Geoscience Reference
In-Depth Information
4.2.5 The magnitude-frequency relationship
Over 10 000 earthquakes with magnitude greater than about 4 occur each year.
4
As might be expected, small earthquakes are much more abundant than large
ones. About twenty earthquakes with
m
b
or
M
S
greater than 7 occur worldwide
each year and on average there is one 'great' earthquake with magnitude 8 or
over per year, while there are over 1100 with
m
b
between 5.0 and 5.5, of which
over 800 are shallower than 70 km. During the period 1968-1995 some 95 000
earthquakes with magnitude greater than 1 were recorded locally around San
Francisco (Fig. 4.14).
It is typically found that there is a straight-line relationship between the surface-
wave magnitude
M
S
and the logarithm of
N
,where
N
is the number of earthquakes
with magnitude exceeding
M
S
occurring in an area per unit of time:
log
N
=
a
−
bM
S
(4.24a)
where
a
is a constant and the value of
b
is a measure of the relative abundance
of large and small earthquakes. This statistical model is often referred to as
the
Gutenberg-Richter 'law'.
The equivalent relationship between number of
earthquakes and seismic moment is
log
N
=
α
−
β
log
M
0
(4.24b)
A large
b
-value in a region indicates that small earthquakes occur frequently,
whereas a small
b
-value indicates that small earthquakes are not so frequent
and that large earthquakes are more likely to occur. An approximate worldwide
average for
b
is 1 (the worldwide average for
3); small
b
-values are
generally those less than 1, and large
b
-values are greater than 1. If the
b
-value
is known (or assumed), then knowledge of
a
(or
β
is 2
/
) means that Eq. (4.24)gives
the maximum expected earthquake magnitude in the region. This is therefore
useful in assessing areas for earthquake risk. Assume that
a
and
b
are known.
Then Eq. (4.24a)gives
N
, the number of earthquakes exceeding magnitude
M
S
each year. If, therefore,
N
is 0.2, we could say that the recurrence time for an
earthquake of this magnitude would be 1
α
/
N
=
1
/
0.2
=
5yr. Alternatively, if
=
b
1, the value of
a
is the maximum expected earthquake magnitude per year
for the region under consideration (since log
10
1
=
0). Globally, since we have
over 10 000 earthquakes each year with magnitude greater than 4, Eq. (4.24a)
implies that we should expect one earthquake each year with magnitude greater
4
The total number of earthquakes occurring each year is obviously variable. However, the sensitivity
of instruments and extent of seismic networks, as well as the criteria used for confirmation of,
and inclusion of, earthquakes in catalogues have changed over the years and continue to change.
This makes it hard to present unambiguous statistics for global rates of earthquake occurrence. In
1931 there were about 350 instruments operating worldwide, now there are over ten times as many.
The International Seismological Centre (ISC) data for 1905 show a total of 11 earthquakes; 84 in
1915; 617 in 1940; 3214 in 1960; 20 135 in 1980; 63 902 in 1990; and 48 596 in 1995. Most of the
variability in these numbers is due to improvements in instrumentation.
