Journal of Seismology

, Volume 20, Issue 3, pp 771–786 | Cite as

Focusing patterns of seismicity with relocation and collapsing

  • Ka Lok LiEmail author
  • Ólafur Gudmundsson
  • Ari Tryggvason
  • Reynir Bödvarsson
  • Bryndís Brandsdóttir
Original Article


Seismicity is generally concentrated on faults or in fault zones of varying, sometimes complex geometry. An earthquake catalog, compiled over time, contains useful information about this geometry, which can help understanding the tectonics of a region. Interpreting the geometrical distribution of events in a catalog is often complicated by the diffuseness of the earthquake locations. Here, we explore a number of strategies to reduce this diffuseness and hence simplify the seismicity pattern of an earthquake catalog. These strategies utilize information about event locations contained in their overall catalog distribution. They apply this distribution as an a priori constraint on relocations of the events, or as an attractor for each individual event in a collapsing scheme, and thereby focus the locations. The latter strategy is not a relocation strategy in a strict sense, although event foci are moved, because the movements are not driven by data misfit. Both strategies simplify the seismicity pattern of the catalog and may help to interpret it. A synthetic example and a real-data example from an aftershock sequence in south west Iceland are presented to demonstrate application of the strategies. Entropy is used to quantify their effect.


Probability distributions Clustering Seismicity Image processing 



We would like to thank an anonymous reviewer for his constructive comments.

Supplementary material

10950_2016_9556_MOESM1_ESM.eps (273 kb)
(EPS 273 KB)


  1. Asanuma H, Ishimoto M, Jones RH, Phillips WS, Niitsuma H (2001) A variation of the collapsing method to delineate structures inside a microseismic cloud. Bull Seismol Soc Am 91(1):154–160. doi: 10.1785/0120000063 CrossRefGoogle Scholar
  2. Brandsdóttir B, Parsons M, White RS, Gudmundsson O, Drew J, Thorbjarnadóttir B (2010) The May 29 2008 earthquake aftershock sequence within the South Iceland Seismic Zone: fault locations and source parameters of aftershocks. Jökull 60:23–46Google Scholar
  3. Decriem J, Árnadóttir T, Hooper A, Geirsson H, Sigmundsson F, Keiding M, Ófeigsson BG, Hreinsdóttir S, Einarsson P, LaFemina P, Bennett RA (2010) The 2008 May 29 earthquake doublet in SW Iceland. Geophys J Int 181(2):1128–1146. doi: 10.1111/j.1365-246X.2010.04565.x Google Scholar
  4. Einarsson P (2010) Mapping of Holocene surface ruptures in the South Iceland Seismic Zone. Jökull 60:117–134Google Scholar
  5. Fehler M, Phillips WS, House L, Jones RH, Aster R, Rowe C (2000) Improved relative locations of clustered earthquakes using constrained multiple event location. Bull Seismol Soc Am 90(3):775–780. doi: 10.1785/0119990095 CrossRefGoogle Scholar
  6. Forbes C, Evans M, Hastings N, Peacock B (2010) Statistical distributions, 4th edn. Wiley, HobokenCrossRefGoogle Scholar
  7. Frohlich C (1979) An efficient method for joint hypocenter determination for large groups of earthquakes. Comput Geosci 5(3-4):387–389. doi: 10.1016/0098-3004(79)90034-7 CrossRefGoogle Scholar
  8. Greenwood PE, Nikulin MS (1996) A Guide to Chi-Squared Testing. Wiley-InterscienceGoogle Scholar
  9. Hreinsdóttir S, Árnadóttir T, Decriem J, Geirsson H, Tryggvason A, Bennett RA, LaFemina P (2009) A complex earthquake sequence captured by the continuous GPS network in SW Iceland. Geophys Res Lett 36(12):L12,309. doi: 10.1029/2009GL038391 CrossRefGoogle Scholar
  10. Ito A (1985) High resolution relative hypocenters of similar earthquakes by cross spectral analysis method. J Phys Earth 33:279–294CrossRefGoogle Scholar
  11. Jones RH, Stewart RC (1997) A method for determining significant structures in a cloud of earthquakes. J Geophys Res 102(B4):8245–8254. doi: 10.1029/96JB03739 CrossRefGoogle Scholar
  12. Kamer Y, Ouillon G, Sornette D, Wössner J (2015) Condensation of earthquake location distributions: optimal spatial information encoding and application to multifractal analysis of south Californian seismicity. Phys Rev E 92(2):022,808. doi: 10.1103/PhysRevE.92.022808 CrossRefGoogle Scholar
  13. Khodayar M, Björnsson S (2014) Fault ruptures and geothermal effects of the second earthquake, 29 May 2008, South Iceland Seismic Zone. Geothermics 50:44–65. doi: 10.1016/j.geothermics.2013.07.002.. CrossRefGoogle Scholar
  14. Lomax A, Michelini A, Curtis A (2009) Earthquake Location, Direct, Global-Search Methods. In: Meyers RA (ed) Encyclopedia of Complexity and Systems Science. Springer, New York, pp 2449–2473. doi: 10.1007/978-0-387-30440-3_150
  15. Martinsson J (2013) Robust Bayesian hypocentre and uncertainty region estimation: the effect of heavy-tailed distributions and prior information in cases with poor, inconsistent and insufficient arrival times. Geophys J Int 192(3):1156–1178.  10.1093/gji/ggs067. CrossRefGoogle Scholar
  16. Nicholson T, Sambridge M, Gudmundsson Ó (2000) On entropy and clustering in earthquake hypocentre distributions. Geophys J Int 142(1):37–51. doi: 10.1046/j.1365-246x.2000.00113.x CrossRefGoogle Scholar
  17. Papoulis A, Pillai SU (2002) Probability,random variables and stochastic processes, 4th edn. McGraw-HillGoogle Scholar
  18. Skilling J (1989) Classic maximum entropy. In: Skilling J (ed) Maximum entropy and bayesian methods. Springer, Netherlands, Dordrecht, pp 45–52, doi: 10.1007/978-94-015-7860-8, (to appear in print)
  19. Slunga R, Rognvaldsson ST, Bodvarsson R (1995) Absolute and relative locations of similar events with application to microearthquakes in southern Iceland. Geophys J Int 123(2):409–419. doi: 10.1111/j.1365-246X.1995.tb06862.x CrossRefGoogle Scholar
  20. Spence W (1980) Relative epicenter determination using P-wave arrival-time differences. Bull Seismol Soc Am 70(1):171–183Google Scholar
  21. Waldhauser F, Ellsworth W (2000) A Double-Difference earthquake location algorithm: method and application to the northern hayward fault, california. Bull Seismol Soc Am 90(6):1353–1368. doi: 10.1785/0120000006 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Earth SciencesUppsala UniversityUppsalaSweden
  2. 2.Science InstituteUniversity of IcelandReykjavikIceland

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