A bayesian approach to the real time estimation of magnitude from the early P- and S-wave displacement peaks

It has been shown that the initial portion of P and S wave signals can provide
information about the final earthquake magnitude in a wide magnitude range. This
observation opens the perspective for the real-time determination of source parameters. In
this paper we describe a probabilistic evolutionary approach for the real-time magnitude
estimation which can have a potential use in earthquake early warning. The technique
is based on empirical prediction laws correlating the low-frequency peak ground
displacement measured in a few seconds after the P and/or S phase arrival and the final
event magnitude. The evidence for such a correlation has been found through the analysis
of 256 shallow crustal events in the magnitude range Mjma 4–7.1 located over the entire
Japanese archipelago. The peak displacement measured in a 2-s window from the
first P phase arrival correlates with magnitude in the range M = [4–6.5]. While a possible
saturation effect above M ’ 6.5 is observed, it is less evident in an enlarged window of 4 s.
The scaling of S peaks with magnitude is instead also observed at smaller time lapses
(i.e., 1 s) after the first S arrival. The different scaling of P and S peaks with magnitude
when measured in a 2-s window is explained in terms of different imaged rupture surface
by the early portion of the body wave signals. We developed a technique to estimate
the probability density function (PDF) of magnitude, at each time step after the event
origin. The predicted magnitude value corresponds to the maximum of PDF, while its
uncertainty is given by the 95% confidence bound. The method has been applied to the
2007 (Mjma = 6.9) Noto Hanto and 1995 (Mjma = 7.3) Kobe earthquakes. The results of
this study can be summarized as follows: (1) The probabilistic algorithm founded on
the predictive model of peak displacement versus final magnitude is able to provide a fast
and robust estimation of the final magnitude. (2) The information available after a few
seconds from the first detection of the P phase at the network can be used to predict the
peak ground motion at a given regional target with uncertainties which are comparable to
those derived from the attenuation law. (3) The near-source S phase data can be used
jointly with P data for regional early warning purposes, thus increasing the accuracy and
reliability of magnitude estimation.

ABS Consulting (2007), Flash report on the Noto Hanto earthquake, technical
report, Houston, Tex.
Aki, K., and P. G. Richards (1980), Quantitative Seismology: Theory and
Methods, W. H. Freeman, San Francisco, Calif.
Allen, R. (2007), The ElarmS earthquake early warning methodology and
application across California, in Earthquake Early Warning System, edited
by P. Gasparini, G. Manfredi, and J. Zhao, pp. 21 – 43, Springer,
Heidelberg, Germany.
Allen, R. M., and H. Kanamori (2003), The potential for earthquake early
warning in southern California, Science, 300, 786– 789.
Allen, R. V. (1978), Tiltmeter observations near a large earthquake, Bull.
Sesimol. Soc. Am., 68(3), 855–857.
Bernard, P., and R. Madariaga (1984), A new asymptotic method for the
modeling of near-field accelerograms, Bull. Seismol. Soc. Am., 74(2),
539– 557.
Campbell, K. W. (1985), Strong motion attenuation relations: A ten-year
perspective, Earthquake Spectra, 1, 759– 804.
City of Kobe Office (2008), The great Hanshin-Awaji earthquake statistics
and restoration progress, technical report, Kobe, Japan.
Cua, G., and T. Heaton (2007), The Virtual Seismologist (VS) method: A
Bayesian approach to earthquake early warning, in Earthquake Early
Warning System, edited by P. Gasparini, G. Manfredi, and J. Zschau,
pp. 97– 132, Springer, Heidelberg, Germany.
Dziewonski, A. M., T. A. Chou, and J. H. Woodhouse (1981), Determination
of earthquake source parameters from waveform data for studies of
global and regional seismicity, J. Geophys. Res., 86, 2825–2852.
Festa, G. (2007), Does the slip in the early steps of the rupture scale with
the final magnitude of the event?, Eos Trans. AGU, 88(52), Fall Meet.
Suppl., Abstract S24B-04.
Font, Y., H. Kao, S. Lallemand, C.-S. Liu, and L.-Y. Chiao (2004), Hypocentre
determination offshore of eastern Taiwan using the maximum
intersection method, Geophys. J. Int., 158(2), 655 – 675, doi:10.1111/
j.1365-246X.2004.02317.x.
Fukuyama, E., W. L. Ellsworth, F. Waldhauser, and A. Kubo (2003),
Detailed fault structure of the 2000 western Tottori, Japan, earthquake
sequence, Bull. Seismol. Soc. Am., 93(4), 1468– 1478.
Goltz, J. D. (2002), Introducing earthquake early warning in california: A
summary of social science and public policy issues, technical report,
Governor’s Off. of Emergency Serv., Pasadena, Calif.
Hellemans, A. (2006), Do early tremors give sneak preview of quake’s
power?, Scienze, 314, 1670, doi:10.1126/science.314.5806.1670.
Hokuriku Electric Power Company (2006), Annual report, technical report,
Toyama City, Japan.
Horiuchi, S., H. Negishi, K. Abe, A. Kamimura, and Y. Fujinawa (2005),
An automatic processing system for broadcasting earthquake alarms,
Bull. Seismol. Soc. Am., 95(2), 708– 718.
Hoshiba, M., O. Kamigaichi, M. Saito, S. Tsukada, and N. Hamada (2008),
Earthquake early warning starts nationwide in Japan, Eos Trans. AGU,
89(8), 73.
Ide, S., M. Takeo, and Y. Yoshida (1996), Source process of the 1995 Kobe
earthquake: Determination of spatio-temporal slip distribution by Bayesian
modeling, Bull. Seismol. Soc. Am., 86, 547– 566.
Iervolino, I., V. Convertito, M. Giorgio, G. Manfredi, and A. Zollo (2006),
Real-time risk analysis in hybrid earthquake early warning systems,
J. Earthquake Eng., 10, 867– 885.
Iervolino, I., M. Giorgio, and G. Manfredi (2007), Expected loss-based
alarm threshold set for earthquake early warning systems, Earthquake
Eng. Struct. Dyn., 36, 1151– 1168, doi:10.1002/eqe.675.
Kamigaichi, O. (2004), JMA earthquake early warning, J. Jpn. Assoc.
Earthquake Eng., 3, 134– 137.
Kanamori, H. (2005), Real-time seismology and earthquake damage mitigation,
Annu. Rev. Earth Planet. Sci., 33, 195– 214.
Kanno, T., A. Narita, N. Morikawa, H. Fujiwara, and Y. Fukushima (2006),
A new attenuation relation for strong ground motion in Japan based on
recorded data, Bull. Seismol. Soc. Am., 96(3), 879– 897.
Katsumata, A. (1996), Comparison of magnitudes estimated by the Japan
Meteorological Agency with moment magnitudes for intermediate and
deep earthquakes, Bull. Seismol. Soc. Am., 86(3), 832–842.
Keilis-Borok, V. (1959), On estimation of the displacement in an earthquake
source and of source dimensions, Ann. Geofis., 12, 205– 214.
Kostrov, B. V. (1964), Selfsimilar problems of propagation of shear cracks,
Appl. Math. Mech., 28(5), 1077– 1087.
Midorikawa, S., K. Fujimoto, and I. Muramatsu (1999), Correlation of new
JMA instrumental seismic intensity with former JMA seismic intensity
and ground motion parameters, J. Inst. Soc. Safety Sci., 1, 51–56.
Murphy, S., and S. Nielsen (2008), Dynamic and kinematic investigation of
earthquake magnitude determination by first few seconds of waveforms,
Bull. Seismol. Soc. Am., in press.
Nakamura, Y. (1988), On the urgent earthquake detection and alarm system
(Uredas), in Proceedings of the 9th World Conference on Earthquake
Engineering, vol. VII, pp. 673–678, Univ. do Porto, Fac. de Eng., Porto,
Portugal.
Odaka, T., K. Ashiya, S. Tsukada, S. Sato, K. Ohtake, and D. Nozaka
(2003), A new method of quickly estimating epicentral distance and
magnitude from a single seismic record, Bull. Seismol. Soc. Am., 93(1),
526– 532.
Olson, E. L., and R. M. Allen (2005), The deterministic nature of earthquake
rupture, Nature, 438–10, 212– 215.
Rydelek, P., and S. Horiuchi (2006), Is the earthquake rupture deterministic?,
Nature, 442–20, E5–E6.
Rydelek, P., C. Wu, and S. Horiuchi (2007), Comment on ‘‘Earthquake
magnitude estimation from peak amplitudes of very early seismic signals
on stron motion records’’ by Aldo Zollo, Maria Lancieri, and Stefan
Nielsen, Geophys. Res. Lett., 34, L20302, doi:10.1029/2007GL029387.
Satriano, C., A. Lomax, and A. Zollo (2008), Real-time evolutionary earthquake
location for seismic early warning, Bull. Seismol. Soc. Am., 98(3),
1482–1494, doi:10.1785/0120060159.
Scholz, C. H. (1990), The Mechanics of Earthquakes and Faulting, Cambridge
Univ. Press, New York.
Sekiguchi, H., K. Irikura, T. Iwata, Y. Kakehi, and M. Hoshiba (1996),
Minute locating of faulting beneath Kobe and the waveform inversion
of the process during the 1995 Hyogo-Ken Nambu, Japan earthquake
using strong ground motion records, J. Phys. Earthquake, 44, 473–487.
Sekiguchi, H., K. Irikura, and T. Iwata (2000), Fault geometry at the rupture
termination of the 1995 Hyogo-Ken Nanbu earthquake, Bull. Seismol.
Soc. Am., 90(1), 133– 177.
Shresta, B. K. (2001), Disaster reduction and response preparedness in
Japan: A Hyogo approach, paper presented at CDC 2001: The Second
Tampere Conference on Disaster Communication, Motorola, Tampere,
Finland.
Spudich, P., and L. N. Frazer (1984), Use of ray theory to calculate highfrequency
radiation from earthquake sources having spatially variable
rupture velocity and stress drop, Bull. Seismol. Soc. Am., 74, 2061–2082.
Tsuboi, C. (1954), Determination of the Gutenberg-Richter’ s magnitude
of earthquakes occurring in and near Japan (in Japanese with English
abstract), J. Seismol. Soc. Jpn., 7, 185– 193.
Tsukada, S. (2006), Earthquake early warning system in Japan, paper presented
at 6th Joint Meeting of UJNR Panel on Earthquake Research,
Coop. Program in Nat. Resour., Tokushima, Japan.
Wald, D. J. (1996), Slip history of the 1995 Kobe, Japan, earthquake
determined from strong motion, teleseismc, and geodetic data, J. Phys.
Earth, 44, 489– 503.
Wells, D., and K. Coppersmith (1994), New empirical relationships among
magnitude, rupture length, rupture width, rupture area, and surface displacement,
Bull. Seismol. Soc. Am., 84(4), 974–1002.
Wu, Y. M., and H. Kanamori (2005a), Rapid assessment of damage potential
of earthquakes in Taiwan from the beginning of P waves, Bull.
Seismol. Soc. Am., 95(3), 1181– 1185.
Wu, Y. M., and H. Kanamori (2005b), Experiment on an onsite early
warning method for the Taiwan early warning system, Bull. Seismol.
Soc. Am., 95(1), 347– 353.
Wu, Y.-M., and L. Zhao (2006), Magnitude estimation using the first three
seconds P-wave amplitude in earthquake early warning, Geophys. Res.
Lett., 33, L16312, doi:10.1029/2006GL026871.
Wu, Y.-M., H.-Y. Yen, L. Zhao, B.-S. Huang, and W.-T. Liang (2006),
Magnitude determination using initial P waves: A single-station approach,
Geophys. Res. Lett., 33, L05306, doi:10.1029/2005GL025395.
Yoshida, S., K. Koketsu, B. Shibazaki, T. Sagiya, and Y. Yoshida (1996),
Joint inversion of near- and far-field waveforms and geodetic data for the
rupture process of the 1995 Kobe earthquake, J. Phys. Earth, 44, 437–
454.
Zhao, D., F. Ochi, A. Hasegawa, and A. Yamamoto (2000), Evidence for
the location and cause of large crustal earthquakes in Japan, J. Geophys.
Res., 105, 13,579– 13,594.
Zollo, A., M. Lancieri, and S. Nielsen (2006), Earthquake magnitude estimation
from peak amplitudes of very early seismic signals on strong
motion records, Geophys. Res. Lett., 33, L23312, doi:10.1029/
2006GL027795.
Zollo, A., M. Lancieri, and S. Nielsen (2007), Reply to comment by P.
Rydelek et al. on ‘‘Earthquake magnitude estimation from peak amplitudes
of very early seismic signals on strong motion records,’’ Geophys.
Res. Lett., 34, L20303, doi:10.1029/2007GL030560.