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Extreme Environmental Events pp 1022–1034Cite as

Tsunamis, Inverse Problem of

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Article Outline

Glossary

Definition of the Subject

Introduction

Tsunami Generation by Earthquakes

Tsunami Propagation

Tsunami Observations

Estimation of Tsunami Source

Estimation of Earthquake Fault Parameters

Future Directions

Bibliography

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Abbreviations

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.

Shallow water (long) waves:

In hydrodynamics, water waves can be treated as shallow water, or long, waves when the wavelength is much larger than the water depth. In such a case, the entire water mass from water bottom to surface moves horizontally and the wave propagation speed is given as a square root of the product of the gravitational acceleration and the water depth.

The 2004 Indian Ocean tsunami:

On December 26, 2004, a gigantic earthquake, the largest in the last half century in the world, occurred off the west coast of Sumatra Island, Indonesia. With the source extending more than 1,000 km through Nicobar and Andaman Islands, the earthquake generated tsunami which attacked the coasts of Indian Ocean and caused the worst tsunami disaster in history. The total casualties were about 230,000 in many countries as far away as Africa.

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 the elastic dislocation theory.

Refraction and inverse refraction diagrams (travel timemap):

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 backwards from observation points. The tsunami source can be estimated from the arcs corresponding to tsunami travel times.

Bibliography

Primary Literature

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  6. 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  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

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

    Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

  12. 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  Google Scholar 

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

    Article  Google Scholar 

  14. Song YT, Fu L-L, Zlotnicki V, Ji C, Hjorleifsdottir V, Shum CK, Yi Y (2008) The role of horizontal impulses of the faulting continental slope in generating the 26 December 2004 tsunami. Ocean Modell 20:362–379

    Article  Google Scholar 

  15. Intergovernmental Oceanographic Commission (1997) IUGG/IOC TIME Project Numerical Method of Tsunami Simulation with the Leap-frog Scheme. UNESCO, Paris

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  18. 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 

  19. 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 Planet Space 52:841–845

    Google Scholar 

  20. 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  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  23. 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 Planet Space 58:195–201

    Google Scholar 

  24. 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 

  25. Intergovernmental Oceanographic Commission (1998) Post‐tsunami survey field guide. UNESCO, Paris

    Google Scholar 

  26. 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. doi:10.1029/2003JB002521

  27. 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 

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

    Article  Google Scholar 

  29. 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  CAS  Google Scholar 

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

    Article  Google Scholar 

  31. 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  Google Scholar 

  32. Miyabe N (1934) An investigation of the Sanriku tunami based on mareogram data. Bull Earthq Res Inst Univ Tokyo Suppl 1:112–126

    Google Scholar 

  33. 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. doi:10.1029/2005GL022610

  34. 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 Planet Space 58:211–215

    Google Scholar 

  35. 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 

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

    Article  Google Scholar 

  37. 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  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  43. 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  Google Scholar 

  44. 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  Google Scholar 

  45. 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  Google Scholar 

  46. 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 

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

    Article  Google Scholar 

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

    Google Scholar 

  49. 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  CAS  Google Scholar 

  50. 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, doi:10.1029/2006GL027286

    Article  Google Scholar 

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

    Article  Google Scholar 

  52. 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  Google Scholar 

  53. 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 Coastal Engin JSCE 46:341–345

    Google Scholar 

  54. Yokota T, Nemoro M, Masuda T (2004) Estimate of slip distribution by tsunami height data inversion. Abst Jpn Earth Planet Sci Joint Meeting S043-P0005

    Google Scholar 

  55. Namegaya Y, Tsuji Y (2007) Distribution of asperities of the 1854 Ansei Nankai earthquake. Abst Jpn Earth Planet Sci Joint Meeting S142-009

    Google Scholar 

  56. Satake K, Baba T, Hirata K, Iwasaki S, Kato T, Koshimura S, Takenaka J, Terada Y (2005) Tsunami source of the 2004 off the Kii peninsula earthquakes inferred from offshore tsunami and coastal tide gauges. Earth Planet Space 57:173–178

    Google Scholar 

Books and Reviews

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

    Google Scholar 

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

    Google Scholar 

  3. Menke W (1989) Geophysical data analysis: Discrete inverse theory (revised edition). Academic Press, San Diego

    Google Scholar 

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

    Google Scholar 

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Author information

Authors and Affiliations

  1. Earthquake Research Institute, University of Tokyo, Tokyo, Japan

    Kenji Satake

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  1. Kenji Satake
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Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Satake, K. (2011). Tsunamis, Inverse Problem of. In: Meyers, R. (eds) Extreme Environmental Events. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7695-6_54

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