Attenuation and GMPE’s for earthquakes in Iceland

Símon Ólafsson

University of IcelandEarthquake Engineering Research Centre

Austurvegur 2a - Selfoss

UPStrat-MAFA Workshop, Selfoss 24-27 July 2012

Not enough data exists for applying regression equations

Applying GMPEs from other regions does not give good results

GMPEs from other regions tend to underestimate close to fault and overestimate far from fault

Applying GMPs to Icelandic data

Developing a GMPE

Basic assumptions:

Strike slip earthquake with near vertical fault plane Strong motion phase modelled Brune’s source model applied High frequency spectral decay modelled with an

exponential term Geometrical spreading function applied

Recent Earthquakes in South Iceland

• Mw 6.0, 25 May 1987

• Mw 6.6, 17 June 2000

• Mw 6.5, 21 June 2000

• Mw 6.3, 28th May 2008

Modelling approach

p 0 20 c c3

c 2c

12

C M R(M , , R , , , ) ( , ) ( , ) ( , ) ( )

21( , ) =

1+ ( / )1( , )

( , ) exp

( )

A B G E S

B Omega squared source model

G Geometrical spreading function

E Spectral attenuation

S Site amplification

R R

R R

Geometric spreading function

d = epicentral distance h = depth parameterD1, D2 and D3 are used to set the limits for the different zones

of the spreading function

12

n nD DD

R 1 2

2 3

D D DD D D

2 2 D d h

Reference:Ólafsson, S. and Sigbjörnsson, R. (1999), “A theoretical attenuation model for earthquake-induced ground motion”, Journal of Earthquake Engineering 3, Imperial College Press, 287-315.

100

101

102

103

10-3

10-2

10-1

100

101

DISTANCE (km)

PEAK G

RO

UND A

CCELE

RATI

ON (g

)

0 20 40 60 80 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

DISTANCE (km)PEAK G

RO

UND A

CCELE

RATI

ON (g

)

Effect of spreading function

Theoretical GMPE

dT2

rmsd 0

1a a(t) dtT

2

rmsd

A( )1a d2 T

Parseval theorem:

Theoretical attenuation model for rms acceleration:

2 2/3 2/3p

rms 3/2 1/2d

0

2.34 (16 / 7) R C 1log(a ) log log22

1 log(M ) log3

T

R

A relationship for peak acceleration is obtained by inserting:

amax = parms

cos3sinsi21sin3cosci

211

dtt

tsin2

dtt

tsinxsix

0x

dtt

1tcosxlndtt

tcosxcix

0x

c

The function

Estimation of parameters

Sub-filter Time domain Frequency domain

B()

D()

E

S

2 21 1 1( ) 2e ( 1) e ( 2) ( )x k x k x k w k

2

1 2(1 e )z

2 1 1 12S

1( ) ( ( ) 2 ( 1) ( 2))x k x k x k x kT

1 2 2S(1 ) /z T

2 1

3 22 21 S

( ) ( )2 / 2

pN n

n

zx k x k nnT

2 2S

2 / 2

n

n

znT

4 4 3( ) ( ) (1 ) ( )c cx k r x k n r x k m

S

S

/

2 /

(1 )1

Tc

Tc

r zr z

Discrete filter equations for GMPE

Earthquake 28 May 2008 - Parameters

Parameter Estimate Units _____________________________________Mo 3.4 ×1018 N mMw 6.26 Fc 0.24 Hzr 6.4 km 0.053 s 73.0 baru 79.4 cm_____________________________________

GMPE for Iceland Mw4.8 – Mw6.6

Parameter Estimate Units Typeo 2.8 g/cm3 Density 6.4 km S-wave velocity 0.04 s Spectral decay 100 bar Stress

dropr Fault radius

D 2 4r Geom. att. param.n 2 Exponenth ≈ r Depthp 2.94 Peak factor

100

101

102

103

10-3

10-2

10-1

100

101

DISTANCE (km )

PG

A (

g)

Magnitude MW6

100

101

102

103

10-3

10-2

10-1

100

101

DISTANCE (km )

PG

A (

g)Magnitude MW6.5

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

DISTANCE (km)

PG

A (

g)

Magnitude MW6.5 – Linear scale

100

101

102

103

10-3

10-2

10-1

100

101

DISTANCE (km)

PG

A (

g)

Magnitude MW6.5 Icelandic model fitted to NGA data

100

101

102

103

10-3

10-2

10-1

100

101

DISTANCE (km )

PG

A (

g)

Magnitude MW6.5 Icelandic strong motion and formulas from Europe and America

100

101

102

103

10-3

10-2

10-1

100

101

DISTANCE (km )

PG

A (

g)

Magnitude MW6.5 NGA data with formulas by Campbell, Ambraseys and Boore

31 2 T

cd

rT c c d

Duration function

Td = duration r = radius of dislocation = S-wave velocity

d = hypocentral distance c1, c2, c3 = model parameters

T = standard deviation of duration

0 20 40 60 80 1000

5

10

15

20

25

30

DISTANCE (km)

DU

RA

TIO

N (s

)

Duration – 90% cumulative energy

Cumulative energy

Cumulative energy

c1 c1 c3 T h (km) G n PGA0 (g)

50% 0.3915 0.1325 0.9977 1.9472 15.5034 5.6848 1.9976 0.2872 0.804955% 0.4721 0.1130 1.0442 1.9309 15.1629

5.5282

1.9967 0.2868 0.7772

60% 0.5394 0.0926 1.1084 1.9424 15.0573 5.4360 1.9949 0.2863 0.755465% 0.6383 0.0767 1.1651 2.0717 14.7577 5.3421 1.9936 0.2858 0.733370% 0.8402 0.0446 1.3072 2.3974 14.0419 5.0856 1.9924 0.2851 0.697675% 0.7524 0.0642 1.2395 2.7453 14.6322 5.2775 1.9909 0.2848 0.716480% 1.1013 0.0371 1.3760 3.1754 13.5552 5.0906

1.9897

0.2842

0.6849

85% 1.3357 0.0255 1.4812 3.8608 13.0368

4.8847

1.9855

0.2847

0.6762

90% 1.8519 0.0080 1.7840 5.4832 12.2003 4.8697 1.9853 0.2833 0.6671

Estimated parameters

100

101

102

10-3

10-2

10-1

100

DISTANCE (km)

PG

A (g

)

GMPE (Mw6.5) with 50 – 90% cumul energy

0 20 40 60 80 1000

5

10

15

20

25

DISTANCE (km)

DU

RA

TIO

N (s

)

50%55%

60%65%

70%75%

80%85%90%

Duration function for 50% - 90% cumulative energy

Macroseismic data and model

Articles regarding attenuation and GMPE for Iceland Sigbjörnsson R, Ólafsson S (2004) Near-source

decay of seismic waves in Iceland, article 4462 in Proceeding of the 15WCEE.

Sigbjörnsson R, Ólafsson S, Snæbjörnsson JT (2007) Macroseismic effects related to strong ground motion: a study of the South Iceland earthquakes in June 2000. Bulletin of Earthquake Engineering 5, 591-608.

Sigbjörnsson R, Ólafsson S (2004) On the South Iceland earthquakes in June 2000: Strong-motion effects and damage. Bollettino di Geofisica Teorica ed Applicata, 45(3), 131-152.

The parameter n defines the rate of attenuation for the geometrical spreading function has been estimated to be very close to the theoretical rate of attenuation, n = 2, for ground motion in the near-field. Based on data from earthquakes Mw6.3 – Mw6.5.

The parameter D2 was estimated 5r. The depth parameter, h, was estimated as to be in the range 15.5 km to 12.2 km.

The standard deviation, , is lowest for the estimation using the 90% duration. This result seem to favour the use of the 90% duration model for the GMPE.

Conclusions

End