Earthquake‐source parameters related to magnitude

Abstract

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, ES is given virtually by ES=M0D/L, where M0 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 (M0D/L) and magnitude M. The following empirical relations are obtained from two different sets of reliable earthquake source data: (Formula Presented.) (r, correlation coefficient) for 54 earthquakes with M≥ 5.5 occurring worldwide (including very large earthquakes), and (Formula Presented.) for 60 moderate California local shocks (2.0 ≤ML≤ 6.8; ML, Richter's local magnitude). The total force drop ΔF defined by ΔF=ΔσS, 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 umax; this suggests that ΔF can be regarded as a measure of the strength of earthquake, and that log ΔF is linearly related to M. The empirical equation (Formula Presented.) is 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 ΔF∝ 10ML and the theoretical proportional relationship between ΔF and umax indicate that umax 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 ΔF∼M0/W for a rectangular fault with width W and length L, the following relations are obtained: (Formula Presented.) 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 ΔF and ML, and between log (M0D/L) (=ES) and M. The empirical equations derived may be useful for practical applications. Copyright © 1978, Wiley Blackwell. All rights reserved