overcome this deficiency, seismologists have introduced a
intensity in the epicentral area. The following illustrate
"physical" parameter called seismic moment, M@, to
such relationships.
describe the size of an earthquake. This parameter is
directly related to the size of the fault rupture area, the
(Gutenberg and Richter, 1956)
average slip on the fault, and the property in shear of the
ruptured zone (recall that the magnitude scale is a relative
M L = 1+ 2 Io
(D-4)
3
scale). M@ is defined as:
(Krinitzky and Chang, 1975)
Mo = G A S
(D-2)
M L = 2.1 + 1 I o
where
(D-5)
2
G = average shear modulus over the rupture zone
(Chinnery and Rogers, 1973) for Northeastern United
A = fault rupture area
States,
S = average slip on the fault during the earthquake.
M L = 2.1 + 0.6I o
(D-6)
(3) Moment magnitude. In order to relate seismic
moment to the existing magnitude scales, a moment
where
to 6, Mw corresponds to ML. Mw is related to seismic moment
ML = Richter magnitude or local magnitude
M@by the following relationship (Hanks and Kanamori,
I@ = Modified Mercalli intensity in the epicentral area
1979).
(c) All such relationships, including those
M w = 2 LogM o - 10.7
(D-3)
derived for specific sites where specific data are available,
3
are extremely approximate and the scatter of data about the
predicted lines is large. Note that much of the scatter is
where Mo is in units of dyne-cm.
due to the necessity of empirically converting site intensity
data to the equivalent I@value in the epicentral area, so as
Comparative values of the moment magnitudes and seismic
to normalize the site distance attenuation effects. Figure D-
moments of some well-known earthquakes are given in
4 (Krinitzky and Chang, 1975) shows the relationships
Table D-1.
given by Equations D-4 and D-5 along with earthquake
data.
(4) Intensity measures. Another means of
describing the size of an earthquake at a given location is
D-2. Ground Motion Recordings and Ground Motion
the intensity scale. The two intensity scales used in the
Characteristics
United States are the Rossi-Forel Scale (RF Scale) and the
Modified Mercalli Scale (MM Scale).
a. Characteristics in the Time Domain. With the
introduction of modern strong motion instruments, the
(a) The Modified Mercalli scale is the most
actual ground motion at a given location is often derived
common. A simplified version of this scale is given in
from instrumentally recorded motions. The most
Table D-2. The RF scale, which was developed in the late
19th century, was used in this century until 1930. Since
commonly used instruments for engineering purposes are
strong motion accelerographs. These instruments record
then, use of the MM scale has become more common. It is
the acceleration time history of ground motion at a site,
important to note that the above scales are subjectively
called an accelerogram. Figure D-5(a) shows a typical
assigned by investigators after observing and reviewing the
accelerogram. By proper analysis of a recorded
earthquake effects in a given region. The assignment of
accelerogram to account for instrument distortion and base
proper intensity value therefore requires a careful analysis
line correction, the resulting corrected acceleration record
of the affected region. Unless the guidelines for assigning
can be used by engineers. This corrected acceleration
intensities are properly and correctly followed, there could
record can yield ground velocity and ground displacement
be an error in the assigned value.
by appropriate integration (Figure D-5(a)).
(b) Empirical relationships are available in the
literature to relate the magnitude of an earthquake and the
D-5
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