## Abstract

This paper lays the theoretical groundwork for a variable period mantle magnitude, M_{m}, based on the measurement of the spectral amplitude X(ω) of very long period Rayleigh waves. We retain the concept of magnitude by restricting ourselves to single-station measurements, ignoring the focal mechanism and the exact depth of the shallow earthquakes considered. Our measurements are made at a series of periods (in all cases greater than 40 s), and the largest value is retained. This procedure effectively avoids the well-known interference effects leading to saturation of magnitude scales defined at a fixed period. Two corrections are used: a period-dependent distance correction C_{p}, and a source correction C_{s}, also period-dependent. The analysis of a data set of 256 records from the broadband seismograph at Papeete, Tahiti, the ultra-long period system at Pasadena, and stations of the GEOSCOPE network, shows that the mean error in the estimation of the seismic moment is on the order of 0.1-0.2 units of magnitude, with the standard deviation at each station also on the order of 0.2 units of magnitude. Both versions of the method lend themselves well to automation. -from Authors

Original language | English (US) |
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Pages (from-to) | 4169-4193 |

Number of pages | 25 |

Journal | Journal of Geophysical Research |

Volume | 94 |

Issue number | B4 |

DOIs | |

State | Published - Jan 1 1989 |

## ASJC Scopus subject areas

- Geophysics
- Forestry
- Oceanography
- Aquatic Science
- Ecology
- Water Science and Technology
- Soil Science
- Geochemistry and Petrology
- Earth-Surface Processes
- Atmospheric Science
- Space and Planetary Science
- Earth and Planetary Sciences (miscellaneous)
- Palaeontology