Reconstruction of Far-Field Tsunami Amplitude Distributions from Earthquake Sources
The probability distribution of far-field tsunami amplitudes is explained in relation to the distribution of seismic moment at subduction zones. Tsunami amplitude distributions at tide gauge stations follow a similar functional form, well described by a tapered Pareto distribution that is parameterized by a power-law exponent and a corner amplitude. Distribution parameters are first established for eight tide gauge stations in the Pacific, using maximum likelihood estimation. A procedure is then developed to reconstruct the tsunami amplitude distribution that consists of four steps: (1) define the distribution of seismic moment at subduction zones; (2) establish a source-station scaling relation from regression analysis; (3) transform the seismic moment distribution to a tsunami amplitude distribution for each subduction zone; and (4) mix the transformed distribution for all subduction zones to an aggregate tsunami amplitude distribution specific to the tide gauge station. The tsunami amplitude distribution is adequately reconstructed for four tide gauge stations using globally constant seismic moment distribution parameters established in previous studies. In comparisons to empirical tsunami amplitude distributions from maximum likelihood estimation, the reconstructed distributions consistently exhibit higher corner amplitude values, implying that in most cases, the empirical catalogs are too short to include the largest amplitudes. Because the reconstructed distribution is based on a catalog of earthquakes that is much larger than the tsunami catalog, it is less susceptible to the effects of record-breaking events and more indicative of the actual distribution of tsunami amplitudes.
KeywordsTsunamis probability distribution seismic moment tsunami amplitude tide gauge
Unable to display preview. Download preview PDF.
- Abe K. (1989), Quanitification of tsunamigenic earthquakes by the Mt scale, Tectonophys., 166, 27–34.Google Scholar
- Bird P., Kagan Y.Y. (2004), Plate-tectonic analysis of shallow seismicity: apparent boundary width, beta-value, corner magnitude, coupled lithosphere thickness, and coupling in 7 tectonic settings, Bull. Seismol. Soc. Am., 94, 2380–2399.Google Scholar
- Engdahl E.R., Villaseñor A. (2002), Global seismicity: 1900-1999. In: Lee WHK, Kanamori H, Jennings PC, Kisslinger C (eds), International Handbook of Earthquake and Engineering Seismology, Part A. Academic Press, San Diego, pp. 665–690.Google Scholar
- Geist E.L. (1999), Local tsunamis and earthquake source parameters, Adv. Geophys., 39, 117–209.Google Scholar
- Geist E.L. (2012), Phenomenology of tsunamis II: scaling, Event Statistics, and Inter-Event Triggering, Adv. Geophys., 53, 35–92.Google Scholar
- Geist E.L., Parsons T. (2011), Assessing historical rate changes in global tsunami occurrence, Geophys. J. Int., 187, 497–509.Google Scholar
- Geist E.L., Parsons T., ten Brink U.S., Lee H.J. (2009), Tsunami Probability. In: Bernard EN, Robinson AR (eds), The Sea, v. 15. Harvard University Press, Cambridge, Massachusetts, pp. 93–135.Google Scholar
- Geller R.J., Kanamori H. (1977), Magnitudes of great shallow earthquakes from 1904 to 1952, Bull. Seismol. Soc. Am., 67, 587–598.Google Scholar
- Gutenberg B., Richter C.F. (1944), Frequency of earthquakes in California, Bull. Seismol. Soc. Am., 34, 185–188.Google Scholar
- Hatori T. (1971), Tsunami sources in Hokkaido and southern Kuril regions, Bulletin of the Earthquake Research Institute, 49, 63–75.Google Scholar
- Horrillo J., Knight W., Kowalik Z. (2008), Kuril Islands tsunami of November 2006: 2. Impact at Crescent City by local enhancement, J. Geophys. Res., 113, doi: 10.1029/2007JC004404.
- Huber P.J. (1967). The behavior of maximum likelihood estimates under nonstandard conditions. In: Proceedings of the fifth Berkeley symposium on mathematica statistics and probability, pp. 221–233.Google Scholar
- Ishimoto M., Iida K. (1939), Observations of earthquakes registered with the microseismograph constructed recently, Bulletin of the Earthquake Research Institute, 17, 443–478.Google Scholar
- Kagan Y.Y. (2010), Earthquake size distribution: power-law with exponent β = 1/2?, Tectonophys., 490, 103–114.Google Scholar
- Kempthorne O., Folks L. (1971), Probability, statistics, and data analysis. Iowa State University Press, Ames, Iowa.Google Scholar
- Main I., Naylor M., Greenhough J., Touati S., Bell A.F., McCloskey J. (2011), Model selection and uncertainty in earthquake hazard analysis. In: Faber M, Köhler J, Nishijima K (eds), Applications of Statistics and Probability in Civil Engineering. CRC Press, Leiden, The Netherlands, pp. 735–743.CrossRefGoogle Scholar
- Okal E.A. (1988), Seismic parameters controlling far-field tsunami amplitudes: a review, Natural Hazards, 1, 67–96.Google Scholar
- Pacheco J.F., Sykes L.R. (1992), Seismic moment catalog of large shallow earthquakes, 1900 to 1989, Bull. Seismol. Soc. Am., 82, 1306–1349.Google Scholar
- Parsons T., Console R., Falcone G., Murru M., Yamashina K. (2012), Comparison of characteristic and Gutenberg-Richter models for time-dependent M ≥ 7.9 earthquake probability in the Nankai-Tokai subduction zone, Japan, Geophys. J. Int., doi: 10.1111/j.1365-1246X.2012.05595.x.
- Pawitan Y. (2001), In all likelihood: statistical modelling and inference using likelihood. Oxford University Press, Oxford.Google Scholar
- Wesnousky S.G. (1994), The Gutenberg-Richter or characteristic earthquake distribution, which is it?, Bull. Seismol. Soc. Am., 84, 1940–1959.Google Scholar