Simplified estimation of seismic moment from seismograms

Abstract

abstract This study proposes a method to estimate the seismic moment of regional and local earthquakes based on simple measurements made directly on Wood-Anderson seismograms. The method parallels the routine estimation of local magnitude in observatory work. The relation used is log M o = a + b log ( C × D × Δ p ) where C is the maximum peak-to-peak amplitude read on a Wood-Anderson seismogram, D is the duration between the S arrival and the onset with amplitude C/d, Δ is epicentral distance, and a, b, p, and d are constants. The form of the logarithmic term is suggested by the analytical expression for moment (Keilis-Borok, 1960). Least-squares fits were made to data from 73 Wood-Anderson records of 16 central California earthquakes with seismic moments already evaluated independently from spectral analysis or broadband displacement records. The values p = 1, d, = 3 proved appropriate and subsequent regression yielded log M o = ( 16.74 ± 0.20 ) + ( 1.22 ± 0.14 ) log ( C × D × Δ ) where Mo is dyne-cm, C in millimeters, D in seconds, and Δ in kilometers. The corresponding moment-magnitude relation is log M o = ( 17.92 ± 1.02 ) + ( 1.11 ± 0.15 ) M L , for 3 ≦ ML ≦ 6.2. The latter fit is close to an earlier empirical result (Johnson and McEvilly, 1974) for central California based on fewer cases and a different range of magnitude (2.4 ≦ ML ≦ 5.1).