Development of a time-domain, variable-period surface-wave magnitude measurement procedure for application at regional and teleseismic distances, part I: Theory

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: [GRAPHICS] To calculate M-s(b), the following steps should be taken: 1. Determine the epicentral distance in degrees to the event A and the period T. 2. Calculate the corner filter frequency f(c) using the preceding inequality. 3. Filter the time series using a zero-phase, third-order Butterworth bandpass filter with corner frequencies 1/T - f(c), 1/T + f(c). 4. Calculate the maximum amplitude ab of the filtered signal and calculate M-s(b). At the reference period of 20 sec, the equation is equivalent to von Seggern's formula (1977) scaled to Vanek (1962) at 50 degrees. For periods 8 <= T <= 25, the equation is corrected to T = 20 sec, accounting for source effects, attenuation, and dispersion.