## Abstract

A combination of surface wave theory and phase-stationary asymptotics is used to relate the time domain amplitude a(t) of a strongly dispersed wave and the moment M_{o} of the source. This approximation is valid at sufficiently large distances, over 10° for 20-s Rayleigh waves. We apply this formalism to justify theoretically the Prague formula for M_{s}. Assuming a Rayleigh Q of 297, we can successfully model the theoretical distance correction as 1.66 log_{10} Δ in the range 20-160°. We also predict a relation of the form log_{10} M_{0}=M_{s} + 19.46, in good agreement with reported empirical values. Finally, we show that the theory requires M_{s} to be described by the product (aT); the use of the ratio (a/T) is a partial and ad hoc compensation for a large number of frequency-dependent terms ignored in the Prague formula. -from Author

Original language | English (US) |
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Pages (from-to) | 4194-4204 |

Number of pages | 11 |

Journal | Journal of Geophysical Research |

Volume | 94 |

Issue number | B4 |

DOIs | |

State | Published - 1989 |

## ASJC Scopus subject areas

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

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