Skip to main content
Earth, Planets and Space
Download PDF

Rupture process by waveform inversion using simulated annealing and simulation of broadband ground motions

Earth, Planets and Space volume 57, pages 571–590 (2005)Cite this article

Abstract

A source inversion method using very fast simulated annealing is proposed to estimate the earthquake rupture process, and associated radiation of broadband strong ground motions. We invert the displacement and velocity motions separately to estimate the spatio-temporal distributions of effective stress and moment. The developed method is applied to the near-source strong motions in the frequency range up to 5 Hz from the 1997 Izu-Hanto Toho-Oki earthquake (Mjma 5.9). Results of the displacement inversion indicate that for this earthquake the seismic moment is mainly released from the shallower region and the northern area from the hypocenter. Similar results are obtained from the velocity inversion, and the variation of the effective stress also exhibits a similar behavior to the moment distribution. Based on the inversion results, we propose a characterized source model that consists of the finite number of asperities and a background area with uniform effective stresses. The broadband ground motion simulation demonstrates that the characterized source model successfully reproduces the observed ground motions in spite of the simplification of actual (inverted) source process. This suggests our proposed inversion method and source characterization process are suitable for the strong-motion prediction that reflects the high-frequency radiation from an actual earthquake.

References

  • Aki, K., Scaling law of seismic spectrum, J. Geophys. Res., 72, 1217–1231, 1967.

    Article  Google Scholar 

  • Boatwright, J., The seismic radiation from composite models of faulting, Bull. Seism. Soc. Am., 78, 489–508, 1988.

  • Boore, D. M., Stochastic simulation of high frequency ground motion based on seismological models of radiated spectra, Bull. Seism. Soc. Am., 73, 1865–1894, 1983.

    Google Scholar 

  • Brune, J., Tectonic stress and the spectra of seismic shear waves from earthquakes, J. Geophys. Res., 75, 4997–5009, 1970.

    Article  Google Scholar 

  • Brune, J., Correction, J. Geophys. Res., 76, 5002, 1971.

    Article  Google Scholar 

  • Claerbout, J. F. and F. Muir, Robust modeling with erratic data, Geophysics, 38, 826–844, 1973.

    Article  Google Scholar 

  • Das, S. and B. V. Kostrov, Inversion for seismic slip rate history and distribution with stabilizing constraints: Application to the 1986 Andreanof Islands earthquake, J. Geophys. Res., 95, 6899–6913, 1

    Article  Google Scholar 

  • Day, S. M., Three-dimensional finite difference simulation of fault dynamics; rectangular faults with fixed rupture velocity, Bull. Seism. Soc. Am., 72, 705–727, 1982.

    Google Scholar 

  • Delous, B., P. Lundgren, J. Salichon, and D. Giardini, Joint inversion of InSAR and teleseismic data for the slip history of the 1999 Izmit (Turkey) earthquake, Geophys. Res. Lett., 27, 3389–3392, 2000.

    Article  Google Scholar 

  • Delous, B., D. Giardini, P. Lundgren, and J. Salichon, Jointinversion of InSAR, GPS, teleseismic, and strong-motion data for the spatial and temporal distribution of earthquake slip: Application to the 1999 Izmit Mainshock, Bull. Seism. Soc. Am., 92, 278–299, 2002.

    Article  Google Scholar 

  • Duijndam, A. J. W., Baysian estimation in seismic inversion. Part I: Principles, Geophysical Prospecting, 36, 878–898, 1988.

    Article  Google Scholar 

  • Eshelby, J. D., The determination of the elastic field of an ellipsoidal inclusion and related problems, Proc. Roy. Soc. Lond., A, 241, 376–396, 1957.

    Article  Google Scholar 

  • Fukuyama, E., Inversion for the rupture details of the 1987 east Chiba earthquake, Japan, using a fault model based on the distribution if relocated aftershocks, J. Geophys. Res., 96, 8205–8217, 1991.

    Article  Google Scholar 

  • Fukuyama, E. and K. Irikura, Heterogeneity of the 1980 Izu-Hanto-toho-Oki earthquake rupture process, Geophys. J. Int., 99, 711–722, 1989.

    Article  Google Scholar 

  • Fukuyama, E., M. Ishida, D. S. Dreger, and H. Kawai, Automated seismic moment tensor determination by using on-line broadband waveforms, Zisin 2 (J. Seism. Soc. Japan), 51, 149–156, 1998 (in Japanese with English abstract).

    Google Scholar 

  • Geman, S. and D. Geman, Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images, IEEE Trans. Patt. Anal. Mach. Int., 6, 721–741, 1

    Article  Google Scholar 

  • Gibert, D. and J. Virieux, Electromagnetic imaging and simulated annealing, J. Geophys. Res., 96, 8057–8067, 1991.

    Article  Google Scholar 

  • Hartzell, S. H., Earthquake aftershocks as Green’s functions, Geophys. Res. Lett., 5, 1–4, 1978.

    Article  Google Scholar 

  • Hartzell, S. H. and T. H. Heaton, Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of the 1979 Imperial Valley, California earthquake, Bull. Seism. Soc. Am., 73, 1553–1583, 1983.

    Google Scholar 

  • Hellweg, M. and J. Boatwright, Mapping the rupture process of moderate earthquakes by inverting accelerograms, J. Geophys. Res., 104, 7319–7328, 1999.

    Article  Google Scholar 

  • Holland, J. H., Adaptation in Natural and Artificial Systems, MIT Press, Cambridge, Massachusetts, 1975.

    Google Scholar 

  • Horikawa, H., Earthquake doublet in Kagoshima, Japan: Rupture of asperities in a stress shadow, Bull. Seism. Soc. Am., 91, 112–127, 2001.

    Article  Google Scholar 

  • Ide, S., Source process of the 1997 Yamaguchi, Japan, earthquake analyzed in different frequency bands, Geophys. Res. Lett., 26, 1973–1976, 1999.

    Article  Google Scholar 

  • Ide, S., Complex source process and the interaction of moderate earthquakes during the earthquake swarm in the Hida-Mountains, Japan, 1998, Tectonophysics, 334, 35–54, 2001.

    Article  Google Scholar 

  • Ide, S. and M. Takeo, Determination of constitutive relations of fault slip based on seismic wave analysis, J. Geophys. Res., 102, 27379–27391, 1997.

    Article  Google Scholar 

  • IhmlĂ©, P. F., Monte Carlo slip inversion in the frequency domain: Application to the 1992 Nicaragua slow earthquake, Geophys. Res. Lett., 9, 913–916, 1996.

    Article  Google Scholar 

  • IhmlĂ©, P. F., and J. C. Ruegg, Source tomography by simulated annealing using broad-band surface waves and geodetic data: Application to the Mw=8.1 Chile 1995 event, Geophys. J. Int., 131, 146–158, 1997.

    Article  Google Scholar 

  • Ingber, L., Very fast simulated re-annealing, Mathl. Comput. Modelling, 12, 967–973, 1989.

    Article  Google Scholar 

  • Irikura, K., Semi-empirical estimation of strong ground motions during large earthquakes, Bull. Disas. Prev. Res. Inst., Kyoto Univ., 33, 63–104, 1983.

    Google Scholar 

  • Irikura, K., Prediction of strong acceleration motions using empirical Green’s function, Proc. 7th Japan Conf. Earthq. Eng., 151–156, 1986.

    Google Scholar 

  • Irikura, K., Recipe for predicting strong ground motion from future large earthquake, Annuals of Disas. Prev. Res. Inst., Kyoto Univ., 47, A, 2004 (in Japanese with English abstract).

  • Iwata, T. and K. Irikura, Source parameters of the 1983 Japan Sea earthquake sequence, J. Phys. Earth, 36, 155–184, 1988.

    Article  Google Scholar 

  • Japan Meteorological Agency, Seismic activity in and around the Izu Peninsula (Novenber, 1996–April, 1997), Rep. Coord. Comm. Earthq. Pred., 58, 229–238, 1997 (in Japanese).

    Google Scholar 

  • Ji, C. D., J. Wald, and D. V. Helmberger, Source description of the 1999 Hector Mine, California, earthquake, Part I: Wavelet domain inversion theory and resolution analysis, Bull. Seism. Soc. Am., 92, 1192–1207, 2002a.

    Article  Google Scholar 

  • Ji, C. D., J. Wald, and D. V. Helmberger, Source description of the 1999 Hector Mine, California, earthquake, Part II: Complexity of slip history, Bull. Seism. Soc. Am., 92, 1208–1226, 2002b.

    Article  Google Scholar 

  • Kakehi, Y. and K. Irikura, Estimation of high-frequency wave radiation areas on the fault plane by the envelope inversion of acceleration seismograms, Geophys. J. Int., 125, 892–900, 1996.

    Article  Google Scholar 

  • Kamae, K. and K. Irikura, Source model of the 1995 Hyogo-ken Nanbu earthquake and simulation of near-source ground motion, Bull. Seism. Soc. Am., 88, 400–412, 1998.

    Google Scholar 

  • Kanamori, H. and D. L. Anderson, Theoretical basis of some empirical relations in seismology, Bull. Seism. Soc. Am., 65, 1073–1095, 1975.

    Google Scholar 

  • Kinoshita, S., Frequency-dependent attenuation of shear waves in the crust of southern Kanto area, Japan, Bull. Seismol. Soc. Am., 84, 1387–1396, 1994.

    Google Scholar 

  • Kirkpatrick, S., C. D. Gelatt, and M. P. Vecchi, Optimization by simulated annealing, Science, 220, 671–680, 1983.

    Article  Google Scholar 

  • Liu, H. L. and D. V. Helmberger, The 23:29 aftershock of the 15 October 1979 Imperial Valley earthquake: More evidence for an asperity, Bull. Seism. Soc. Am., 75, 689–708, 1985.

    Google Scholar 

  • Mai, P. M. and G. C. Beroza, Source scaling properties from finite-fault rupture models, Bull. Seism. Soc. Am., 90, 604–615, 2000.

    Article  Google Scholar 

  • Metropolis, N., A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, Equation of state calculations by fast computing machines, J. Chem. Phys., 21, 1087–1092, 1953.

    Article  Google Scholar 

  • Miyake, H., T. Iwata, and K. Irikura, Strong ground motion simulation and source modeling of the Kagoshima-ken Hokuseibu earthquakes of March 26 (Mjma 6.5) and May 13 (Mjma 6.3), 1997, using empirical Green’s function method, Zisin 2 (J. Seism. Soc. Japan), 51, 431–442, 1999 (in Japanese with English abstract).

    Google Scholar 

  • Miyake, H., T. Iwata, and K. Irikura, Source characterization for broadband ground-motion simulation: Kinematic heterogeneous source model and strong motion generation area, Bull. Seism. Soc. Am., 93, 2531–2545, 2003.

    Article  Google Scholar 

  • Miyakoshi, K., T. Kagawa, H. Sekiguchi, T. Iwata, and K. Irikura, Source characterization of inland earthquakes in Japan using source inversion results, Proc. 12th World Conf. Earthq. Eng., 1850, 2000.

    Google Scholar 

  • Mori, J. and S. Hartzell, Source inversion of the 1988 Upland, California, earthquake: Determination of a fault plane for a small event, Bull. Seism. Soc. Am., 80, 507–518, 1990.

    Google Scholar 

  • Mosegaard, K. and A. Tarantola, Monte Carlo sampling of solutions to inverse problems, J. Geophys. Res., 100, 12431–12447, 1995.

    Article  Google Scholar 

  • Mosegaard, K. and P. D. Vestergaard, A simulated annealing approach to seismic model optimization with sparse prior information, Geophys. Prospect., 39, 599–611, 1991.

    Article  Google Scholar 

  • Nakahara, H., T. Nishimura, H. Sato, M. Ohtake, S. Kinoshita, and H. Hamaguchi, Broadband source rupture process of the 1998 Iwate Prefecture, Japan, earthquake as revealed from inversion analysis of seismic waveforms and envelopes, Bull. Seism. Soc. Am., 92, 1708–1720, 2002.

    Article  Google Scholar 

  • Okada, T., N. Umino, T. Matsuzawa, A. Hasegawa, and M. Kamiyama, Source processes of 15 September 1998 M5.0 Sendai, NE Japan, earthquake and its M3.8 foreshock by waveform inversion, Bull. Seism. Soc. Am., 91, 1607–1618, 2001.

    Article  Google Scholar 

  • Olson, A. H. and R. J. Aspel, Finite Faults and inverse theory with application to the 1979 Imperial Valley earthquake, Bull. Seism. Soc. Am., 72, 1969–2001, 1982.

    Google Scholar 

  • Reeves, C. R., Modern Heuristic Techniques for Combinatorial Problems, McGraw-Hill, 1993.

    Google Scholar 

  • Sekiguchi, H., K. Irikura, T. Iwata, Y. Kakehi, and M. Hoshiba, Minute locating of fault planes and source process of the 1995 Hyogo-ken Nanbu, Japan, earthquake from the waveform inversion of strong ground motion, J. Phys. Earth, 44, 473–487, 1996.

    Article  Google Scholar 

  • Somerville, P. G., K. Irikura, R. Graves, S. Sawada, D. Wald, N. Abrahamson, Y. Iwasaki, T. Kagawa, N. Smith, and A. Kowada, Characterizing crustal earthquake slip models for the prediction of strong ground motion, Seism. Res. Lett., 70, 59–80, 1999.

    Article  Google Scholar 

  • Takeo, M., Rupture process of the 1980 Izu-Hanto-Toho-Oki earthquake deduced from strong motion seismograms, Bull. Seism. Soc. Am., 78, 1074–1091, 1988.

    Google Scholar 

  • Trifunac, M. D., A three dimensional dislocation model for the San Fernando, California earthquake of February 9, 1971, Bull. Seism. Soc. Am., 64, 149–172, 1974.

    Google Scholar 

  • Wessel, P. and W. H. F. Smith, New version of the Generic Mapping Tools released, Eos Trans. Am. Geophys. Union, 76, 329, 1995.

    Article  Google Scholar 

  • Yamanaka, H., Application of simulated annealing to inversion of surface wave phase velocity—Comparison of performances between SA and GA inversions, Butsuri-Tansa a(Geophys. Explor.), 54, 197–206, 2001 (in Japanese with English abstract).

    Google Scholar 

  • Yoshida, S. and K. Koketsu, Simultaneous inversion of waveform and geodetic data for rupture process of the 1984 Naganoken-Seibu, Japan, earthquake, Geophys. J. Int., 103, 355–362, 1990.

    Article  Google Scholar 

  • Zeng, Y., K. Aki, and T. Teng, Mapping of the high-frequency source radiation for the Loma Prieta earthquake, California, J. Geophys. Res., 98, 11981–11993, 1993.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Central Research Institute of Electric Power Industry, 1646 Abiko, Abiko-shi, Chiba, 270-1194, Japan

    Yoshiaki Shiba

  2. Kyoto University, Yoshida, Sakyo-ku, Kyoto, 606-8501, Japan

    Kojiro Irikura

Authors
  1. Yoshiaki Shiba
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kojiro Irikura
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yoshiaki Shiba.

Rights and permissions

Open Access  This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shiba, Y., Irikura, K. Rupture process by waveform inversion using simulated annealing and simulation of broadband ground motions. Earth Planet Sp 57, 571–590 (2005). https://doi.org/10.1186/BF03351837

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1186/BF03351837

Key words