Objective Determination of Source Parameters and Similarity of Earthquakes of Different Size

The omega-squared spectral model with two independent parameters (stress drop, moment) provides a simple parameterization of ground motion spectra for statistical analysis. Accurate determination of source parameters of small earthquakes requires accounting for distortion of the source spectrum by each site response spectrum. Record spectra are inverted here to find separate station and event spectra. Source parameters are found by an automated objective method using integrals of each event spectrum. Quantitative estimates of error are carried through the entire analysis. These methods are applied to digital records of aftershocks of the 1980 Mammoth Lakes California earthquake sequence. Stress drop is found to be independent of source radius for the 90 events with best-determined source parameters. The ratio of Hanks to Brune stress drop is remarkably constant and independent of source radius, showing that the spectra, on average, have a constant shape that is scaled by two parameters, corner frequency and low-frequency level. Stress drops have a log-normal distribution with the standard deviation being about a factor of 2.