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....
In many waves (light, sound) energy intensity is proportional to the
square of the wave amplitude. This is true of earthquakes as well.
"Because of the logarithmic basis of the scale, each whole number increase in
magnitude represents a tenfold increase in measured amplitude; as an estimate of
energy, each whole number step in the magnitude scale corresponds to the release
of about 31 times more energy than the amount associated with the preceding
whole number value. "