Evidence for ω-cube scaling from amplitudes and periods of the Rat Island sequence (1965)

An attempt has been made to deduce seismic scaling information from the amplitudes A and periods T of P waves from 868 earthquakes of the Rat Island sequence of 1965, with m_b values ranging from ∼4 to 5. Consistently reliable data were reported in the Earthquake Data Reports from five VELA array stations in the U.S., falling in an azimuthal sector of 60° to 80° from the source region with distances ranging from 44° to 68°. The most striking feature of the data is the strong linear trend of log (A/T) with T at each station over a wide period range of 0.5 to >1.5 sec. Using a subset of 245 events reported jointly at all five VELA stations we calculated a least squares magnitude versus period relation given by m_b = (3.24 ± 0.08) + (1.32 ± 0.09) T. In order to interpret this trend in terms of source models, synthetic records, including earth attenuation were calculated for ω-square models of Sharpe and Brune, and an ω-cube model suggested by Savage. Under the assumption of geometric similarity, whereby the zero-frequency source level is proportional to source volume, the measured trend of log (A/T) on the synthetic records indicates that an ω-cube rather than either ω-square model is more appropriate for the Rat Island data.

Extrapolation of the synthetic source spectra to D.C. for m_b 4.7 yields a moment of 6.65 × 10²² dyne cm and for the sequence a stress drop of ∼25 bars, in reasonable agreement with previous results obtained from long-period P-wave spectra.

These results indicate that crude seismic scaling information for moderate-sized earthquakes can be extracted from good bulletin data without using spectral analysis. Large amounts of data are required, however, to establish a reliable trend for interpretation.