dreger (UCB)

Ques.ons for Resource Expert •  Summarize ground mo.on simula.on models •  Provide an overview of the technical bases for the methods considered.

•  What features are common among the methods •  What features are specific to a given method? •  What models are ready for forward simula.ons applica.on?

•  Which models or types of models are most appropriate for what range of magnitude and distance?

•  What part of the valida.on is most informa.ve in the assignment of a pass/fail grade?

Models Considered •  Point-‐Source Stochas.c

–  SMSIM (Boore, 1983, 2005, 2014) •  Finite-‐Source

–  Stochas.c Finite Fault Method (Silva et al., 1990) –  EXSIM (Motazedian and Atkinson, 2005; Atkinson and Assatourians,

2014) – G&P (Graves and Pitarka, 2010, 2014) –  SDSU (Mena et al., 2010; Mai et al., 2010; Olsen and Takedatsu, 2014)

– UCSB (Liu et al., 2006; Schmedes, 2010, 2013; Crempien and Archuleta, 2014)

–  CSM (Zeng et al., 1994, 1995, 1996; Anderson, 2014)



–  Stochas.c Finite Fault Method (Silva et al., 1990, 1997) –  EXSIM (Motazedian and Atkinson, 2005; Atkinson and Assatourians,




Stochas.c Simula.on of Time Histories

1)  Employs linear filter theory and simplified propaga.on models to scale and shape random phase .me histories and spectra.

Y M0,R, f( ) = E M0, f( )P R, f( )S f( ) I f( )

From SCEC BBP EXSIM Documentation

Stochas.c Simula.on of Time Histories 2) Empirically calibrated shape and scaling func.ons include:

A)  Region specific geometrical spreading

B)  Region specific Q C)  Site correc.ons D)  Applica.on of site

kappa or fmax E)  Correc.ons for a

magnitude-‐dependent double corner frequency

Y M0,R, f( ) = E M0, f( )P R, f( )S f( ) I f( )


Stochas.c Simula.on of Time Histories


EXSIM – Stochas.c Simula.on of Time Histories

EXSIM introduces a dynamic corner frequency to model a propaga.ng slip pulse..


Sa is calculated from the .me histories. Bias (ln residual) plots are used to compare the observed and simulated Sa. BBP V13.6 valida.on compared simulated mo.ons for 7 earthquakes recorded at ~40 sta.ons each.

SMSIM – New Generalized Double Corner Frequency Models

A∝M 0 f2 1

1+ f fa( )pfa"

#$%&'

pda

1

1+ f fb( )pfb"

#$%&'

pdb

Mul.plica.ve

A∝M0 f

2 1−ε( )

1+ ffa( )

pfa#

$%

&

'(

pda+

M0 f2ε

1+ ffb( )

pfb#

$%

&

'(

pdb

Addi.ve

fa < fc < fb

fc = 4.906x106β Δσ

M0( )1/3

fb = fa

fcfa( )

2

− 1−ε( )

ε

log fa =C1 fa +C2 fa M −M fa( )logε =C1ε +C2ε M −Mε( )

Boore, Di Alessandro, and Abrahamson, 2014


Behavior of Mul.plica.ve Model



Behavior of Addi.ve Model


SMSIM – ADCF



–  Stochas.c Finite Fault Method (Silva et al., 1990) –  EXSIM (Motazedian and Atkinson, 2005; Atkinson and Assatourians,




Classes of Finite-‐Fault Simula.on Approaches

•  Stochas.c (EXSIM, Silva & Darragh) –  U.lizes temporally and spectrally shaped white noise to generate .me series

used to es.mate Sa. –  Shape func.ons are empirically calibrated

•  Determinis.c (CSM and UCSB) –  Applies the representa.on theorem for a fault disloca.on u.lizing Green’s

func.ons for simplified 1D velocity structures –  Differences in the methods are in terms of the descrip.on of the kinema.c

source model •  Hybrid (G&P and SDSU)

–  Applies representa.on theorem for the low frequency determinis.c part –  Uses a stochas.c component to characterize high frequency por.on of the

spectrum •  G&P uses a stochas.c approach following Boore (1983) & Frankel (1995) •  SDSU uses scamering func.ons Zeng et al. (1991, 1993)

Seismic Representa.on Theorem

Displacement discon.nuity across fault

Isotropic elas.c tensor

Unit-‐force Green’s func.on represen.ng source to receiver transfer func.on for prescribed velocity model

Composite Source Model – V13.6 1)  U.lizes Green’s func.ons that are

complete in terms of body and surface waves, and near-‐, intermediate-‐ and far-‐field terms.

2)  1D velocity models are used with a frequency independent Q model.

3)  The source model is built from a distribu.on of randomly placed point-‐sources in which the distribu.on sa.sfies a Gutenberg-‐Richter rela.onship and radius-‐frequency self-‐similarity.

4)  The .ming of the subevents is controlled by a constant velocity rupture front ini.a.ng from a hypocenter.

5)  Subevents are allowed to overlap.

Composite Source Model-‐ V13.6 1)  U.lizes Green’s func.ons that are

complete in terms of body and surface waves, and near-‐, intermediate-‐ and far-‐field terms.

2)  1D velocity models are used with a frequency independent Q model.

3)  The source model is built from a distribu.on of randomly placed point-‐sources in which the distribu.on sa.sfies a Gutenberg-‐Richter rela.onship and radius-‐frequency self-‐similarity.

4)  The .ming of the subevents is controlled by a constant velocity rupture front ini.a.ng from a hypocenter.

5)  Subevents are allowed to overlap.

Composite Source Model – V13.6

1.  Informed from dynamic simula.ons 2.  U.lizes 1D Green’s func.ons with a

frequency dependent Q(f). a.  Layered structure use for f < 2 Hz b.  Single crustal layer structure used

for f>= 2 Hz 3.  PDF and correla.on func.ons between

key kinema.c parameters are obtained from more than 300 dynamic simula.ons a.  Slip b.  Rise .me c.  Peak .me d.  Peak slip rate e.  Rupture velocity

4.  A random slip model assuming a k-‐2 spa.al distribu.on is used with slip amplitude scaled by empirical rela.on is then itera.vely adjusted to conform to the PDF and correla.on func.ons.

5.  A 2d finite-‐difference algorithm is used to determine subfault trigger .mes from the locally prescribed rupture velocity.

UCSB Method – V14.3

11/22/2013 COSMOS Technical Session

UCSB Method – V14.3

UCSB Method

V14.3

Graves & Pitarka Method – V14.3 Computes determinis.c long-‐period mo.ons (T > 1 sec) using 1D Green’s func.ons (frequency independent Q), and a kinema.c model based on empirically calibrated theore.cal forms for kinema.c parameter scaling.

•  Fault area/dimensions scale with magnitude (Leonard, 2010)

•  Correla.on of slip heterogeneity scales with magnitude (Mai and Beroza, 2002) in which the coefficient of varia.on is set at 0.85

•  Average rise .me scales with M00.33 (Somerville et

al., 1999) but is double for z<5 km and z>15 km •  Background rupture speed scales with local Vs. •  Local rise .me scales with square root of local slip

plus a small random component •  Local rupture speed scales with local slip and

M00.33

Short-‐period (T < 1 sec) mo.ons are generated using a stochas.c approach very similar to that used by SMSIM

Graves & Pitarka Method

Graves & Pitarka Method

V14.3

SDSU Method

U.lizes the same low-‐frequency Green’s func.ons and source generator as Graves and Pitarka (2010). Calculates high frequency stochas.c response from isotropic radia.on scamering func.ons from Zeng et al. (1991, 1993) The low-‐frequency and high-‐frequency and combined at 1 Hz similarly to G&P

SDSU Method

SDSU Method

V14.3

Comparison of Run 10000005v13.6 G&P and SDSU: Loma Prieta

Comparison of Best Fit Simula.ons: Loma Prieta LEX sta.on -‐ V14.3

Comparison of Best Fit Simula.ons: Loma Prieta LEX sta.on – V14.3

Evalua.on of Methods •  Evalua.on performed within the computa.onal framework of the BBP and was based on median pseudo specral accelera.on.

•  Part A: Event/sta.on specific PSA comparsions •  Part B: Comparisons with GMPE

•  Eight member evalua.on panel held workshops with modelers, reviewed wrimen documenta.on, and simula.on results from the BBP

•  Valida.on report for V13.6 was submimed to SCEC on August 1, 2013.

•  Documenta.on of the process and an update for V14.3 was submimed for publica.on in an SRL Special Issue

•  Part A: Mean Bias •  Combined Goodness of

Fit (CGOF) •  Pass 0.35 ln units •  Fail 0.70 ln units

•  Performance is very good for 5<R<300 km and 0.01 < T < 1 second

•  <= 20% of cases exceed failure threshold

•  ~80% are bemer than a factor of 2

•  ~40% are bemer than the 1.41x pass threshold

CGOF = 12ln data

model( ) +12ln data

model( )

•  Part A: Method / GMPE •  Pass < 1 •  Fail > 1.5

•  Performance is very good for 5<R<300 km and 0.01 < T < 3 second

Part A: Distance Metric Ln residual is plomed for each event in discrete distance bins. Ideally the slope is zero. Test: If a slope of zero lies within the 95% confidence of the slope es.mate there is no systema.c distance bias and the method passes. Distance metric is the abs(slope)/95%confidence_slope

Part B Evalua.on

Ques.ons for Resource Expert •  Summarize ground mo.on simula.on models •  Provide an overview of the technical bases for the methods considered. •  What features are common among the methods •  What features are specific to a given method? •  What models are ready for forward simula.ons applica.on?

–  SMSIM, EXSIM, G&P, SDSU and UCSB •  Which models or types of models are most appropriate for what range

of magnitude and distance? –  All V14.3 methods within M range of valida.on (M 4.6 – 7.2) –  All V14.3 methods for 0 < R <= (200 or 300) km

•  What part of the valida.on is most informa.ve in the assignment of a pass/fail grade?

–  Part B defines a rigid pass/fail, however there is no one metric that is perfect for this purpose. –  A combina.on of metrics as implemented provides a more comprehensive analysis of the

performance of these complex methods. –  Addi.onal metrics should be introduced including Fourier amplitude spectra fits, consistency

with net omega-‐2 spectral shape, component specific measures, and limits of sta.c slip to zero fault distance.

References •  Anderson, J. G. (2014). The composite source model for broadband simula.ons of strong ground mo.ons,

submimed to Seism. Res. Lem. •  Atkinson, G. M., and K. Assatourians (2014). Implementa.on and valida.on of EXSIM (a stochas.c finite-‐fault

ground-‐mo.on simula.on algorithm) on the SCEC broadband plavorm, submimed to Seism. Res. Lem. •  Boore, D. M. (1983). Stochas.c simula.on of high-‐frequency ground mo.ons based on seismological models of

the radiated spectra, Bull. Seism. Soc. Am., 73, 1865-‐1894. •  Boore, D. M. (2005). SMSIM – Fortran programs for simula.on ground mo.ons from earthquakes: Version 2.3

– A revision of OFR 96-‐80-‐A, US Geological Survey Open-‐File Report, 00-‐509, revised 15 August 2005, 55pp. •  Boore, D. M. (2009). Comparing stochas.c point-‐source and finite-‐source ground-‐mo.on simula.ons: SMSIM

and EXSIM, Bull. Seism. Soc. Am., 99, 3202-‐3216. •  Boore, D. M., C. Di Alessandro, and N. A. Abrahamson (2014). A generaliza.on of the double-‐corner-‐frequency

source spectral model and its use in the SCEC BBP valida.on exercise, submimed to Bull. Seism. Soc. Am. •  Crempien J. G. F., and R. J. Archuleta (2014). UCSB Method for Broadband Ground Mo.on from Kinema.c

Simula.ons of Earthquakes, submimed to Seism. Res. Lem. •  Dreger, D. S., G. C. Beroza, S. M. Day, C. A. Goulet, T. H. Jordan, P. A. Spudich, and J. P. Stewart (2014).

Valida.on of the SCEC broadband plavorm V14.3 simula.on methods using pseudo spectral accelera.on data, submimed to Seism. Res. Lem.

•  Dreger, D. S., G. C. Beroza, S. M. Day, C. A. Goulet, T. H. Jordan, P. A. Spudich, and J. P. Stewart (2013). Evalua.on of SCEC Broadband Plavorm Phase 1 Ground Mo.on Simula.on Results, SCEC Report No. X, 33 pages.

•  Graves, R., and A. Pitarka (2014). Refinements to the Graves and Pitarka (2010) Broadband Ground Mo.on Simula.on Method, submimed to Seism. Res. Lem.

•  Graves, R. W., and A. Pitarka (2010). Broadband Ground-‐Mo.on Simula.on Using a Hybrid Approach, Bull. Seism. Soc. Am., 100, 2095-‐2123, doi:10.1785/0120100057.

•  Liu, P. and R. J. Archuleta (2004). A new nonlinear finite fault inversion with 3D Green’s func.ons: Applica.on to 1989 Loma Prieta, California, earthquake, J. Geophys. Res., 109, B02318, doi:10.1029/2003JB002625.

References •  Liu, P. R. J. Archuleta, and S. H. Hartzell (2006). Predic.on of broadband ground-‐mo.on .me histories: Hybrid low/high-‐

frequency method with correlated random source parameters, Bull. Seism. Soc. Am., 96(6), 2118-‐2130, doi:10.1785/0120060036.

•  Mai, P. M., W. Imperatori, and K. B. Olsen (2010). Hybrid broadband ground-‐mo.on simula.ons: combining long-‐period determinis.c synthe.cs with high-‐frequency mul.ple S-‐toS backscamering, Bull. Seism. Soc. Am., 100, 5A, 2124-‐2142, doi:10.1785/0120080194.

•  Mena, B., P. M. Mai, K. B. Olsen, M. D. Purvance, and J. N. Brune (2010). Hybrid broadband ground-‐mo.on simula.on using scamering Green’s func.ons: applica.on to large-‐magnitude events, Bull. Seism. Soc. Am., 100, 5A, doi:10.1785/0120080318.

•  Motazedian, D., and G. M. Atkinson (2005). Stochas.c finite-‐fault modeling based on a dynamic corner frequency, Bull. Seism. Soc. Am., 95, 995-‐1010.

•  Olsen, K., and R. Takedatsu (2014). The SDSU Broadband Ground Mo.on Genera.on Module Bbtoolbox Version 1.5, submimed to Seism. Res. Lem.

•  Schmedes, J., R. J. Archuleta, and D. Lavallée (2010). Correla.on of earthquake source parameters inferred from dynamic rupture simula.ons, J. Geophys. Res., 115, B03304, doi:10.1029/2009JB006689.

•  Schmedes, J., R. J. Archuleta, and D. Lavallée (2013). A kinema.c rupture model generator incorpora.ng spa.al interdependency of earthquake source parameters, Geophys. J. Int. 192 (3), 1116-‐1131. doi: 10.1093/gji/ggs02.

•  Schneider, J. F., W. J. Silva, and C. L. Stark (1993). Ground mo.on model for the 1989 M6.9 Loma Prieta earthquake including effects of source, path, and site, Earthquake Spectra 9, 251–287.

•  Silva, W., R. Darragh, C. Stark, I. Wong, J. Stepp, J. Schneider, and S. Chiou (1990). A methodology to es.mate design response spectra in the near-‐source region of large earthquakes using the Band-‐Limited-‐White-‐Noise ground mo.on model, in Proc. Fourth U.S. Na<onal Conference on Earthquake Engineering, Vol. 1, 487–494.

•  Silva, W. J., Abrahamson, N., Toro, G., and Costan.no, C. (1997). “Descrip.on and valida.on of the stochas.c ground mo.on model, Final Report.” Brookhaven Na<onal Laboratory, Contract No. 770573, Associated Universi.es, Inc. Upton, New York

•  Zeng, Y., J. G. Anderson and G. Yu (1994). A composite source model for compu.ng realis.c synthe.c strong ground mo.ons, Geophysical Research Lemers 21, 725-‐728.

•  Zeng, Y., J. G. Anderson and F. Su (1995). Subevent rake and random scamering effects in realis.c strong ground mo.on simula.on, Geophysical Research Lemers 22, 17-‐20.

•  Zeng, Y. and J. G. Anderson (1996). A composite source model of the 1994 Northridge earthquake using gene.c algorithms, Bull. Seism. Soc. Am. 86, No. 1B, pages S71-‐S83.

Comparison of Best Fit Simula.ons: Loma Prieta V13.6

Comparison of Best Fit Simula.ons: Loma Prieta – V13.6

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