Pure and Applied Geophysics

, Volume 175, Issue 12, pp 4241–4252 | Cite as

Visibility Graph Analysis of Alaska Crustal and Aleutian Subduction Zone Seismicity: An Investigation of the Correlation between b Value and kM Slope

  • Shima Azizzadeh-RoodpishEmail author
  • Chris H. Cramer


Statistical methods are useful tools to aid the recognition of patterns and extract information from a large amount of data available through resources such as earthquake catalogs. Visibility graph analysis is one of these relatively new statistical techniques that can be applied on data in the form of time series, and map them into a graph of nodes and connections, which makes it possible to use network theory for characterizing the original data. We present a study applying visibility graph analysis to a seismicity catalog for the Alaska crust and the Aleutian subduction zone. The catalog is gathered from the United States Geological Survey database, for the years between 1900 and mid 2017. A history of several earthquakes and a variety in seismic features, both near surface and at depth, make this region one of the richest areas to investigate possible seismic patterns and correlations. The focus here is on examining the previously suggested correlation between b value of the Gutenberg–Richter relation and the kM slope from a visibility graph analysis. The visibility graph method defines a k degree or connectivity degree for each event according to its magnitude and position in time series. The kM slope represents the slope of the regression line of these pairs of magnitude and connectivity degree, as a single number for each zone. We calculate the kM slope for selected zones for Alaska and the Aleutians and add it to the data from previous worldwide studies and the results verify and improve the linear universal relationship between b value and kM slope suggested by past studies, which indicates that the visibility graph analysis can work as an alternative approach for studying earthquake sequence.


Visibility graph analysis b value statistical seismicity Alaska and Aleutian subduction zone 



The data for this study was obtained from the United State Geological Survey, USGS, ( This research was possible thanks to support from the Center for Earthquake Research and Information (CERI) at the University of Memphis. CERI is designated as a Center of Excellence by the Tennessee Board of Regents and is funded in part by the State of Tennessee under State Sunset Laws (SB 1510 and HB 1608, 2015–2016).


  1. AEIS website. (2018). Accessed 12 July 2018.
  2. Aki, K. (1965). Maximum likelihood estimate of b in the formula log N = a − bM and its confidence limits. Bulletin Earthquake Research Institute Tokyo University, 43, 237–239.Google Scholar
  3. Azizzadeh-Roodpish, S., Khoshnevis, N., & Cramer, C. H. (2017). Visibility graph analysis of southern California. In Proceedings annual meeting of the seismological society of America, Denver, Colorado (Vol. 10).
  4. Chen, S., Hu, Y., Mahadevan, S., & Deng, Y. (2014). A visibility graph averaging aggregation operator. Physica A: Statistical Mechanics and its Applications, 403, 1–12.CrossRefGoogle Scholar
  5. Cheng, C., Sa-Ngasoongsong, A., Beyca, O., Le, T., Yang, H., Kong, Z., et al. (2015). Time series forecasting for nonlinear and non-stationary processes: A review and comparative study. IIE Transactions, 47(10), 1053–1071.CrossRefGoogle Scholar
  6. Coonrad, W. L. (1982). The United States geological survey in Alaska: Accomplishments during 1981. Circular, 844, 1.Google Scholar
  7. Das, R., Wason, H. R., & Sharma, M. L. (2011). Global regression relations for conversion of surface wave and body wave magnitudes to moment magnitude. Natural Hazards, 59(2), 801–810.CrossRefGoogle Scholar
  8. Elsner, J. B., Jagger, T. H., & Fogarty, E. A. (2009). Visibility network of United States hurricanes. Geophysical Research Letters, 36, L16702. Scholar
  9. Gutenberg, B., & Richter, C. F. (1944). Frequency of earthquakes in California. Bulletin of the Seismological Society of America, 34(4), 185–188.Google Scholar
  10. Jiang, W., Wei, B., Zhan, J., Xie, C., & Zhou, D. (2016). A visibility graph power averaging aggregation operator: A methodology based on network analysis. Computers & Industrial Engineering, 101, 260–268.CrossRefGoogle Scholar
  11. Khoshnevis, N., Taborda, R., Azizzadeh-Roodpish, S., & Telesca, L. (2017). Analysis of the 2005–2016 earthquake sequence in Northern Iran using the visibility graph method. Pure and Applied Geophysics, 174(11), 4003–4019.CrossRefGoogle Scholar
  12. Kisslinger, C., & Jones, L. M. (1991). Properties of aftershock sequences in southern California. Journal of Geophysical Research: Solid Earth, 96(B7), 11947–11958.CrossRefGoogle Scholar
  13. Kutliroff, J. R. (2017). Estimating the Proportions of Large to Small Earthquakes in Seismic Regions with a Short Span of Earthquake Magnitudes (Doctoral dissertation, The University of Memphis).Google Scholar
  14. Lacasa, L., Luque, B., Ballesteros, F., Luque, J., & Nuno, J. C. (2008). From time series to complex networks: The visibility graph. Proceedings of the National Academy of Sciences, 105(13), 4972–4975.CrossRefGoogle Scholar
  15. Long, Y. (2013). Visibility graph network analysis of gold price time series. Physica A: Statistical Mechanics and its Applications, 392(16), 3374–3384.CrossRefGoogle Scholar
  16. Masehian, E., & Amin-Naseri, M. R. (2004). A Voronoi diagram-visibility graph-potential field compound algorithm for robot path planning. Journal of Field Robotics, 21(6), 275–300.Google Scholar
  17. National Research Council. (1976). Predicting earthquakes: A scientific and technical evaluation, with implications for society. Washington, DC: National Academies.Google Scholar
  18. Nilanjana, P., Anirban, B., Susmita, B., & Dipak, G. (2016). Non-invasive alarm generation for sudden cardiac arrest: A pilot study with visibility graph technique. Translational Biomedicine. Scholar
  19. Page, R. A., Biswas, N. N., Lahr, J. C., & Pulpan, H. (1991). Seismicity of continental Alaska. In D. B. Slemmons, E. R. Engdahl, M. D. Zoback, D. D. Blackwell (Eds.), Neotectonics of North America, (Vol. 1, pp. 47–68). Boulder, CO: Geological Society of AmericaGoogle Scholar
  20. Pearson, K. (1895). Note on regression and inheritance in the case of two parents. Proceedings of the Royal Society of London, 58, 240–242.CrossRefGoogle Scholar
  21. Qian, M. C., Jiang, Z. Q., & Zhou, W. X. (2010). Universal and nonuniversal allometric scaling behaviors in the visibility graphs of world stock market indices. Journal of Physics A: Mathematical and Theoretical, 43(33), 335002.CrossRefGoogle Scholar
  22. Reasenberg, P. A., & Jones, L. M. (1989). Earthquake hazard after a mainshock in California. Science, 243(4895), 1173–1176.CrossRefGoogle Scholar
  23. Tarr, R. S., & Martin, L. (1912). The earthquakes at Yakutat Bay, Alaska, in September, 1899 (No. 69). US Gov’t. Print. Off..Google Scholar
  24. Telesca, L., & Lovallo, M. (2012). Analysis of seismic sequences by using the method of visibility graph. EPL (Europhysics Letters), 97(5), 50002.CrossRefGoogle Scholar
  25. Telesca, L., Lovallo, M., Ramirez-Rojas, A., & Flores-Marquez, L. (2013). Investigating the time dynamics of seismicity by using the visibility graph approach: Application to seismicity of Mexican subduction zone. Physica A: Statistical Mechanics and its Applications, 392(24), 6571–6577.CrossRefGoogle Scholar
  26. Telesca, L., Lovallo, M., Ramirez-Rojas, A., & Flores-Marquez, L. (2014a). Relationship between the frequency magnitude distribution and the visibility graph in the synthetic seismicity generated by a simple stick-slip system with asperities. PLoS ONE, 9(8), e106233.CrossRefGoogle Scholar
  27. Telesca, L., Lovallo, M., & Toth, L. (2014b). Visibility graph analysis of 2002–2011 Pannonian seismicity. Physica A: Statistical Mechanics and its Applications, 416, 219–224.CrossRefGoogle Scholar
  28. Utsu, T. (1965). A method for determinating the value of b in a formula logN = a − bM showing the magnitude-frequency relation for earthquakes. Geophysics Bill Hokkaido University, 13, 99–103.Google Scholar
  29. Utsu, T. (2002). Relationships between magnitude scales. International geophysics (Vol. 81, pp. 733–746). New York: Academic.Google Scholar
  30. Wang, N., Li, D., & Wang, Q. (2012). Visibility graph analysis on quarterly macroeconomic series of China based on complex network theory. Physica A: Statistical Mechanics and its Applications, 391(24), 6543–6555.CrossRefGoogle Scholar
  31. Wesson, R. L., Boyd, O. S., Mueller, C. S., Bufe, C. G., Frankel, A. D., & Petersen, M. D. (2007). Revision of time-independent probabilistic seismic hazard maps for Alaska (No. 2007-1043). Geological Survey (US).Google Scholar
  32. Wiemer, S., & Wyss, M. (2002). Mapping spatial variability of the frequency-magnitude distribution of earthquakes. Advances in geophysics (Vol. 45, p. 259). Oxford: Elsevier.Google Scholar
  33. Yu, M., Hillebrand, A., Gouw, A. A., & Stam, C. J. (2017). Horizontal visibility graph transfer entropy (HVG-TE): A novel metric to characterize directed connectivity in large-scale brain networks. NeuroImage, 156, 249–264.CrossRefGoogle Scholar
  34. Zhang, R., Ashuri, B., Shyr, Y., & Deng, Y. (2018). Forecasting construction cost index based on visibility graph: A network approach. Physica A: Statistical Mechanics and its Applications, 493, 239–252.CrossRefGoogle Scholar
  35. Zhu, G., Li, Y., & Wen, P. P. (2012). An efficient visibility graph similarity algorithm and its application on sleep stages classification. International conference on brain informatics (pp. 185–195). Berlin: Springer.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Center for Earthquake Research and Information (CERI)University of MemphisMemphisUSA

Personalised recommendations