A major problem with time-domain measurements of seismic surface waves is the significant effect of nondispersed Rayleigh waves and Airy phases, which can occur at both regional and teleseismic distances. This article derives a time-domain method for measuring surface waves with minimum digital processing by using zero-phase Butterworth filters. The method can effectively measure surface- wave magnitudes at both regional and teleseismic distances, at variable periods between 8 and 25 sec, while ensuring that the magnitudes are corrected to accepted formulae at 20-sec reference periods, thus providing historical continuity. For applications over typical continental crusts, the proposed magnitude equation is, for zero- to-peak measurements in millimicrons:
Ms(b) = log(ab) + 1/2 log(sin(Δ)) + 0.0031(20/T)1.8Δ
− 0.66 log (20/T) − log(fc) − 0.43,
fc ≤ 0.6/T√Δ.
To calculate Ms(b), the following steps should be taken:
Determine the epicentral distance in degrees to the event Δ and the period T.
Calculate the corner filter frequency fc using the preceding inequality.
Filter the time series using a zero-phase, third-order Butterworth bandpass filter with corner frequencies 1/T − fc, 1/T + fc.
Calculate the maximum amplitude ab of the filtered signal and calculate Ms(b).
Online material: Design and realization of Butterworth filters.