David R. Russell

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: M s(b) = log( a b ) + 1/2 log(sin(Δ)) + 0.0031(20/ T ) 1.8 Δ − 0.66 log (20/ T ) − log( f c ) − 0.43, where: f c ≤ 0.6/ T √Δ. To calculate M s(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 f c using the preceding inequality. Filter the time series using a zero-phase, third-order Butterworth bandpass filter with corner frequencies 1/ T − f c , 1/ T + f c . Calculate the maximum amplitude a b 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 Vanĕk (1962) at 50 degrees. For periods 8 ≤ T ≤ 25, the equation is corrected to T = 20 sec, accounting for source effects, attenuation, and dispersion. Online material: Design and realization of Butterworth filters.

Development of a Time-Domain, Variable-Period Surface-Wave Magnitude Measurement Procedure for Application at Regional and Teleseismic Distances, Part II: Application and Ms–mb Performance

The Russell surface-wave magnitude formula, developed in Part I of this two-part article, and the M_s(VMAX) measurement technique, discussed in this article, provide a new method for estimating variable-period surface-wave magnitudes at regional and teleseismic distances. The M_s(VMAX) measurement method consists of applying Butterworth bandpass filters to data at center periods between 8 and 25 sec. The filters are designed to help remove the effects of nondispersed Airy phases at regional and teleseismic distances. We search for the maximum amplitude in all of the variable-period bands and then use the Russell formula to calculate a surface-wave magnitude. In this companion article, we demonstrate the capabilities of the method by using applications to three different datasets. The first application utilizes a dataset that consists of large earthquakes in the Mediterranean region. The results indicate that the M_s(VMAX) technique provides regional and teleseismic surface-wave magnitude estimates that are in general agreement except for a small distance dependence of −0.002 magnitude units per degree. We also find that the M_s(VMAX) estimates are less than 0.1 magnitude unit different than those from other formulas applied at teleseismic distances such as Rezapour and Pearce (1998) and Vanĕk et al. (1962). In the second and third applications of the method, we demonstrate that measurements of M_s(VMAX) versus m_b provide adequate separation of the explosion and earthquake populations at the Nevada and Lop Nor Test Sites. At the Nevada Test Site, our technique resulted in the misclassification of two earthquakes in the explosion population. We also determined that the new technique reduces the scatter in the magnitude estimates by 25% when compared with our previous studies using a calibrated regional magnitude formula. For the Lop Nor Test Site, we had no misclassified explosions or earthquakes; however, the data were less comprehensive. A preliminary analysis of Eurasian earthquake and explosion data suggest that similar slopes are obtained for observed M_s(VMAX) versus m_b data with m_b <5. Thus the data are not converging at lower magnitudes. These results suggest that the discrimination of explosions from earthquakes can be achieved at lower magnitudes using the Russell (2006) formula and the M_s(VMAX) measurement technique.