** Empirical
Relationships For Estimating Peak Ground Acceleration
**

Commonly
used empirical relationships for estimating peak ground acceleration (PGA)
values from hypocentral parameters and magnitude data are listed below. Here,
the seismological nomenclature of magnitudes M_{L}, m_{b}, M_{S}
and M_{W} have been used for the local magnitude, the body wave
magnitude, the surface wave magnitude and the moment magnitude, respectively. M
has been used where the magnitude scale is not specified, explicitly. R_{e},
R_{h}, and R_{f} have been used for epicentral distance,
hypocentral distance and distance from the causative fault (on which the
hypocenter of the earthquake is located), respectively, has been used. R has
been used when no distinction is made between the different representations for
the term distance. H has been used
for focal depth in kilometers, __a__ is used for the peak ground acceleration
(horizontal component), __v__ is used for the peak ground velocity and __d__
for the peak ground displacement. Subscript h and z have been used for
characterizing the horizontal and vertical components of ground motion
respectively. The symbol s
represents the standard deviation of the relationship, wherever available.
Unless specified differently, all distances are in kilometers (kms), __a__ in
units of 'g', __v__ in cms/s and __d__ in cms.

1.
__Milne and Davenport (1969). __The
peak ground acceleration in units of g is given by:

__a__
= 0.0069 exp (1.64 M)/{1.1 exp (1.1 M) + R_{e}^{2}}

The database used in the
derivation of this relationship pertained to the Western United States, Central
America and Chile. Scatter of the data is not reported.

__ 2.
Mickey (1971).__
Peak value of particle acceleration is related to the hypocentral distance and
body wave magnitude of the earthquake. (Expressions for velocity and
displacement have also been derived.)

__a__
= (3.04.100.74 m_{b} - 4)/R_{h}^{1.4}

__3.
Davenport (1972).__ The value of the peak ground
acceleration in units of g is given by:

__a__
= 279 x 10-6 Exp (1.8 * M)/R_{e}^{1.64}

__4.
Donovan (1973).__ World wide average values of
the peak ground acceleration in units of g are given by:

__a__
= 1.320 Exp (0.58M)/(R + 25)^{1.52}

The
relationship does not distinguish between the epicentral distance, the
hypocentral distance or the distance from the causative fault. Standard
deviation of the estimated value is given by:

s(log_{e}
__a__) = 0.84

5.
__Donovan (1974).__ Donovan derived several relationships to describe
the values of the peak ground acceleration from the San Fernando earthquake of
1971, recorded under different site conditions. Magnitude did not appear
explicitly in these relationships. A magnitude dependent relationship, which may
be applied for other geographical areas and for earthquakes of different
magnitudes, is based on data from Western North America, Japan and Papua New
Guinea. In this relationship the peak ground acceleration is given by:

__a__
= 1.080 Exp (0.5M)/(R + 25)^{1.32}

The standard deviation is given
by:

s(log_{e}
a) = 0.707

__ 6.
McGuire (1974).__ Values of peak ground
acceleration is given in terms of earthquake magnitude and hypocentral distance

__a__
= 0.472 x 100.28M/(R_{h} + 25)^{1.3}

s(log_{10}
__a__) = 0.222

__7.
Orphal and Lahoud (1974).__ The
relationship gives the values of peak ground acceleration in terms of the
magnitude and hypocentral distance.

__a__
= 0.066 x 100.4M/R_{h}^{1.39}

__8.
Esteva and Villaverde (1974).__
Values of the peak ground acceleration and velocity can be estimated in terms of
the magnitude of the earthquake and the Hypocentral distance

__a__
= 5.6 Exp(0.8M)/(R_{h} + 40)^{2}

s(log_{e}
__a__) = 0.64

__9.
Trifunac and Brady (1976).__ Using data
in the magnitude range 4.8 < M < 7.5 a relationship in the following form
was derived

log __a__ = M + log Ao(R) -
log {yo (M, p, s', v')} -log(980)

p specifies
the confidence limit, s' specifies the site classification (s'= 0 for alluvium,
= 1 for intermediate and = 2 for rock). The expression for yo is written as
follows:

log yo = AA p + AB M + AC + ADs'
+ AE V' + AF M2

AA, AB, AC,
AD, AE and AF are coefficients derived from regression analysis for acceleration
values. V' = 0 for horizontal motion and V' = 1 for vertical motion. p = 0.5 for
the mean and p = 0.8 for the 84th percentile values. log Ao(R) is a function
which accounts for the attenuation with distance R, and has been tabulated by
Trifunal at discrete values of R. Within 100 kilometers distance the values can
be computed using the following polynomial:

log10 Ao(R) = Co + C1X + C2X2 +
C3X3 + C4X4

where X = log10(R) ; Co =
-1.399793 ; C1 = 1.3615414;

C2 = -3.315589 ; C3 = 2.729386 ; C4 =
-0.601832

The values of the coefficients
AA, AB ...VA, VB,... DA, DB... are given below:

AA = -0.898 ; AB = -1.789 ; AC = 6.217

AD = 0.06; AE = 0.331; AF = 0.186

__10.
McGuire (1978).__ For the Western United States a
relationship was given distinguishing between rock and soil sites using
earthquake data between magnitude 4.5 and 7.7 and distances between 10 and 200
kms. The peak ground acceleration is given by:

__a__
= 0.0306 [Exp(0.89M)/R_{h}^{1.17}]Exp(-0.2b)

s(log_{e}__a__)
= 0.62

b
= 0 for rock and b
= 1 for soil.

__11.
Donovan and Bornstein (1978).__ A graphical relationship valid
between magnitudes 5 and 7.7 and a distance range (distance to the
center of energy release) between 5 and 300 kilometers is given
below:

__a__ = A Exp (BM)/(R + 25)C

A = 2198/R2.1 ; B = 0.046 + 0.193 log_{e}(R)

C = -2.515 + 0.211 log_{e}(R)

__12.
Cornell, Banon and Shakal (1979).__ For Western United States for
earthquakes having magnitudes between 3 and 7.7 and hypocentral distance between
20 and 200 kms

__a__
= 0.863 Exp(0.86M)/(R_{h} + 25)^{1.80}

s(log_{e}__a__)
= 0.57

__13.
Espinosa (1980).__
For the western United States, relationships were derived between PGA, local
magnitude, ML and epicentral distance. Separate relations were given for
distances less than 10 kms, between 10 and 60 kms, between 60 and 300 kms and
between 5 and 300 kms. The relationship between 10 and 60 kms distance is given
below:

__a__=1.776x10-5xExp(2.3M_{L})/R_{e}^{1.59}

The scatter of the PGA values is not
available.

__14.
Battis (1981).__ Two separate relations for the north
American Continent for peak ground acceleration are given. One is for the
California region:

__a__
= 0.348 Exp(1.21m_{b})/(R_{e} + 25)^{2.08} ;

s(log_{e}__a__)
= 0.71

The other relationship is for the
Central United States

__a__
= 0.0239 Exp(1.24m_{b})/(R_{e} + 25)^{1.24}

s(log_{e}__a__)
= 0.71

The relationships are based on 5<m_{b}<
6.5.

__15.
Campbell (1981).__ This relationship estimates the peak
ground acceleration in terms of the closest distance to the causative fault. The
peak ground acceleration is given by:

__a__
= 0.0159 Exp(0.868M)/[R + C(M)]^{1.09}

C(M)
= 0.0606 Exp(0.7M)

s(log_{e}__a__)
= 0.37

__16,17.
Hasegava, Basham and Berry (1981).__ The
relationships for peak ground acceleration and velocity were derived using body
wave magnitudes between 4 and 7 and hypocentral distances between 10 and 200 kms.
Separate relationships were derived for the eastern and western regions of
Canada.

(16) Eastern Canada

__a__
= 4.0 x 10-4 Exp(2.3m_{b})/R^{1.3}

(17) Western Canada

__a__
= (1.02/100) Exp(1.3m_{b})/R_{h}^{1.5}

__18.
Joyner and Boore (1981)__. The closest distance to the surface
projection of the fault rupture (R_{s}) was used for distance. Peak
ground acceleration and velocity are given for soil and rock:

__a__
= 0.0955 Exp(0.573 M).D-1 e-0.00587D

D
= û(R_{s}^{2} + 7.32);

b(log_{e}__a__)=0.60

19. Nuttli and Hermann (1984). Relationships were derived for a and v for earthquake data from Mississippi valley. The relationship for PGA is given below:

a=3.79x103xExp(1.15mb)xD-0.83Exp(-0.00159R)

D=(R2+Hmin2)_{0.5}
and Hmin =0.0186Exp(1.05m_{b})

b(log_{e}__a__)
= 0.55

__20.
Abrahamson and Lithehiser (1989).__ A
distinction is made between intraplate and interplate earthquakes and reverse
and normal faults. The peak ground acceleration for the horizontal component
is given by

log10__a__={
-0.62 + 0.177M - 0.982 log10(r + e0.284M)+

0.132F
- 0.0008Er}

b(log_{10}
__a__) = 0.277

E
= 1 for interplate earthquakes

0 for intraplate earthquakes

F = 1 for reverse and oblique faults 0 otherwise

The vertical component of ground
acceleration is given by:

log_{10}(a_{v})=
{-1.15 + 0.245M - 1.096 log10(r + e0.256M) +
0.096F - 0.0011 Er}

b(log_{10}
a_{v}) = 0.296