Empirical attenuation formula for estimating PGA, PGV and response spectra

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 M_L<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)
Component	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	M_J, Mw, Ms	M_J	Mw	Mw	Mw	M_J
Distance *1)		B	A	A	A, D	A, E	E	D
Component	H	○(geometric mean)	○(average)	○(larger)	○(geometric mean)	○(larger)	○(independent data)	○(average)
Component	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	M_J	Mw	M_J
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)	○
Component	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<M_J<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<M_J<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		M_L	M_L	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	○	○	○	○	○
Component	V		○	○
Source Data		Southern California, 1991-2001, 5.0<M<7.5, 38events, 522records	Eastern Alps, 1976-2002, 2.5<M_L<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<M_L<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
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.