Reliable determination of earthquake magnitude is a fundamental building block of seismic hazard assessment. The seismicity catalog for Puerto Rico is dominated by small earthquakes (M < 5), mostly MD (a local magnitude based on duration) and mb (body-wave magnitude). There is considerable uncertainty over the interpretation of MD. To reduce this uncertainty, we evaluate moment magnitude (M) and M1, (1-Hz magnitude) for events within the catalog and develop relationships between these and other magnitude measures. The available seismographic data are most ly short-period records, because broadband instruments in Puerto Rico have been installed only recently. A difficulty with the calculation of moment magnitude is that short-period data do not generally extend to sufficiently low frequencies to reliably obtain the displacement spectrum at low frequencies. Moment magnitudes for small earthquakes in Puerto Rico are thus estimated from a single broadband station and subject to much uncertainty. To get around this difficulty, we used M1, which closely tracks moment magnitude for small to moderate events (Chen and Atkinson, 2002). M1 is obtained from the spectral amplitude at 1 Hz and is defined such that it will equal moment magnitude for earthquakes following a Brune point-source model. Unlike moment magnitude, M1 can be determined from short-period seismograms. Our values of M and M1 are in close agreement with each other for small to moderate earthquakes. There is a systematic difference between M1 or M and catalog magnitudes mb or Md, with the catalog magnitude exceeding moment magnitude by about 0.4 units on average. It is recommended that M1 be used as a regional magnitude scale for earthquakes in Puerto Rico, and as an estimate of M for events of M < 5.

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Journal Bulletin of the Seismological Society of America
Motazedian, D, & Atkinson, G.M. (Gail M.). (2005). Earthquake magnitude measurements for Puerto Rico. Bulletin of the Seismological Society of America, 95(2), 725–730. doi:10.1785/0120040083