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Tsunamis, Inverse Problem of

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Glossary

Fault parameters:

Earthquake source is modeled as a fault motion, which can be described by nine static parameters. Once these fault parameters are specified, the seafloor deformation due to faulting, or initial condition of tsunamis, can be calculated by using elastic dislocation theory.

Inverse problem:

Unlike a forward problem, which starts from a tsunami source then computes propagation in the ocean and predicts travel times and/or water heights on coasts, an inverse problem starts from tsunami observations to study the generation process. While forward modeling is useful for tsunami warning or hazard assessments, inverse modeling is a typical approach for geophysical problems.

Refraction and inverse refraction diagrams (travel-time map):

Refraction diagram is a map showing isochrons or lines of equal tsunami travel times calculated from the source toward coasts. Inverse refraction diagram is a map showing arcs calculated backward from observation points. The tsunami...

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Bibliography

Primary Literature

  • Abe K (1973) Tsunami and mechanism of great earthquakes. Phys Earth Planet Inter 7:143–153

    Article  ADS  Google Scholar 

  • Abe K (1979) Size of great earthquakes of 1873–1974 inferred from tsunami data. J Geophys Res 84:1561–1568

    Article  ADS  Google Scholar 

  • Abe K (1981) Physical size of tsunamigenic earthquakes of the northwestern Pacific. Phys Earth Planet Inter 27:194–205

    Article  ADS  Google Scholar 

  • Abe K (1989) Quantification of tsunamigenic earthquakes by the Mt scale. Tectonophysics 166:27–34

    Article  ADS  Google Scholar 

  • Aida I (1978) Reliability of a tsunami source model derived from fault parameters. J Phys Earth 26:57–73

    Article  Google Scholar 

  • Ammon CJ, Ji C, Thio HK, Robinson D, Ni SD, Hjorleifsdottir V, Kanamori H, Lay T, Das S, Helmberger D, Ichinose G, Polet J, Wald D (2005) Rupture process of the 2004 Sumatra-Andaman earthquake. Science 308:1133–1139

    Article  ADS  Google Scholar 

  • Annaka T, Ohta K, Motegi H, Yoshida I, Takao M, Soraoka H (1999) A study on the tsunami inversion method based on shallow water theory. Proc Coast Eng JSCE 46:341–345

    Article  Google Scholar 

  • Atwater BF, Musumi-Rokkaku S, Satake K, Tsuji Y, Ueda K, Yamaguchi DK (2005) The orphan tsunami of 1700. USGS Prof Paper 1707:133

    Google Scholar 

  • Baba T, Cummins PR, Hori T (2005) Compound fault rupture during the 2004 off the Kii Peninsula earthquake (M 7.4) inferred from highly resolved coseismic sea-surface deformation. Earth Planets Space 57:167–172

    Article  ADS  Google Scholar 

  • Dawson AG, Shi SZ (2000) Tsunami deposits. Pure Appl Geophys 157:875–897

    Article  ADS  Google Scholar 

  • Fujii Y, Satake K (2007) Tsunami source model of the 2004 Sumatra-Andaman earthquake inferred from tide gauge and satellite data. Bull Seismol Soc Am 97:S192–S207

    Article  Google Scholar 

  • Fujii Y, Satake K, Sakai S, Shinohara M, Kanazawa T (2011) Tsunami source of the 2011 off the Pacific coast of Tohoku earthquake. Earth Planets Space 63:815–820

    Article  ADS  Google Scholar 

  • Geist E (1998) Local tsunamis and earthquake source parameters. Adv Geophys 39:117–209

    Article  ADS  Google Scholar 

  • Gonzalez FI, Bernard EN, Meinig C, Eble MC, Mofjeld HO, Stalin S (2005) The NTHMP tsunameter network. Nat Hazards 35:25–39

    Article  Google Scholar 

  • Gusman AR, Sheehan AF, Satake K, Heidarzadeh M, Mulia IE, Maeda T (2016) Tsunami data assimilation of Cascadia seafloor pressure gauge records from the 2012 Haida Gwaii earthquake. Geophys Res Lett 43:4189–4196

    Article  ADS  Google Scholar 

  • Hanks T, Kanamori H (1979) A moment magnitude scale. J Geophys Res 84:2348–2350

    Article  ADS  Google Scholar 

  • Hirata K, Satake K, Tanioka Y, Kuragano T, Hasegawa Y, Hayashi Y, Hamada N (2006) The 2004 Indian Ocean tsunami: tsunami source model from satellite altimetry. Earth Planets Space 58:195–201

    Article  ADS  Google Scholar 

  • Imamura F (2009) Tsunami modeling: calculating inundation and hazard maps. In: Bernard EN, Robinson AR (eds) Tsunamis. Harvard University Press, Cambridge, pp 321–332

    Google Scholar 

  • Intergovernmental Oceanographic Commission (1997) IUGG/IOC TIME project numerical method of tsunami simulation with the leap-frog scheme. UNESCO, Paris. http://www.jodc.go.jp/info/ioc_doc/Manual/122367eb.pdf

  • Intergovernmental Oceanographic Commission (1998) Post-tsunami survey field guide. UNESCO, Paris

    Google Scholar 

  • Kanamori H (1977) The energy release in great earthquakes. J Geophys Res 82:2981–2987

    Article  ADS  Google Scholar 

  • Kato T, Terada Y, Kinoshita M, Kakimoto H, Isshiki H, Matsuishi M, Yokoyama A, Tanno T (2000) Real-time observation of tsunami by RTK-GPS. Earth Planets Space 52:841–845

    Article  ADS  Google Scholar 

  • Kikuchi M, Fukao Y (1985) Iterative deconvolution of complex body waves from great earthquakes – the Tokachi-oki earthquake of 1968. Phys Earth Planet Inter 37:235–248

    Article  ADS  Google Scholar 

  • Lay T, Kanamori H (1981) An asperity model of large earthquake sequences. In: Simpson DW, Richards PG (eds) Earthquake prediction – an international review. American Geophysical Union, Washington, DC, pp 579–592

    Google Scholar 

  • Lay T, Kanamori H, Ammon CJ, Nettles M, Ward SN, Aster RC, Beck SL, Bilek SL, Brudzinski MR, Butler R, DeShon HR, Ekstrom G, Satake K, Sipkin S (2005) The great Sumatra-Andaman earthquake of 26 December 2004. Science 308:1127–1133

    Article  ADS  Google Scholar 

  • Mader CL (1988) Numerical modeling of water waves. University of California Press, Berkeley

    MATH  Google Scholar 

  • Maeda T, Obara K, Shinohara M, Kanazawa T, Uehira K (2015) Successive estimation of a tsunami wavefield without earthquake source data: a data assimilation approach toward real-time tsunami forecasting. Geophys Res Lett 42:7923–7932

    Article  ADS  Google Scholar 

  • Mansinha L, Smylie DE (1971) The displacement fields of inclined faults. Bull Seismol Soc Am 61:1433–1440

    MATH  Google Scholar 

  • Mei CC (1989) The applied dynamics of ocean surface waves. World Scientific, Singapore

    MATH  Google Scholar 

  • Merrifield MA, Firing YL, Aarup T, Agricole W, Brundrit G, Chang-Seng D, Farre R, Kilonsky B, Knight W, Kong L, Magori C, Manurung P, McCreery C, Mitchell W, Pillay S, Schindele F, Shillington F, Testut L, Wijeratne EMS, Caldwell P, Jardin J, Nakahara S, Porter FY, Turetsky N (2005) Tide gauge observations of the Indian Ocean tsunami, December 26, 2004. Geophys Res Lett 32. https://doi.org/10.1029/2005GL022610

  • Mikada H, Mitsuzawa K, Matsumoto H, Watanabe T, Morita S, Otsuka R, Sugioka H, Baba T, Araki E, Suyehiro K (2006) New discoveries in dynamics of an M8 earthquake-phenomena and their implications from the 2003 Tokachi-oki earthquake using a long term monitoring cabled observatory. Tectonophysics 426:95–105

    Article  ADS  Google Scholar 

  • Miyabe N (1934) An investigation of the Sanriku tsunami based on mareogram data. Bull Earthquake Res Inst 1:112–126

    Google Scholar 

  • Mori J, Shimazaki K (1985) Inversion of intermediate-period Rayleigh waves for source characteristics of the 1968 Tokachi-oki earthquake. J Geophys Res 90:11374–11382

    Article  ADS  Google Scholar 

  • Murotani S, Satake K, Fujii Y (2013) Scaling relations of seismic moment, rupture area, average slip, and asperity size for M ~ 9 subduction-zone earthquakes. Geophys Res Lett 40:5070–5074

    Article  ADS  Google Scholar 

  • Nagarajan B, Suresh I, Sundar D, Sharma R, Lal AK, Neetu S, Shenoi SSC, Shetye SR, Shankar D (2006) The great tsunami of 26 December 2004: a description based on tide-gauge data from the Indian subcontinent and surrounding areas. Earth Planets Space 58:211–215

    Article  ADS  Google Scholar 

  • Nanayama F, Satake K, Furukawa R, Shimokawa K, Atwater BF, Shigeno K, Yamaki S (2003) Unusually large earthquakes inferred from tsunami deposits along the Kuril trench. Nature 424:660–663

    Article  ADS  Google Scholar 

  • Neetu S, Suresh I, Shankar R, Shankar D, Shenoi SSC, Shetye SR, Sundar D, Nagarajan B (2005) Comment on “The great Sumatra-Andaman earthquake of 26 December 2004”. Science 310:1431a

    Article  Google Scholar 

  • Okada Y (1985) Surface deformation due to shear and tensile faults in a half-space. Bull Seismol Soc Am 75:1135–1154

    Google Scholar 

  • Piatanesi A, Tinti S, Gavagni I (1996) The slip distribution of the 1992 Nicaragua earthquake from tsunami run-up data. Geophys Res Lett 23:37–40

    Article  ADS  Google Scholar 

  • Pires C, Miranda PMA (2001) Tsunami waveform inversion by adjoint methods. J Geophys Res 106:19773–19796

    Article  ADS  Google Scholar 

  • Rabinovich AB, Thomson RE (2007) The 26 December 2004 Sumatra tsunami: analysis of tide gauge data from the world ocean part 1, Indian Ocean and South Africa. Pure Appl Geophys 164:261–308

    Article  ADS  Google Scholar 

  • Saito T, Satake K, Furumura T (2010) Tsunami waveform inversion including dispersive waves: the 2004 off Kii Peninsula earthquake. J Geophys Res 115:B06303. https://doi.org/10.1029/2009JB006884

    Article  ADS  Google Scholar 

  • Satake K (1988) Effects of bathymetry on tsunami propagation – application of ray tracing to tsunamis. Pure Appl Geophys 126:27–36

    Article  ADS  Google Scholar 

  • Satake K (1989) Inversion of tsunami waveforms for the estimation of heterogeneous fault motion of large submarine earthquakes – the 1968 Tokachi-Oki and 1983 Japan Sea earthquakes. J Geophys Res 94:5627–5636

    Article  ADS  Google Scholar 

  • Satake K, Tanioka Y (2003) The July 1998 Papua New Guinea earthquake: mechanism and quantification of unusual tsunami generation. Pure Appl Geophys 160:2087–2118

    Article  ADS  Google Scholar 

  • Satake K, Wang KL, Atwater BF (2003) Fault slip and seismic moment of the 1700 Cascadia earthquake inferred from Japanese tsunami descriptions. J Geophys Res 108. https://doi.org/10.1029/2003JB002521

  • Satake K, Fujii Y, Harada T, Namgaya Y (2013) Time and space distribution of coseismic slip of the 2011 Tohoku earthquake as inferred from tsunami waveform data. Bull Seismol Soc Am 103:1473–1492

    Article  Google Scholar 

  • Sawai Y, Namegaya Y, Okamura Y, Satake K, Shishikura M (2012) Challenges of anticipating the 2011 Tohoku earthquake and tsunami using coastal geology. Geophys Res Lett 39:L21309. https://doi.org/10.1029/2012GL053692

    Article  ADS  Google Scholar 

  • Smith WHF, Scharroo R, Titov VV, Arcas D, Arbic BK (2005) Satellite altimeters measure tsunami, early model estimates confirmed. Oceanography 18:10–12

    Google Scholar 

  • Stein S, Okal EA (2005) Speed and size of the Sumatra earthquake. Nature 434:581–582

    Article  ADS  Google Scholar 

  • Steketee JA (1958) On Volterra’s dislocations in a semi-infinite elastic medium. Can J Phys 36:192–205

    Article  ADS  MathSciNet  Google Scholar 

  • Synolakis CE, Okal EA (2005) 1992–2002: perspective on a decade of post-tsunami surveys. In: Satake K (ed) Tsunamis: case studies and recent developments. Springer, Dordrecht, pp 1–29

    Google Scholar 

  • Tanioka Y, Satake K (1996) Tsunami generation by horizontal displacement of ocean bottom. Geophys Res Lett 23:861–864

    Article  ADS  Google Scholar 

  • Tanioka Y, Yudhicara KT, Kathiroli S, Nishimura Y, Iwasaki S-I, Satake K (2006) Rupture process of the 2004 great Sumatra-Andaman earthquake estimated from tsunami waveforms. Earth Planets Space 58:203–209

    Article  ADS  Google Scholar 

  • Titov VV, Gonzalez FI, Bernard EN, Eble MC, Mofjeld HO, Newman JC, Venturato AJ (2005) Real-time tsunami forecasting: challenges and solutions. Nat Hazards 35:41–58

    Article  Google Scholar 

  • Tsai VC, Nettles M, Ekstrom G, Dziewonski AM (2005) Multiple CMT source analysis of the 2004 Sumatra earthquake. Geophys Res Lett 32. https://doi.org/10.1029/2005GL023813

  • Tsushima H, Hino R, Fujimoto H, Tanioka Y, Imamura F (2009) Near-field tsunami forecasting from cabled ocean bottom pressure data. J Geophys Res 114:B06309

    Article  ADS  Google Scholar 

  • Velasco AA, Ammon CJ, Lay T (2006) Search for seismic radiation from late slip for the December 26, 2004 Sumatra-Andaman (Mw = 9.15) earthquake. Geophys Res Lett 33:L18305. https://doi.org/10.1029/2006GL027286

    Article  ADS  Google Scholar 

  • Wang Y, Satake K, Maeda T, Gusman AR (2017) Green’s Function-based Tsunami Data Assimilation: a fast data assimilation approach toward tsunami early warning. Geophys Res Lett 44:10282–10289

    Article  ADS  Google Scholar 

  • Yamanaka Y, Kikuchi M (2004) Asperity map along the subduction zone in northeastern Japan inferred from regional seismic data. J Geophys Res 109:B07307. https://doi.org/10.1029/2003JB002683

    Article  ADS  Google Scholar 

  • Yamashita T, Sato R (1974) Generation of tsunami by a fault model. J Phys Earth 22:415–440

    Article  Google Scholar 

  • Yanagisawa K, Imamura F, Sakakiyama T, Annaka T, Takeda T, Shuto N (2007) Tsunami assessment for risk management at nuclear power facilities in Japan. Pure Appl Geophys 164:565–576

    Article  ADS  Google Scholar 

  • Yeh H, Liu P, Synolakis C (1996) Long-wave runup models. World Scientific, Singapore

    Google Scholar 

Books and Reviews

  • Lawson CL, Hanson RJ (1974) Solving least squares problems. Prentice-Hall, Englewood Cliffs. (Republished by Society for Industrial and Applied Mathematics, 1995)

    MATH  Google Scholar 

  • Lay T, Wallace TC (1995) Modern global seismology. Academic, San Diego

    Google Scholar 

  • Menke W (1989) Geophysical data analysis: discrete inverse theory (revised edition). Academic, San Diego

    MATH  Google Scholar 

  • Satake K (2007) Tsunamis. In: Kanamori H (ed) Treatise on geophysics, vol 4. Elsevier, Amsterdam

    Google Scholar 

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Satake, K. (2019). Tsunamis, Inverse Problem of. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_570-3

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  • DOI: https://doi.org/10.1007/978-3-642-27737-5_570-3

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Chapter history

  1. Latest

    Tsunamis, Inverse Problem of
    Published:
    01 August 2019

    DOI: https://doi.org/10.1007/978-3-642-27737-5_570-3

  2. Original

    Tsunamis, Inverse Problem of
    Published:
    14 October 2015

    DOI: https://doi.org/10.1007/978-3-642-27737-5_570-2