Pure and Applied Geophysics

, Volume 176, Issue 4, pp 1561–1577 | Cite as

Dynamic Multifractality of Seismic Activity in Northeast India

  • S. Sri LakshmiEmail author
  • Puja Banerjee


In recent years, the study of earthquakes has proven to be of great interest, particularly to understand the hidden processes underlying earthquake generation. The multifractal characteristics of frequency–time series of earthquakes of magnitude M ≥ 3 and M ≥ 4 that occurred in Northeast India (NEI) from January 1973 to December 2016 are studied in the present work. The Hurst exponent calculated for the NEI earthquake data is larger than 0.5, presenting long-range correlations and persistent behavior. In the present study, multifractal detrended fluctuation analysis (MFDFA) is used to study the multifractal properties of the data. The results show different shapes of multifractal spectra and corresponding distinct properties. This indicates that the degree of multifractality exhibits strong variation with time, which is associated with the dynamic evolution of earthquake activity in this region. The singularity spectrum is left-skewed and shows a long left tail, suggesting that the multifractal structures are sensitive to local fluctuations of large numbers of events. The singularity spectra of the four blocks of NEI also show a long left tail but with different width of the spectrum, indicating variation in the strength of multifractality in different blocks of the study area.


Fractal dimension generalized Hurst coefficient multifractal detrended fluctuation analysis (MFDFA) seismic activity earthquakes seismogenesis 



The authors acknowledge the Head of the Centre for Earth, Ocean and Atmospheric Sciences, University of Hyderabad for providing the facilities to carry out this work.


  1. Aki, K. (1987). Magnitude–frequency relation for small earthquakes: A clue to the origin of fmax of large earthquakes. Journal of Geophysical Research, 92, 1349–1355.CrossRefGoogle Scholar
  2. Bettinelli, P., Avouac, J.-P., Flouzat, M., Bollinger, L., Ramillien, G., Rajaure, S., & Sapkota, S. (2008). Seasonal variations of seismicity and geodetic strain in the imalaya induced by surface hydrology. Earth and Planetary Science Letters, 266, 332–344. Scholar
  3. Bhattacharya, P. M., & Kayal, J. R. (2003). Mapping the b-value and its correlation with the fractal dimension in the northeast region of India. Geological Society of India, 62(6), 680–695.Google Scholar
  4. Bhattacharya, P. M., Kayal, J. R., Baruah, S., & Arefiev, S. S. (2010). Earthquake source zones in northeast India: seismic tomography, fractal dimension and b value mapping. Pure and Applied Geophysics, 167(8–9), 999–1012.CrossRefGoogle Scholar
  5. Bollinger, L., Avouac, J. P., Cattin, R., & Pandey, M. R. (2004). Stress buildup in the Himalaya. Journal of Geophysical Research, 109, B11405. Scholar
  6. Bollinger, L., Perrier, F., Avouac, J.-P., Sapkota, S., Gautam, U., & Tiwari, D. R. (2007). Seasonal modulation of seismicity in the Himalaya of Nepal. Geophysical Research Letters, 34, L08304. Scholar
  7. Christiansen, L. B., Hurwitz, S., & Inge-britsen, S. (2007). Annual modulation of seismicity along the San Andreas Fault near Parkfield, CA. Geophysical Research Letters, 34, L04306. Scholar
  8. Costain, J. K., & Bollinger, G. A. (1996). Climatic changes, streamflow, and long-term forecasting of intraplate seismicity. Journal of Geodynamics, 22, 97–117.CrossRefGoogle Scholar
  9. Enescu, B., Ito, K., & Struzik, Z. R. (2006). Wavelet-based multiscale resolution analysis of real and simulated time-series of earthquakes. Geophysical Journal International, 164(1), 63–74.CrossRefGoogle Scholar
  10. Esteller, R., Vachtsevanos, G., Echauz, J., & Litt, B. (2001). A comparison of waveform fractal dimension algorithms. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 48(2), 177–183.CrossRefGoogle Scholar
  11. Feder, J. (1988). Fractals. New York: Plenum.CrossRefGoogle Scholar
  12. Gadano, C., Alonzo, M. L., & Vilardo, G. (1997). Multifractal approach to time clustering of earthquakes, application to Mt. Vesuvio seismicity, Pure and Applied Geophysics, 149, 375–390.CrossRefGoogle Scholar
  13. Gao, S. S., Silver, P. G., Linde, A. T., & Sacks, I. S. (2000). Annual modulation of triggered seismicity following the 1992 Landers earthquake in California. Nature, 406, 500–504.CrossRefGoogle Scholar
  14. Godano, C., & Caruso, V. (1995). Multifractal analysis of earthquake catalogues. Geophysical Journal International, 121(2), 385–392.CrossRefGoogle Scholar
  15. Grapenthin, R., Sigmundsson, F., Geirsson, H., Árnadóttir, T., & Pinel, V. (2006). Icelandic rhythmics: annual modulation of land elevation and plate spreading by snow load. Geophysical Research Letters, 33, L24305.CrossRefGoogle Scholar
  16. Gutenberg, R., & Richter, C. F. (1944). Frequency of earthquakes in California. Bulletin of Seismological Society of America, 34, 185–188.Google Scholar
  17. Gupta, H. K., Rajendran, K., & Singh, H. N. (1986). Seismicity of the Northeast Indian Region. Journal of the Geological Society of India, 28, 345–365.Google Scholar
  18. Hainzl, S., Kraft, T., Wassermann, J., Igel, H., & Schmedes, E. (2006). Evidence for rainfall-triggered earthquake activity. Geophysical Research Letters, 33, L19303. Scholar
  19. Heki, K. (2003). Snow load and seasonal variation of earthquake occurrence in Japan. Earth and Planetary Science Letters, 207, 159–164.CrossRefGoogle Scholar
  20. Helmstetter, A., & Sornette, D. (2003). Foreshocks explained by cascades of triggered seismicity. Journal of Geophysical Research: Solid Earth, 108(B10), 2457.Google Scholar
  21. Higuchi, T. (1988). Approach to an irregular time series on the basis of fractal theory. Physica D: Nonlinear Phenomena, 31, 277–283.CrossRefGoogle Scholar
  22. Hirata, T. (1989). A correlation between the b-value and the fractal dimension of earthquakes. Journal of Geophysical Research: Solid Earth, 94, 7507–7514.CrossRefGoogle Scholar
  23. Huc, M., & Main, I. G. (2003). Anomalous stress diffusion in earthquake triggering: Correlation length, time dependence, and directionality. Journal of Geophysical Research: Solid Earth, 108(B7), 2324.CrossRefGoogle Scholar
  24. Hurst, H. E. (1951). Long-term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers, 116, 770–808.Google Scholar
  25. Idziak, A., & Teper, L. (1996). Fractal dimension of faults network in the upper Silesian coal basin (Poland): Preliminary studies. Pure and Applied Geophysics, 147(2), 239–247.CrossRefGoogle Scholar
  26. Ihlen, E. A. (2012). Introduction to multifractal detrended fluctuation analysis in matlab. Frontiers in Physiology. Scholar
  27. Kagan, Y. Y., & Knopoff, L. (1980). Spatial distribution of earthquakes: The two-point correlation function. Geophysical Journal International, 62, 303–320.CrossRefGoogle Scholar
  28. Kantelhardt, J. W., Koscielny-Bunde, E., Rego, H. A. A., Havlin, S., & Bunde A. (2001). Detecting long-range correlation with detrended fluctuation analysis. Physica A, 295, 441–454.CrossRefGoogle Scholar
  29. Kantelhardt, J. W., Zschiegner, S. A., Koscielny-Bunde, E., Havlin, S., Bunde, A., & Stanley, H. E. (2002). Multifractal detrended fluctuation analysis of nonstationary time series. Physica A: Statistical Mechanics and Its Applications, 316(1), 87–114.CrossRefGoogle Scholar
  30. Katz, M. (1988). Fractals and the analysis of waveforms. Computers in Biology and Medicine, 18, 145–156.CrossRefGoogle Scholar
  31. Kayal, J. R. (1996). Earthquake source process in northeast India: A review. Journal of Himalayan Geology, 17, 53–69.Google Scholar
  32. Kayal, J. R. (2001). Microearthquake activity in some parts of the Himalaya and the tectonic model. Tectonophysics, 339, 331–351.CrossRefGoogle Scholar
  33. Kayal, J. R., & Banerjee, B. (1988). Anomalous behaviour of the precursor resistivity in the Shillong area, Northeast India. Geophysics Journal International, 94, 97–103.CrossRefGoogle Scholar
  34. King, G. (1983). The accommodation of large strains in the upper lithosphere of the earth and other solids by self-similar fault system: The geometrical origin of b-value. Pure and Applied Geophysics, 121, 761–815.CrossRefGoogle Scholar
  35. Main, I. G. (1996). Statistical physics, seismogenesis, and seismic hazard. Reviews of Geophysics, 34, 433–462.CrossRefGoogle Scholar
  36. Mandelbrot, B. B. (1983). The fractal geometry of nature (2nd ed.). San Francisco: W. H. Freeman.Google Scholar
  37. Mandelbrot, B., & Wallis, J. R. (1969). Robustness of the rescaled range R/S in the measurement of noncyclic long-run statistical dependence. Water Resources Research, 5, 967–988.CrossRefGoogle Scholar
  38. McCloskey, J. (1993). A hierarchical model for earthquake generation on coupled segments of a transform fault. Geophysical Journal International, 115(2), 538–551.CrossRefGoogle Scholar
  39. Michas, G., Sammonds, P., & Vallianatos, F. (2014). Dynamic multifractality in earthquake time series: Insights from the Corinth rift, Greece. Pure and Applied Geophysics, 172(7), 1909–1921.CrossRefGoogle Scholar
  40. Michas, G., Vallianatos, F., & Sammonds, P. (2013). Non-extensivity and long-range correlations in the earthquake activity at the West Corinth rift (Greece). Nonlinear Processes in Geophysics, 20(5), 713–724.CrossRefGoogle Scholar
  41. Nakaya, S., & Hashimoto, T. (2002). Temporal variation of multifractal properties of seismicity in the region affected by the mainshock of the October 6, 2000 Western Tottori Prefecture, Japan, earthquake (M = 7.3). Geophysical Research Letters, 29, 133–141.CrossRefGoogle Scholar
  42. Ogata, Y. (1983). Likelihood analysis of point processes and its application to seismological data. Bulletin of the International Statistical Institute, 50(2), 943–961.Google Scholar
  43. Oike, K. (1978). On the relation between rainfall and the occurrence of earthquakes. Disaster Prevention Research Institute, 20B–1, 35–45.Google Scholar
  44. Oncel, A. O., & Wilson, T. H. (2002). Space-time correlations of seismotectonic parameters: Example from Japan and from Turkey preceding the Izmith earthquake. Bulletin of the Seismological Society of America, 92, 339–349.CrossRefGoogle Scholar
  45. Oncel, A. O., & Wilson, T. (2006). Evaluation of earthquake potential along the northern Anatolian Fault zone in the Marmara Sea using comparisons of 160 GPS strain and seismotectonics parameters. Tectonophysics, 418, 205–218.CrossRefGoogle Scholar
  46. Peng, C. K., Havelin, S., Stanley, H. E., & Goldberger, A. L. (1995). Quantification of scaling exponents and crossover phenomena in nonstationary time series. Chaos, 5, 82–89. Scholar
  47. Peng, C. K., Mietus, J., Hausdorff, J. M., Havlin, S., Stanley, H. E., & Goldberger, A. L. (1993). Long range anti-correlations and non-Gaussian behavior of the heartbeat. Physical Review Letters, 70, 1343–1346. Scholar
  48. Petrosian, A. (1995). Kolmogorov complexity of finite sequences and recognition of different preictal EEG patterns. In Computer-Based Medical Systems, 1995., Proceedings of the Eighth IEEE Symposium on (pp. 212–217). IEEE.Google Scholar
  49. Raghavendra, B. S., & Dutt, D. N. (2010). Computing fractal dimension of signals using multiresolution Box-counting method. International Journal of Information and Mathematical Sciences, 6(1), 50–65.Google Scholar
  50. Roy, P. N. S., & Mondal, S. K. (2009). Fractal nature of earthquake occurrence in Northwest Himalayan region. The Journal of Indian Geophysical Union, 13(2), 63–68.Google Scholar
  51. Roy, P. N. S., & Mondal, S. K. (2012). Fractal and multifractal study of earthquakes for analysis of stress pattern in Kumaun Himalaya and its surrounding region. Journal of Earth System Science, 121(4), 1033–1047.CrossRefGoogle Scholar
  52. Roy, P. N. S., Mondal, S. K., & Joshi, M. (2012). Seismic Hazards Assessment of Kumaun Himalaya and adjacent region. Natural Hazards. Scholar
  53. Roy, P. N. S., & Nath, S. K. (2007). Precursory correlation dimensions for three great earthquakes. Current Science, 93(11), 1522–1529.Google Scholar
  54. Rundle, J. B. (1989). Derivation of the complete Gutenberg-Richter magnitude–frequency relation using the principle of scale invariance. Journal of Geophysical Research, 94(B9), 12337–12342. (September).CrossRefGoogle Scholar
  55. Saar, M. O., & Manga, M. (2003). Seismicity induced by seasonal groundwater recharge at Mt. Hood, Oregon. Earth and Planetary Science Letters, 214, 605–618.CrossRefGoogle Scholar
  56. Sri Lakshmi, S., & Tiwari, R. K. (2007). Are northeast and western Himalayas earthquake dynamics better “organized” than Central Himalayas: An artificial neural network approach. Geofísica Internacional, 46(1), 63–73.Google Scholar
  57. Sri Lakshmi, S., & Tiwari, R. K. (2009). Model dissection from earthquake time series: A comparative analysis using modern non-linear forecasting and artificial neural network approaches. Computers & Geosciences, 35(2), 191–204.CrossRefGoogle Scholar
  58. Srivastava, H. N., Bhattacharya, S. N., & Sinha Ray, K. C. (1996). Strange attractor characteristics of earthquakes in Shillong plateau and adjoining regions. Geophysical Research Letters, 23(24), 3519–3522.CrossRefGoogle Scholar
  59. Telesca, L., Lapenna, V., & Vallianatos, F. (2002). Monofractal and multifractal approaches in investigating scaling properties in temporal patterns of the 1983-2000 seismicity in the western Corinth graben, Greece. Physics of the Earth and Planetary Interiors, 131, 63–79.CrossRefGoogle Scholar
  60. Tiwari, R. K., Srilakshmi, S., & Rao, K. N. N. (2003). Nature of earthquake dynamics in the central Himalayan region: a nonlinear forecasting analysis. Journal of Geodynamics, 35(3), 273–287.CrossRefGoogle Scholar
  61. Tiwari, R. K., Srilakshmi, S., & Rao, K. N. N. (2004). Characterization of earthquake dynamics in the Northeastern India regions: a modern nonlinear forecasting analysis. Pure and Applied Geophysics, 161, 865–880.CrossRefGoogle Scholar
  62. Tosi, P. (1998). Seismogenic structure behaviour revealed by spatial clustering of seismicity in the Umbria-Marche Region (Central Italy). Annali di Geofisica, 41(2), 215–224.Google Scholar
  63. van Stiphout, T., Zhuang, J., & Marsan, D. (2012). Seismicity declustering. Community Online Resource for Statistical Seismicity Analysis. Scholar
  64. Wiemer, S., & Wyss, M. (2000). Minimum magnitude of complete reporting in earthquake catalogs: examples from Alaska, the western United States, and Japan. Bulletin of the Seismological Society of America, 90, 859–869.CrossRefGoogle Scholar
  65. Yoder, M., Holliday, J. R., Turcotte, D. L., & Rundle, J. (2012). A geometric frequency–magnitude scaling transition: Measuring b= 1.5 for large earthquakes. Tectonophysics, 532–535, 162–174.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Centre for Earth, Ocean and Atmospheric Sciences, University of HyderabadHyderabadIndia

Personalised recommendations