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Bulletin of the Seismological Society of America; June 1973; v. 63; no. 3; p. 959-968
© 1973 Seismological Society of America
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The maximum acceleration of seismic ground motion

YOSHIAKI IDA*

DEPARTMENT OF EARTH AND PLANETARY SCIENCES MASSACHUSETTS INSTITUTE OF TECHNOLOGY, CAMBRIDGE, MASSACHUSETTS 02139

Abstract

A prediction of earthquake strong motion is attempted by studying the initial form of the seismic source-time function associated with a fracturing process described under idealized physical conditions. The effect of cohesive force on the source function is examined in detail, and the following relations are derived for the maximum particle velocity u•M and the maximum acceleration üM


Formula

where {sigma}o is the strength of material, Do is the slip displacement required for the initial formation of crack surface, c is the rupture velocity, and µ is the rigidity. Using these relations, it is concluded that the earthquake source motion is not directly governed by the interatomic cohesion, but rather by the gross strength of rocks. In fact, if 1 kbar for {sigma}o and 10 cm for Do are assumed, reasonable results, such as u•M ~ 1 m/sec and üM ~ 1 g, are obtained, with the characteristic period and distance 0.1 sec and 100 meters, respectively. This result implies that the specific surface energy for the earthquake may be as large as 1010 erg/cm2, which is much larger than the typical values (103) observed for rocks in the laboratory.

Footnotes

* Now at the Institute for Solid State Physics, University of Tokyo, Roppongi, Minato-ku, Tokyo 106, Japan.




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