To determine the total seismic energy radiated from 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, M_{o}) and a uniform decrease
with increasing frequency above some corner frequency (F_{c}),
so the seismic energy is a function of both M_{o} and
F_{c}. For a given moment,
the radiated energy will increase as F_{c} 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:

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 FM_{o}= u D A where: u = shear modulus (3 - 6 x 10^{11}) dyn/cm^{2}D = average displacement A = area of rupture

Having said this, however, if only an earthquake's moment is known
the radiated seismic 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 (M_{o}) and moment magnitude
(M_{W}) are
related by the following equations (Kanamori, H., 1977, The Energy
Release in Great Earthquakes, Journal of Geophysical Research,
v82, p. 2981- 2987):

The energy released by TNT (trinitrotoluene) and the TNT equivalent of the Hiroshima nuclear bomb (McGraw-Hill Encyclopedia of Science and Technology, 1992):E = M_{o}/(2 x 10^{4}) erg (1 erg = 1 dyn cm) log E = 1.5 M_{W}+ 11.8 (Gutenberg-Richter magnitude-energy relation) Then: log M_{o}- log(2 x 10^{4}) = 1.5 M_{W}+ 11.8 M_{w}= (log M_{o}- 16.1) / 1.5

Energy per ton of TNT = 4.18 x 10^{9}Joules = 4.18 x 10^{16}ergs Energy per megaton of TNT = 4.18 x 10^{15}Joules

According to the Sandia National Laboratories' web site, the energy equivalent of the Hiroshima fission bomb was 15,000 tons of TNT.

Example -- consider an earthquake with moment magnitude Mw = 4.0

The total seismic energy radiated from the source, **E(4),
**would be:

**E(4)**_{ }
= 10**(1.5*4 + 11.8) = 10**17.8 ergs = 10**10.8 Joules = 6.3 x 10^{11}
Joules

The moment, **
Mo(4), **would be:

**Mo(4) = E x (2 x 10 ^{4}) =
1.26 x 10^{16} Joules**

It has been found that a 1 kton explosion will generate seismic waves approximately equivalent to a magnitude 4 earthquake. Therefore, the amount of energy dissipated by TNT to yield seismic waves similar to a magnitude 4 is:

**Energy of TNT(4) = 4.18 x 10 ^{12}
Joules**

Back to 'Everything you wanted to know ....'

Reference: http://www.cwp.mines.edu/~john/empirical/node4.html

Handy for units conversion: http://www.thomasglobal.com/tools/