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Technical Description-2

Magnitude Determination

  Generation of tsunamis heavily depends on the magnitude of the earthquakes. Hence, it is essential for tsunami forecast to estimate the magnitude as quickly as possible with highest accuracy. The JMA NWPTAC computes Mjma, Mwp (Tsuboi), and Mwp (Nishimae). Mjma is used for local earthquakes (generally < 600 km from Japanese main islands while Mwp is used for regional and teleseismic earthquakes). The first tsunami message is based on these initial magnitudes.

(1) Local Earthquakes : Mjma
  JMA operates around 200 seismic stations in Japan to determine the location and magnitude of earthquakes in and around the country. Local earthquakes can therefore be seen as events for which JMA can calculate the hypocenter and magnitude precisely using domestic networks only. Local earthquakes are usually located within 600 km of the Japanese coast. Magnitudes determined using the JMA seismic network are described as Mjma [Katsumata (2004), Funasaki et al. (2004)]; when a local earthquake occurs, JMA determines the Mjma value, which then appears on domestic and international tsunami messages including NWPTAs.
Mjma is computed using body waves of period < 30s with the formula:
Mjma = log(AD)+βD(Δ,H)+CD ,
where
AD :maximum displacement amplitude derived by the integration of acceleration record
(in 10-6m)
Δ : epicentral distance (km)
H : source depth (km)
βD : decay correction
CD : constant.

Theoretically, Mjma can be applied for earthquakes of Δ ≤ 2000 km.

When earthquakes meet the specific conditions, JMA uses the Earthquake Early Warning (EEW) magnitude as Mjma, with the formula:
Mjma = log(AD)+log Δ+a1 Δ +a2 ,
where a1, a2 are constant.

The conditions are:
  • Magnitude > 6.5 and depth ≤ 100 km
  • Earthquake occurs near coasts (approximately within 150 ~ 200 km)
  • Hypocenter and magnitude are determined in certain level of curacy.

Reference:
  • Katsumata, A., Revision of the JMA displacement magnitude, 2004, Quarterly Journal of Seismology, 67, 1-10 (Japanese)
  • Funasaki, J. and Earthquake Prediction Information Division, Revision of the JMA velocity magnitude, 2004, Quarterly Journal of Seismology, 67, 11-20 (Japanese)



    (2) Teleseismic Earthquakes : Mwp (Tsuboi and Nishimae)
      The moment magnitude (Mw), which is derived from the long-period components of the seismic signal, is useful for tsunami forecast because it is more accurate for large earthquakes than the traditional Richter magnitude. In order to obtain Mw more rapidly, JMA calculates Mwp, which is equivalent with Mw, from the signals of the first arriving seismic P-waves using two techniques proposed by Nishimae (2002), and Tsuboi (1995) with the correction of Whitmore (2002).

    Mwp (Nishimae) is calculated using band-pass filtered STS-1(~360s), STS-2 (~ 120s),
    CMG (~ 100s) data (Fig.1), with the formula:
    Mwp (Nishimae) = a*log(A)+b*sin(Δ/2)+c ,

    where
    a, b, c : Empirically estimated coefficients for relating the amplitude and the epicentral             distance with the magnitude. They are determined by the least square method
                to meet the Harvard moment magnitude.
    A        : Root mean square (RMS) of vertical component of P wave potion. As the
               window length for RMS, one of time length of 2, 3, 4, or 5 min. is chosen
    Δ        : epicentral distance(deg)

    Theoretically, Mwp (Nishimae) can be applied magnitude > 5.5 and 20º ≤ Δ ≤ 80º .

    Fig.1 Band-pass filter for calculation of Mwp(Nishimnae)
    Fig. 1 Band-pass filter for calculation of Mwp(Nishimnae)

    As for Tsuboi Mwp, see reference below. Reference:
  • Nishimae, Y., K. Nakasoko, and M. Okada, Empirical formulas for quick estimation of the moment magnitude of teleseismic earthquakes with STS2 seismometer, 2002, Technical Reports of the Matsushiro Seismological Observatory, 19, 57-79 (Japanese)
  • Tsuboi, S., K. Abe, K. Takano, and Y. Yamanaka, Rapid Determination of Mw from Broadband P waveforms, 1995, Bull. Seism. Soc. Am., 85, 606-613
  • Whitmore, P., S. Tsuboi, B. Hirshorn, T. Sokolowski, Magnitude-Dependent Correction for Mwp, 2002, Science of Tsunami Hazards, 20, No. 4, 187-192

    • Comparison of Mwp_tsuboi calculated by JMA with Mw (Global CMT) for earthquakes from March 2005 to December 2006


    Comparison of Mwp_nishimae with Mw (Global CMT) for earthquakes from March 2005 to December 2006




    (3) Some Additional Notes
    i) Tsunami Earthquake
    "Tsunami earthquakes" are defined as earthquakes which generate tsunamis greatly larger than that estimated from their normal magnitudes. Generally, the ground motion is small compared to that which is expected from the actually observed tsunami record. Usual method often underestimates the magnitude for those earthquakes and unexpected large tsunamis strike the coast. When a long-period wave is found predominant in the seismic record, JMA takes the possibility of a tsunami earthquake into consideration and takes actions according to the situation if necessary.

    ii) Earthquake Early Warning (EEW)
    The EEW technique is developed to announce estimated seismic intensity and arrival time before the strong motion reaches each area. When an earthquake occurs, seismographic data near the hypocenter are analyzed to estimate the location and magnitude immediately. The arrival time of the main movement and the seismic intensity in various places are estimated, and information is announced as quickly as possible. Even after the issuance of the first EEW message, JMA continues to update the hypocenter and magnitude determination as more data becomes available. Accordingly, EEWs are disseminated repeatedly with improved accuracy and reliance with time.

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The figures on this page were created using Generic Mapping Tools open-source software (GMT; Wessel, P. and W. H. F. Smith, New, improved version of Generic Mapping Tools released, EOS Trans. Amer. Geophys. U., Vol. 79 (47), pp. 579, 1998).