Average properties of Southern California

earthquake ground motions envelopes…

G. Cua, T. Heaton

Caltech

Main Points

saturation of rock vs soil sites attenuation characteristics of P vs S-

waves importance of station corrections

Motivation: Seismic Early Warning

Q1: Given available data, what ismost probable magnitude andlocation estimate?

Q2: Given a magnitude and location estimate, what are the expected ground motions?

Full acceleration time history

envelope definition– max.absolute value over 1 second window

Ground motion envelope: our definition

P,S-wave envelopes – rise time, duration, constant amplitude, 2 decay parameters

Noise - constant

model for observed envelope

Modeling ground motion envelopes

2 2 2OBS P S NOISEE E E E

70 events 2 < M <=7.3 0 < R < 200 km

9 channels Z, EW, NS acc, vel, disp

binary classfication rock - NEHRP BC, above soil - NEHRP C, below

log10(distance in km)

M

ag

nit

ud

e

Database

Functional form for M, R-dependence of ground motion amplitudes

C(M) term “turns on”amplitude saturation forM > 5

Magnitude

C(M

)

* Modified from Campbell (1981)

10 1 10 1

ground motion amplitudes

1,...[9 channels 2 (rock and soil) 2 (P-, S-wave)]

or for 5;

for 5

epicentral distance for 5

log ( ) ( ( )) log ( ( ))

b l

W

i i i i i i

A

i

M m m M

M M

R M

A a M b R C M d R C M e

21

1 2

2i

closest distance to fault (when available) for 5

9

( ) (arctan( 5) 1.4) ( exp( ( 5))) *

constant + station corrections

statistical error, ~ (0, )

i

M

R R

C M M c c M

e

N

Main Points

saturation of rock vs soil sites attenuation characteristics of P vs S-

waves importance of station corrections

ROCKS-wave

SOILS-wave

Scaling for small magnitudes-

10 1 10 1log ( ) ( ( )) log ( ( ))i i i i i iA a M b R C M d R C M e

0.81.4

1~ 10 MU

R

Saturation of rms horizontal acceleration S-wave (rock vs soil)

Saturation is most pronounced in acceleration in close to large events Also present to some degree in velocity and displacement Rock and soil approach similar amplitude levels in close to large events Displacements are high-passed filtered

Acceleration Velocity

(filtered)Displacement

Main Points

saturation of rock vs soil sites

attenuation characteristics of P vs S-waves

importance of station corrections

S-wave acceleration (ROCK)

P-wave acceleration (ROCK)

scaling for small magnitudes, 0.7

1.2

0.81.4

1~ 10

1~ 10

MP

MS

UR

UR

horizontal P-wave amplitudes saturate more than horizontal S-wave difference between P- and S-waves is more pronounced in horizontal than vertical uniquely decomposing P and S wave at close distances is problematic, particularly on horizontal

Vertical P and S waveHorizontal P and S wave

Something curious …

Average Rock and Soil envelopes as functions of M, R ACCELERATION

Main Points

saturation of rock vs soil sites attenuation characteristics of P vs S-

waves

importance of station corrections

rock only= 0.308

rock w/ station corr= 0.243

~21% reduction in

How much do station corrections improve standard deviation?

rock + soil= 0.315

22 ( )

#obs predA A

dof

Acceleration Amplification Relative to Average Rock Station

Velocity Amplification Relative to Average Rock Station

Conclusions Saturation of rock and soil sites

Soil sites saturate ground motions more than rock Stronger saturation at higher frequencies Difference between rock and soil sites decreases

with increasing ground motion amplitude

P-waves appear to have higher degree of saturation than S-waves ?

Station-specific data contributes to ~20% variance reduction

Rock versus Soil

CDMG map of Preliminary Surface Geologic Material (Wald) and SCEC Phase III Report Velocity Calculator

NEHRP Class

Maximum Shear Wave Velocity in Upper 30 m (m/s)

A (Hard Rock)

1400

B (Soft Rock) 724

BC 686

C 464

CD (Alluvium)

372

D 301

DE 298

E (Mud) 163

30 CISN ROCK Stations

120 CISN SOIL Stations

Our Binary Classification

Average Rock and Soil envelopes as functions of M, R VELOCITY

Average Rock and Soil envelopes as functions of M, R (filtered) DISPLACEMENT

ROCK SOILa 0.7789 0.8354b -2.56E-03 -2.32E-03c1 1.4775 1.768c2 1.1054 1.03d -1.352 -1.563e -0.645 -0.338

magnitude-dependence

saturation

anaelastic attenuation

geometric attenuationconstant

S-wave S-wave

10 1 10 1log ( ) ( ( )) log ( ( ))i i i i i iA a M b R C M d R C M e

P-wave S-wavea 0.718 0.779b -3.27E-03 -2.56E-03c1 1.6 1.478c2 1.045 1.105d -1.195 -1.105e -1.064 -0.645

S-wave acceleration (ROCK)

P-wave acceleration (ROCK)

Station Corrections

Average residual at a given station relative to expected ground motion amplitude given by attenuation relationship

Defined for stations with 2 or more available records

Consistent with generally known station behavior

PAS, PFO are typically used as hard rock reference sites SVD anomalous due to proximity to San Andreas

Some “average” rock stations are: DGR, JCS, HEC, MWC, AGA, EDW