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Earthquake Science

, Volume 23, Issue 4, pp 309–323 | Cite as

Seismicity pattern of the Betic Cordillera (Southern Spain) derived from the fractal properties of earthquakes and faults

  • J Henares RomeroEmail author
  • C López Casado
  • J Badal
  • J A Peláez
Article

Abstract

Several studies on earthquake occurrence and associated faulting have demonstrated that both phenomena have a scale-invariant behavior which can be analyzed by means of a set of non-integer dimensions (D q ) describing their fractal properties and the calculation of multi-fractal spectra. It is the case that the behavior of these spectra is asymptotic at the ends of the variation interval of q, which is a real number that enters into the definition of the partition function of the dataset. The difference between the extreme values, called multi-fractal spectrum slope, is used to investigate the heterogeneity of the spatial distribution of earthquakes and fault systems. In this paper we focus on the Betic Cordillera, southeastern Spain, which is commonly considered the contact between the Eurasian and African plates and has an important seismic activity in the context of the Iberian Peninsula. Some of the most conspicuous Iberian earthquakes, such as the 1829 mb6.3 Torrevieja and the 1884 mb6.1 Alhama de Granada earthquakes occurred in this mountain range and both reached intensity X. The present work implies a new analysis based on the slope of multi-fractal spectra and referred to the historical seismicity of the region, specifically b-value (frequency distribution of earthquakes respect to magnitude), epicentral location, seismic energy and faulting. On this basis we propose a seismotectonic zonation that is contrasted with the stress state and the geodynamical evolution of the Betic Cordillera.

Key words

fractal dimensions multi-fractal spectrum slope seismotectonic Betic Cordillera 

CLC number

P315.5 

References

  1. Aki K (1965). Maximum likelihood estimate of b in the formula logN=a-bM and its confidence limits. Bull Earthq Res Inst43: 237–239.Google Scholar
  2. Alfaro P, Rueda J, Delgado J, Estévez A, López Casado C and Giner J (1999). Seismotectonics of the lower Segura basin (Betic Cordillera). Proceedings of the 1st Hispano-Portuguese Assembly of Geodesy and Geophysics. University of Almeria and National Geographic Institute, Madrid (in Spanish).Google Scholar
  3. Bhattacharya P M, Majumdar R K and Kayal J R (2002). Fractal dimension and b-value mapping in northeast India. Current Science82(12): 1486–1491.Google Scholar
  4. Bhattacharya P M and Kayal J R (2003). Mapping the b-value and its correlation with the fractal dimension in the northeast region of India. J Geol Soc India62: 680–695.Google Scholar
  5. Bezzeghoud M and Buforn E (1999). Source parameters of the 1992 Melilla (Spain, MW=4.8), 1994 Alhoceima (Morocco, MW=5.8) and 1994 Mascara (Algeria, MW=4.7) earthquakes and seismotectonic implications. Bull Seism Soc Amer89(2): 359–372.Google Scholar
  6. Buforn E, Udías A and Mézcua J (1988a). Seismicity and focal mechanisms in South Spain. Bull Seism Soc Amer78(6): 2008–2024.Google Scholar
  7. Buforn E, Udías A and Colombás M A (1988b). Seismicity, source mechanisms and tectonics of the Azores-Gibraltar plate boundary. Tectonophysics152(1–2): 89–118.CrossRefGoogle Scholar
  8. Buforn E, Sanz de Galdeano C and Udías A (1995). Seismotectonics of the Ibero-Maghrebian region. Tectonophysics248(3–4): 247–261.CrossRefGoogle Scholar
  9. Carpinteri A, Chiaia B and Invernizzi S (2002). Applications of fractal geometry and renormalization group to the Italian seismic activity. Chaos Solitons and Fractals14(6): 917–928.CrossRefGoogle Scholar
  10. Coca P and Buforn E (1994). Focal mechanisms in South Spain: Period 1965–1985. Estudios Geológicos50: 33–45 (in Spanish).CrossRefGoogle Scholar
  11. Cortés A L and Maestro A (1998). Recent intraplate stress field in the eastern Duero Basin (North Spain). Terra Nova10(5): 287–294.CrossRefGoogle Scholar
  12. Dimri V P (2000). Application of fractals in seismology with reference to Koyna earthquakes. In: Dimri V P ed. Application of Fractals in Earth Sciences. A.A. Balkema, USA/Oxford, and IBH Pub. Co., New Delhi, pp. 139–147.Google Scholar
  13. Falconer K J (1990). Fractal Geometry: Mathematical Foundations and Applications. John Wiley & Sons, England, pp. 366.Google Scholar
  14. Galindo-Zaldívar J, González Lodeiro F and Jabaloy A (1993). Stress and palaeostress in the Betic-Rif cordilleras (Miocene to the present). Tectonophysics227(1–4): 105–126.CrossRefGoogle Scholar
  15. Giaquinta A, Boccaletti S, Boccaletti M, Piccardi L and Arecchi F T (1999). Investigating the fractal properties of geological fault systems: The main Ethiopian Rift case. Geophys Res Lett26(11): 1 633–1 636.CrossRefGoogle Scholar
  16. Grassberger P (1983). Generalized dimensions of strange attractors. Phys Lett A97(6): 227–231.CrossRefGoogle Scholar
  17. Grimison N and Chen W (1986). The Azores-Gibraltar plate boundary: Focal mechanisms, depths of earthquakes and their tectonic implications. J Geophys Res91(B2): 2029–2047.CrossRefGoogle Scholar
  18. Gutenberg B and Richter C F (1944). Frequency of earthquakes in California. Bull Seism Soc Amer34(4): 185–188.Google Scholar
  19. Gutenberg B and Richter C F (1956). Earthquake magnitude, intensity, energy, and acceleration. Bull Seism Soc Amer46(2): 105–145.Google Scholar
  20. Gutscher M A, Malod J, Rehault J P, Contrucci I, Klingelhoefer F, Mendes-Victor L and Spackman W (2002). Evidence for active subduction beneath Gibraltar. Geology30(12): 1 071–1 074.CrossRefGoogle Scholar
  21. Hatzfeld D and Boloix M (1976). Preliminary results of deep seismic profiles in the Alboran Sea. Meeting on Geodynamics of the Betic Cordillera and Alboran Sea, Granada, Spain, pp. 19–23 (in Spanish).Google Scholar
  22. Henares Romero J (2009). Multi-fractal characterization of the seismotectonic of the Betic Cordillera. [PhD Dissertation]. University of Granada, Spain, pp. 215 (in Spanish).Google Scholar
  23. Henares J, López Casado C, Sanz de Galdeano C, Delgado J and Peláez J A (2003). Stress fields in the Ibero-Maghrebian region. J Seism7(1): 65–78.CrossRefGoogle Scholar
  24. Hentschel H and Procaccia I (1983). The infinite number of generalized dimensions of fractals and strange attractors. Physica D8(3): 435–444.CrossRefGoogle Scholar
  25. Hernández J, Larouzière F D, Bolze J and Bordet P (1987). The Neogene magmatism of the Betic-Rif complex and the slipping corridor of Alboran. Bull Soc Géol Fr3(2): 257–267 (in French).Google Scholar
  26. Herráiz M, De Vicente G, Lindo Ñaupari R, Giner J, Simón J L, González Casado J M, Vadillo O, Rodríguez-Pascua M A, Cicuéndez J I, Casas A, Cabañas L, Rincón P, Cortés A L, Ramírez M and Lucini M (2000). The recent (upper Miocene to Quaternary) and present tectonic stress distributions in the Iberian Peninsula. Tectonics19(4): 762–786.CrossRefGoogle Scholar
  27. Hirabayashi T, Ito K and Yoshii T (1992). Multi-fractal analysis of earthquakes. Pageoph138(4): 591–610.CrossRefGoogle Scholar
  28. Jolivet L, Faccenna C and Piromallo C (2009). From mantle to crust: Stretching the Mediterranean. Earth Planet Sci Lett285(1–2): 198–209.CrossRefGoogle Scholar
  29. Kagan Y Y and Knopoff L (1980). Spatial distribution of earthquakes: The two point correlation function. J Geophys R Astron Soc62(2): 303–320.CrossRefGoogle Scholar
  30. Li D, Zheng Z and Wang B (1994). Research into the multi-fractal earthquake spatial distribution. Tectonophysics233(1–2): 91–97.CrossRefGoogle Scholar
  31. López Casado C, Sanz de Galdeano C, Delgado J and Peinado M A (1995). The b parameter in the Betic Cordillera, Rif and nearby sectors: Relations with the tectonics of the region. Tectonophysics248(3–4): 277–292.CrossRefGoogle Scholar
  32. López Casado C, Molina S, Giner J and Delgado J (2000). Magnitude-intensity relationships in the Ibero-Maghrebian region. Natural Hazards22(3): 269–294.CrossRefGoogle Scholar
  33. L’opez Casado C, Sanz de Galdeano C, Molina Palacios S and Henares Romero J (2001). The structure of the Alboran Sea: An interpretation from seis mological and geological data. Tectonophysics338(2): 79–95.CrossRefGoogle Scholar
  34. Main I G, Meredith P G, Sammonds P R and Jones C (1990). Influence of fractal flaw distributions of rock deformation in the brittle field. In: Knipe R J and Rutter E H eds. Deformation Mechanisms, Rheology and Tectonics. Geol Soc London Special Publication 54: 81–96.Google Scholar
  35. Mandelbrot B B (1982). The Fractal Geometry of Nature. Freeman, San Francisco, pp. 468.Google Scholar
  36. Mandelbrot B B (1989). Multi-fractal measures, especially for the geophysicist. Pageoph131(1–2): 5–42.CrossRefGoogle Scholar
  37. Martínez Solares J M (2003). Historical seismicity of the Iberian Peninsula. Física de la Tierra15: 13–28 (in Spanish).Google Scholar
  38. Martínez López F, Cabrerizo Vilchez M A and Hidalgo Álvarez R (2001). Multi-fractal behaviour of the estimated natural measure for colloidal cluster-cluster aggregation in 2-D. Physica A291(1–4): 1–12.CrossRefGoogle Scholar
  39. Medina F and Cherkaoui T E (1991). Focal mechanisms of the Atlas earthquakes and tectonic implications. Geologische Rundschau80(3): 639–648.CrossRefGoogle Scholar
  40. Mézcua J and Martínez Solares J M (1983). Seismicity of the Ibero-Maghrebian area, National Geographic Institute, Madrid, Publ. 203, pp. 300 (in Spanish).Google Scholar
  41. Mézcua J and Rueda J (1997). Seismological evidence for a delamination process in the lithosphere under the Alboran Sea. Geophys J Int129(1): 256–264.Google Scholar
  42. Mézcua J, Rueda J and García Blanco R M (2004). Reevaluation of historic earthquakes in Spain. Seism Res Lett75(1): 75–81.CrossRefGoogle Scholar
  43. Molina S (1998). Seismotrctonics and seismic hazard of the contact area between Iberia and Africa. [PhD Dissertation]. University of Granada, Spain, pp. 288 (in Spanish).Google Scholar
  44. M.O.P.T. (1992). Seismotrctonic Analysis of the Iberian Peninsula, Balearic and Canary Islands. Ed. National Geographic Institute, Madrid, Tech. Publ. 26 (in Spanish).Google Scholar
  45. Morales J, Serrano I, Jabaloy A, Galindo-Zaldívar J, Zhao D, Torcal J, Vidal F and González Lodeiro F (1999). Active continental subduction beneath the Betic Cordillera and the Alboran Sea. Geology27(8): 735–738.CrossRefGoogle Scholar
  46. Moreira V S (1985). Seismotectonics of Portugal and its adjacent area in the Atlantic, Tectonophysics117(1–2): 85–96.CrossRefGoogle Scholar
  47. Narenberg M A H and Essex C (1990). Correlation dimension and systematic geometric effects. Phys Rev A42(12): 7065–7074.CrossRefGoogle Scholar
  48. Öncel A O, Wilson T H and Nishizawa O (2001). Size scaling relationships in the active fault networks of Japan and their correlation with Gutenberg-Richter b values. J Geophys Res106(B10): 21827–21841.CrossRefGoogle Scholar
  49. Öncel A O and Wilson T (2006). Evaluation of earthquake potential along the Northern Anatolian Fault Zone in the Marmara Sea using comparisons of GPS strain and seismotectonic parameters. Tectonophysics418(3–4): 205–218.CrossRefGoogle Scholar
  50. Peláez J A (2000). Aggregation and disaggregation of expected accelerations in the Iberian Peninsula using background seismicity. [PhD Dissertation]. University of Granada, Spain, pp. 183 (in Spanish).Google Scholar
  51. Peláez J A and López Casado C (2002). Seismic hazard estimate in the Iberian Peninsula. Pageoph159(11–12): 2699–2713.Google Scholar
  52. Proyecto Sigma (1998). Analysis of the recent and current tectonic stress state from populations of faults and focal mechanisms of earthquakes. Methodology and application to the Iberian Peninsula. Collection “Other Documents”, Nuclear Security Council, Madrid (in Spanish).Google Scholar
  53. Sanz de Galdeano C and López Casado C (1988). Seismic sources in the Betic-Rif zone. Rev Geofís44: 175–198 (in Spanish).Google Scholar
  54. Sanz de Galdeano C, López Casado C and Peláez J A (2003). Seismic potential of the main active faults in the Granada Basin (Southern Spain). Pageoph160(8): 1537–1556.CrossRefGoogle Scholar
  55. Sanz de Galdeano C, Shanov S, Galindo-Zaldívar J, Radulov A and Nikolov G (2010). A new tectonic discontinuity in the Betic Cordillera deduced from active tectonics and seismicity in the Tabernas Basin. J Geodyn (in press).Google Scholar
  56. Scholz C H (1968). The frequency-magnitude relation of micro-fracturing in rock and its relation to earthquakes. Bull Seism Soc Amer58(1): 399–415.Google Scholar
  57. Sherman S I and Gladkov A S (1999). Fractals in studies of faulting and seismicity in the Baikal rift zone. Tectonophysics308(1–2): 133–142.CrossRefGoogle Scholar
  58. Shivakumar K and Rao M V M S (2000). Application of fractals to the study of rock fracture and rockburst-associated seismicity. In: Dimri V P ed. Application of Fractals in Earth Sciences. A.A. Balkema, USA/Oxford, and IBH Pub. Co., New Delhi, pp. 171–188.Google Scholar
  59. Singh Ch, Bhattacharya P M and Chadha R K (2008). Seismicity in the Koyna-Warna reservoir site in western India: Fractal and b-value mapping. Bull Seism Soc Amer98(1): 476–482.CrossRefGoogle Scholar
  60. Singh Ch, Singh A and Chadha R K (2009). Fractal and b-value mapping in Eastern Himalaya and Southern Tibet. Bull Seism Soc Amer99(6): 3529–3533.CrossRefGoogle Scholar
  61. Smith L A (1988). Intrinsic limits on dimension calculations. Phys Lett A113(6): 283–288.CrossRefGoogle Scholar
  62. Stanley H E, Amaral L A N, Goldberger A L, Havlin S, Ivanov P Ch and Peng C K (1999). Statistical physics and physiology: Monofractal and multi-fractal approaches. Physica A270(1–2): 309–324.CrossRefGoogle Scholar
  63. Teotia S S (2000). Multi-fractal analysis of earthquakes: An overview. In: Dimri V P ed. Application of Fractals in Earth Sciences. A.A. Balkema, USA/Oxford, and IBH Pub. Co., New Delhi, pp. 161–170.Google Scholar
  64. Udías A (1982). Seismicity and seismotectonic stress field in the Alpine Mediterranean region. In: Berckhemer H and Hsu K eds. Alpine-Mediterranean Geodynamics. AGU-GSA Geodynamics Series7, pp. 75–82.Google Scholar
  65. Udías A and Buforn E (1991). Regional stresses along the Eurasia-Africa plate boundary derived from focal mechanisms of large earthquakes. Pageoph136(4): 433–448.CrossRefGoogle Scholar
  66. Utsu T (1965). A method for determining the b-value in the formula logN=a-bM showing the magnitude-frequency relation for earthquakes. Geophys Bull Hokkaido Univ13: 99–103 (in Japanese).Google Scholar
  67. Utsu T (1966). A statistical significant test of the difference in b-value between two earthquake groups. J Phys Earth14: 37–40.CrossRefGoogle Scholar
  68. Utsu T (1967). Some problems with respect to the magnitude-frequency relation of earthquakes. Geophys Bull Hokkaido Univ17: 85–112 (in Japanese).Google Scholar
  69. Vicsek T (1992). Fractal Growth Phenomena: Second Edition. World Scientific Publishing Co., pp. 495.Google Scholar
  70. Xu Y and Burton P W (1999). Spatial fractal evolutions and hierarchies for microearthquakes in central Greece. Pageoph154(1): 73–99.CrossRefGoogle Scholar

Copyright information

© The Seismological Society of China and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • J Henares Romero
    • 1
    Email author
  • C López Casado
    • 1
  • J Badal
    • 2
  • J A Peláez
    • 3
  1. 1.Department of Theoretical Physics and CosmosUniversity of GranadaGranadaSpain
  2. 2.Physics of the Earth, Sciences BUniversity of ZaragozaZaragozaSpain
  3. 3.Department of Physics, Higher Polytechnic SchoolUniversity of JaénJaénSpain

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