Among the earthquake generated energy, traveled through the earth producing disruption, the only quantity that can be measured is that which is radiated through the earth. The total energy from an earthquake includes energy required to create new cracks in rock, energy dissipated as heat through friction, and energy elastically radiated through the earth. Of these, the radiated energy that shakes buildings and is recorded by seismographs.
The radiated energy can be obtained in various ways. Historically, the radiated energy was estimated empirically (from observations) from magnitude Ms through the Richter formula, log Es = 4.8 + 1.5Ms, where Es is seismic energy in Joules. In this formula, magnitude is measured first, after which the formula is used to obtain Es. With modern instrumentation, energy can be measured directly from velocity seismograms and converted to a magnitude. If Es is energy in joules, the energy magnitude Me is obtained by Me = (2/3) log Es -2.9. If Me is not available, the seismic moment Mo of an earthquake can provide an empirical estimate of radiated energy. After Mo is measured, it is converted to a moment magnitude Mw by Mw = (2/3) log Mo – 6.0 where Mo is in Newton-meters (Joules). Mw is then used as the magnitude in the Richter formula to obtain an estimate of radiated energy.
It should be noticed that Me and Mw do not necessarily have the same numerical value because they measure different physical quantities. Mw is a magnitude that is derived from low-frequency displacement spectra whereas Me is measured from higher frequency velocity spectra. Mw is a measure of the area of rupture and the average slip across the fault, whereas is Me is a measure of the shaking from an earthquake.
Magnitudes and corresponding energy (Joules and tons of TNT)
The radiated energy can be obtained in various ways. Historically, the radiated energy was estimated empirically (from observations) from magnitude Ms through the Richter formula, log Es = 4.8 + 1.5Ms, where Es is seismic energy in Joules. In this formula, magnitude is measured first, after which the formula is used to obtain Es. With modern instrumentation, energy can be measured directly from velocity seismograms and converted to a magnitude. If Es is energy in joules, the energy magnitude Me is obtained by Me = (2/3) log Es -2.9. If Me is not available, the seismic moment Mo of an earthquake can provide an empirical estimate of radiated energy. After Mo is measured, it is converted to a moment magnitude Mw by Mw = (2/3) log Mo – 6.0 where Mo is in Newton-meters (Joules). Mw is then used as the magnitude in the Richter formula to obtain an estimate of radiated energy.
It should be noticed that Me and Mw do not necessarily have the same numerical value because they measure different physical quantities. Mw is a magnitude that is derived from low-frequency displacement spectra whereas Me is measured from higher frequency velocity spectra. Mw is a measure of the area of rupture and the average slip across the fault, whereas is Me is a measure of the shaking from an earthquake.
Magnitudes and corresponding energy (Joules and tons of TNT)
Magnitude
|
Es (from Me)
|
Es (from Ms or Mw)
| Tons of TNT |
Nuclear Bomb Equivalence (# of bombs)
|
| 4 | 0.22E+11 | 0.63E+11 | 15. | 0.00 |
| 5 | 0.71E+12 | 0.20E+13 | 475. | 0.02 |
| 6 | 0.22E+14 | 0.63E+14 | 15023. | 0.79 |
| 7 | 0.71E+15 | 0.20E+16 | 475063. | 25.0 |
| 8 | 0.22E+17 | 0.63E+17 | 15022833. | 790.6 |
| 9 | 0.71E+18 | 0.20E+19 | 475063712. | 25,003.3 |
Once the energy is known in Joules, it can be compared to the explosive energy of TNT. One ton of TNT has an energy of 4.2*10E09 Joules. In July 16, 1945 the first atomic bomb, or A-bomb, exploded on , Alamogordo, N.Mex. It produced an explosion equal to that of 19,000 short tons (17,000 metric tons) of TNT."
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