Environmental Engineering Reference
In-Depth Information
and E
S
is proportional to the seismic moment:
quantifying very large tremors. In addition, there is no
universal ratio between the seismic wave energy and the
total energy released by an earthquake. Total energy re-
lease by the Sumatra-Andaman earthquake was put by
Bilham (2005) at 4.3 EJ, roughly four times the seismic
energy flux. An illustrative global aggregate derived
by using average annual frequency of earthquakes in the
three highest categories (much more common, smaller
earthquakes account for less than 1% of all seismic
energy)—1 of M
W
8.0 or higher, 17 between 7 and
7.9, 134 between 6 and 6.9—and applying conserva-
tive E
S
averages adds up to releases of about 800 PJ
(USGS 2005). Quintupling this to account for strain
energy accumulated in irreversible deformations and
for friction-generated heat along the faults would yield
roughly 125 GW, less than 0.3% of the Earth's conduc-
tive heat flow.
Verhoogen (1980) estimated that the average seismic
power may be about 300 GW and that the addition of
accumulated strain energy and of friction-generated heat
may raise the total to about 1 TW. The Sumatra-
Andaman earthquake was equivalent to a 1-Gt bomb, or
as many as 68,000 Hiroshima bombs. Earthquakes of
M
W
8-9 last usually 30-90 s (and have a serious impact
over areas with diameters of 80-160 km), and those with
magnitudes 7-7.9 last only 2-50 s with strong ground
shaking within radii of 50-120 km. A 30-s M
W
9 earth-
quake rates nearly 67 PW, and its power density (prorat-
ing over the area with radius of 80 km subjected to
strong ground shaking) could be as high as 3.3 MW/
m
2
. A much more common M
W
6 tremor of the same
duration with shocks felt over 100 km
2
would have a
surface power density of about 21 kW/m
2
. In contrast,
the Sumatra-Andaman earthquake lasted about 500 s,
and the strongest recorded earthquake in Chile in 1960
E
S
¼
5
10
5
M
0
:
Modern seismographs record digitally across a broad
bandwidth (0.01-5 H), and this makes it possible to cal-
culate radiated seismic energy by direct integration of
records (Boatwright and Choy 1986). Energy magni-
tude, M
e
, in J, can be calculated (Choy and Boatwright
1995) as
M
e
¼
3
log
10
E
S
2
:
9
;
with E
S
in Nm.
Seismic energies derived from the recordings of
broadband waves and those calculated from M
W
(or
M
S
) will not be identical: the measures capture two dif-
ferent quantities, shaking from higher-velocity spectra vs.
low-frequency displacement spectra due to the area of
rupture and the slip across the fault (USGS 2005). Mag-
nitude 5 corresponds to E
S
of 710 GJ from broadband
measurements and to 2 TJ when derived from M
W
(or
M
S
). But all estimates of E
S
become difficult for great
earthquakes with long duration because the established
empirical conversions do not work in the case of the
strongest events. The Sumatra-Andaman earthquake had
M
0
of 4
:
0
10
22
Nm (maximum slip of about 20 m) or
M
W
of 9.0 for the main shock (empirically derived E
S
is
as high as 2 EJ). This is precisely the value used by the
USGS (2005), but Lay et al. (2005) assigned M
W
of
9.2 and offered 1.1 EJ as the best estimate of seismic en-
ergy. Banerjee, Pollitz, and B¨rgmann (2005) concluded
that M
W
did not exceed 9.2.
These discrepancies, amounting to a twofold difference
in overall energy discharge, illustrate the difficulties of
