Comparison of earthquake energy to nuclear explosion energy.
J.C. Lahr, Revised 8/28/00
To determine the seismic energy of an earthquake one would have to
integrate the energy radiated at all frequencies over the entire
focal sphere. The spectrum of the average radiation over the focal
sphere can be approximated by a constant level at low frequencies
(which is proportional to the moment, Mo) and a uniform decrease
with increasing frequency above some corner frequency (Fc), so the
seismic energy is a function of both Mo and Fc. For a given moment,
the energy will increase as Fc increases. Consider, for example,
two earthquakes with the same displacement and rupture area that
occur within rocks with the same shear modulus. They would have
the same moment, which can be computed from: Mo = u D A,
where:
u = shear modulus (3 - 6 x 1011) dyn/cm2
D = average displacement
A = area of rupture
If one event were a "slow" earthquake with "more or less creep-like
deformation" (Kanamori, H., 1972, Mechanism of Tusnami Earthquakes,
Phys. Earth Planet. Interiors, v6, p. 346-359) while the other had
a more typical rupture velocity near the shear wave velocity, much
more energy would be radiated from the latter earthquake due to its
rich high frequency radiation corresponding larger Fc than from the
"slow" event.
Having said this, however, if only an earthquake's moment is known
the energy can still be approximated because, if a large set of
earthquakes is considered, the average corner frequency varies
systematically with the moment. For the average earthquake, the
seismic wave energy (E), moment (Mo) and moment magnitude (Mw) are
related by the following equations (Kanamori, H., 1977, The Energy
Release in Great Earthquakes, JGR, v82, p. 2981- 2987):
E = Mo/(2 x 104) erg (1 erg = 1 dyn cm)
log E = 1.5 Mw + 11.8 (Gutenberg-Richter magnitude-energy
relation)
Then:
log Mo - log(2 x 104) = 1.5 Mw + 11.8
Mw = (log Mo - 16.1) / 1.5
The energy released by TNT (trinitrotoluene) and the TNT equivalent
of the Hiroshima nuclear bomb (McGraw-Hill Encyclopedia of Science
and Technology, 1992):
Energy per ton of TNT = 4.18 x 109 Joules
= 4.18 x 1016 ergs
Energy per megaton of TNT = 4.18 x 1022 ergs
TNT equivalent of the Hiroshima nuclear bomb was 13 kilotons.
RICHTER EARTHQUAKE MAGNITUDE
The Richter Magnitude Scale is a measure of the amplitude of the
seismic waves produced by an earthquake. An increase of one unit
on the Richter Scale, for example from magnitude 6.0 to 7.0,
corresponds to a 10-fold increase in the amplitude of the seismic
waves that shake the ground. Magnitude is related to the energy
radiated from the earthquake source as seismic waves. An increase
of one unit on the Richter Scale corresponds to approximately a
30-fold increase in the total energy released.
A little background information:
The Richter Scale was devised by Charles F. Richter in 1935 for
local earthquakes in southern California. Today, seismologists use
a number of different magnitude scales, such as surface wave
magnitude (Ms), body wave magnitude (mb) and moment magnitude (Mw),
which are founded upon extensions of the original Richter Scale.
An earthquake's magnitude may be computed more than one way at each
seismic station that records the event. These different estimates
often vary by as much as half a magnitude unit, and the final
magnitude reported is the average of many estimates.
Magnitude Notes
-3.0 1.5 foot-pounds (18 inch-pounds)
-2.0 47 foot-pounds
-1.0 1,500 foot-pounds
2.0 Felt only nearby, if at all
4.0 Often felt up to 10's of miles away
6.9 1995 Kobe, Japan, Earthquake
7.3 1933 Salcha Earthquake
9.2 1964 Alaska Earthquake
9.5 1960 Chile - Largest Recorded Earthquake
Magnitude Energy Energy TNT TNT TNT Hiroshima
Joules ft-lbs tons megatons equiv. tons bombs
-3.0 0.200E+01 0.147E+01 0.477E-09 0.477E-15 0.318E-07 0.212E-11
-2.0 0.631E+02 0.465E+02 0.151E-07 0.151E-13 0.101E-05 0.671E-10
-1.0 0.200E+04 0.147E+04 0.477E-06 0.477E-12 0.318E-04 0.212E-08
0.0 0.631E+05 0.465E+05 0.151E-04 0.151E-10 0.101E-02 0.671E-07
1.0 0.200E+07 0.147E+07 0.477E-03 0.477E-09 0.318E-01 0.212E-05
2.0 0.631E+08 0.465E+08 0.151E-01 0.151E-07 0.101E+01 0.671E-04
3.0 0.200E+10 0.147E+10 0.477E+00 0.477E-06 0.318E+02 0.212E-02
4.0 0.631E+11 0.465E+11 0.151E+02 0.151E-04 0.101E+04 0.671E-01
5.0 0.200E+13 0.147E+13 0.477E+03 0.477E-03 0.318E+05 0.212E+01
6.0 0.631E+14 0.465E+14 0.151E+05 0.151E-01 0.101E+07 0.671E+02
6.9 0.141E+16 0.104E+16 0.338E+06 0.338E+00 0.225E+08 0.150E+04
7.0 0.200E+16 0.147E+16 0.477E+06 0.477E+00 0.318E+08 0.212E+04
8.0 0.631E+17 0.465E+17 0.151E+08 0.151E+02 0.101E+10 0.671E+05
8.5 0.355E+18 0.262E+18 0.849E+08 0.849E+02 0.566E+10 0.377E+06
8.6 0.501E+18 0.370E+18 0.120E+09 0.120E+03 0.799E+10 0.533E+06
8.7 0.708E+18 0.522E+18 0.169E+09 0.169E+03 0.113E+11 0.753E+06
8.8 0.100E+19 0.738E+18 0.239E+09 0.239E+03 0.159E+11 0.106E+07
9.0 0.200E+19 0.147E+19 0.477E+09 0.477E+03 0.318E+11 0.212E+07
9.1 0.282E+19 0.208E+19 0.674E+09 0.674E+03 0.450E+11 0.300E+07
9.2 0.398E+19 0.294E+19 0.952E+09 0.952E+03 0.635E+11 0.423E+07
9.5 0.112E+20 0.828E+19 0.268E+10 0.268E+04 0.179E+12 0.119E+08
c /home/lahr/outreach/makequak 8/28/00 jcl
c correct size of Hiroshima bomb from 13 to 15 ktons. 11/2/98
c see the Sandia National Laboratories' web page:
c http://www.ca.sandia.gov/outreach/2020/FAQs/nukeeffectfaq.html
c change energy in table from ergs to Joules. 11/2/98
print *,
* ' Magnitude Energy Energy TNT ',
* 'TNT TNT Hiroshima'
print *,
* ' Joules ft-lbs tons ',
* 'megatons equiv. tons bombs'
do 100 i = 1, 13
amag = i - 4
call enrg(amag)
100 continue
call enrg(6.9)
call enrg(8.5)
call enrg(8.5)
call enrg(8.6)
call enrg(8.7)
call enrg(8.8)
call enrg(9.1)
call enrg(9.2)
call enrg(9.5)
stop
end
subroutine enrg(amag)
c energy in ergs for magnitude = i
energy = 10.**(1.5*amag + 11.8)
c equivalent tons of TNT
tnt_ton = energy/(4.18*(10.**16))
c increase tnt_ton to account for the inefficiency of TNT to
c generate seismic waves.
tnt_ton_equiv = tnt_ton*1000./15.
c equivalent mtons of TNT
tnt_mton = tnt_ton/(10.**6)
c equivalent number of Hiroshima bombs
bombs = tnt_ton_equiv/(1.5*(10.**4))
c foot-pounds = 7.376*(10.**-8) * ergs
ftlbs = energy*7.376/(10.**8)
c convert energy to Joules
energy = energy * 10.**-7
write(6, '(f12.1, 6e12.3)')
* amag, energy, ftlbs, tnt_ton, tnt_mton, tnt_ton_equiv, bombs
return
end