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