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, 15 formulas which are summarized in Table 1.1 are selected and following 10 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