A high-frequency magnitude scale

A high-frequency magnitude scale (m) is proposed: m=2log⁡a˜hf+3, where ãhf is the high-frequency level of the Fourier amplitude spectrum of acceleration in cm/sec (average or random horizontal component), at a hypocentral or closest fault distance of 10 km. m can be determined from either instrumental data or the felt area of an earthquake. The definition of m has been arranged such that m = M (moment magnitude) for events of “average” stress drop, in both eastern North America (ENA) and California. m provides a measure of the stress drop if M is also known. The observed relationship between m and M indicates that the average stress drop is about 150 bars for ENA earthquakes, and about 70 bars for California earthquakes. The variability of stress drop is much larger in ENA than in California. The chief justification for the m scale is its utility in the interpretation of the large preinstrumental earthquakes that are so important to seismic hazard estimation in eastern North America. For such events, m can be determined more reliably than can M or mN (Nuttli magnitude), and forms a much better basis for estimating high-frequency ground motions. When used as a pair, m and M provide a good index of ground motion over the entire engineering frequency band. If both of these magnitudes can be defined for an earthquake then a ground-motion model, such as the stochastic model, can be used to obtain reliable estimates of response spectra and peak ground motions.

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