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M m: A variable-period mantle magnitude for intermediate and deep earthquakes

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Abstract

We extend to the case of intermediate and deep earthquakes the mantle magnitude developed for shallow shocks byokal andTalandier (1989). Specifically, from the measurement of the spectral amplitude of Rayleigh waves at a single station, we obtain a mantle magnitude,M m, theoretically related to the seismic moment of the event through

$$M_m = \log _{10} M_0 - 20.$$

The computation ofM minvolves two corrections. The distance correction is the same as for shallow shocks. For the purpose of computing the frequency-dependent source correction, we define three depth windows: Intermediate (A) (75 to 200 km); Intermediate (B) (200–400 km) and Deep (over 400 km). In each window, the source correctionC S is modeled by a cubic spline of log10 T.

Analysis of a dataset of 200 measurements (mostly from GEOSCOPE stations) shows that the seismic moment of the earthquakes is recovered with a standard deviation of 0.23 units of magnitude, and a mean bias of only 0.14 unit. These figures are basically similar to those for shallow events. Our method successfully recognizes truly large deep events, such as the 1970 Colombia shock, and errors due to the potential misclassification of events into the wrong depth window are minimal.

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Refernces

  • Abe, K., andKanamori, H. (1979),Temporal Variation of the Activity of Intermediate and Deep Focus Earthquakes, J. Geophys. Res.84, 3589–3595.

    Google Scholar 

  • Dziewonski, A. M., andAnderson, D. L. (1981),Preliminary Reference Earth Model, Phys. Earth Planet. Inter.25, 297–356.

    Google Scholar 

  • Dziewonski, A. M., Friedman, A., Giardini, D., andWoodhouse, J. H. (1983a),Global Seismicity of 1982: Centroid Moment Tensor Solutions for 308 Earthquakes, Phys. Earth Planet. Inter.33, 76–90.

    Google Scholar 

  • Dziewonski, A. M., Friedman, A., andWoodhouse, J. H. (1983b),Centroid Moment-tensor Solutions for January–March 1983, Phys. Earth Planet. Inter.33, 71–75.

    Google Scholar 

  • Dziewonski, A. M., Franzen, J. E., andWoodhouse, J. H. (1983c),Centroid Moment-tensor Solutions for April–June 1983, Phys. Earth Planet. Inter.33, 243–249.

    Google Scholar 

  • Dziewonski, A. M., Franzen, J. E., andWoodhouse, J. H. (1984a),Centroid Moment-tensor Solutions for October–December 1983, Phys. Earth Planet. Inter.34, 129–136.

    Google Scholar 

  • Dziewonski, A. M., Franzen, J. E., andWoodhouse, J. H. (1984b),Centroid Moment-tensor Solutions for January–March 1984, Phys. Earth Planet. Inter.34, 209–219.

    Google Scholar 

  • Dziewonski, A. M., Franzen, J. E., andWoodhouse, J. H. (1985a),Centroid Moment-tensor Solutions for April–June 1984, Phys. Earth Planet. Inter.37, 87–96.

    Google Scholar 

  • Dziewonski, A. M., Franzen, J. E., andWoodhouse, J. H. (1985b),Centroid Moment-tensor Solutions for October–December 1984, Phys. Earth Planet. Inter.39, 147–156.

    Google Scholar 

  • Dziewonski, A. M., Franzen, J. E., andWoodhouse, J. H. (1985c),Centroid Moment-tensor Solutions for July–September 1984, Phys. Earth Planet. Inter.38, 203–213.

    Google Scholar 

  • Dziewonski, A. M., Franzen, J. E., andWoodhouse, J. H. (1986a),Centroid Moment-tensor Solutions for April–June 1985, Phys. Earth Planet. Inter.41, 215–224.

    Google Scholar 

  • Dziewonski, A. M., Franzen, J. E., andWoodhouse, J. H. (1986b),Centroid Moment-tensor Solutions for July–September 1985, Phys. Earth Planet. Inter.42, 205–214.

    Google Scholar 

  • Dziewonski, A. M., Ekström, G., Franzen, J. E., andWoodhouse, J. H. (1987a),Global Seismicity of 1978; Centroid Moment-tensor Solutions for 512 Earthquakes, Phys. Earth Planet. Inter.46, 316–342.

    Google Scholar 

  • Dziewonski, A. M., Ekström, G., Franzen, J. E., andWoodhouse, J. H. (1987b),Global Seismicity of 1979; Centroid Moment-tensor Solutions for 524 Earthquakes, Phys. Earth Planet. Inter.48, 18–46.

    Google Scholar 

  • Dziewonski, A. M., Franzen, J. E., andWoodhouse, J. H. (1987c),Centroid Moment-tensor Solutions for January–March 1986, Phys. Earth Planet. Inter.45, 1–10.

    Google Scholar 

  • Dziewonski, A. M., Ekström, G., Franzen, J. E., andWoodhouse, J. H. (1987d),Centroid Moment-tensor Solutions for July–September 1986, Phys. Earth Planet. Inter.46, 305–315.

    Google Scholar 

  • Dziewonski, A. M., Ekström, G., Woodhouse, J. H., andZwart, G. (1987e),Centroid Moment-tensor Solutions for October–December 1986, Phys. Earth Planet. Inter.48, 5–17.

    Google Scholar 

  • Dziewonski, A. M., Ekström, G., Franzen, J. E., andWoodhouse, J. H. (1987f),Centroid Moment-tensor Solutions for April–June 1986. Phys. Earth Planet. Inter.48, 229–239.

    Google Scholar 

  • Dziewonski, A. M., Ekström, G., Franzen, J. E., andWoodhouse, J. H. (1988a),Global Seismicity of 1980; Centroid Moment-tensor Solutions for 515 Earthquakes. Phys. Earth Planet. Inter.50, 127–154.

    Google Scholar 

  • Dziewonski, A. M., Ekström, G., Woodhouse, J. H., andZwart, G. (1988b),Centroid Moment-tensor Solutions for January–March 1987, Phys. Earth Planet. Inter.,50, 116–126.

    Google Scholar 

  • Dziewonski, A. M., Ekström, G., Franzen, J. E. andWoodhouse, J. H. (1988c),Global Seismicity of 1981; Centroid Moment-tensor Solutions for 542 Earthquakes, Phys. Earth Planet. Inter.50, 155–182.

    Google Scholar 

  • Furumoto, M., andFukao, Y. (1976),Seismic Moments of Great Deep Shocks, Phys. Earth Planet. Inter.11, 352–357.

    Google Scholar 

  • Gilbert, J. F., andDziewonski, A. M. (1975),An Application of Normal Mode Theory to the Retrieval of Structural Parameters and Source Mechanism from Seismic Spectra, Phil. Trans. Roy. Soc. London278A, 187–269.

    Google Scholar 

  • Okal, E. A. (1979),Higher Mode Rayleigh Waves Studied as an Individual Seismic Phase, Earth Plan. Sci. Lett.43, 162–167.

    Google Scholar 

  • Okal, E. A., andGeller, R. J. (1979),On the Observability of Isotropic Seismic Sources: The July 31, 1970 Colombian Earthquake, Phys. Earth Planet Inter.18, 176–196.

    Google Scholar 

  • Okal, E. A., andJo, B.-G. (1983),Regional Dispersion of First-order Overtone Rayleigh Waves, Geophys. J. Roy. Astr. Soc.72, 461–481.

    Google Scholar 

  • Okal, E. A., andTalandier, J. (1989),M m: A Variable Period Mantle Magnitude, J. Geophys. Res.94, 4169–4193.

    Google Scholar 

  • Okal, E. A., andTalandier, J. (1990),M m: Extension to Love Waves of the Concept of a Vairable-period Mantle Magnitude, Pure Appl. Geophys.,134, 355–384.

    Google Scholar 

  • Strelitz, R. A.,Source Processes of Three Complex Deep-focus Earthquakes, Ph. D. Dissertation, (Princeton University, Princeton, N.J. 1977), 259 pp.

    Google Scholar 

  • Talandier, J., andOkal, E. A. (1989),An Algorithm for Automated Tsunami Warning in French Polynesia, Based on Mantle Magnitudes, Bull. Seismol. Soc. Am.79, 1177–1193.

    Google Scholar 

  • Vaněk, J., Zátopek, A., Kárník, V., Kondorskaya, N. V., Riznichenko, Yu. V., Savarenskii, E. F., Solov'ev, S. L., andShebalin, N. V. (1962),Standardization of Magnitude Scales, Izv. Akad. Nauk SSSR, Ser. Geofiz.,2, 153–158.

    Google Scholar 

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  1. Department of Geological Sciences, Northwestern University, 60208, Evanston, Illinois, USA

    Emile A. Okal

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  1. Emile A. Okal
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Okal, E.A. M m: A variable-period mantle magnitude for intermediate and deep earthquakes. PAGEOPH 134, 333–354 (1990). https://doi.org/10.1007/BF00878737

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  • DOI: https://doi.org/10.1007/BF00878737

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