Earthquake‐source parameters related to magnitude

Summary. On the basis of theoretical prediction, relations between earthquake‐source parameters and magnitude are examined. For propagating shear faults (circular or rectangular), the total seismic energy radiated, E S is given virtually by E S = M 0 D/L , where M 0 is the total seismic moment, D is the seismic slippage and L is the fault length. The above relation suggests that a linear relation holds between log ( M 0 D/L ) and magnitude M. The following empirical relations are obtained from two different sets of reliable earthquake source data:( r , correlation coefficient) for 54 earthquakes with M ≥ 5.5 occurring worldwide (including very large earthquakes), andfor 60 moderate California local shocks (2.0 ≤ M L ≤ 6.8; M L , Richter's local magnitude). The total force drop Δ F defined by Δ F =Δσ S , where Δσ is the stress drop averaged over the fault area S , is found to be directly proportional to the maximum amplitude of the far‐field displacement u max ; this suggests that Δ F can be regarded as a measure of the strength of earthquake, and that log Δ F is linearly related to M. The empirical equationis obtained for the 60 moderate California local shocks. This relation is better correlated and less scattered than any other empirical equations examined. The empirical relation Δ F ∝ 10 M L and the theoretical proportional relationship between Δ F and u max indicate that u max is proportional to the maximum trace amplitude recorded on a Wood—Anderson seismometer within the error involved in the determination of magnitude and source parameters. For the 54 earthquakes with M ≥ 5.5 , recalling that Δ F ∼ M 0 / W for a rectangular fault with width W and length L , the following relations are obtained:These results indicate that the similarity assumption for aspect ratio is generally reasonable for large earthquakes. Relations between other faulting parameters and magnitude are also examined. Although many source parameters can be related to magnitude, no other relations examined are better than the linear relations between log Δ F and M L , and between log ( M 0 D/L ) (= E S ) and M. The empirical equations derived may be useful for practical applications.