Journal of Seismology

, Volume 14, Issue 3, pp 565–600 | Cite as

DIRDOP: a directivity approach to determining the seismic rupture velocity vector

  • Bento Caldeira
  • Mourad Bezzeghoud
  • José F. Borges
Open Access
Original Article


Directivity effects are a characteristic of seismic source finiteness and are a consequence of the rupture spread in preferential directions. These effects are manifested through seismic spectral deviations as a function of the observation location. The directivity by Doppler effect method permits estimation of the directions and rupture velocities, beginning from the duration of common pulses, which are identified in waveforms or relative source time functions. The general model of directivity that supports the method presented here is a Doppler analysis based on a kinematic source model of rupture (Haskell, Bull Seismol Soc Am 54:1811–1841, 1964) and a structural medium with spherical symmetry. To evaluate its performance, we subjected the method to a series of tests with synthetic data obtained from ten typical seismic ruptures. The experimental conditions studied correspond with scenarios of simple and complex, unilaterally and bilaterally extended ruptures with different mechanisms and datasets with different levels of azimuthal coverage. The obtained results generally agree with the expected values. We also present four real case studies, applying the method to the following earthquakes: Arequipa, Peru (M w = 8.4, June 23, 2001); Denali, AK, USA (M w = 7.8; November 3, 2002); Zemmouri–Boumerdes, Algeria (M w = 6.8, May 21, 2003); and Sumatra, Indonesia (M w = 9.3, December 26, 2004). The results obtained from the dataset of the four earthquakes agreed, in general, with the values presented by other authors using different methods and data.


Directivity Doppler effect Seismic source Rupture parameters Inversion 


  1. Ammon CJ, Chen J, Hong-Kie T, Robinson D, Ni S, Hjorleifsdottir V, Kanamori H, Lay T, Das S, Helmberger D, Ichinose G, Polet J, Wald D (2005) Rupture process of the 2004 Sumatra–Andaman earthquake. Science 308:1133–1139. doi: 10.1126/science.1112260 CrossRefGoogle Scholar
  2. Aki K, Richards PG (1980) Quantitative seismology: theory and methods, vol 2. Freeman and Co., San FranciscoGoogle Scholar
  3. Ayadi A, et al (2003) Strong Algerian earthquake strikes near capital city. Eos Trans AGU 84(50):561–568. doi: 10.1029/2003EO500002 CrossRefGoogle Scholar
  4. Ayadi A, Dorbath C, Ousadou F, Maouche S, Chikh M, Bounif MA, Meghraoui M (2008) Zemmouri earthquake rupture zone (Mw 6.8, Algeria): aftershocks sequence relocation and 3-D velocity model. J Geophys Res 113:B09301. doi: 10.1029/2007JB005257 CrossRefGoogle Scholar
  5. Baumont D, Courboulex F, Scotti O, Melis NS, Stavrakakis G (2002) Slip distribution of the Mw 5.9, 1999 Athens earthquake inverted from regional seismological data. Geophys Res Lett 29(1720):15.1–15.4. doi: 10.1029/2001GL014261 Google Scholar
  6. Beck S, Silver P, Wallace T, James D (1995) Directivity analysis of the deep Bolivian earthquake of June 9, 1994. Geophys Res Lett 22:2257–2260CrossRefGoogle Scholar
  7. Belabbès S, Wicks CZ, Akir C, Meghraoui M (2009) Rupture parameters of the 2003 Zemmouri (Mw 6.8), Algeria, earthquake from joint inversion of interferometric synthetic aperture radar, coastal uplift, and GPS. J Geophys Res 114:B03406. doi: 10.1029/2008JB005912 CrossRefGoogle Scholar
  8. Benioff H (1955) Mechanism and strain characteristics of the white wolf fault as indicated by the aftershock sequence. Calif Div Mines Bull 171:199–202Google Scholar
  9. Ben-Menahem A (1961) Radiation of seismic surface-waves from finite moving sources. Bull Seismol Soc Am 51:401–435Google Scholar
  10. Ben-Menahem A, Singh SJ (1981) Seismic waves and sources. Springer, New YorkGoogle Scholar
  11. Beresnev IA (2003) Uncertainties in finite-fault slip inversions: to what extend to believe? (A critical review). Bull Seismol Soc Am 93:2445–2458CrossRefGoogle Scholar
  12. Bezzeghoud M, Buforn E (1999) Source parameters of 1992 Melilla (Spain, Mw = 4.8), 1994 Alhoceima (Morocco, Mw = 5.8) and 1994 Mascara (Algeria, Mw = 5.7) earthquakes and seismotectonic implications. Bull Seismol Soc Am 89(2):359–372Google Scholar
  13. Bilham R, Engdahl ER, Feldl N, Satyabala SP (2005) Partial and complete rupture of the Indo-Andaman plate boundary 1847–2004. Seismol Res Lett 76(3):299–311. doi: 10.1785/gssrl.76.3.299 CrossRefGoogle Scholar
  14. Bilek S, Ruff L (2002) Analysis of the 23 June 2001 Mw = 9.4 Peru underthrusting earthquake and its aftershocks. Geophys Res Lett 29(20):21.1–21.4. doi: 10.1029/2002GL015543 CrossRefGoogle Scholar
  15. Boore D, Joyner W (1978) The influence of rupture incoherence on seismic directivity. Bull Seismol Soc Am 68:283–300Google Scholar
  16. Borges J (2003) Fonte Sísmica Em Portugal-Algumas Implicações Na Geodinâmica Da Região Açores-Gibraltar. PhD thesis, Évora UniversityGoogle Scholar
  17. Bouchon M, Toksöz N, Karabulut H, Bouin M, Dietrich M, Aktar M, Edie M (2002) Space and time evolution of rupture and faulting during the 1999 Izmit (Turkey) earthquake. Bull Seismol Soc Am 92:256–266CrossRefGoogle Scholar
  18. Buforn E, Bezzeghoud M, Udias A, Pro C (2004) Seismic source in the Iberian–African plate boundary. Pageoph 161(3):623–646CrossRefGoogle Scholar
  19. Bullen KE, Bolt B (1985) Introduction to the theory of seismology. Cambridge University Press, CambridgeGoogle Scholar
  20. Caldeira B (2004) Caracterização espaço-temporal da fonte sísmica—Processos de rupture e directividade. PhD thesis, Évora UniversityGoogle Scholar
  21. Caldeira B, Bezzeghoud M, Borges J (2004) Contributo da directividade para a caracterização da Fonte do sismo de Boumerdes (Argélia) de 21 de Maio de 2003, Mw = 6.7. 4 Assembleia Luso-Espanhola de Geodesia e Geofísica, pp 251–252Google Scholar
  22. Cipar J (1979) Source processes of the Haicheng, China earthquake from observations of P and S waves. Bull Seismol Soc Am 69:1903–1916Google Scholar
  23. Das S, Kostrov BV (1990) Inversion for seismic slip rate history and distribution with stabilizing constraints application to the 1986 Andrean of islands earthquake. J Geophys Res 95(B5):6899–6913CrossRefGoogle Scholar
  24. Day S (1982) Three dimensional simulation of spontaneous rupture: the effect of nonuniform pre-stress. Bull Seismol Soc Am 72:1881–1901Google Scholar
  25. Delouis B, Vallée M, Meghraoui M, Calais E, Mahsas S, Briole P, Benhamouda F, Yelles K (2004) Slip distribution of the 2003 Boumerdes–Zemmouri earthquake, Algeria, from teleseismic, GPS, and coastal uplift data. Geophys Res Lett 31:L18607. doi: 10.1029/2004GL020687 CrossRefGoogle Scholar
  26. Douglas A, Hudson J, Pearce R (1988) Directivity and the Doppler effect. Bull Seismol Soc Am 78:1367–1372Google Scholar
  27. Dunham M, Archuleta RJ (2004) Evidence for a supershear transient during the 2002 Denali fault earthquake. Bull Seismol Soc Am 94:S256–S268CrossRefGoogle Scholar
  28. Eberhart-Phillips D, Haeussler P et al (2003) The 2002 Denali fault earthquake, Alaska: a large magnitude, slip-partitioned event. Science 300:1113–1118. doi: 10.1126/science.1082703 CrossRefGoogle Scholar
  29. Frankel A (2004) Rupture process of the M 7.9 Denali fault, Alaska, earthquake: subevents, directivity, and scaling of high-frequency ground motions. Bull Seismol Soc Am 94:S234–S255CrossRefGoogle Scholar
  30. French AP (1974) Vibrations and waves. Norton, New YorkGoogle Scholar
  31. Fukao Y (1972) Source process of a large deep-focus earthquake and its tectonic implications—the western Brazil earthquake of 1963. Phys Earth Planet Inter 5:61–76CrossRefGoogle Scholar
  32. Grach SM, Komrakov GP, Yurishchev MA, Thid B, Leyser TB, Carozzi T (1997) Multifrequency Doppler radar observations of electron gyroharmonic effects during electromagnetic pumping of the ionosphere. Phys Rev Lett 78(5):883–886. doi: 10.1103/PhysRevLett78.883 CrossRefGoogle Scholar
  33. Haskell NA (1964) Total energy and energy spectral density of elastic wave radiation from propagating faults. Bull Seismol Soc Am 54:1811–1841Google Scholar
  34. Hoshiba M (2003) Fluctuation of wave amplitude even when assuming convolution of source, path and site factors—effect of rupture directivity. Phys Earth Planet Inter 137:45–65CrossRefGoogle Scholar
  35. Ihmlé PF (1998) On the interpretation of subevents in teleseismic waveforms: the 1994 Bolivia deep earthquake revisited. J Geophys Res 103(B8):17,919–17,932CrossRefGoogle Scholar
  36. Ishii M, Shearer P, Houston H, Vidale J (2005) Extend, duration and speed of the 2004 Sumatra–Andaman earthquake imaged by the Hi-Net array. Nature 435:933–936. doi: 10.1038/nature03675 Google Scholar
  37. Kasahara K (1981) Earthquakes mechanics. Cambridge Univ. Press, CambridgeGoogle Scholar
  38. Kennett B, Engdahl E (1991) Traveltimes for global earthquake location and phase identification. Geophys J Int 105:429–465CrossRefGoogle Scholar
  39. Kikuchi M, Kanamori H (1991) Inversion of complex body waves—III. Bull Seismol Soc Am 81:2335–2350Google Scholar
  40. Kikuchi M, Yamanaka Y (2002) Source rupture processes of the central Alaska earthquake of Nov. 3, 2002, inferred from teleseismic body waves, EIC Seismological Note. No. 129, Nov. 4Google Scholar
  41. Kraeva N (2004) Tikhonov’s regularization for deconvolution in the empirical green function method and vertical directivity effect. Tectonophysics 383:29–44CrossRefGoogle Scholar
  42. Krüger F, Ohrnberger M (2005a) Tracking the rupture of the Mw = 9.3 Sumatra earthquake over 1,150 km at teleseismic distance. Nature 435:937–939. doi: 10.1038/nature03696 Google Scholar
  43. Krüger F, Ohrnberger M (2005b) Spatio-temporal source characteristics of the 26 December 2004 Sumatra earthquake as imaged by teleseismic broadband arrays. Geophys Res Lett 32:L24312. doi: 10.1029/2005GL023939 CrossRefGoogle Scholar
  44. Lambotte S, Rivera L, Hinderer J (2007) Constraining the overall kinematics of the 2004 Sumatra and the 2005 Nias earthquakes using the earth’s gravest free oscillations. Bull Seismol Soc Am 97(1A):S128-S138. doi: 10.1785/0120050621 CrossRefGoogle Scholar
  45. Lay T, Kanamori H, Ammon C, Nettles M, Wald SN, Aster RC, Beck S, Bilek S, Brudzinski MR, ButlerR, DeShon HR, Ekstrom G, Satake K, Sipkin S (2005) The great Sumatra–Andaman earthquake of 26 December 2004. Science 308(5725):1127–1133. doi: 10.1126/science.1112250 CrossRefGoogle Scholar
  46. Le Pichon A, Guilbert J, Vega A, Garce’s M, Brachet N (2002) Ground-coupled air waves and diffracted infrasound from the Arequipa earthquake of June 23, 2001. Geophys Res Lett 29(18):33.1–33.4. doi: 10.1029/2002GL015052 Google Scholar
  47. Liao BY, Huang H (2008) Rupture process of the 2002 Mw 7:9 Denali earthquake, Alaska, using a newly devised hybrid blind deconvolution method. Bull Seismol Soc Am 98:162–179. doi: 10.1785/0120050065 CrossRefGoogle Scholar
  48. Loupas T, Gill RW (1994) Multifrequency Doppler: improving the quality of spectral estimation by making full use of the information present in scattered RF echoes. Ultrason Ferroelectr Freq Control 41(4):522–531. doi: 10.1109/58.294114 CrossRefGoogle Scholar
  49. Menke W (1984) Geophysical data analysis: discrete inverse theory. Academic, OrlandoGoogle Scholar
  50. Ni S, Hiro K, Don H (2005) Seismology: energy radiation from the Sumatra earthquake. Nature 434:582. doi: 10.1038/434582a CrossRefGoogle Scholar
  51. Ozacar AA, Beck SL (2004) The 2002 Denali fault and 2001 Kunlun fault earthquakes: complex rupture processes of two large strike-slip events. Bull Seismol Soc Am 94(6B):S278–292. doi: 10.1785/0120040604 CrossRefGoogle Scholar
  52. Pritchard M, Norabuena E, Ji C, Boroschek R, Comte D, Simons M, Dixon TH, Rosen PA (2007) Geodetic, teleseismic, and strong motion constraints on slip from recent southern Peru subduction zone earthquakes. J Geophys Res 112:B03307. doi: 10.1029/2006JB004294 CrossRefGoogle Scholar
  53. Pro MC (2002) Estudio del efecto de directividad en la forma de ondas. PhD thesis, Universidad Compultense de MadridGoogle Scholar
  54. Pro C, Buforn E, Udías A (2007) Rupture length and velocity for earthquakes in the Mid-AtlanticRidge from directivity effect in body and surface waves. Tectonophysics V 433:65–79CrossRefGoogle Scholar
  55. Rao IS, Anandan VQ, Kumar MS (2009) Multifrequency decoding of a phased array Doppler sodar. J Atmos Ocean Technol 26(4):759–768CrossRefGoogle Scholar
  56. Rhie J, Dreger D, Bürgmann R, Romanowicz B (2007) Slip of the 2004 Sumatra–Andaman earthquake from joint inversion of long period global seismic waveforms and GPS static offsets. Bull Seismol Soc Am 97(1A):S115–S127CrossRefGoogle Scholar
  57. Russell D, Brucher R (2002) Multifrequency Doppler discriminates between baseous and solid microemboli. Ann Thorac Surg 73(1):S369CrossRefGoogle Scholar
  58. Robinson DP, Das S, Watts AB (2006) Earthquake rupture stalled by a subducting fracture zone. Science 312:1203–1205CrossRefGoogle Scholar
  59. Semmane F, Campillo M, Cotton F (2005) Fault location and source process of the Boumerdes, Algeria, earthquake inferred from geodetic and strong motion data. Geophys Res Lett 32:L01305. doi: 10.1029/2004GL021268 CrossRefGoogle Scholar
  60. Sekiguchi H, Iwata T (2002) Rupture process of the 1999 Kocaeli, Turkey, earthquake estimated from strong-motion waveforms. Bull Seismol Soc Am 92:300–311CrossRefGoogle Scholar
  61. Tavera H, Buforn E, Bernal I, Antayhua Y, Vilacapoma L (2002) The Arequipa (Peru) earthquake of June 23, 2001. J Seismol 6(2):279–283CrossRefGoogle Scholar
  62. Tibi R, Estabrook C, Bock G (1999) The 1996 June 17 Flores sea and 1994 March 9 Fiji–Tonga earthquakes: source processes and deep earthquake mechanisms. Geophys J Int 138:625–642CrossRefGoogle Scholar
  63. Tregoning P, Brunner FK, Bock YS, Puntodewo SO, McCaffrey R, Genrich JF, Calais E, Rais J, Subarya C (1994) First geodetic measurement of convergence across the Java Trench. Geophys Res Lett 21:2135–2139CrossRefGoogle Scholar
  64. Tumarkin A, Archuleta R (1994) Empirical ground motion prediction. Ann Geofis XXXVII:1691–1720Google Scholar
  65. Udias A (1971) Source parameters of earthquakes from spectra of Rayleigh waves. Geophys J R Astron Soc 22:253–276Google Scholar
  66. Vallée M (2007) Rupture properties of the giant Sumatra earthquake imaged by empirical green function analysis. Bull Seismol Soc Am 97(1A):S103–S114CrossRefGoogle Scholar
  67. Velasco A, Ammon CJ, Farrell J, Pankow K (2004) Rupture directivity of the 3 November 2002 Denalifault earthquake determined from surface waves. Bull Seismol Soc Am 94(6B):S293–S299. doi: 10.1785/0120040624 CrossRefGoogle Scholar
  68. Vigny C, Simons W, Abu S, Bamphenyu R, Satirapod C, Choosakul N, Subarya C, Socquet A, Omar K, Abidin HZ, Ambrosius BA (2005) Insight into the 2004 Sumatra–Andaman earthquake from GPS measurements in southeast Asia. Nature 436:201–206CrossRefGoogle Scholar
  69. Yagi Y (2003) Source process of large and significant earthquakes in 2003. Bull Int Inst Seismol Earthq Eng v.37:145–153. Google Scholar

Copyright information

© The Author(s) 2009

Authors and Affiliations

  • Bento Caldeira
    • 1
  • Mourad Bezzeghoud
    • 1
  • José F. Borges
    • 1
  1. 1.Centro de Geofísica de Évora (CGE) e Departamento de FísicaUniversidade de ÉvoraÉvoraPortugal

Personalised recommendations