Abstract
We define a new magnitude scale, M TSU, allowing the quantification of the seismic moment M0 of an earthquake based on recordings of its tsunami in the far field by ocean-bottom pressure sensors (“tsunameters”) deployed in ocean basins, far from continental or island shores which are known to affect profoundly and in a nonlinear fashion the amplitude of the tsunami wave. The formula for M TSU, M TSU=log10 M O‒20=log10 X (ω) + C TSU D + C TSU S +C O, where X(ω) is the spectral amplitude of the tsunami, C TSUD a distance correction and C TSUS a source correction, is directly adapted from the mantle magnitude M m introduced for seismic surface waves by Okal and Talandier. Like M m, its corrections are fully justified theoretically based on the representation of a tsunami wave as a branch of the Earth's normal modes. Even the locking constant C 0, which may depend on the nature of the recording (surface amplitude of the tsunami or overpressure at the ocean floor) and its units, is predicted theoretically. M TSU combines the power of a theoretically developed algorithm, with the robustness of a magnitude measurement that does not take into account such parameters as focal geometry and exact depth, which may not be available under operational conditions in the framework of tsunami warning. We verify the performance of the concept on simulations of the great 1946 Aleutian tsunami at two virtual gauges, and then apply the algorithm to 24 records of 7 tsunamis at DART tsunameters during the years 1994–2003. We find that M TSU generally recovers the seismic moment M 0 within 0.2 logarithmic units, even under unfavorable conditions such as excessive focal depth and refraction of the tsunami wave around continental masses. Finally, we apply the algorithm to the JASON satellite trace obtained over the Bay of Bengal during the 2004 Sumatra tsunami, after transforming the trace into a time series through a simple ad hoc procedure. Results are surprisingly good, with most estimates of the moment being over 1029 dyn-cm, and thus identifying the source as an exceptionally large earthquake.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abe, K. (1981), A new scale of tsunami magnitude, M t, Phys. Earth Planet. Inter. 27, 194–205.
Alterman, Z., Jarosch, H., and Pekeris, C.L. (1959), Oscillations of the Earth, Proc. Roy. Soc. Ser. A, 252, 80–95.
Artru, J., Dučić, V., Kanamori, H., Lognonné, P., and Murakami, M. (2005), Ionospheric detection of gravity waves induced by tsunamis, Geophys. J. Intl. 160, 840–848.
Ben-Menahem, A., and Rosenman, M. (1972), Amplitude patterns of tsunami waves from submarine earthquakes, J. Geophys. Res. 77, 3097–3128.
Geller, R.J. (1976), Scaling relations for earthquake source parameters and magnitudes, Bull. Seismol. Soc. Amer. 66, 1501–1523.
Gilbert, F. (1970), Excitation of the normal modes of the Earth by earthquake sources, Geophys. J. Roy. astr. Soc. 22, 223–226.
González, F.I., Bernard, E.N., Meinig, C., Eble, M.C., Mofjeld, H.O., and Stalin, S. (2005), The NTHMP Tsunameter network, Natural Hazards 35, 25–39.
Guibourg, S., Heinrich, P., and Roche, R. (1997), Numerical modeling of the 1995 Chilean tsunami; impact on French Polynesia, Geophys. Res. Letts. 24, 775–778.
Hanson, J.A. and Bowman, J.R. (2005), Dispersive and reflected tsunami signals from the 2004 Indian Ocean tsunami observed on hydrophones and seismic stations, Geophys. Res. Letts. 32(17), L17608, 5 pp.
Kanamori, H. (1977), The energy release in great earthquakes, J. Geophys. Res. 82, 2981–2987.
Kanamori, H. and Cipar, J.J. (1974), Focal process of the great Chilean earthquake, May 22, 1960, Phys. Earth Planet. Inter. 9, 128–136.
López, A.M. and Okal, E.A. (2006), A seismological reassessment of the source of the 1946 Aleutian “tsunami” earthquake, Geophys. J. Intl. 165, 835–849.
Love, A.E.H., Some Problems in Geodynamics (Cambridge Univ. Press, 1911).
Mansinha, L. and Smylie, D.E. (1971), The displacement fields of inclined faults, Bull. Seismol. Soc. Amer. 61, 1433–1440.
Occhipinti, G., Lognonné, P., Kherani, A., and Hébert, H. (2005), Modeling and detection of ionospheric perturbation associated with the Sumatra tsunami of December 26th, 2004, Eos, Trans. Amer. Geophys. Un. 86(52), U11A–0829 (abstract).
Okal, E.A. (1982), Mode-wave equivalence and other asymptotic problems in tsunami theory, Phys. Earth Planet. Inter. 30, 1–11.
Okal, E.A. (1988), Seismic parameters controlling far-field tsunami amplitudes: A review, Natural Hazards 1, 67–96.
Okal, E.A. (1990), Single forces and double-couples: A theoretical review of their relative efficiency for the excitation of seismic and tsunami waves, J. Phys. Earth 38, 445–474.
Okal, E.A. (2003), Normal mode energetics for far-field tsunamis generated by dislocations and landslides, Pure Appl. Geophys. 160, 2189–2221.
Okal, E.A. and Hébert, H. (2007), Far-field modeling of the 1946 Aleutian tsunami, Geophys. J. Intl. in press.
Okal, E.A. and Talandier, J. (1989), M m: Avariable period mantle magnitude, J. Geophys. Res. 94, 4169–4193.
Okal, E.A. and Talandier, J. (1991), Single-station estimates of the seismic moment of the 1960 Chilean and 1964 Alaskan earthquakes, using the mantle magnitude M m, Pure Appl. Geophys. 136, 103–126.
Okal, E.A., Piatanesi, A., and Heinrich, P. (1999), Tsunami detection by satellite altimetry, J. Geophys. Res. 104, 599–615.
Okal, E.A., Synolakis, C.E., Fryer, G.J., Heinrich, P., Borrero, J.C., Ruscher, C., Arcas, D., Guille, G., and Rousseau, D. (2002), A field survey of the 1946 Aleutian tsunami in the far field, Seismol. Res. Letts. 73, 490–503.
Okal, E.A., Talandier, J., and Reymond, D. (2007), Quantification of hydrophone records of the 2004 Sumatra tsunami, Pure Appl. Geophys. 164, 309–323.
Peltier, W.P. and Hines, C.O. (1976), On a possible ionospheric technique for tsunami detection, Geophys. J. Roy. astr. Soc. 46, 669–706.
Saito, M. (1967), Excitation of free oscillations and surface waves by a point source in a vertically heterogeneous Earth, J. Geophys. Res. 72, 3689–3699.
Scharroo, R., Smith, W.H.F., Titov, V.V., and ARCAS, D. (2005), Observing the Indian Ocean tsunami with satellite altimetry, Geophys. Res. Abstr. 7, 230, (abstract).
Sladen, A. and Hébert, H., Inversion of satellite altimetry to recover the Sumatra 2004 earthquake slip distribution, Eos, Trans. Amer. Geophys. Un. 86(52), U22A–07, (2005) (abstract).
Stein, S. and Okal, E.A. (2005), Size and speed of the Sumatra earthquake, Nature 434, 581–582.
Synolakis, C.E., Tsunami and seiche, In Earthquake Engineering Handbook (eds.) W.-F. Chen and C. Scawthron pp. 9_1–9_90, (CRC Press, Boca Raton, 2002).
Tanioka, Y., Ruff, L.J., and Satake, K. (1995), The great Kurile earthquake of October 4, 1994 tore the slab, Geophys. Res. Letts. 22, 1661–1664.
Titov, V.V. and Arcas, D. (2005), Indian Ocean tsunami generation and propagation from modeling and observations, Geol. Soc. Amer. Abstr. with Programs 37(7), p.93, (abstract).
Titov, V.V. and Synolakis, C.E. (1998), Numerical modeling of tidal wave run-up, J. Waterw. Port, Coastal and Ocean Eng. 124, 157–171.
Titov, V.V., González, F.I., Bernard, E.N., Eble, M.C., Mofjeld, H.O., Newman, J.C., and Venturato, A.J. (2005), Real-time tsunami forecasting: Challenges and solutions, Natural Hazards 35, 41–58.
Tsai, V.C., Nettles, M., Ekström, G., and Dziewoński, A.M. (2005), Multiple CMT source analysis of the 2004 Sumatra earthquake, Geophys. Res. Letts. 32(17), L17304, 4 pp.
Ward, S.N. (1980), Relationships of tsunami generation and an earthquake source, J. Phys. Earth 28, 441–474.
Ward, S.N. (1981), On tsunami nucleation: I. A point source, J. Geophys. Res. 86, 7895–7900.
Ward, S.N. (1982a), On tsunami nucleation: II. An instantaneous modulated line source, Phys. Earth Planet. Inter. 27, 273–285.
Ward, S.N. (1982b), Earthquake mechanism and tsunami generation: the Kurile Islands event of October 13, 1963, Bull. Seismol. Soc. Amer. 72, 759–777.
Weaver, P.F., Yuen, P.C., Prölss, G.W., and Furumoto, A.S. (1970), Acoustic coupling into the ionosphere from seismic waves of the earthquake at Kurile Islands on August 11, 1969, Nature 226, 1239–1241.
Yeh, H., Titov, V.V., Gusiakov, V., Pelinovsky, E., Khramushin, V., and Kaistrenko, V. (1995), The 1994 Shikotan earthquake tsunamis, Pure Appl. Geophys. 144, 855–874.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Birkhaüser Verlag, Basel
About this paper
Cite this paper
Okal, E.A., Titov, V.V. (2007). M TSU : Recovering Seismic Moments from Tsunameter Records. In: Satake, K., Okal, E.A., Borrero, J.C. (eds) Tsunami and Its Hazards in the Indian and Pacific Oceans. Pageoph Topical Volumes. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8364-0_5
Download citation
DOI: https://doi.org/10.1007/978-3-7643-8364-0_5
Received:
Accepted:
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8363-3
Online ISBN: 978-3-7643-8364-0
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)