A relation between surface-wave magnitude M_s and fault area S for great earthquakes has been proposed;
logS≈2M_s-11.5 (M_s>7.5).
A similar formula has been also derived for body-wave magnitude m_b* redetermined from maximum amplitudes of short-period P-wave trains;
logS∝1.7m_b*.
These are quite different from a theoretical relation expected on the basis of long wave approximation. The statistical theory of extreme values has been applied to understand the relations considering that the component waves which consititute the wave trains for m_b*-M_s determinations originate from the random fracture of fault heterogeneities.