Size of Strained Region Prior

A previous formula of the author's has been adapted to give the volume V of the region in which the material is near breaking-point, just prior to an extreme earthquake, in terms of the released energy and breaking-strength near the focus. In the light of recent earthquake energy-magnitude data of Gutenberg, Richter, and Benioff, it is inferred that V is at least of the order of the volume of a sphere of radius 25 km. Comparison with other estimates of the size of strained regions in earthquakes suggests that V may possibly reach the order of the volume of a sphere of radius 50 km. It is suggested that a factor in the occurrence of extreme earthquakes is the existence, in the zone of strain, of strength rather greater than in the majority of major earthquakes of magnitude one unit or more less than the extreme value. 1. Let E be the energy released in seismic waves in an earthquake, and let qE be the distortional strain energy in the focal region just prior to the occurrence of the earthquake. Let V denote the volume of the strained region, assuming the material to have been at breaking-point throughout the whole volume. Then if S and tt are the Mises strength and the rigidity assumed constant throughout V, it follows, from work in a previous paper, 1 that 12 qt, E = S2V . (1) On plausible assumptions, the formula (1) sets an upper bound to the value of E / S 2 in the greatest earthquakes. In paper 1, this result was considered in relation to the tentative earthquake energy-magnitude formula of Gutenberg and Richter, 2