Skip to main content

Tsunamis: Stochastic Models of Occurrence and Generation Mechanisms

  • Living reference work entry
  • Latest version View entry history
  • First Online:
Encyclopedia of Complexity and Systems Science

Glossary

Aleatory Uncertainty:

The uncertainty in seismic and tsunami hazard analysis due to inherent random variability of the quantity being measured. Aleatory uncertainties cannot be reduced by refining modeling or analytical techniques. Modified from Bormann et al. (2013).

Dynamic Earthquake Model:

A model of time-dependent and spontaneous fault rupture that produces time-dependent 3-D seismic wave and displacement fields on and around the fault, including deformation of the seafloor. A friction evolution equation is specified on the fault during the rupture process.

Dynamic Tsunami Generation Model:

A model of time-dependent displacement of the water column above the source region computed from the dynamic earthquake model (q.v.). It includes propagation of seismic waves in the solid earth and the water column. In contrast to static and kinematic models (q.v.), slip is not prescribed; it is computed from time-dependent stress conditions on the fault.

Moment Magnitude (Earthquake):

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Bibliography

  • Aitkin M (2010) Statistical inference: an integrated Bayesian/likelihood approach, vol 116. CRC Press, Boca Raton, p 236

    Google Scholar 

  • Akaike H (1980) Likelihood and the Bayes procedure. Trab Estad Investig Oper 31:143–166

    Article  MathSciNet  MATH  Google Scholar 

  • Aki K, Chouet B (1975) Origin of coda waves: source, attenuation, and scattering effects. J Geophys Res 80:3322–3342

    Article  ADS  Google Scholar 

  • Allen TI, Hayes GP (2017) Alternative rupture-scaling relationships for subduction Interface and other offshore environments. Bull Seismol Soc Am 107:1240–1253

    Article  Google Scholar 

  • Andrews DJ (1976) Rupture velocity of plane strain shear cracks. J Geophys Res 81:5679–5687

    Article  ADS  Google Scholar 

  • Andrews DJ (1980) A stochastic fault model 1. Static case. J Geophys Res 85:3867–3877

    Article  ADS  Google Scholar 

  • Andrews DJ, Barall M (2011) Specifying initial stress for dynamic heterogeneous earthquake source models. Bull Seismol Soc Am 101:2408–2417

    Article  Google Scholar 

  • Andrews DJ, Ma S (2016) Validating a dynamic earthquake model to produce realistic ground motion. Bull Seismol Soc Am 106:665–672

    Article  Google Scholar 

  • Annaka T, Satake K, Sakakiyama T, Yanagisawa K, Shuto N (2007) Logic-tree approach for probabilistic tsunami hazard analysis and it applications to the Japanese coasts. Pure Appl Geophys 164:577–592

    Article  ADS  Google Scholar 

  • Aochi H, Fukuyama E, Matsu’ura M (2000) Selectivity of spontaneous rupture propagation on a branched fault. Geophys Res Lett 27:3635–3638

    Article  ADS  Google Scholar 

  • Babeyko A, Hoechner A, Sobolev S (2010) Source modeling and inversion with near real-time GPS: a GITEWS perspective for Indonesia. Nat Hazards Earth Syst Sci 10:1617

    Article  ADS  Google Scholar 

  • Bartlett MS (1978) An introduction to stochastic processes, 3rd edn. Cambridge University Press, Cambridge, p 388

    Google Scholar 

  • Bebbington M (2013) Volcanic eruptions: stochastic models of occurrence patterns. In: Meyers R (ed) Encyclopedia of complexity and systems science. Springer, Berlin/Heidelberg

    Google Scholar 

  • Beichelt FE, Fatti LP (2002) Stochastic processes and their applications. Taylor & Francis, London

    Google Scholar 

  • Blaser L, Krüger F, Ohrnberger M, Scherbaum F (2010) Scaling relations of earthquake source parameter estimates with special focus on subduction environment. Bull Seismol Soc Am 100:2914–2926

    Article  Google Scholar 

  • Blaser L, Ohrnberger M, Riggelsen C, Babeyko A, Scherbaum F (2011) Bayesian networks for tsunami early warning. Geophys J Int 185:1431–1443

    Article  ADS  Google Scholar 

  • Bormann P, Aki K, Lee WHK, Schweitzer J (2013) Glossary. In: Bormann P (ed) New manual of seismological observatory practice 2 (NMSOP2). Deutsches GeoFoschungsZentrum GFZ, Potsdam, pp 1–200. https://doi.org/10.2312/GFZ.NMSOP-2_Glossary

    Chapter  Google Scholar 

  • Burbridge D, Cummins PR, Mleczko R, Thio HK (2008) A probabilistic tsunami hazard assessment for western Australia. Pure Appl Geophys 165:2059–2088

    Article  ADS  Google Scholar 

  • Burroughs SM, Tebbens SF (2005) Power law scaling and probabilistic forecasting of tsunami runup heights. Pure Appl Geophys 162:331–342

    Article  ADS  Google Scholar 

  • Candela T, Renard F, Klinger Y, Mair K, Schmittbuhl J, Brodsky EE (2012) Roughness of fault surfaces over nine decades of length scales. J Geophys Res 117. https://doi.org/10.10029/2011JB009041

  • Carrier GF (1970) Stochastically driven dynamical systems. J Fluid Mech 44:249–264

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Carrier GF (1995) On-shelf tsunami generation and coastal propagation. In: Tsuchiya Y, Shuto N (eds) Tsunami: Progress in prediction, disaster prevention and warning, vol 4. Kluwer, Dordrecht, pp 1–20

    Chapter  Google Scholar 

  • Cienfuegos R, Catalán PA, Urrutia A, Benavente R, Aránguiz R, González G (2018) What can we do to forecast tsunami hazards in the near field given large epistemic uncertainty in rapid seismic source inversions? Geophys Res Lett 45:4944–4955

    Article  ADS  Google Scholar 

  • Corral A (2009) Point-occurrence self-similarity in crackling-noise systems and in other complex systems. J Stat Mech Theor Exp 2009. https://doi.org/10.1088/1742-5468/2009/01/P01022

    Article  Google Scholar 

  • Daley DJ, Vere-Jones D (2003) An introduction to the theory of point processes, vol 1, 2nd edn. Springer, New York

    Google Scholar 

  • Das S (1981) Three-dimensional spontaneous rupture propagation and implications for the earthquake source mechanism. Geophys J R Astron Soc 67:375–393

    Article  ADS  Google Scholar 

  • Davies G, Horspool N, Miller V (2015) Tsunami inundation from heterogeneous earthquake slip distributions: evaluation of synthetic source models. J Geophys Res Solid Earth 120:6431–6451

    Article  ADS  Google Scholar 

  • Day SM (1982) Three-dimensional simulation of spontaneous rupture: the effect of nonuniform prestress. Bull Seismol Soc Am 72:1881–1902

    Google Scholar 

  • DeDontney N, Rice JR, Dmowska R (2012) Finite element modeling of branched ruptures including off-fault plasticity. Bull Seismol Soc Am 102:541–562

    Article  Google Scholar 

  • Duan B, Oglesby DD (2007) Nonuniform prestress from prior earthquakes and the effect on dynamics of branched fault systems. J Geophys Res 112:B05308. https://doi.org/10.1029/2006JB004443

    Article  ADS  Google Scholar 

  • Fukutani Y, Suppasri A, Imamura F (2015) Stochastic analysis and uncertainty assessment of tsunami wave height using a random source parameter model that targets a Tohoku-type earthquake fault. Stoch Env Res Risk A 29:1763–1779

    Article  Google Scholar 

  • Geist EL (2002) Complex earthquake rupture and local tsunamis. J Geophys Res 107. https://doi.org/10.1029/2000JB000139

  • Geist EL (2009) Phenomenology of tsunamis: statistical properties from generation to runup. Adv Geophys 51:107–169

    Article  ADS  Google Scholar 

  • Geist EL (2012a) Near-field tsunami edge waves and complex earthquake rupture. Pure Appl Geophys. https://doi.org/10.1007/s00024-012-0491-7

    Article  ADS  Google Scholar 

  • Geist EL (2012b) Phenomenology of tsunamis II: scaling, event statistics, and inter-event triggering. Adv Geophys 53:35–92

    Article  ADS  Google Scholar 

  • Geist EL (2014) Explanation of temporal clustering of tsunami sources using the epidemic-type aftershock sequence model. Bull Seismol Soc Am 104:2091–2103

    Article  Google Scholar 

  • Geist EL (2016) Non-linear resonant coupling of tsunami edge waves using stochastic earthquake source models. Geophys J Int 204:878–891

    Article  ADS  Google Scholar 

  • Geist EL (2018) Effect of dynamical phase on the resonant interaction among tsunami edge wave modes. Pure Appl Geophys 175:1341–1354

    Article  ADS  Google Scholar 

  • Geist EL, Oglesby DD (2014) Earthquake mechanism and seafloor deformation for tsunami generation. In: Beer M, Patelli E, Kougioumtzoglou IA, Au IS-K (eds) Encyclopedia of earthquake engineering. Springer, Berlin, p 17

    Google Scholar 

  • Geist EL, Parsons T (2006) Probabilistic analysis of tsunami hazards. Nat Hazards 37:277–314

    Article  Google Scholar 

  • Geist EL, Parsons T (2008) Distribution of tsunami inter-event times. Geophys Res Lett 35:L02612. https://doi.org/10.1029/2007GL032690

    Article  ADS  Google Scholar 

  • Geist EL, Parsons T (2010) Estimating the empirical probability of submarine landslide occurrence. In: Mosher DC, Shipp C, Moscardelli L, Chaytor J, Baxter C, Lee HJ, Urgeles R (eds) Submarine mass movements and their consequences IV. Springer, Heidelberg, pp 377–386

    Chapter  Google Scholar 

  • Geist EL, Parsons T (2011) Assessing historical rate changes in global tsunami occurrence. Geophys J Int 187:497–509

    Article  ADS  Google Scholar 

  • Geist EL, Parsons T (2014) Undersampling power-law size distributions: effect on the assessment of extreme natural hazards. Nat Hazards 72:565–595

    Article  Google Scholar 

  • Geist EL, Parsons T, ten Brink US, Lee HJ (2009) Tsunami Probability. In: Bernard EN, Robinson AR (eds) The sea, vol 15. Harvard University Press, Cambridge, pp 93–135

    Google Scholar 

  • Geist EL, Chaytor JD, Parsons T, ten Brink U (2013) Estimation of submarine mass failure probability from a sequence of deposits with age dates. Geosphere 9:287–298

    Article  ADS  Google Scholar 

  • Goda K, Song J (2016) Uncertainty modeling and visualization for tsunami hazard and risk mapping: a case study for the 2011 Tohoku earthquake. Stoch Env Res Risk A 30:2271–2285

    Article  Google Scholar 

  • Goda K, Mai PM, Yasuda T, Mori N (2014) Sensitivity of tsunami wave profiles and inundation simulations to earthquake slip and fault geometry for the 2011 Tohoku earthquake. Earth Planets Space 66:105

    Article  ADS  Google Scholar 

  • Goda K, Li S, Mori N, Yasuda T (2015a) Probabilistic tsunami damage assessment considering stochastic source models: application to the 2011 Tohoku earthquake. Coast Eng J 57:1550015

    Article  Google Scholar 

  • Goda K, Yasuda T, Mori N, Mai PM (2015b) Variability of tsunami inundation footprints considering stochastic scenarios based on a single rupture model: application to the 2011 Tohoku earthquake. J Geophys Res Oceans 120:4552–4575

    Article  ADS  Google Scholar 

  • Goda K, Yasuda T, Mori N, Maruyama T (2016) New scaling relationships of earthquake source parameters for stochastic tsunami simulation. Coast Eng J 58:1650010-1–1650010-40

    Article  Google Scholar 

  • González FI, Kulikov YA (1993) Tsunami dispersion observed in the deep ocean. In: Tinti S (ed) Tsunamis in the world. Kluwer Academic Publishers, Dordrecht, pp 7–16

    Chapter  Google Scholar 

  • González FI, Geist EL, Jaffe BE, Kânoglu U, Mofjeld HO, Synolakis CE et al (2009) Probabilistic tsunami hazard assessment at seaside, Oregon for near- and far-field seismic sources. J Geophys Res 114. https://doi.org/10.1029/2008JC005132

  • Greenhough J, Main IG (2008) A Poisson model for earthquake frequency uncertainties in seismic hazard analysis. Geophys Res Lett 35. https://doi.org/10.1029/2008GL035353

  • Grezio A, Babeyko AY, Baptista AM, Behrens J, Costa A, Davies G et al (2017) Probabilistic tsunami Hazard analysis (PTHA): multiple sources and global applications. Rev Geophys 55:1158–1198

    Article  ADS  Google Scholar 

  • Griffin JD, Pranantyo IR, Kongko W, Haunan A, Robiana R, Miller V et al (2017) Assessing tsunami hazard using heterogeneous slip models in the Mentawai Islands, Indonesia. Geol Soc Lond, Spec Publ 441:47–70

    Article  Google Scholar 

  • Guatteri M, Mai PM, Beroza GC (2004) A pseudo-dynamic approximation to dynamic rupture models for strong ground motion prediction. Bull Seismol Soc Am 94:2051–2063

    Article  Google Scholar 

  • Gutenberg B, Richter CF (1944) Frequency of earthquakes in California. Bull Seismol Soc Am 34:185–188

    Google Scholar 

  • Harris RA, Archuleta RJ, Day SM (1991) Fault steps and the dynamic rupture process – 2-D numerical simulations of a spontaneously propagating shear fracture. Geophys Res Lett 18:893–896

    Article  ADS  Google Scholar 

  • Hergarten S (2003) Landslides, sandpiles, and self-organized criticality. Nat Hazards Earth Syst Sci 3:505–514

    Article  ADS  Google Scholar 

  • Hergarten S, Neugebauer HJ (1998) Self-organized criticality in a landslide model. Geophys Res Lett 25:801–804

    Article  ADS  Google Scholar 

  • Herrero A, Bernard P (1994) A kinematic self-similar rupture process for earthquakes. Bull Seismol Soc Am 84:1216–1228

    Google Scholar 

  • Hisada Y (2000) A theoretical omega-square model considering the spatial variation in slip and rupture velocity. Bull Seismol Soc Am 90:387–400

    Article  Google Scholar 

  • Hisada Y (2001) A theoretical omega-square model considering the spatial variation in slip and rupture velocity. Part 2: case for a two-dimensional source model. Bull Seismol Soc Am 91:651–666

    Article  Google Scholar 

  • Hogben N (1990) Long term wave statistics. In: Le Méhauté B, Hanes DM (eds) Ocean engineering science, vol 9. Wiley, New York, pp 293–333

    Google Scholar 

  • Horspool N, Pranantyo I, Griffin J, Latief H, Natawidjaja DH, Kongko W et al (2014) A probabilistic tsunami hazard assessment for Indonesia. Nat Hazards Earth Syst Sci 14:3105–3122

    Article  ADS  Google Scholar 

  • Huang NE, Tung CC, Long SR (1990) The probability structure of the ocean surface. In: Le Méhauté B, Hanes DM (eds) Ocean engineering science, vol 9. Wiley, New York, pp 335–366

    Google Scholar 

  • Ishimoto M, Iida K (1939) Observations of earthquakes registered with the microseismograph constructed recently. Bull Earthquake Res Inst 17:443–478

    Google Scholar 

  • Jha AK, Winterstein SR (2000) Nonlinear random ocean waves: prediction and comparison with data. In: Proceedings of the ETCE/OMAE2000 joint conference: energy for the new Millennium. ASME, New Orleans, pp 1–12

    Google Scholar 

  • Kagan YY (1973) Statistical methods in the study of seismic processes. Bull Int Stat Inst 45:437–453

    Google Scholar 

  • Kagan YY (1991) Seismic moment distribution. Geophys J Int 106:123–134

    Article  ADS  Google Scholar 

  • Kagan YY (2002) Seismic moment distribution revisited: I. statistical results. Geophys J Int 148:520–541

    Article  ADS  Google Scholar 

  • Kagan YY (2007) Why does theoretical physics fail to explain and predict earthquake occurrence? In: Bhattacharyya P, Chakrabarti BK (eds) Modelling critical and catastrophic phenomena in geoscience. Springer, Berlin, pp 303–359

    Google Scholar 

  • Kagan YY (2010) Statistical distributions of earthquake numbers: consequence of branching process. Geophys J Int 180:1313–1328

    Article  ADS  Google Scholar 

  • Kagan YY, Jackson DD (2000) Probabilistic forecasting of earthquakes. Geophys J Int 143:438–453

    Article  ADS  Google Scholar 

  • Kame N, Rice JR, Dmowska R (2003) Effects of pre-stress state and rupture velocity on dynamic fault branching. J Geophys Res 108:2265. https://doi.org/10.1029/2002JB002189

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  • Kirby JT, Putrevu U, Özkan-Haller HT (1998) Evolution equations for edge waves and shear waves on longshore uniform beaches. In: Proceedings of 26th international conference on coastal engineering. ASCE, Copenhagen, pp 203–216

    Google Scholar 

  • Koshimura S, Hayashi Y, Munemoto K, Imamura F (2008) Effect of the emperor seamounts on trans-oceanic propagation of the 2006 Kuril Island earthquake tsunami. Geophys Res Lett 35. https://doi.org/10.1029/2007GL032129

  • Kowalik Z, Horrillo J, Knight W, Logan T (2008) Kuril Islands tsunami of November 2006: 1. Impact at Crescent City by distant scattering. J Geophys Res 113. https://doi.org/10.1029/2007JC004402

  • Lavallée D (2008) On the random nature of earthquake sources and ground motions: a unified theory. Adv Geophys 50:427–461

    Article  Google Scholar 

  • Lavallée D, Liu P, Archuleta RJ (2006) Stochastic model of heterogeneity in earthquake slip spatial distributions. Geophys J Int 165:622–640

    Article  ADS  Google Scholar 

  • Lavallée D, Miyake H, Koketsu K (2011) Stochastic model of a subduction-zone earthquake: sources and ground motions for the 2003 Tokachi-oki, Japan, earthquake. Bull Seismol Soc Am 101:1807–1821

    Article  Google Scholar 

  • Lay T, Kanamori H, Ammon CJ, Hutko AR, Furlong K, Rivera L (2009) The 2006-2007 Kuril Islands great earthquake sequence. J Geophys Res 114. https://doi.org/10.1029/2008JB006280

  • LeVeque RJ, Waagan K, González FI, Rim D, Lin G (2016) Generating random earthquake events for probabilistic tsunami Hazard assessment. Pure Appl Geophys 173:3671–3692

    Article  ADS  Google Scholar 

  • Liu-Zeng J, Heaton TH, DiCaprio C (2005) The effect of slip variability on earthquake slip-length scaling. Geophys J Int 162:841–849

    Article  ADS  Google Scholar 

  • Longuet-Higgins MS (1952) On the statistical distribution of the heights of sea waves. J Mar Res 11:245–266

    Google Scholar 

  • Lorito S, Selva J, Basili R, Romano F, Tiberti MM, Piatanesi A (2015) Probabilistic hazard for seismically induced tsunamis: accuracy and feasibility of inundation maps. Geophys J Int 200:574–588

    Article  ADS  Google Scholar 

  • Løvholt F, Pedersen G, Bazin S, Kühn D, Bredesen RE, Harbitz C (2012) Stochastic analysis of tsunami runup due to heterogeneous coseismic slip and dispersion. J Geophys Res 117. https://doi.org/10.1029/2011JC007616

    Article  Google Scholar 

  • Ma S, Beroza GC (2008) Rupture dynamics on a bimaterial interface for dipping faults. Bull Seismol Soc Am 98:1642–1658

    Article  Google Scholar 

  • Mai PM, Beroza GC (2002) A spatial random field model to characterize complexity in earthquake slip. J Geophys Res 107. https://doi.org/10.1029/2001JB000588

    Article  Google Scholar 

  • Main I (2000) Apparent breaks in scaling in the earthquake cumulative frequency-magnitude distribution: fact or artifact? Bull Seismol Soc Am 90:86–97

    Article  Google Scholar 

  • Malamud BD, Turcotte DL, Guzzetti F, Reichenbach P (2004) Landslide inventories and their statistical properties. Earth Surf Process Landf 29:687–7111

    Article  ADS  Google Scholar 

  • Massel SR (1996) Ocean surface waves: their physics and prediction, vol 11. World Scientific, Singapore

    Book  Google Scholar 

  • McCloskey J, Antonioli A, Piatanesi A, Sieh K, Steacy S, Nalbant S et al (2008) Tsunami threat in the Indian Ocean from a future megathrust earthquake west of Sumatra. Earth Planet Sci Lett 265:61–81

    Article  ADS  Google Scholar 

  • McKane AJ (2016) Stochastic processes. In: Meyers RA (ed) Encyclopedia of complexity and systems science. Springer, Berlin/Heidelberg, pp 1–22

    Google Scholar 

  • Meerschaert MM, Roy P, Shao Q (2012) Parameter estimation for exponentially tempered power law distributions. Commun Stat Theor Models 41:1839–1856

    Article  MathSciNet  MATH  Google Scholar 

  • Mei CC, Stiassnie M, Yue DK-P (2005) Theory and applications of ocean surface waves. Part 2: nonlinear aspects. World Scientific, Singapore

    MATH  Google Scholar 

  • Mikumo T, Miyatake T (1993) Dynamic rupture processes on a dipping fault, and estimates of stress drop and strength excess from the results of waveform inversion. Geophys J Int 112:481–496

    Article  ADS  Google Scholar 

  • Mofjeld HO, González FI, Bernard EN, Newman JC (2000) Forecasting the heights of later waves in Pacific-wide tsunamis. Nat Hazards 22:71–89

    Article  Google Scholar 

  • Mofjeld HO, Titov VV, González FI, Newman JC (2001) Tsunami scattering provinces in the Pacific Ocean. Geophys Res Lett 28:335–337

    Article  ADS  Google Scholar 

  • Mueller C, Power W, Fraser S, Wang X (2015) Effects of rupture complexity on local tsunami inundation: implications for probabilistic tsunami hazard assessment by example. J Geophys Res Solid Earth 120:488–502

    Article  ADS  Google Scholar 

  • Muraleedharan G, Rao AD, Kurup PG, Nair NU, Sinha M (2007) Modified Weibull distribution for maximum and significant wave height simulation and prediction. Coast Eng 54:630–638

    Article  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 

  • Ochi MK (2005) Ocean waves: the stochastic approach. Cambridge University Press, Cambridge, p 332

    Google Scholar 

  • Ogata Y (1988) Statistical models for earthquake occurrences and residual analysis for point processes. J Am Stat Assoc 83:9–27

    Article  Google Scholar 

  • Ogata Y (1999) Estimating the hazard of rupture using uncertain occurrence times of paleoearthquakes. J Geophys Res 104:17,995–18,014

    Article  ADS  Google Scholar 

  • Oglesby DD (1999) Earthquake dynamics on dip-slip faults[Thesis]. Type, University of California, Santa Barbara

    Google Scholar 

  • Oglesby DD, Archuleta RJ, Nielsen SB (1998) Earthquakes on dipping faults: the effects of broken symmetry. Science 280:1055–1059

    Article  ADS  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 

  • Olsen KB, Archuleta RJ, Matarese JR (1995) Three-dimensional simulation of a magnitude 7.75 earthquake on the San Andreas fault. Science 270:1628–1632

    Article  ADS  Google Scholar 

  • Parsons T (2002) Global Omori law decay of triggered earthquakes: large aftershocks outside the classical aftershock zone. J Geophys Res 107:2199. https://doi.org/10.1029/2001JB000646

    Article  Google Scholar 

  • Parsons T (2008) Monte Carlo method for determining earthquake recurrence parameters from short paleoseismic catalogs: example calculations for California. J Geophys Res 113. https://doi.org/10.1029/2007JB004998

  • Parsons T, Geist EL (2009) Tsunami probability in the Caribbean region. Pure Appl Geophys 165:2089–1226

    Article  ADS  Google Scholar 

  • Peitgen H-O, Jürgens H, Saupe D (1992) Chaos and fractals: new Frontiers of science. Springer, New York

    Book  MATH  Google Scholar 

  • Power W, Wang X, Lane E, Gillibrand P (2013) A probabilistic tsunami hazard study of the Auckland region, part I: propagation modelling and tsunami hazard assessment at the shoreline. Pure Appl Geophys 170:1621–1634

    Article  ADS  Google Scholar 

  • Prevosto M, Kogstad HE, Robin A (2000) Probability distributions for maximum wave and crest heights. Coast Eng 40:329–360

    Article  Google Scholar 

  • Rabinovich AB, Candella RN, Thomson RE (2011) Energy decay of the 2004 Sumatra tsunami in the World Ocean. Pure Appl Geophys 168:1919–1950

    Article  ADS  Google Scholar 

  • Rayleigh JWS (1880) On the resultant of a large number of vibrations of the same pitch and of arbitrary phase. Philos Mag 10:73–78

    Article  Google Scholar 

  • Ruiz JA, Fuentes M, Riquelme S, Campos J, Cisternas A (2015) Numerical simulation of tsunami runup in northern Chile based on non-uniform k−2 slip distributions. Nat Hazards 79:1177–1198

    Article  Google Scholar 

  • Ryan KJ, Geist EL, Barall M, Oglesby DD (2015) Dynamic models of an earthquake and tsunami offshore Ventura, California. Geophys Res Lett 42:6599–6606

    Article  ADS  Google Scholar 

  • Rychlik I, Leadbetter MR (1997) Analysis of ocean waves by crossing and oscillation intensities. In: Proceedings of the seventh international offshore and polar engineering conference (ISOPE), vol 3, Golden, pp 206–213

    Google Scholar 

  • Rychlik I, Johannesson P, Leadbetter MR (1997) Modelling and statistical analysis of ocean-wave data using transformed Gaussian processes. Mar Struct 10:13–47

    Article  Google Scholar 

  • Saito T, Furumura T (2009) Scattering of linear long-wave tsunamis due to randomly fluctuating sea-bottom topography: coda excitation and scattering attenuation. Geophys J Int 177:958–965

    Article  ADS  Google Scholar 

  • Satake K (2007) Tsunamis. In: Kanamori H, Schubert G (eds) Treatise on geophysics, volume 4-earthquake seismology, vol 4. Elsevier, Amsterdam, pp 483–511

    Chapter  Google Scholar 

  • Satake K, Kanamori H (1991) Use of tsunami waveforms for earthquake source study. Nat Hazards 4:193–208

    Article  Google Scholar 

  • Satake K, Yoshida Y, Abe K (1992) Tsunami from the Mariana earthquake of April 5, 1990: its abnormal propagation and implications for tsunami potential from outer-rise earthquakes. Geophys Res Lett 19:301–304

    Article  ADS  Google Scholar 

  • Satake K, Fujii Y, Harada T, Namegaya 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 

  • Savage JC (1994) Empirical earthquake probabilities from observed recurrence intervals. Bull Seismol Soc Am 84:219–221

    Google Scholar 

  • Selva J, Tonini R, Molinari I, Tiberti MM, Romano F, Grezio A et al (2016) Quantification of source uncertainties in seismic probabilistic tsunami Hazard analysis (SPTHA). Geophys J Int 205:1780–1803

    Article  ADS  Google Scholar 

  • Sepúlveda I, Liu PL-F, Grigoriu M, Pritchard M (2017) Tsunami hazard assessments with consideration of uncertain earthquake slip distribution and location. J Geophys Res Solid Earth 122:7252–7271

    Article  ADS  Google Scholar 

  • Sornette D, Sornette A (1999) General theory of the modified Gutenberg-Richter law for large seismic moments. Bull Seismol Soc Am 89:1121–1130

    Google Scholar 

  • Stark CP, Hovius N (2001) The characterization of landslide size distributions. Geophys Res Lett 28:1091–1094

    Article  ADS  Google Scholar 

  • Strasser FO, Arango MC, Bommer JJ (2010) Scaling of the source dimensions of interface and intraslab subduction-zone earthquakes with moment magnitude. Seismol Res Lett 81:941–950

    Article  Google Scholar 

  • Takahara M, Yomogida K (1992) Estimation of coda Q using the maximum likelihood method. Pure Appl Geophys 139:255–268

    Article  ADS  Google Scholar 

  • Tamura S, Ide S (2011) Numerical study of splay faults in subduction zones: the effects of bimaterial interface and free surface. J Geophys Res 116. https://doi.org/10.1029/2011JB008283

  • Tanioka Y, Satake K (1996) Tsunami generation by horizontal displacement of ocean bottom. Geophys Res Lett 23:861–865

    Article  ADS  Google Scholar 

  • ten Brink US, Geist EL, Andrews BD (2006) Size distribution of submarine landslides and its implication to tsunami hazard in Puerto Rico. Geophys Res Lett 33. https://doi.org/10.1029/2006GL026125

  • Titov VV, González FI, Bernard EN, Ebel JE, Mofjeld HO, Newman JC et al (2005) Real-time tsunami forecasting: challenges and solutions. Nat Hazards 35:40–58

    Article  Google Scholar 

  • Tsai CP (1997) Slip, stress drop and ground motion of earthquakes: a view from the perspective of fractional Brownian motion. Pure Appl Geophys 149:689–706

    Article  ADS  Google Scholar 

  • Turcotte DL (1992) Fractals and chaos in geology and geophysics. Cambridge University Press, Cambridge, p 221

    MATH  Google Scholar 

  • Turcotte D (2013) Fractals in geology and geophysics. In: Meyers R (ed) Encyclopedia of complexity and systems science. Springer, Berlin/Heidelberg

    Google Scholar 

  • van Dorn WG (1984) Some tsunami characteristic deducible from tide records. J Phys Oceanogr 14:353–363

    Article  ADS  Google Scholar 

  • Vere-Jones D (2013) Earthquake occurrence and mechanisms, stochastic models for. In: Meyers R (ed) Encyclopedia of complexity and systems science. Springer, Berlin/Heidelberg

    Google Scholar 

  • Vere-Jones D, Robinson R, Yang W (2001) Remarks on the accelerated moment release model: problems of model formulation, simulation and estimation. Geophys J Int 144:517–531

    Article  ADS  Google Scholar 

  • Wendt J, Oglesby DD, Geist EL (2009) Tsunamis and splay fault dynamics. Geophys Res Lett 36. https://doi.org/10.1029/2009GL038295

    Article  Google Scholar 

  • Werner M, Sornette D (2013) Seismicity, statistical physics approaches to. In: Meyers R (ed) Encyclopedia of complexity and systems science. Springer, Berlin/Heidelberg

    Google Scholar 

  • Whirley RG, Engelmann BE (1993) DYNA3D: a nonlinear, explicit, three-dimensional finite element code for solid and structural mechanics – user manual. University of California, Lawrence Livermore National Laboratory

    Google Scholar 

Download references

Acknowledgment

The authors gratefully acknowledge careful readings of the first edition of this paper and constructive comments by Martin Mai, Mark Bebbington, Kenji Satake, Tom Parsons, and the Encyclopedia Section Editor William H. K. Lee. Data used in this study include DART bottom-pressure recorder data from the event archive at NOAA’s National Data Buoy Center and digital tide gauge records from NOAA’s National Tsunami Warning Center. Analysis of tsunami records was performed in part using the Wave Analysis for Fatigue and Oceanography (WAFO) package developed at Lund University, Sweden.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Eric L. Geist .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Geist, E.L., Oglesby, D.D., Ryan, K.J. (2019). Tsunamis: Stochastic Models of Occurrence and Generation Mechanisms. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_595-2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-27737-5_595-2

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27737-5

  • Online ISBN: 978-3-642-27737-5

  • eBook Packages: Springer Reference Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics

Publish with us

Policies and ethics

Chapter history

  1. Latest

    Tsunamis: Stochastic Models of Occurrence and Generation Mechanisms
    Published:
    22 August 2019

    DOI: https://doi.org/10.1007/978-3-642-27737-5_595-2

  2. Original

    Tsunamis: Stochastic Models of Occurrence and Generation Mechanisms
    Published:
    15 October 2014

    DOI: https://doi.org/10.1007/978-3-642-27737-5_595-1