OICC Press Journal of Theoretical and Applied Physics 2251-7235 11 4 2023 11 17 A frequency-based parameter for rapid estimation of magnitude 10.1007/s40094-018-0273-4 EN OICC Press Authors Various OICC Press Authors Journal Article 2023 11 17 AbstractThis study introduce a new frequency parameter called τfcwtdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ au_{ ext{fcwt}}$$end{document}, which can be used to estimate earthquake magnitude on the basis of the first few seconds of P-waves, using the waveforms of earthquakes occurring in Japan. This new parameter is introduced using continuous wavelet transform as a tool for extracting the frequency contents carried by the first few seconds of P-wave. The empirical relationship between the logarithm of τfcwtdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ au_{ ext{fcwt}}$$end{document} within the initial 4 s of a waveform and magnitude was obtained. To evaluate the precision of τfcwtdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ au_{ ext{fcwt}}$$end{document}, we also calculated parameters τpmaxdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ au_{ ext{p}}^{ hbox{max} }$$end{document} and τcdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ au_{ ext{c}}$$end{document}. The average absolute values of observed and estimated magnitude differences (|Mest-Mobs|documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$|M_{ ext{est}} - M_{ ext{obs}} |$$end{document}) were 0.43, 0.49, and 0.66 units of magnitude, as determined using τpmaxdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ au_{ ext{p}}^{ hbox{max} }$$end{document}, τcdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ au_{ ext{c}}$$end{document}, and τfcwtdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ au_{ ext{fcwt}}$$end{document}, respectively. For earthquakes with magnitudes greater than 6, these values were 0.34, 0.56, and 0.44 units of magnitude, as derived using τpmaxdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ au_{ ext{p}}^{ hbox{max} }$$end{document}, τcdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ au_{ ext{c}}$$end{document}, and τfcwtdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ au_{ ext{fcwt}}$$end{document}, respectively. The τfcwtdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ au_{ ext{fcwt}}$$end{document} parameter exhibited more precision in determining the magnitude of moderate- and small-scale earthquakes than did the τcdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ au_{ ext{c}}$$end{document}-based approach. For a general range of magnitudes, however, the τpmaxdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ au_{ ext{p}}^{ hbox{max} }$$end{document}-based method showed more acceptable precision than did the other two parameters.