Physical basis of earthquake magnitudes: an extreme value of seismic amplitudes from incoherent fracture of random fault patches

Physics

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Scientific paper

A relation between surface-wave magnitude Ms and fault area S for great earthquakes has been proposed log S ⋍ 2Ms - 11.5 (Ms > 7.5) A similar formula has been also derived for body-wave magnitude mb* redetermined from maximum amplitudes of short-period P-wavetrains log S ~ 1.7 mb* These are quite different from a theoretical relation expected on the basis of long-wave approximation. Because wavelengths of seismic waves used for the above magnitudes are very short compared to the size of earthquake sources, these relations represent the short-period nature of the earthquake process. The statistical theory of extreme values has been applied to understand the relations considering that the component waves which constitute the wavetrains for mb* and Ms determinations originate from the random fracture of fault heterogeneities.

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