Skip to main content

Earth System Modeling Through Chaos

  • Chapter
Book cover Fractal Behaviour of the Earth System

Summary

Modeling parameters using deterministic chaos have been discussed for Earth system through atmospheric pressure, maximum and minimum temperature, monsoon rainfall, cyclonic storm tracks, long term climate, ozone, radio refractive index, magnetosphere ionosphere system, volcanoes, earthquakes and fluid flows in core and mantle using the method of Grassberger and Procaccia and Lyapunov exponents. It was found that the atmospheric phenomena generally showed a strange attractor dimension of 6 to 7 implying at least 7 to 8 parameters for modeling the system. On the other hand, the magnetosphere-ionosphere system had a low dimension. Most interesting results were found for earthquakes whose strange attractor dimension provides a methodology for differences between interplate and intraplate Indian region. It also provides a dynamical justification for delineation of seismicity patterns based on epicenters of earthquakes on different closely located fault systems up to 500 km radius from the impending earthquake.

Another interesting result pertains to the Koyna region, India where a low strange attractor dimension of 4.5 provides justification for earthquake predictability programme in this region.

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

Access this chapter

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 PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.00
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Baker DN, Klimas AJ, Roberts DA (1991) Examination of time-variable input effects in a nonlinear analogue magnetosphere model. Geophy Res Lett 18:1631–1634

    Google Scholar 

  • Bauer ST, Brown MB (1992) Empirical Low-order Enso dynamics. Geophys Res Lett 19: 2055–2058

    Google Scholar 

  • Beltrami H, Mareschal JC (1993) Strange seismic attractor? Pure Appl Geophys 141: 71–81

    Article  Google Scholar 

  • Bhattacharya SN, Srivastava HN (1992) Earthquake predictability in Hindukush region using chaos and seismicity pattern. Bull Ind Soc Earthq Tech 29: 23–25

    Google Scholar 

  • Elsner JB, Tsonis AA (1993) Non-linear dynamics established in the EN-SO. Geophys Res Lett 20: 213–216

    Google Scholar 

  • Elsner JB, Tsonis AA (1992) Non-linear prediction as a way of distinguishing chaos from random fractal sequences. Nature 358: 217–220

    Google Scholar 

  • Fraedrich K (1987) Estimating weather and climate predictability on attractors. Jr Atmosph Sci 44: 722–728

    Google Scholar 

  • Grassberger P, Procaccia I (1983) Characteristics of strange attractors. Phys Rev Lett 50: 346–349

    Article  Google Scholar 

  • Gutenberg B (1959) Physics of the Earth’s interior. Academic Press, New York

    Google Scholar 

  • Horowitz FG (1989) A Strange attractor underlying Parkfield seismicity EOS 70: 1359

    Google Scholar 

  • Julian BR (1990) Are earthquakes chaotic? Nature 345: 481–482

    Article  Google Scholar 

  • Lowrie W (1997) Fundamentals of geophysics. Cambridge University Press, UK

    Google Scholar 

  • Nicolis C (1982) Stochastic aspects of climatic transitions-response to a periodic forcing. Tellus 34:1–9

    Google Scholar 

  • Pal PK (1991) Cyclone track prediction over the north Indian ocean. Mon Wea Rev Notes and Correspondence 119: 3095–3098

    Google Scholar 

  • Polvos GP, Karakatsanis L, Latoussakis LB, Dialetis D, Papaisannou G (1994) Chaotic analysis of a time series composed of seismic events recorded in Japan. Intern Jr Bifurc & Chaos 4: 87–98

    Google Scholar 

  • Rikitake T (1958) Oscillations of a system of disk dynamos. Proc Cambridge Phil Soc 54:89:105

    Article  Google Scholar 

  • Ruelle D (1990) Deterministic chaos: the science and the fiction. Proc Roy Soc Lond A-427: 241–248

    Google Scholar 

  • Satyan V (1988) Is there a strong attractor in monsoon rainfall? Proc Indian Acad Sci EPS 97: 49–52

    Google Scholar 

  • Sharma AS, Vassiliadis D, Papadopoulos K (1993) Reconstruction of Low-Dimensional Magnetospheric Dynamics by Singular Spectrum Analysis. Geophys Res Lett 20: 335

    Google Scholar 

  • Singh R, Moharir PS, Maru VM (1996) Compound chaos. Int Jr Bifurc Chaos 6:383–393

    Google Scholar 

  • Sornette A, Dubois J, Cheminee JL, Sornette D (1991) Are Sequences of Volcanic Eruptions Deterministically Chaotic? J Geophys Res 96:11931

    Google Scholar 

  • Srivastava HN, Pathak RB (1970) Regional models of Radio atmosphere over India. Jr Inst Telecom Engrs 16: 171–180

    Google Scholar 

  • Srivastava HN, Singh SS (1993) Empirical orthogonal functions associated with parameters used in long range forecasting of Indian summer monsoon. Mausam 44: 29–34

    Google Scholar 

  • Srivastava HN, Bhattacharya SN, Sinha Ray KC (1994a) Strange attractor dimension as a new measure of seismotectonics around Koyna reservoir India. Earth Plan Sci Lett 124: 57–62

    Article  Google Scholar 

  • Srivastava HN, Sinha Ray KC, Bhattacharya SN (1994b) Strange attractor dimension of surface radio refractivity over Indian stations. Mausam 45: 171–176

    Google Scholar 

  • Srivastava HN, Bhattacharya SN, Sinha Ray KC, Mahmoud SM, Yunga S (1995) Reservoir associated characteristics using deterministic chaos in Aswan, Nurek and Koyna reservoirs. PAGEPOH 145: 209–217

    Google Scholar 

  • Srivastava HN, Bhattacharya SN, Sinha Ray KC (1996) Strange attractor characteristics of earthquakes in Shillong plateau and adjoining regions. Geophy Res Lett 23: 3519–3522

    Article  Google Scholar 

  • Srivastava HN (1997) Compounding meteorological parameters in long range weather forecasting using deterministic chaos. IAMAP-IAPSO Symposium Melbourne Australia

    Google Scholar 

  • Srivastava HN, Sinha Ray (1997) Predictability of geophysical phenomena using deterministic chaos. Proc Nat Acad Sci LXVII Part VI: 305–345

    Google Scholar 

  • Srivastava HN, Bhattacharya SN (1998) Application of principal component analysis to some earthquake related data in the Koyna region, India. Eng Geology 50: 141–151

    Google Scholar 

  • Srivastava HN, Sinha Ray KC (1999) Deterministic chaos in earthquake occurrence in Parkfield California region and characteristic earthquakes. Mausam 49: 104

    Google Scholar 

  • Stewart CA, Turcotte DL (1989) The route to chaos in thermal convection at infinite Prandtl number 1 some trajectories and bifurcations. Jour Geophys Res 94: 13707

    Google Scholar 

  • Takalo J, Timonen J, Koskinen H (1993) Correlation dimension and affinity of AE data and bicolored noise. Geophys Res Lett 20: 525–550

    Google Scholar 

  • Tiwari RK, Rao KNN (2001) Power law random behaviour and seasonality bias of northeastern India earthquakes. J Geol Soc India 57: 369–376

    Google Scholar 

  • Tiwari RK, Srilakshmi S, Rao KNN (2003) Nature of earthquake dynamics in the central Himalayan region: a non-linear forecasting analysis. J Geodyn 35: 273–287

    Article  Google Scholar 

  • Tziperman E, Saher H, Zebiak SE, Cane MA (1997) Controlling spatio temporal chaos in a realistic El Nino prediction model. Phy Rev Lett 79: 1034–1038

    Google Scholar 

  • Vassiliadis D, Sharma AS, Papadopoulos K (1992) Low dimensionality of magnetospheric activity. EOS Trans AGU Spring Meeting Supp l 73: 270

    Google Scholar 

  • Wolf A, Swift JB, Swinney LH, Vastano JA (1985) Determining Lyapunov exponents from a time series. Physica 16 D: 285–317

    Google Scholar 

  • Yongqing P, Shaojin Y (1994) Seasonal variation features of Western North Pacific tropical cyclone tracks with their predictability. Advances in atmospheric sciences 11: 463–469

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Srivastava, H.N. (2005). Earth System Modeling Through Chaos. In: Dimri, V.P. (eds) Fractal Behaviour of the Earth System. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26536-8_9

Download citation

Publish with us

Policies and ethics