Skip to main content
SpringerLink
Log in

The Nonlinear and Linear Modes of Growth of the Cumulative Seismic Moment

  • Chapter
  • First Online:
Book cover Heavy-Tailed Distributions in Disaster Analysis

Part of the book series: Advances in Natural and Technological Hazards Research ((NTHR,volume 30))

  • 782 Accesses

Abstract

In the previous chapter it was shown that the nonlinear mode of growth of cumulative effects takes place in all cases when the distribution function obeys the power-law distribution with β ≤ 1. The distribution of seismic moments obeys this law, and it is this very character of the distribution which causes serious difficulties in seismic risk assessment [PSS, BP, BK, EL, K2, K7, Ki, LTPK, MKP, TLP, WuPS1]. The modes of nonlinear and linear increase in cumulative seismic moments are examined below using the world Harvard seismic moment catalog. The catalog includes substantially more data than are available in the case of loss values examined in the previous chapter. The availability of data permits a more comprehensive examination of the distribution behavior in the range of rare large events.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Abe K (1982) Magnitude, seismic moment and apparent stress for major deep earthquakes. J Phys Earth 30(4):321–330

    Article  Google Scholar 

  2. Bender BK, Perkins DM (1993) Treatment of parameter uncertainty and variability for a single seismic hazard map. Earthq Spectra 9(2):165–195

    Article  Google Scholar 

  3. Bird P, Kagan YY (2004) Plate-tectonic analysis of shallow seismicity: apparent boundary width, beta, corner magnitude, coupled lithosphere thickness, and coupling in seven tectonic settings. Bull Seismol Soc Am 94(6):2380–2399

    Article  Google Scholar 

  4. Brune JN (1968) Seismic moment, seismicity, and rate of slip along major fault zones. J Geophys Res 73:777–784

    Article  Google Scholar 

  5. Bullen KE (1975) The earth’s density. Wiley, New York

    Book  Google Scholar 

  6. Davison FC, Scholz CH (1985) Frequency-moment distribution of earthquakes in the Aleutian Arc: a test of the characteristic earthquake model. Bull Seismol Soc Am 75(5):1349–1361

    Google Scholar 

  7. Embrechts P, Kluppelberg C, Mikosch T (1997a) Modelling extremal events. Berlin-Heidelberg, Springer-Verlag, 645 pp

    Book  Google Scholar 

  8. Efron B (1988) Unconventional methods of multivariate statistical analysis. Finansy i Statistika, Moscow, 264 pp, in Russian

    Google Scholar 

  9. Galadini F, Galli P, Giraudi C (1997) Geological investigations of Italian earthquakes: new paleoseismic data from the Fucino plain (central Italy). J Geophys 24:87–103

    Google Scholar 

  10. Godano C, Pingue F (2000) Is the seismic moment-frequency relation universal? Geophys J Int 142:193–198

    Article  Google Scholar 

  11. Grachev AF, Magnitskii VA, Mukhamediev SA, Yunga SL (1996) Determination of possible maximum magnitudes of earthquakes in the East European Platform. Physica Zemli 7:3–20, in Russian

    Google Scholar 

  12. Ho C-H, Smith EI (1997) Volcanic hazard assessment incorporating expert knowledge: application to the Yucca Mountain region, Nevada, USA. Math Geol 29:615–627

    Article  Google Scholar 

  13. Jarrard RD (1986) Relations among subduction parameters. Rev Geophys 24(2):217–284

    Article  Google Scholar 

  14. Kagan YY (1993) (1993) Statistics of characteristic earthquakes. Bull Seismol Soc Am 83(1):7–24

    Google Scholar 

  15. Kagan YY (1994) Observational evidence for earthquakes as a nonlinear dynamic process. Physica D 77:160–192

    Article  Google Scholar 

  16. Kagan YY (1999) Universality of the seismic moment-frequency relation. Pure Appl Geophys 1:537–573

    Article  Google Scholar 

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

    Article  Google Scholar 

  18. Kagan YY (2002b) Seismic moment distribution revisited: II Moment conservation principle. Geophys J Int 149:731–754

    Article  Google Scholar 

  19. Kagan YY, Schoenberg F (2001) Estimation of the upper cutoff parameter for the tapered distribution. J Appl Probab 38A:901–918

    Article  Google Scholar 

  20. Kijko A, Graham G (1998) Parametric-historic procedure for probabilistic seismic hazard analysis, Part I, Estimation of Maximum Regional Magnitude Mmax. Pure Appl Geophys 152:413–442

    Article  Google Scholar 

  21. Laherrere J, Sornette D (1998) Streched exponential distributions in nature and economy: “fat tails” with characteristic scales. Eur Phys J 2:525–539

    Google Scholar 

  22. Molchan G, Kronrod T, Panza GF (1997) Multi-scale seismicity model for seismic risk. Bull Seis Soc Am 87:1220–1229

    Google Scholar 

  23. Morozov VN, Rodkin MV, Tatarinov VN (2001) On the problem of geodynamic safety of object nuclear-fuel circle. Geoecology 3:125–137

    Google Scholar 

  24. Nikonov AA (1994) On Great Caucasus strong earthquakes in the A.D. first millennium: a revision of the initial data and catalogue. Physica Zemli 7–8:107–112, in Russian

    Google Scholar 

  25. Nurmagambetov A, Mikhailova NN, Golinsky GL, Plotnikova LM, Frolova AG, Negmatullaev SK (2000) Comparative seismic hazard estimation for the capitals of the countries of Central Asia. J Earthq Prediction Res 8:496–505

    Google Scholar 

  26. Pacheco JF, Scholz C, Sykes L (1992) Changes in frequency-size relationship from small to large earthquakes. Nature 355:71–73

    Article  Google Scholar 

  27. Pisarenko VF, Sornette D (2003) Characterization of the Frequency of Extreme Earthquake Events by the Generalized Pareto Distribution. Pure Appl Geophys 160:2343–2364

    Article  Google Scholar 

  28. Pisarenko VF, Sornette D (2004) Statistical detection and characterization of a deviation from the Gutenberg-Richter distribution above magnitude 8. Pure Appl Geophys 161:839–864

    Article  Google Scholar 

  29. Plate-Tectonic Map of the Circum-Pacific Region (1981) Scale 1:10 000 000. Circum-Pacific Council for energy and mineral resources, the American Association of Petroleum Geologists, Tulsa, Oklahoma, USA, 1981

    Google Scholar 

  30. Reisner GI, Nikonov AA (1996) Reappraisal of seismic potential of the Caucasus region. Physica Zemli 8:3–12

    Google Scholar 

  31. Rodkin MV, Pisarenko VF (2006) Extreme earthquake disasters – verification of the method of parameterization of the character of distribution of the rare major events, Ch 08. Adv Geosci 1: 75–89

    Google Scholar 

  32. Romanovicz B, Rundle JB (1993) On scaling relation for large earthquakes. Bull Seismol Soc Am 83(4):1294–1297

    Google Scholar 

  33. Scholz CH (1991) Earthquakes and faulting: self-organized critical phenomena with a characteristic dimension. In: Riste T, Sherrington D (eds) Spontaneous formation of spase-time structures and criticallity. Kluwer, Netherlands, pp 41–56

    Chapter  Google Scholar 

  34. Silva PG, Goy JL, Zazo C, Lario J, Barbaji T (1997) Paleoseismin indications along “aseismic” fault in the Guadalentin depression (SE Spain). J Geophys 24(1):105–115

    Google Scholar 

  35. Sornette D, Knopoff L, Kagan YY, Vanneste C (1996) Rank-ordering statistics of extreme events: application to the distribution of large earthquakes. J Geophys Res 101(6):13883–13893

    Article  Google Scholar 

  36. Streltsov MI (2005) The May 27 (28), 1995 Neftegorsk earthquake on Sakhalin island. “Yanus-K”, Moscow, 178 pp

    Google Scholar 

  37. Tsapanos TM, Lyubushin AA, Pisarenko VF (2001) Application of a Bayesian Approach for estimation of seismic hazard parameters in some regions of Circum-Pacific Belt. Pure Appl Geophys 158:859–875

    Article  Google Scholar 

  38. Wesnousky SG (1994) The Gutenberg-Richter or characteristic earthquake distribution, which is it? Bull Seism Soc Am 84:1940–1959

    Google Scholar 

  39. Wu ZL (2000) Frequency-size distribution of global seismicity seen from broad-band radiated energy. Geophys J Int 142:59–66

    Article  Google Scholar 

  40. Kagan YY (1997a) Seismic moment-frequency relation for shallow earthquakes: Regional comparison. J Geophys Res 102:2835–2852

    Article  Google Scholar 

  41. Kagan YY (1997b) Earthquake size distribution and earthquake insurance. Commun Statist Stachastic Models 13(4):775–797

    Article  Google Scholar 

  42. Shapoval A., Shnirman M (2001) Prediction in a Two-polarity Model of Sandpile Type, Comp. Seism. V. 32, 225–236(In Russian).

    Google Scholar 

  43. Hill, B.M. (1975) A simple general approach to inference about the tail of a distribution. Ann.Statist., 3, 1163–1174

    Google Scholar 

  44. Rogojin EA, Reisner GI, Besstrashnov VM, et al. (2002) Seismotectonic situation of Sakhalin Island. Physica Zemli, 3, 35–44 (In Russian).

    Google Scholar 

  45. Ulomov V. I., Polyakova TP, Medvedeva NS (2002) On the Long-Term Prediction of Strong Earthquakes in Central Asia and the Black Sea-Caspian Region. Izvestiya, Physics of the Solid Earth, Vol. 38, No. 4, pp. 276–290.

    Google Scholar 

  46. Sobolev GA (1993)Principles of Earthquake Prediction. Nauka, Moscow, 313 pp. (In Russian).

    Google Scholar 

  47. Ruff L, Kanamori H (1980) Seismicity and the subduction process// Phys. Earth Pl. Int., v.23, 240–252

    Google Scholar 

  48. Ruff L, Kanamori H (1980) Seismicity and the subduction process// Phys. Earth Pl. Int., v.23, 240–252

    Google Scholar 

  49. Rautian TG, Khalturin VI (1991) Focal earthquake spectra. In: Earthquakes and processes of their preparation. Nauka, Moscow, pp 82–93, in Russian

    Google Scholar 

  50. Rodkin MV (2005a) Linear and nonlinear increase regimes of the cumulative seismic moment. Phys Solid Earth 41(2):95–103

    Google Scholar 

  51. Simkin T, Siebert L (1994) Volcanoes of the world. Geoscence Press, Tucson

    Google Scholar 

  52. Ulomov V. I., Polyakova T. P., Medvedeva N. S. On the Long-Term Prediction of Strong Earthquakes in Central Asia and the Black Sea-Caspian Region. Izvestiya, Physics of the Solid Earth, Vol. 38, No. 4, 2002, pp. 276–290

    Google Scholar 

  53. Epstein BC, Lomnitz C (1966) A model for the occurrence of large earthquakes. Nature 211:954–956

    Article  Google Scholar 

  54. Kijko A (2004) Estimation of the maximum earthquake magnitude, Mmax. Pure Appl Geophys 161:1–27

    Article  Google Scholar 

  55. Lyubushin AA, Tsapanos TM, Pisarenko VF, Koravos GC (2002) Seismic hazard for selected sites in Greece: a Bayesian estimate of seismic peak ground acceleration. Nat Hazards 25:83–98

    Article  Google Scholar 

  56. Rodkin MV (2005b) The model of synergetic effect development upon severe disasters. Geoecology 1:81–87, in Russian

    Google Scholar 

  57. Rodkin MV, Pisarenko VF (2003) Earthquake loss. Moscow, GEOS, Comput Seismol 34:205–209, in Russian

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, Moscow, Russia

    Dr. V. Pisarenko & Dr. M. Rodkin

Authors
  1. Dr. V. Pisarenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dr. M. Rodkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. Pisarenko .

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Netherlands

About this chapter

Cite this chapter

Pisarenko, V., Rodkin, M. (2010). The Nonlinear and Linear Modes of Growth of the Cumulative Seismic Moment. In: Heavy-Tailed Distributions in Disaster Analysis. Advances in Natural and Technological Hazards Research, vol 30. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9171-0_5

Download citation

Publish with us

Policies and ethics

Search

Navigation