Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Earthquake Location, Direct, Global-Search Methods

  • Anthony Lomax
  • Alberto Michelini
  • Andrew Curtis
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_150-2

Definition of the Subject

An earthquake location specifies the place and time of occurrence of energy release from a seismic event. A location together with a measure of size forms a concise description of the most important characteristics of an earthquake. The location may refer to the earthquake’s epicenter, hypocenter, or centroid or to another observed or calculated property of the earthquake that can be spatially and temporally localized. A location is called absolute if it is determined or specified within a fixed, geographic coordinate system and a fixed time base (e.g., Coordinated Universal Time, UTC); a location is called relative if it is determined or specified with respect to another spatiotemporal object (e.g., an earthquake or explosion) which may have unknown or uncertain absolute location.

For rapid hazard assessment and emergency response, an earthquake location provides information such as the locality of potential damage or the source region of a possible tsunami,...


Earthquake location hypocenter epicenter seismicity early warning experimental design inverse problem global search probabilistic 
This is a preview of subscription content, log in to check access.


  1. Aki K, Richards PG (1980) Quantitative seismology. Freeman, New YorkGoogle Scholar
  2. Anderson K (1981) Epicentral location using arrival time order. Bull Seismol Soc Am 71:541–545Google Scholar
  3. Baker T, Granat R, Clayton RW (2005) Real-time earthquake location using Kirchhoff reconstruction. Bull Seismol Soc Am 95:699–707CrossRefGoogle Scholar
  4. Billings SD (1994) Simulated annealing for earthquake location. Geophys J Int 118:680–692ADSCrossRefGoogle Scholar
  5. Buland R (1976) The mechanics of locating earthquakes. Bull Seismol Soc Am 66:173–187Google Scholar
  6. Calvert A, Gomez F, Seber D, Barazangi M, Jabour N, Ibenbrahim A, Demnati A (1997) An integrated geophysical investigation of recent seismicity in the Al-Hoceima region of North Morocco. Bull Seismol Soc Am 87:637–651Google Scholar
  7. Cervený V (2001) Seismic ray theory. Cambridge University Press, CambridgeCrossRefzbMATHGoogle Scholar
  8. Cua G, Heaton T (2007) The Virtual Seismologist (VS) method: a Bayesian approach to earthquake early warning. In: Gasparini P, Gaetano M, Jochen Z (eds) Earthquake early warning systems. Springer, BerlinGoogle Scholar
  9. Curtis A (1999a) Optimal experiment design: cross-borehole tomographic examples. Geophys J Int 136:637–650ADSCrossRefGoogle Scholar
  10. Curtis A (1999b) Optimal design of focussed experiments and surveys. Geophys J Int 139:205–215ADSCrossRefGoogle Scholar
  11. Curtis A (2004a) Theory of model-based geophysical survey and experimental design part A – linear problems. Lead Edge 23(10):997–1004CrossRefGoogle Scholar
  12. Curtis A (2004b) Theory of model-based geophysical survey and experimental design part B – nonlinear problems. Lead Edge 23(10):1112–1117CrossRefGoogle Scholar
  13. Curtis A, Michelini A, Leslie D, Lomax A (2004) A deterministic algorithm for experimental design applied to tomographic and microseismic monitoring surveys. Geophys J Int 157:595–606ADSCrossRefGoogle Scholar
  14. Dreger D, Uhrhammer R, Pasyanos M, Frank J, Romanowicz B (1998) Regional and far-regional earthquake locations and source parameters using sparse broadband networks: a test on the Ridgecrest sequence. Bull Seismol Soc Am 88:1353–1362Google Scholar
  15. Ekström G (2006) Global detection and location of seismic sources by using surface waves. Bull Seismol Soc Am 96:1201–1212. doi:10.1785/0120050175CrossRefGoogle Scholar
  16. Font Y, Kao H, Lallemand S, Liu CS, Chiao LY (2004) Hypocentral determination offshore eastern Taiwan using the Maximum Intersection method. Geophys J Int 158:655–675ADSCrossRefGoogle Scholar
  17. Geiger L (1912) Probability method for the determination of earthquake epicenters from the arrival time only (translated from Geiger’s 1910 German article). Bull St Louis Univ 8:56–71Google Scholar
  18. Gentili S, Michelini A (2006) Automatic picking of P and S phases using a neural tree. J Seismol 10:39–63. doi:10.1007/s10950-006-2296-6CrossRefGoogle Scholar
  19. Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley, ReadingzbMATHGoogle Scholar
  20. Hammersley JM, Handscomb DC (1967) Monte Carlo methods. Methuen, LondonGoogle Scholar
  21. Horiuchi S, Negishi H, Abe K, Kamimura A, Fujinawa Y (2005) An automatic processing system for broadcasting earthquake alarms. Bull Seismol Soc Am 95:708–718CrossRefGoogle Scholar
  22. Husen S, Smith RB (2004) Probabilistic earthquake relocation in three-dimensional velocity models for the Yellowstone National Park region, Wyoming. Bull Seismol Soc Am 94:880–896CrossRefGoogle Scholar
  23. Husen S, Kissling E, Deichmann N, Wiemer S, Giardini D, Baer M (2003) Probabilistic earthquake location in complex three-dimensional velocity models: application to Switzerland. J Geophys Res 108:2077–2102CrossRefGoogle Scholar
  24. Johnson CE, Lindh A, Hirshorn B (1994) Robust regional phase association. US Geol Surv Open-File Rep 94–621Google Scholar
  25. Kawakatsu H (1998) On the real-time monitoring of the long-period seismic wavefield. Bull Earthq Res Inst 73:267–274Google Scholar
  26. Kennett BLN (1992) Locating oceanic earthquakes – the influence of regional models and location criteria. Geophys J Int 108:848–854ADSCrossRefGoogle Scholar
  27. Kennett BLN (2006) Non-linear methods for event location in a global context. Phys Earth Planet Inter 158:46–54ADSCrossRefGoogle Scholar
  28. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680ADSCrossRefzbMATHMathSciNetGoogle Scholar
  29. Lahr JC (1999) Hypoellipse: a computer program for determining local earthquake hypocentral parameters, magnitude, and first-motion pattern (Y2K compliant version) 1999 Version 1.0. US Geological Survey Open-File Report, 99–23. http://jclahr.com/science/software/hypoellipse/hypoel/hypoman/hypomst_pdf.pdf
  30. Lepage GP (1978) A new algorithm for adaptive multi-dimensional integration. J Comput Phys 27:192–203ADSCrossRefzbMATHGoogle Scholar
  31. Lomax A (2005) A reanalysis of the hypocentral location and related observations for the great 1906 California Earthquake. Bull Seismol Soc Am 91:861–877CrossRefGoogle Scholar
  32. Lomax A (2008) Location of the focus and tectonics of the focal region of the California earthquake of 18 April 1906. Bull Seismol Soc Am 98:846–860CrossRefGoogle Scholar
  33. Lomax A, Curtis A (2001) Fast, probabilistic earthquake location in 3D models using oct-tree importance sampling. Geophys Res Abstr 3:955, www.alomax.net/nlloc/octtree Google Scholar
  34. Lomax A, Virieux J, Volant P, Berge C (2000) Probabilistic earthquake location in 3D and layered models: Introduction of a Metropolis-Gibbs method and comparison with linear locations. In: Thurber CH, Rabinowitz N (eds) Advances in seismic event location. Kluwer, AmsterdamGoogle Scholar
  35. Lomax A, Zollo A, Capuano P, Virieux J (2001) Precise, absolute earthquake location under Somma-Vesuvius volcano using a new 3D velocity model. Geophys J Int 146:313–331ADSCrossRefGoogle Scholar
  36. Maurer HR, Boerner DE (1998) Optimized and robust experimental design. Geophys J Int 132:458–468ADSCrossRefGoogle Scholar
  37. Milne J (1886) Earthquakes and other earth movements. Appelton, New YorkGoogle Scholar
  38. Mosegaard K, Tarantola A (1995) Monte Carlo sampling of solutions to inverse problems. J Geophys Res 100:12431–12447ADSCrossRefGoogle Scholar
  39. Moser TJ, van Eck T, Nolet G (1992a) Hypocenter determination in strongly heterogeneous earth models using the shortest path method. J Geophys Res 97:6563–6572ADSCrossRefGoogle Scholar
  40. Moser TJ, Nolet G, Snieder R (1992b) Ray bending revisited. Bull Seismol Soc Am 82:259–288Google Scholar
  41. Myers SC, Schultz CA (2000) Improving sparse network seismic location with Bayesian Kriging and teleseismically constrained calibration events. Bull Seismol Soc Am 90:199–211CrossRefGoogle Scholar
  42. Nicholson T, Gudmundsson Ó, Sambridge M (2004a) Constraints on earthquake epicentres independent of seismic velocity models. Geophys J Int 156:648–654ADSCrossRefGoogle Scholar
  43. Nicholson T, Sambridge M, Gudmundsson Ó (2004b) Three-dimensional empirical traveltimes: construction and applications. Geophys J Int 156:307–328ADSCrossRefGoogle Scholar
  44. Podvin P, Lecomte I (1991) Finite difference computations of traveltimes in very contrasted velocity models: a massively parallel approach and its associated tools. Geophys J Int 105:271–284ADSCrossRefGoogle Scholar
  45. Press WH, Flannery BP, Saul AT, Vetterling WT (1992) Numerical recipes, 2nd edn. Cambridge University Press, New YorkGoogle Scholar
  46. Presti D, Troise C, De Natale G (2004) Probabilistic location of seismic sequences in heterogeneous media. Bull Seismol Soc Am 94:2239–2253CrossRefGoogle Scholar
  47. Pujol J (2000) Joint event location – the JHD technique and applications to data from local seismic networks. In: Thurber CH, Rabinowitz N (eds) Advances in seismic event location. Kluwer, AmsterdamGoogle Scholar
  48. Rabinowitz N (2000) Hypocenter location using a constrained nonlinear simplex minimization method. In: Thurber CH, Rabinowitz N (eds) Advances in seismic event location. Kluwer, AmsterdamGoogle Scholar
  49. Rabinowitz N, Steinberg DM (2000) A statistical outlook on the problem of seismic network configuration. In: Thurber CH, Rabinowitz N (eds) Advances in seismic event location. Kluwer, AmsterdamGoogle Scholar
  50. Rawlinson N, Sambridge M (2004a) Wave front evolution in strongly heterogeneous layered media using the fast marching method. Geophys J Int 156:631–647ADSCrossRefGoogle Scholar
  51. Rawlinson N, Sambridge M (2004b) Multiple reflection and transmission phases in complex layered media using a multistage fast marching method. Geophysics 69:1338–1350ADSCrossRefGoogle Scholar
  52. Reid HF (1910) The mechanics of the earthquake. vol II of: The California earthquake of 18 April 1906. Report of the State Earthquake Investigation Commission, Lawson AC (Chairman). Carnegie Institution of Washington Publication, vol 87 (reprinted 1969)Google Scholar
  53. Rothman DH (1985) Nonlinear inversion, statistical mechanics, and residual statics estimation. Geophysics 50:2784–2796ADSCrossRefGoogle Scholar
  54. Rydelek P, Pujol J (2004) Real-time seismic warning with a two-station subarray. Bull Seismol Soc Am 94:1546–1550CrossRefGoogle Scholar
  55. Sambridge M (1998) Exploring multi-dimensional landscapes without a map. Inverse Probl 14:427–440ADSCrossRefzbMATHMathSciNetGoogle Scholar
  56. Sambridge M (1999a) Geophysical inversion with a neighbourhood algorithm, vol I. Searching a parameter space. Geophys J Int 138:479–494ADSCrossRefGoogle Scholar
  57. Sambridge M (1999b) Geophysical inversion with a neighbourhood algorithm, vol II. Appraising the ensemble. Geophys J Int 138:727–746ADSCrossRefGoogle Scholar
  58. Sambridge M (2003) Nonlinear inversion by direct search using the neighbourhood algorithm. In: Lee HK, Kanamori H, Jennings PC, Kisslinger C (eds) International handbook of earthquake and engineering seismology, vol 81B. Academic, Amsterdam, pp 1635–1637CrossRefGoogle Scholar
  59. Sambridge M, Drijkoningen G (1992) Genetic algorithms in seismic waveform inversion. Geophys J Int 109:323–342ADSCrossRefGoogle Scholar
  60. Sambridge M, Gallagher K (1993) Earthquake hypocenter location using genetic algorithms. Bull Seismol Soc Am 83:1467–1491Google Scholar
  61. Sambridge M, Kennett BLN (1986) A novel method of hypocentre location. Geophys J R Astron Soc 87:679–697CrossRefGoogle Scholar
  62. Sambridge M, Mosegaard K (2002) Monte Carlo methods in geophysical inverse problems. Rev Geophys 40:1009–1038ADSCrossRefGoogle Scholar
  63. Satriano C, Lomax A, Zollo A (2007a) Optimal, real-time earthquake location for early warning. In: Gasparini P, Gaetano M, Jochen Z (eds) Earthquake early warning systems. Springer, BerlinGoogle Scholar
  64. Satriano C, Lomax A, Zollo A (2007b) Real-time evolutionary earthquake location for seismic early warning. Bull Seismol Soc Am 98:1482–1494CrossRefGoogle Scholar
  65. Sen M, Stoffa PL (1995) Global optimization methods in geophysical inversion. Elsevier, Amsterdam, p 281zbMATHGoogle Scholar
  66. Sethian JA (1999) Level set methods and fast marching methods. Cambridge University Press, CambridgezbMATHGoogle Scholar
  67. Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423CrossRefzbMATHMathSciNetGoogle Scholar
  68. Shearer PM (1994) Global seismic event detection using a matched filter on long-period seismograms. J Geophys Res 99:13713–13735ADSCrossRefGoogle Scholar
  69. Shearer PM (1997) Improving local earthquake locations using the L1 norm and waveform cross correlation: application to the Whittier Narrows, California, aftershock sequence. J Geophys Res 102:8269–8283ADSCrossRefGoogle Scholar
  70. Steinberg DM, Rabinowitz N, Shimshoni Y, Mizrachi D (1995) Configuring a seismographic network for optimal monitoring of fault lines and multiple sources. Bull Seismol Soc Am 85:1847–1857Google Scholar
  71. Stummer P, Maurer HR, Green AG (2004) Experimental design: electrical resistivity data sets that provide optimum subsurface information. Geophysics 69:120–139ADSCrossRefGoogle Scholar
  72. Tarantola A (1987) Inverse problem theory: methods for data fitting and model parameter estimation. Elsevier, AmsterdamzbMATHGoogle Scholar
  73. Tarantola A (2005) Inverse problem theory and methods for model parameter estimation. SIAM, PhiladelphiaCrossRefzbMATHGoogle Scholar
  74. Tarantola A, Valette B (1982) Inverse problems = quest for information. J Geophys Res 50:159–170Google Scholar
  75. Thurber CH, Kissling E (2000) Advances in travel-time calculations for three-dimensional strucutres. In: Thurber CH, Rabinowitz N (eds) Advances in seismic event location. Kluwer, AmsterdamCrossRefGoogle Scholar
  76. Uhrhammer RA (1980) Analysis of small seismographic station networks. Bull Seismol Soc Am 70:1369–1379Google Scholar
  77. Um J, Thurber C (1987) A fast algorithm for two-point seismic ray tracing. Bull Seismol Soc Am 77:972–986Google Scholar
  78. van den Berg J, Curtis A, Trampert J (2003) Bayesian, nonlinear experimental design applied to simple, geophysical examples. Geophys J Int 55(2):411–421, Erratum (2005) Geophys J Int 161(2):265CrossRefGoogle Scholar
  79. Vidale JE (1988) Finite-difference calculation of travel times. Bull Seismol Soc Am 78:2062–2078Google Scholar
  80. Winterfors E, and Curtis A (2008) Numerical detection and reduction of non-uniqueness in nonlinear inverse problems. Inverse Problems, 24(2):1–14CrossRefMathSciNetGoogle Scholar
  81. Winterfors E, and Curtis A (2012) A Bifocal Measure of Expected Ambiguity in Bayesian Nonlinear Parameter Estimation. Technometrics, 54(2):179–190CrossRefMathSciNetGoogle Scholar
  82. Withers M, Aster R, Young C, Beiriger J, Harris M, Moore S, Trujillo J (1998) A comparison of select trigger algorithms for automated global seismic phase and event detection. Bull Seismol Soc Am 88:95–106Google Scholar
  83. Withers M, Aster R, Young C (1999) An automated local and regional seismic event detection and location system using waveform correlation. Bull Seismol Soc Am 8:657–669Google Scholar
  84. Wittlinger G, Herquel G, Nakache T (1993) Earthquake location in strongly heterogeneous media. Geophys J Int 115:759–777ADSCrossRefGoogle Scholar
  85. Zhou H (1994) Rapid 3-D hypocentral determination using a master station method. J Geophys Res 99:15439–15455ADSCrossRefGoogle Scholar

Books and Reviews

  1. Gasparini P, Gaetano M, Jochen Z (eds) (2007) Earthquake early warning systems. Springer, BerlinGoogle Scholar
  2. Lee WHK, Stewart SW (1981) Principles and applications of microearthquake networks. Academic, New YorkGoogle Scholar
  3. Lomax A, Satriano C, Vassallo M (2012) Automatic picker developments and optimization: FilterPicker—a robust, broadband picker for teal-time seismic monitoring and earthquake early warning. Seismol Res Lett 83:531–540CrossRefGoogle Scholar
  4. Myers SC, Johannesson G, Hanley W (2009) Incorporation of probabilistic seismic phase labels into a Bayesian multiple-event seismic locator. Geophys J Int 177:193–204ADSCrossRefGoogle Scholar
  5. Rosenberger A (2009) Arrival-time order location revisited. Bull Seismol Soc Am 99:2027–2034CrossRefGoogle Scholar
  6. Thurber CH (2011) Earthquakes: location techniques. In: Gupta H (ed) Encyclopedia of solid earth geophysics. Springer, DordrechtGoogle Scholar
  7. Thurber CH, Rabinowitz N (eds) (2000) Advances in seismic event location. Kluwer, AmsterdamzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Anthony Lomax
    • 1
  • Alberto Michelini
    • 2
  • Andrew Curtis
    • 3
  1. 1.ALomax ScientificMouans-SartouxFrance
  2. 2.Istituto Nazionale di Geofisica e VulcanologiaRomeItaly
  3. 3.ECOSSE (Edinburgh Collaborative of Subsurface Science and Engineering), Grant Institute of GeoSciencesThe University of EdinburghEdinburghUK