Geoscience Reference
In-Depth Information
quake locations in Fig. 4.140 are for those with “Richter”
magnitudes greater than 4.5. The Richter magnitude scale
is logarithmic to take account of the large variation in wave
amplitudes from the smallest to largest earthquakes: the
logarithm means that a
M
L
for focal depth, and sometimes for local conditions. Since
deep focus earthquakes do not generate particularly
impressive surface waves, the body-wave magnitude,
m
b
, is
also in use. It is more correctly referred to as the
Gutenberg-Richter scale of body-wave magnitude and
makes use of
P-, PP
, and
S
-wave signals of 12 s period.
The magnitude of any earthquake is perhaps best under-
stood physically by considering the magnitude of the fault
rupture that produces it. The extent of the slipping motion
that occurs is given by the area of the fault plane involved in
the motion,
A
, and the magnitude of the motion, the
measured rupture displacement,
h
.
A
may be routinely
determined from the depth of the mainshock focus and
from the pattern of aftershocks. When the two observable
parameters are multiplied by the shear modulus (see above
and Section 3.13),
K
, the total magnitude of the earth-
quake may be considered as a moment of force, rather like
the force acting at the end of a lever arm. Thus we have the
seismic moment
as
M
0
4 earthquake is 10 times
greater than a magnitude
M
L
3 event and 100 times less
than a
M
L
6 event. All such
magnitude scales
(Box 4.3)
are arbitrary in some way for they depend upon the type of
wave selected to represent the magnitude; either body and
surface waves may be used for the original Richter scale
but the technique is only suitable and accurate for local
(within 500 km of epicenter) events. The surface-wave
magnitude is
M
s
and is measured from the maximum hor-
izontal magnitude of the Rayleigh surface wave signal in
the range of periods 17-23 s. It is useful for relatively shal-
low foci earthquakes (order 50 km deep or less). It needs
corrections for distance traveled from focus to recorder,
KAh
with units of Newton meter
that we can relate directly and proportionally to the energy
released by an earthquake (Fig. 4.141). It may not be pos-
sible to measure the rupture displacement part of the seis-
mic moment expression for many fault ruptures, for
example, those in remote locations or underwater, but it
has the tremendous advantage that it can also be calculated
by an integration of the whole seismogram of an earth-
quake. It is thus widely used as the basis for the
moment
magnitude
scale,
M
w
, of earthquakes. Nowadays in research
it is common to quote both
M
s
and
M
w
for a particular
earthquake event; the two values are not usually identical.
Box
4.3 Earthquake magnitude expressions
have a general form
M
= log
10
(
A
/
T)
+
q
(
∆
,
h
) +
a,
where
A
is maximum wave amplitude in 10
-6
m,
T
is wave period in seconds,
q
is a correction
factor to describe wave decay with distance (
∆
)
and focal depth,
h
and
a
is some constant. Thus
M
s
= log
10
(
A/T
) + 1.66log
10
∆
+3.3.
Moment magnitude is
M
W
= 0.66log
10
M
o
- 10.7.
meteorite impact (10 km
diam, 20 km s
-1
)
daily solar energy
annual heat flow
typical
hurricane
1.10
24
1.10
19
Chile 1960
7.55
1.10
20
mean annual
seismic energy
Mt. St. Helens
eruption
5
1.10
16
1 megaton
nuclear explosion
Alaska 1964
2.5
San
Francisco
1906
typical
thunderstorm
(electrical energy)
1.10
12
1.10
18
10.0
6.0
8.0
moment magnitude, M
W
lightening bolt
1.10
8
2.0
4.0
6.0
8.0
10.0 12.0
moment magnitude, M
W
Fig. 4.141
Measures of energy generated by earthquake compared to other energetic natural phenomena.
Search WWH ::
Custom Search