Geology Reference
In-Depth Information
from the source was 1 mm. A calibration of these
curves using the reference event led to the
following expression for local magnitude:
combined with estimates of rigidity to yield the
seismic moment. Moreover, the magnitudes
of many earthquakes today are reported as
“moment magnitudes,”
M
w
, and are based on the
seismic energy released during an earthquake,
that is, the seismic moment,
M
0
:
M
w
=
(2/3) log
M
0
−
10.73
M
L
=
log
A
−
2.48
+
2.76 log
D
(6.4)
The original Richter magnitude scale was
developed based on measurements of southern
Californian earthquakes during the 1930s using
a certain type of seismometer (Wood-Anderson
torsion instruments), and the equation above is
only strictly applicable to these seismometers in
this setting. Today, however, local magnitudes are
calculated in many areas using a variety of seis-
mometers. The coefficients in Eqn 6.4 have been
modified to yield consistent estimates of the local
magnitude, despite differences in instrumenta-
tion and regional contrasts in the transmission of
seismic waves due to geological variability.
Several other magnitude estimates are
commonly used. Surface-wave magnitudes,
M
s
,
are typically calculated for events at distances
exceeding 600 km by measuring amplitudes of
surface waves with a period of approximately
20 s. Body-wave magnitudes,
m
b
, are based on
the amplitude of direct compressional waves
(P waves) measured from short-period seismo-
grams, typically with periods of about 1 s.
Empirical relationships have been established
between these earthquake magnitudes and
seismic energy,
E
s
, released:
log
E
s
=
11.8
+
1.5
M
s
(6.8)
In theory, the seismic moment is a single,
definable quantity that reliably characterizes
seismic energy release. As a consequence,
moment magnitudes should theoretically pro-
vide a direct means for comparing different earth-
quakes. In reality, today, seismic moments are
calculated both from the actual characteristics
of the rupture and from empirically derived
functions that relate body- or surface-wave
forms to seismic energy and moment.
Because the amplitude of shaking in prehistoric
earthquakes cannot be quantitatively recon-
structed, the magnitudes of ancient earthquakes
are difficult to estimate directly based on
paleoseismological studies. What can be measured,
however, are rupture lengths, mean displacements,
and approximate rupture areas. These observations
provide a means of determining the absolute size
of past earthquakes for which no instrumental
records exist. Such a quantification through
paleoseismological studies represents a powerful
basis for comparing ancient and modern earth-
quakes. Modern studies have defined relation-
ships between the seismic moment and the
amount of ground displacement and shaking.
Building on these relationships, paleoseis-
mological determinations of rupture lengths,
fault geometry, and coseismic fault displacement
provide key constraints on the assessment of
modern seismic hazards along faults.
(6.5)
and
log
E
s
=
5.8
+
2.4
m
b
(6.6)
A different measure of the energy released in an
earthquake is the seismic moment (
M
0
, measured
in dyne cm), which is equivalent to the product of
the rupture area,
a
, average displacement,
d
, and
rigidity,
m
, or shear modulus of elasticity of the
crustal material involved in the rupture:
Direct observations of paleoseismic
displacements
M
0
=
m
da
(6.7)
where
m
is commonly taken as 3 × 10
11
dyne/cm
2
for the crust and 7 × 10
11
dyne/cm
2
for the upper
mantle. Thus, instead of measuring the amplitude
of a deflection on a seismograph, observations of
the rupture length, the probable total area
of rupture, and the mean displacement are
Two types of data can be brought to bear on the
reconstruction of the history of past earthquakes.
Direct observations of displaced or cross-cutting
features provide unambiguous information about
displacements. Such information can be strati-
graphic, structural, or geomorphic in nature, and
