Theoretical basis on relationships between focal parameters and earthquake magnitude.

Not only for a real earthquake but also for a hypothetical earthquake, it is very convenient if we can estimate the first approximations of focal parameters, such as fault area, dislocation, seismic moment, rise time, etc. , by using empirical relations. It is desirable that these relations have as simple forms as possible, explain previous observations even rather roughly, can be predicted From the theory on the fault model available, and also are consistent with each other. In this paper, relationships between some focal parameters and earthquake magnitude proposed by several investigators are theoretically reexamined based upon the dislocation theory. The following new empirical relations for Shallow and large earthquakes (M_? ? ₅), which favor the theoretical considerations, axe suggested; logS (km2) =M-4. 07, logD0 (cm) =0. 502M-1. 40, logM0 (dyne·cm) =1. 50logS (km2) +22. 3, where M is earthquake magnitude, S fault area, D0 mean dislocation and M0 seismic moment. These relations provide a constant strain drop on the fault plane, dynamic similarity, proportionality of rise time to S, proportionality of M0 to seismic energy (constant apparent stress) and the relation log T0-0. 5M, T0 being the predominant period of particle velocity. Of course these relations must be modified when many refined data are accumulated in the future and the theoretical studies on focal process are well developed.