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 only quantity that can be measured is that which is radiated through the earth. It is the radiated energy that shakes buildings and is recorded by seismograph.
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.
[Note 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.
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