1. Empirical attenuation formula for estimating PGA, PGV and response spectra

 

Many researchers have studied the attenuation characteristics of strong ground motion for a long time. They proposed many empirical attenuation formulas to estimate peak ground acceleration (PGA), peak ground velocity (PGV) and response spectra. Several formulas are selected and shown in this page according to the following criterion;

              - Published recently,

              - Applicable to near-source region,

              - Based on the observed record in wide area,

              - Referred or applied frequently.

 

Finally, thirty-one formulas which are summarized in Table 1.1 are selected and following ten items are compiled.

 

1) Reference

2) Estimated physical parameter

3) Used strong motion data

4) Style of faulting

5) Ground condition

6) Definition of magnitude

7) Definition of source distance

8) Definition of horizontal component

9) Applicability written in the paper

10) Empirical attenuation formula

 

Table 1.1  Summary of empirical attenuation formula

Abrahamson & Silva(1997)

Boore et al.(1997)

Spudich
et al.(1999)

Sabetta & Pugliese(1996)

Youngs et al. (1997)

Rinaldis et al. (1998)

Ambraseys (1995)

Ambraseys et al. (1996)

Tectonic Environment

Shallow Crustal

Shallow Crustal

Shallow Crustal

Subduction

Extension and Compression

Shallow (h<25km)

Shallow (h<30km)

Style of Faulting

- Reverse
- Reverse/Oblique
- Otherwise

- Strike slip
- Reverse slip
- Mechanism not specified

- Extensional

- Interface
- Intra slab

- Normal
- Thrust/Strike slip

Ground Condition

- Rock or shallow soil
- Deep soil

evaluated by average shear velocity over upper 30m

- Rock
- Soil

- Stiff
- Shallow Alluvium
- Deep Alluvium

- Rock
- Shallow soil
- Deep soil

- Rock
- Alluvium

- Rock
- Stiff soil
- Soft soil

Other Effect

Hanging Wall

Acceleration

Velocity

Sa (5%)


(0.1 - 5.0sec)


(0.1 - 2.0sec)


(0.075 - 3.0 sec)


(0.1 - 2.0sec)

Sv (5%)


(0.1 - 2.0sec)


(0.04 - 4.0sec)

Magnitude

Mw

Mw

Mw

5.5£Ms
ML<5.5

Mw

Ms, Mw

Ms

Ms

Distance *1)

A

B

B

B, D

A

D

B, D

B, D

Component

H

(geometric mean)

(random horizontal component)

(geometric mean)

(larger)

(geometric mean)

(larger)

V

SourceData

World Wide,
1940-1994,
4.4<M<7.4,
0.1-100km,
58events,
655records

Western North America,
1940-1992,
5.2<M<7.4,
0-118km,
19events,
271records

World Wide,
1940-1995,
5.1<M<7.2,
0-100km,
39events,
142records

Italia,
1940-1992,
4.6<M<6.8,
1.5-110km,
17events,
95records

Alaska, Chile, Cascadia, Japan, Mexico, Peru, Solomon Islands,
1940-1992,
5.0<M<8.2,
8.5-550km,
19events,
271records

Italia&Greece,
4.5<M<7.0,
7-138km,
310records

Europe,
4.5<M<7.0,
1-310km,
334events,
830components

Europe,
1972-1994,
4.0<M<7.9,
0-212km,
157events,
422components

Applicability

5.5<M<7.5,
R<80km

R<100km

4.6<M<6.8,
R<100km

5<M,
10<R<500km

4.5<M<7,
10<R<100km

 

 

 

 

 

 

 

 

 

 

Campbell &Bozorgnia (2003)

Fukushima & Tanaka (1990,1992)

Molas & Yamazaki (1995)

Takahashi et al. (2000)

Si & Midorikawa(2000)

Ohno et al. (2001)

Nishimura & Horike (2003), Horike & Nishimura(2004)

 

Tectonic Environment

Shallow Crustal Earthquakes

Subduction Earthquakes

Shallow

 

Style of Faulting

- Strike slip/Normal
- Reverse
- Thrust

 

Ground Condition

- Firm rock
- Soft rock
- Very Firm soil
- Firm soil

several ground condition

- Rock
- Hard soil
- Medium soil
- Soft soil

- Rock
- Hard soil
- Medium soil
- Soft soil

Firm ground
Vs 600m/s
(average over the upper 30m)

- Tertially
- Pleistocene
- Holocene

AVS20
- 0-250m/s
- 250-400m/s
- 400-700m/s
- 700m/s -

 

Other Effect

Hanging Wall

 

Acceleration

(ground surface)

 

Velocity

 

Sa (5%)


(0.05 - 4.0sec)


(0.2 - 5.0 sec)

 

Sv (5%)


(0.05 - 5.0 sec)

 

Magnitude

Mw

MJ, Mw, Ms

MJ

Mw

Mw

Mw

MJ

 

Distance *1)

B

A

A

A, D

A, E

E

D

 

Component

H

(geometric mean)

(average)

(larger)

(geometric mean)

(larger)

(independent data)

(average)

 

V

 

SourceData

World Wide,
1957-1995,
4.7<M<7.7,
3-60km,
85events, 1403records

Japan & World Wide,
1960-1990,
5.1<M<7.9,
0.1-300km,
Japan 32events, 555records,
World 20events, 278records

Japan(JMA-87),
1988-1993,
4.1<M<7.8,
1-200km,
387events, 2166pairs,
depth
£200km

Japan 1166 records,
5.0<M<8.25,
0.8-300km,
California 166records+Chile 2records,
5.8<M<8.0,
1-200km

Japan,
1968-1997,
5.8<M<8.2,
0-118km,
21events,
acc.1137records,
vel.543records

California,
1940-1994,
4.9<M<7.5,
4-174km,
58events, 662records

Japan(K-NET),
1996-2002,
5.4<M<7.3,
10-200km,
53events

 

Applicability

5.0<M,
R<60km,
shallow crustal earthquake in western
North America and in similor seismically active tectonic regimes world wide

0.1<R<300km

subduction zone earthquake,
depth<200km

0<R<200km

5.5<M<6.5 and depth<100km,
or
6.5<M<7.3 and crustal,
10<R<300km

 

*1)

A : shortest distance to the rupture surface

 

B : closest horizontal distance to the surface projection of the rupture plane

 

C : shortest distance to the seismogenic zone on the rupture plane

 

D : epicentral distance or hypocentral distance

 

E : Equivalent hypocentral distance

 

Author

Field

(2000)

Kalkan & Gülkan

(2004)

Kalkan & Gülkan

(2004)

Midorikawa &Ohtake

(2004)

Sunuwar et al.

(2004)

Takahashi et al.

(2004)

Takai et al.

(2004)

Tectonic

Environment

 

Sallow crustal

Shallow crustal

Crustal

Intra-plate

Inter-plate

 

Crustal

Interface

Slab

Shallow crustal

Intra-plate

Inter-plate

Style of Faulting

- Strike-slip

- Reverse-slip

- Reverse

- Strike-slip

- Normal

- Unknown

- Reverse

- Strike-slip

- Normal

- Unknown

 

 

- Reverse

- Strike-slip

- Normal

- Unknown

 

Ground

Condition

 

- Rock

- Soil

- Soft soil

- Rock

- Soil

- Soft soil

Stiff site (AVS30 is about 600m/s)

 

- Rock

- Hard soil

- Medium soil

- Soft soil

 

Other Effect

 

 

 

 

 

 

 

Acceleration

 

 

Velocity

 

 

 

 

 

Sa (5%)

(0.3, 1.0, 3.0sec)

 

 

 

(0.05-3.00sec)

(0.02-5.00sec)

 

Sv (5%)

 

 

 

 

 

 

 

Magnitude

Mw

Mw

Mw

Mw

MJ

Mw

MJ

Distance

closest distance to the vertical projection of rupture

closest horizontal distance

closest horizontal distance

fault distance

hypocentral distance

source distance

hypocentral distance

Component

H

(average)

 

(larger)

(larger)

(geometric mean)

V

 

 

 

 

 

Source Data

Southern California,

1934-1994,

5.1<Mw<7.5,

28events,

Turkey,

1976-2002,

4.5<Mw<7.4,

47events,

100records

Turkey,

1976-2003,

4.0<Mw<7.4,

57events,

112records

Japan,

1968-2001,

5.5<M<8.3,

depth3-120km,

33events,

PGA 3335redords, PGV 1980redords

Japan(K-NET),

1996 June

-2003 December,

4.0<MJ<5.6,

depth8-43km,

42events,

acc.667records,

Japan,

Iran,

Western USA,

Mw>5.0,

depth<162km,

Japan

249events, 4192records,

Iran and Western 21events, 208records

Japan(K-NET, Tohoku

and Hokkaido),

1997-2003,

5.0<MJ<8.0,

depth8-122km,

65events

Applicability

 

closest horizontal distance <200km

Mw4.5-7.5,

closest horizontal distance <250km,

Mw 4.0-7.5

 

eastern margin of Sea of Japan in the north-eastern part of Japan in Okhotsk-Amur plates boundary.

depth <120km

 

 

Author

Yanxiang YU & Yuxian HU

(2004)

Bragato and Slejko

(2005)

Liu & Tsai

(2005)

Kanno et al.

(2006)

Kataoka et al.

(2006)

Tectonic

Environment

 

 

Crustal earthquake

 

 

Style of Faulting

 

 

 

 

 

Ground

Condition

Rock

 

TWN area : whole Taiwan region

CHY area :

southwestern Taiwan IWA area :

 northeastern Taiwan NTO area :

 central Taiwan

 

 

Other Effect

 

 

 

 

 

Acceleration

 

Velocity

 

 

Sa (5%)

(0.04-20sec)

(0.05-2sec)

 

(0.05-5.00sec)

 

Sv (5%)

 

 

 

 

(1%)

(2-20sec)

Magnitude

ML

ML

Mw

Mw

Mw

Distance

epicentral distance

epicentral distance or closest horizontal distance to the vertical projection of the rupture

hypocentral distance

source distance

source distance

Component

H

V

 

 

 

Source Data

Southern California,

1991-2001,

5.0<M<7.5,

38events,

522records

Eastern Alps,

1976-2002,

2.5<ML<6.3,

240events,

PVA 3168records,

horizontal components 1402records

Taiwan,

1993-2002,

4.0<Mw<7.1,

depth2.7-30km,

51events,

three components

>7900

Japan(K-NET,KiK-net), California, Turkey

Japan 1963-2003,

California 1971-1994

Turkey 1999,

Mw>5.5,

Japan

184events, 11542records,

California and Turkey 10events, 377records

Japan,

1964-2004,

6.9<Mw<8.2(Subduction),

5.8<Mw<6.9(Crustal),

depth0-58.5km

21event,

Applicability

 

2.5<ML<6.3,

0<R<130km

 

 

 

 

Author

Morikawa et al.

(2006)

Uchiyama & Midorikawa

(2006)

Zhao et al.

(2006)

Campbell & Bozorgnia

(2008)

Tectonic

Environment

Inter-plate

Slab

 

Crustal

Interface

Slab

Shallow crustal

Style of Faulting

 

 

- Reverse

- Strike-slip

- Normal

- Unknown

Normal-Normal Oblique (30deg. < rake < 150deg.)

Reverse-Reverse Oblique (-150deg. < rake < -30deg.)

Ground

Condition

 

Vs 500m/s

(average over the upper 30m)

- Rock

- Hard soil

- Medium soil

- Soft soil

Represented by AVS30

Other Effect

 

 

 

Hanging-wall effect

Basin response effect

Linear-Non Linear site response

Acceleration

 

Velocity

 

 

Sa (5%)

(0.05-0.45sec)

(0.02-5.0sec)

(0.05-5.00sec)

(0.01-10.00sec)

Sv (5%)

 

 

 

 

Magnitude

Mw

Mw

Mw

Mw

Distance

source distance

shortest distance to the rupture surface

source distance

AB

Component

H

 

(geometric mean)

(geometric mean)

GMRot150 (Boore etal., 2006): Orientation-independent geometrio mean horizontal component

V

 

 

 

×

Source Data

Japan(Pacific plate),

1996-2003,

5.5<Mw<8.0,

depth30-150km,

35events

Japan,

1968-2003,

5.5<Mw<8.3

depth3-122km,

52events,

3198records

Japan, Iran,

Western USA,

-2003,

depth

Japan <162km,

Western USA <20km,

Japan

249events,

4518records,

Iran and Western

20events,

208records

- Area: World wide

- Period: 1952-2003 years

- Number of events: 64

- Numver of records: 1561

- Magnitude: 4.3-7.9

- rupture distance: 0.1-199km

Applicability

correction coefficient for empirical attenuation relations by Kanno et al.(2005).

 

depth < 120km

The model to be appropriate for estimating PGA. PGV. PGD and linear elastic response spectra (T=0.01!! 10 s) for shallow continental earthquakes occurring in westem North America and other regimes of similar active tectonics.