Journal of Seismology

, Volume 15, Issue 1, pp 147–164 | Cite as

Rapid directivity detection by azimuthal amplitude spectra inversion

  • Simone CescaEmail author
  • Sebastian Heimann
  • Torsten Dahm
Original Article


An early detection of the presence of rupture directivity plays a major role in the correct estimation of ground motions and risks associated to the earthquake occurrence. We present here a simple method for a fast detection of rupture directivity, which may be additionally used to discriminate fault and auxiliary planes and have first estimations of important kinematic source parameters, such as rupture length and rupture time. Our method is based on the inversion of amplitude spectra from P-wave seismograms to derive the apparent duration at each station and on the successive modelling of its azimuthal behaviour. Synthetic waveforms are built assuming a spatial point source approximation, and the finite apparent duration of the spatial point source is interpreted in terms of rupture directivity. Since synthetic seismograms for a point source are calculated very quickly, the presence of directivity may be detected within few seconds, once a focal mechanism has been derived. The method is here first tested using synthetic datasets, both for linear and planar sources, and then successfully applied to recent Mw 6.2–6.8 shallow earthquakes in Peloponnese, Greece. The method is suitable for automated application and may be used to improve kinematic waveform modelling approaches.


Directivity Earthquake source Kinematic model Amplitude spectra 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Beck SL, Silver P, Wallace TC, James D (1995) Directivity analysis of the deep Bolivian earthquake of June 9, 1994. Geophys Res Lett 22:2257–2260CrossRefGoogle Scholar
  2. Ben-Menahem A (1961) Radiation of seismic surface waves from finite moving sources. Bull Seismol Soc Am 51:401–453Google Scholar
  3. Ben-Menahem A, Singh SJ (1981) Seismic waves and sources. Springer, New YorkGoogle Scholar
  4. Bernard P, Madariaga R (1984) A new asymptotic method for the modelling of near-field accelerograms. Bull Seismol Soc Am 74:539–557Google Scholar
  5. Beroza GC, Spudich P (1988) Linearized inversion for fault rupture behaviour: application to the 1984 Morgan Hill, California, earthquake. J Geophys Res 93:6275–6296CrossRefGoogle Scholar
  6. Boore D, Joyner W (1978) The influence of rupture incoherence on seismic directivity. Bull Seismol Soc Am 68:283–300Google Scholar
  7. Brüstle W, Müller G (1987) Stopping phases in seismograms and the spatiotemporal extent of earthquakes. Bull Seismol Soc Am 1:47–68Google Scholar
  8. Caldeira B, Bezzeghoud M, Borges JF (2009) DIRDOP: a directivity approach to determining the seismic rupture velocity vector. J Seismol 14:565–600. doi: 10.1007/s10950-009-9183-x CrossRefGoogle Scholar
  9. Cassidy JF (1995) Rupture directivity and slip distribution for the Ms 6.8 earthquake of 6 April 1992, Offshore British Columbia: an application of the empirical Green’s function method using surface waves. Bull Seismol Soc Am 85:736–746Google Scholar
  10. Cesca S, Heimann S, Stammler K, Dahm T (2010) Automated procedure for point and kinematic source inversion at regional distances. J Geophys Res 115:B06304. doi: 10.1029/2009JB006450 CrossRefGoogle Scholar
  11. Chouliaras G (2009) Seismicity anomalies prior to 8 June 2008, Mw 6.4 earthquake in Western Greece. Nat Hazards Earth Syst Sci 9:327–335CrossRefGoogle Scholar
  12. Dahm T, Krüger F (1999) Higher-degree moment tensor inversion using far-field broad-band recordings: theory and evaluation of the method with application to the 1994 Bolivia deep earthquake. Geophys J Int 137:35–50CrossRefGoogle Scholar
  13. Dahm T, Kruger F, Stammler K, Klinge K, Kind R, Wylegalla K, Grasso JR (2007) The 2004 Mw 4.4 Rotenburg, Northern Germany, Earthquake and its possible relationship with Gas Recovery. Bull Seismol Soc Am 97:691–704CrossRefGoogle Scholar
  14. Dreger D, Kaverina A (2000) Seismic remote sensing for the earthquake source process and near-source strong shaking: a case study of the October 16, 1999 Hector mine earthquake. Geophys Res Lett 27:1941–1944CrossRefGoogle Scholar
  15. Dziewonski AM, Anderson DL (1981) Preliminary reference earth model. Phys Earth Planet Int 25:297–356CrossRefGoogle Scholar
  16. Eshghi S, Zare M (2003) Reconnaisance report on 26 December 2003 Bam earthquake. International Institute of Earthquake Engineering (IIEES)Google Scholar
  17. Gallovic F, Zahradnik J, Krizova D, Plicka V, Sokos E, Serpetsidaki A, Tselentis GA (2009) From earthquake centroid to spatial-temporal rupture evolution: Mw 6.3 Movri Mountain earthquake, June 8, 2008, Greece. Geophys Res Lett 36:L21310. doi: 10.1029/2009GL040283 CrossRefGoogle Scholar
  18. Ganas A, Serpelloni E, Drakatos G, Kolligri M, Adamis I, Tsimi C, Batsi E (2009) The Mw 6.4 SW-Achaia (western Greece) earthquake of 8 June 2008: seismological, field, GPS, observations and stress modeling. J Earthq Eng 8:1101–1124Google Scholar
  19. Hartzell SH (1978) Earthquake aftershocks as Green’s functions. Geophys Res Lett 5:1–4CrossRefGoogle Scholar
  20. Hartzell S, Heaton DV (1983) Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of the 1979 Imperial Valley, California, earthquake. Bull Seismol Soc Am 83:1553–1583Google Scholar
  21. Hartzell S, Helmberger DV (1982) Strong-motion modelling of the Imperial Valley earthquake of 1979. Bull Seismol Soc Am 72:571–596Google Scholar
  22. Haskell NA (1964) Total energy and energy spectral density of elastic wave radiation from propagating faults. Bull Seismol Soc Am 54:1811–1841Google Scholar
  23. Heimann S (2010) A robust method to estimate kinematic earthquake source parameters. PhD Thesis, University of Hamburg, Germany, pp 145Google Scholar
  24. Imanishi K, Takeo M (1998) Estimates of fault dimensions for small earthquakes using stopping phases. Geophys Res Lett 25:2897–2900CrossRefGoogle Scholar
  25. Imanishi K, Takeo M (2002) An inversion method to analyze rupture process of small earthquakes using stopping phases. J Geophys Res 107:ESE2.1–ESE2.16. doi: 10.1029/2001JB000201 CrossRefGoogle Scholar
  26. Kostantinou KI, Melis NS, Lee SJ, Evangelidis CP, Boukouras K (2009) Rupture process and aftershock relocation of the 8 June 2008 Mw 6.4 earthquake in Northwest Peloponnese, Western Greece. Bull Seismol Soc Am 99:3374–3389CrossRefGoogle Scholar
  27. Li Y, Toksöz MN (1993) Study of the source process of the 1992 Columbia Ms = 7.3 earthquake with the empirical Green’s function method. Geophys Res Lett 20:1087–1090CrossRefGoogle Scholar
  28. Madariaga R (1977) High-frequency radiation from crack (stress drop) models of earthquake faulting. Geophys J R Astron Soc 51:625–651Google Scholar
  29. Madariaga R (1983) High-frequency radiation from dynamic earthquake fault models. Ann Geophys 1:17–23Google Scholar
  30. McGuire JJ, Zhao L, Jordan TH (2001) Teleseismic inversion for the second-degree moments of earthquake space-time distributions. Geophys J Int 145:661–678CrossRefGoogle Scholar
  31. McGuire JJ, Zhao L, Jordan TH (2002) Predominance of unilateral rupture for a global catalog of large earthquakes. Bull Seismol Soc Am 92:3309–3317CrossRefGoogle Scholar
  32. Müller CS (1985) Source pulse enhancement by deconvolution of empirical Green’s functions. Geophys Res Lett 12:33–36CrossRefGoogle Scholar
  33. Nadim F, Moghtaderi-Zadeh M, Lindholm C, Andresen A, Remseth S, Bolourchi MJ, Mokhtari M, Tvedt T (2004) The Bam earthquake of 26 December 2003. Bull Earthquake Eng 2:119–153CrossRefGoogle Scholar
  34. Nielsen S, Madariaga R (2003) On the self-healing fracture mode. Bull Seismol Soc Am 93:2375–2388CrossRefGoogle Scholar
  35. Olson AJ, Apsel RJ (1982) Finite faults and inverse theory with applications to the 1979 Imperial Valley earthquake. Bull Seismol Soc Am 72:1969–2001Google Scholar
  36. Pro C, Buforn E, Udías A (2007) Rupture length and velocity for earthquakes in the Mid-Atlantic Ridge from directivity effects in body and surface waves. Tectonophysics 433:65–79CrossRefGoogle Scholar
  37. Roumelioti Z, Benetatos C, Kiratzi A (2009) the 14 February 2008 earthquake (M6.7) sequence offshore south Peloponnese (Greece): source models of the three strongest events. Tectonophysics 471:272–284CrossRefGoogle Scholar
  38. Selby N, Eshun E, Patton H, Douglas A (2005) Unusual long-period Rayleigh wave from a vertical dip-slip source: the 7 May 2001, North Sea earthquake. J Geophys Res 110:B10304. doi: 10.1029/2005JB003721 CrossRefGoogle Scholar
  39. Sokos E, Serpetsidaki A, Tselentis GA, Zahradnik J (2008) Quick assessment of the fault plane, for the recent strike-slip event in the North-Western Peloponnese, Greece, (8 June 2008, Mw 6.3). EMSC-CSEM ReportGoogle Scholar
  40. Spudich P, Frazer LN (1984) Use of ray theory to calculate high-frequency radiation from earthquake sources having spatially variable rupture velocity and stress drop. Bull Seismol Soc Am 74:2061–2082Google Scholar
  41. Underhill JR (1999) Late Cenozoic deformation of the Hellenide forelands, Western Greece. Geol Soc Am Bull 101:613–634CrossRefGoogle Scholar
  42. Vallée M (2007) Rupture properties of the giant sumatra earthquake imaged by empirical Green’s function analysis. Bull Seismol Soc Am 97:103–114CrossRefGoogle Scholar
  43. Vallée M, Bouchon M (2004) Imaging coseismic rupture in the far field by slip patches. Geophys J Int 156:615–630CrossRefGoogle Scholar
  44. Velasco AA, Ammon CJ, Lay T (1994) Empirical green function deconvolution of broadband surface waves: Rupture directivity of the 1992 Landers, California (Mw = 7.3), earthquake. Bull Seismol Soc Am 84:735–750Google Scholar
  45. Velasco AA, Ammon CJ, Farrell J, Pankow K (2004) Rupture directivity of the 3 November 2002 denali fault earthquake determined from surface waves. Bull Seismol Soc Am 94:293–299CrossRefGoogle Scholar
  46. Warren LM, Shearer PM (2006) Systematic determination of earthquake rupture directivity and fault planes from analysis of long-period P-wave spectra. Geophys J Int 164:46–62CrossRefGoogle Scholar
  47. Wells DL, Coppersmith KJ (1994) New empirical relations among magnitude, rupture length, rupture width, rupture area and surface displacements. Bull Seismol Soc Am 84:974–1002Google Scholar
  48. Wessel P, Smith WHF (1998) New improved version of the generic mapping tools released. Eos Trans AGU 79:579CrossRefGoogle Scholar
  49. Zahradnik J, Gallovic F, Sokos E, Serpetsidaki A, Tselentis GA (2008) Quick fault-plane identification by geometrical method: application to Mw 6.2 Leonidio earthquake, January 6, 2008, Greece. Seismol Res Lett 79:653–662CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Institut für GeophysikUniversität HamburgHamburgGermany

Personalised recommendations