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

Many researchers have studied the attenuation characteristic 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;

Paper published year 2004-2005;

13^th World Conference on Earthquake Engineering

Journal of Structural and Construction Engineering AIJ

Structure Engineering Symposium

Journal of the Japan society of Civil Engineers

Journal of Japan Association for Earthquake Engineering

Bulletin of the Seismological Society of America

Earthquake Spectra

Based on the observed record in wide area

Finally, 15 formulas which are summarized in Table 1.1 are selected and 10 items are compiled.

1) Reference

2) Estimated physical parameters

3) Used strong motion dada

4) Style of faulting

5) Ground condition

6) Definition of magnitude

7) Definition of source distance

8) Definition of horizontal components

9) Applicability written in this paper

10) Empirical attenuation formula

Figure 1-1 Object area of empirical attenuation formula (red area)

Table 1-1 Summary of empirical attenuation formula

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)
Tectonic Environment		Inter-plate Slab		Crustal Interface Slab
Style of Faulting				- Reverse - Strike-slip - Normal - Unknown
Ground Condition			Vs 500m/s (average over the upper 30m)	- Rock - Hard soil - Medium soil - Soft soil
Other Effect
Acceleration		○		○
Velocity		○
Sa (5%)		○ (0.05-0.45sec)	○ （0.02-5.0sec）	○ (0.05-5.00sec)
Sv (5%)
Magnitude		Mw	Mw	Mw
Distance		source distance	shortest distance to the rupture surface	source distance
Component	H		○ (geometric mean)	○ (geometric mean)
	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
Applicability		correction　coefficient for empirical attenuation relations by Kanno et al.(2005).		depth < 120km