A theoretical discussion of time domain magnitudes: the Prague formula for Ms and the mantle magnitude Mm

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26 Scopus citations

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 Mo 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 Ms. Assuming a Rayleigh Q of 297, we can successfully model the theoretical distance correction as 1.66 log10 Δ in the range 20-160°. We also predict a relation of the form log10 M0=Ms + 19.46, in good agreement with reported empirical values. Finally, we show that the theory requires Ms 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 languageEnglish (US)
Pages (from-to)4194-4204
Number of pages11
JournalJournal of Geophysical Research
Volume94
Issue numberB4
DOIs
StatePublished - 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

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