Pure and Applied Geophysics

, Volume 171, Issue 3–5, pp 425–437 | Cite as

Cross-correlation Coefficients for the Study of Repeating Earthquakes: An Investigation of Two Empirical Assumptions/Conventions in Seismological Interpretation Practice

  • Libo Han
  • Zhongliang Wu
  • Yutong Li
  • Changsheng Jiang


For the identification and analysis of ‘repeating earthquakes,’ there are two empirical concepts. The first is the assumption that the cross-correlation coefficient of the filtered seismograms of closely spaced ‘repeaters’ depends exponentially on the inter-event separation distance. The second is the convention that in processing regional seismograms, a 0.5–5.0-Hz band pass filter is used. In this article, using a simple layered structure model, we investigated the cross-correlation coefficient of the filtered synthetic seismograms of two closely located events, that is, a ‘doublet.’ We investigated the relation between the cross-correlation coefficient and the inter-event separation distance. Simulation shows that in the 0.5–5.0-Hz frequency band, even if for simple synthetic seismograms without considering lateral heterogeneity or scattering, the exponential dependence is only a first order approximation concept. To check the frequency dependence of the cross-correlation coefficient, we analyzed a group of seismograms of a ‘multiplet’ in Xiuyan, Liaoning, northeast China, recorded by the Regional Seismographic Network of Liaoning Province. The cross-correlation coefficients were observed to be relatively stable against frequency for the 0.5–5.0-Hz frequency band.


  1. Aki, K. and Richards, P. G.: Quantitative Seismology: Theory and Methods, W. H. Freeman, San Francisco, 1980.Google Scholar
  2. Baisch, S., Ceranna, L., Harjes, H.-P.: Earthquake cluster: what can we learn from waveform similarity? Bull. Seismol. Soc. Amer., 98, 2806–2814, doi:10.1785/0120080018, 2008.
  3. Båth, M.: Spectral Analysis in Geophysics, Elsevier, Amsterdam, 1974.Google Scholar
  4. Cheng, X., Niu, F., Silver, P. G., Horiuchi, S., Takai, K., Iio, Y., and Ito, H.: Similar microearthquakes observed in western Nagano, Japan, and implications for rupture mechanics, J. Geophys. Res., 112, B04306, doi:10.1029/2006JB004416, 2007.
  5. Geller, R. J., Mueller, C. S.: Four similar earthquake in central California, Geophys. Res. Lett., 10, 821–824, 1980.Google Scholar
  6. Igarashi, T. Matsuzawa, T., and Hasegawa, A.: Repeating earthquakes and interplate aseismic slip in the northeastern Japan subduction zone, J. Geophys. Res., 108, 2249, doi:10.1029/2002JB001920, 2003.
  7. Jiang, C. S. and Wu, Z. L.: Location accuracy of the China National Seismograph Network estimated by repeating events, Earthquake Research in China, 20, No. 1, 67–74, 2006.Google Scholar
  8. Jiang, C. S., Wu, Z. L. and Li, Y. T.: Estimating the location capability of the Beijing Capital Digital Seismograph Network using repeating events, Chin. J. Geophys., 51, 817–827, 2008, in Chinese with English abstract.Google Scholar
  9. Jiang, C. S., Wu, Z. L., Li, Y. T and Ma, T. F.: ‘Repeating Events’ as estimator of location precision: the China National Seismograph Network, Pure Appl. Geophys., Accepted, 2012.Google Scholar
  10. Kikuchi, M. and Kanamori, H.: Inversion of complex body waves-III, Bull. Seismol. Soc. Amer., 81, 2335–2350, 1991.Google Scholar
  11. Li, L., Chen, Q. F., Cheng, X., and Niu, F. L.: Spatial clustering and repeating of seismic events observed along the 1976 Tangshan fault, north China, Geophys. Res. Lett., 34, L23309, doi: 10.1029/2007GL031594, 2007.
  12. Li, Y. T., Wu, Z. L., Peng, H. P., Jiang, C. S. and Li, G. P.: Time-lapse slip variation associated with a medium-size earthquake revealed by “repeating” micro-earthquakes: the 1999 Xiuyan, Liaoning, M S = 5.4 earthquake, Nat. Hazards Earth Syst. Sci., 11, 1969–1981, doi:10.5194/nhess-11-1969-2011, 2011.
  13. Lu, Z.-X., Jiang, X.-Q., Pan, K., Bai, Y., Jiang, D.-L., Xiao, L.-P., Liu, J.-H., Liu, F.-T., Chen, H. and He, J.-K.: Seismic tomography in the northeast margin area of Sino-Korean platform, Chin. J. Geophys., 45, 338–351, 2002, in Chinese with English abstract.Google Scholar
  14. Menke, W.: Using waveform similarity to constrain earthquake locations, Bull. Seismol. Soc. Amer., 89, 1143–1146, 1999.Google Scholar
  15. Menke, W., Lerner-Lam, A. L., Dubendorff, B. and Pacheco, J.: Polarization and coherence of 5 to 30 Hz seismic wave fields at a hard-rock site and their relevance to velocity heterogeneities in the crust, Bull. Seismol. Soc. Amer., 80, 430–449, 1990.Google Scholar
  16. Nadeau, R. M., Foxall, W. and McEvilly, T. V.: Clustering and periodic recurrence of microearthquakes on the San Andreas fault at Parkfield, California, Science, 267, 503–507, doi: 10.1126/267.5197.503, 1995.
  17. Nadeau, R. M. and Johnson, L. R.: Seismological studies at Parkfield VI: Moment release rates and estimates of source parameters for small repeating earthquakes, Bull. Seismol. Soc. Amer., 88, 790–814, 1998.Google Scholar
  18. Nadeau, R. M. and McEvilly, T. V.: Fault slip rates at depth from recurrence intervals of repeating microearthquakes, Science, 285, 718–721, doi:10.1126/science.285.5428.718, 1999.
  19. Rau, R. J., Chen, K. H., and Ching, K. E.: Repeating earthquakes and seismic potential along the northern Longitudinal Valley fault of eastern Taiwan. Geophys. Res. Lett., 34, L24301, doi:10.1029/2007GL031622, 2007.
  20. Richards, P., Waldhauser, F., Schaff, D. And Kim, W.-Y.: The applicability of modern methods of earthquake location, Pure appl. Geophys., 163, 351–372, 2006.Google Scholar
  21. Schaff, D.: Semiempirical statistics of correlation-detector performance, Bull. Seismol. Soc. Amer., 98, 1495–1507, 2008.Google Scholar
  22. Schaff, D.: Improvements to detection capability by cross-correlating for similar events: a case study of the 1999 Xiuyan, China, sequence and synthetic sensitivity tests, Geophys. J. Int., 180, 829–846, 2010.Google Scholar
  23. Schaff, D. P. and Richards, P. G.: Repeating seismic events in China, Science, 303, 1176–1178, 2004.Google Scholar
  24. Schaff, D. P. and Richards, P. G.: On finding and using repeating seismic events in and near China, J. Geophys. Res., 116, B03309, doi:10.1029/2010JB007895, 2011.
  25. Schaff, D. P. and Waldhauser, F.: One magnitude unit reduction in detection threshold by cross correlation applied to Parkfield (California) and China seismicity, Bull. Seismol. Soc. Amer., 100, 3224–3238, doi:10.1785/0120100042, 2010.
  26. Vidale, J. E., Ellsworth, W. L., Cole, A., and Marone, C.: Variations in rupture process with recurrence interval in a repeated small earthquake, Nature, 36, 8624–8626, 1994.Google Scholar
  27. Wu, Z. L. and Richards, P. G.: Seismology, Monitoring of CTBT—scientific and technical advances in seismology and their relevance, In: Gupta, H. K. (eds.) Encyclopedia of Solid Earth Geophysics, 2nd Edition, Springer, Amsterdam, 1340–1343, 2011.Google Scholar
  28. Zhao, L. and Helmberger, D. V.: Source estimation from broadband regional seismograms, Bull. Seismol. Soc. Amer., 84, 91–104, 1994.Google Scholar
  29. Zhu, L. and Helmberger, D. V.: Advancement in source estimation techniques using broadband regional seismograms, Bull. Seismol. Soc. Amer., 86, 1634–1641, 1996.Google Scholar
  30. Zhu, L. and Rivera L. A.: A note on the dynamic and static displacements from a point source in multilayered media, Geophys. J. Int., 148, 619–627, 2002.Google Scholar

Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  • Libo Han
    • 1
  • Zhongliang Wu
    • 1
    • 2
  • Yutong Li
    • 3
  • Changsheng Jiang
    • 1
  1. 1.Institute of GeophysicsChina Earthquake AdministrationBeijingChina
  2. 2.Laboratory of Computational GeodynamicsGraduate University of the Chinese Academy of SciencesBeijingChina
  3. 3.Earthquake Administration of Liaoning ProvinceShenyangChina

Personalised recommendations