Pure and Applied Geophysics

, Volume 172, Issue 11, pp 3247–3263 | Cite as

Retrieving the Stress Field Within the Campi Flegrei Caldera (Southern Italy) Through an Integrated Geodetical and Seismological Approach

  • Luca D’Auria
  • Bruno Massa
  • Elena Cristiano
  • Carlo Del Gaudio
  • Flora Giudicepietro
  • Giovanni Ricciardi
  • Ciro Ricco


We investigated the Campi Flegrei caldera using a quantitative approach to retrieve the spatial and temporal variations of the stress field. For this aim we applied a joint inversion of geodetic and seismological data to a dataset of 1,100 optical levelling measurements and 222 focal mechanisms, recorded during the bradyseismic crisis of 1982–1984. The inversion of the geodetic dataset alone, shows that the observed ground deformation is compatible with a source consisting of a planar crack, located at the centre of the caldera at a depth of about 2.56 km and a size of about 4 × 4 km. Inversion of focal mechanisms using both analytical and graphical approaches, has shown that the key features of the stress field in the area are: a nearly subvertical σ 1 and a sub-horizontal, roughly NNE-SSW trending σ 3. Unfortunately, the modelling of the stress fields based only upon the retrieved ground deformation source is not able to fully account for the stress pattern delineated by focal mechanism inversion. The introduction of an additional regional background field has been necessary. This field has been determined by minimizing the difference between observed slip vectors for each focal mechanism and the theoretical maximum shear stress deriving from both the volcanic (time-varying) and the regional (constant) field. The latter is responsible for a weak NNE-SSW extension, which is consistent with the field determined for the nearby Mt. Vesuvius volcano. The proposed approach accurately models observations and provides interesting hints to better understand the dynamics of the volcanic unrest and seismogenic processes at Campi Flegrei caldera. This procedure could be applied to other volcanoes experiencing active ground deformation and seismicity.

Key words

Stress field inversion Campi Flegrei volcano deformation volcanic seismicity joint inversion 



This work has been realised in the framework of an MED-SUV project. MED-SUV has received funding from the European Union’s Seventh Programme for research, technological development and demonstration under grant agreement No. 308665.


  1. Angelier, J. (1984), Tectonic analysis of fault slip data sets, J. Geophys. Res., 89, 5835–5848.Google Scholar
  2. Angelier, J. (1990), Inversion of Field Data in Fault Tectonics to Obtain the Regional Stress. 3. A New Rapid Direct Inversion Method by Analytical Means, Geophys. J. Int., 103, 363–376.Google Scholar
  3. Angelier, J. T., and Mechler, P. (1977), Sur une methode graphique de recherche des contraintes principales egalement utilisables en tectonique et en seismologie: la methode des diedres droits. Bulletin de la Société géologique de France (7), t.XIX, n°6, 1309–1318.Google Scholar
  4. Angelier, J., and Manoussis, S. (1980), Classification automatique et distinction des phases superposées en tectonique de failles. CR Acad. Sci. Paris, 290, 651–654.Google Scholar
  5. Aster, R. C., and Meyer, R. P. (1988), Three-dimensional velocity structure and hypocenter distribution in the Campi Flegrei caldera, Italy. Tectonophysics, 149(3), 195–218.Google Scholar
  6. Aster, R. C., Borchers, B., and Thurber, C. H. (2013), Parameter estimation and inverse problems (Academic Press).Google Scholar
  7. Brandsdottir, B., and Einarsson, P. (1979). Seismic activity associated with the September 1977 deflation of the Krafla central volcano in northern Iceland, J. Volc. Geotherm. Res., 6, 197–212.Google Scholar
  8. Barberi, F., Corrado, G., Innocenti, F. and Luongo, G. (1984), Phlegraean Fields 1982-1984: brief chronicle of a volcano emergency in a densely populated area. Bull. Volcanol., 47(2): 175–185.Google Scholar
  9. Battaglia, M., Troise, C., Obrizzo, F., Pingue, F., and De Natale, G. (2006), Evidence for fluid migration as the source of deformation at Campi Flegrei caldera (Italy). Geophysical Research Letters, 33(1), L01307.Google Scholar
  10. Bianco, F., Del Pezzo, E., Saccorotti, G., and Ventura, G. (2004), The role of hydrothermal fluids in triggering the July–August 2000 seismic swarm at Campi Flegrei, Italy: evidence from seismological and mesostructural data. Journal of Volcanology and Geothermal Research, 133(1), 229–246.Google Scholar
  11. Bishop (1966), The strength of solids as engineering materials, Geotechnique, 16, pp. 91–130.Google Scholar
  12. Bonafede, M. (1991), Hot fluid migration, an efficient source of ground deformation: Application to the 1982–1985 crisis at Campi Flegrei‐Italy, J. Volcanol. Geotherm. Res., 48, 187–198.Google Scholar
  13. Bott, M. H. P. (1959), The mechanics of oblique slip faulting, Geol. Mag., 96, 109–117.Google Scholar
  14. Burnham, K. P., and Anderson, D. R. (2002), Model selection and multimodel inference: a practical information-theoretic approach. Springer.Google Scholar
  15. Camacho, A. G., P. J. González, J. Fernández, and G. Berrino (2011), Simultaneous inversion of surface deformation and gravity changes by means of extended bodies with a free geometry: Application to deforming calderas, J. Geophys. Res., 116, B10401, doi: 10.1029/2010JB008165.
  16. Cannavò, F., Scandura, D., Palano, M. and Musumeci C. (2014), A Joint Inversion of Ground Deformation and Focal Mechanisms Data for Magmatic Source Modelling. Pure and Applied Geophysics, doi: 10.1007/s00024-013-0771-x.
  17. Chiodini, G., Frondini, F., Cardellini, C., Granieri, D., Marini, L., and Ventura, G. (2001), CO 2 degassing and energy release at Solfatara volcano, Campi Flegrei, Italy. Journal of Geophysical Research: Solid Earth (1978–2012), 106(B8), 16213–16221.Google Scholar
  18. Chiodini, G., M. Todesco, S. Caliro, C. Del Gaudio, G. Macedonio, and M. Russo (2003), Magma degassing as a trigger of bradyseismic events: The case of Phlegrean Fields (Italy), Geophys. Res. Lett., 30(8), 1434, doi: 10.1029/2002GL016790.
  19. D’Auria, L., Giudicepietro, F., Aquino, I., Borriello, G., Del Gaudio, C., Lo Bascio, D., Martini M., Ricciardi G.P., Ricciolino P. and Ricco, C. (2011), Repeated fluid‐transfer episodes as a mechanism for the recent dynamics of Campi Flegrei caldera (1989–2010). Journal of Geophysical Research: Solid Earth (1978–2012), 116(B4).Google Scholar
  20. D’Auria, L., Giudicepietro, F., Martini, M., and Lanari, R. (2012), The 4D imaging of the source of ground deformation at Campi Flegrei caldera (southern Italy). Journal of Geophysical Research: Solid Earth (1978–2012), 117 (B8).Google Scholar
  21. D’Auria, L., Martini, M., Esposito, A., Ricciolino, P., and Giudicepietro, F. (2008), A unified 3D velocity model for the Neapolitan volcanic areas, In Conception, Verification and Application of Innovative Techniques to Study Active Volcanoes (ed. Marzocchi W. and Zollo A.), pp. 375–390, ISBN 978-88-89972-09-0.Google Scholar
  22. D’Auria, L., B. Massa, and A. De Matteo (2014), The stress field beneath a quiescent stratovolcano: The case of Mount Vesuvius. J. Geophys. Res. Solid. Earth., 119. doi: 10.1002/2013JB010792.
  23. Deino, A.L., Orsi, G., Piochi, M. and de Vita, S. (2004), The age of the neapolitan Yellow Tuff caldera-forming eruption (Campi Flegrei caldera–Italy) assessed by 40ar/39ar dating method. Journal of Volcanology and Geothermal Research, 133, 157–170.Google Scholar
  24. Del Gaudio, C., Aquino, I., Ricciardi, G. P., Ricco, C., and Scandone, R. (2010), Unrest episodes at Campi Flegrei: A reconstruction of vertical ground movements during 1905–2009. Journal of Volcanology and Geothermal Research, 195(1), 48-56.Google Scholar
  25. Dietrich, J. (1994), A constitutive law for rate of earthquake production and its application to earthquake clustering. J. Geophys. Res. 99, 2601–2618.Google Scholar
  26. Di Vito, M. A., Isaia, R., Orsi, G., Southon, J., De Vita, S., d’Antonio, M., Pappalardo L. and Piochi, M. (1999), Volcanism and deformation since 12,000 years at the Campi Flegrei caldera (Italy). Journal of Volcanology and Geothermal Research, 91(2), 221–246.Google Scholar
  27. Dzurisin, D. (2006), Volcano Deformation: Geodetic Monitoring Techniques. Berlin, Springer, Springer-Praxis Books in Geophysical Sciences, 441 p.Google Scholar
  28. Efron, B. (1979), Bootstrap methods: Another look at the jackknife. The Annals of Statistics 7(1): 1–26.Google Scholar
  29. Fialko, Y., Khazan, Y., and Simons, M. (2001), Deformation due to a pressurized horizontal circular crack in an elastic half‐space, with applications to volcano geodesy. Geophysical Journal International, 146(1), 181–190.Google Scholar
  30. Frohlich, C. (1992), Triangle diagrams: Ternary graphs to display similarity and diversity of earthquake focal mechanisms, Phys. Earth. Planet. Inter., 75, 193–198.Google Scholar
  31. Gaeta, F. S., Peluso, F., Arienzo, I., Castagnolo, D., De Natale, G., Milano, G., Albanese C. and Mita, D. G. (2003), A physical appraisal of a new aspect of bradyseism: The miniuplifts. Journal of Geophysical Research: Solid Earth (1978–2012), 108(B8).Google Scholar
  32. Gaudiosi, G., and Iannaccone, G. (1984), A preliminary study of stress pattern at Phlegraean Fields as inferred from focal mechanisms. Bulletin volcanologique, 47(2), 225–231.Google Scholar
  33. Gebauer, S., Schmitt, A.K., Pappalardo, L., Stockli, D.F., and Lovera, O.M. (2014), Crystallization and eruption ages of Breccia Museo (Campi Flegrei caldera, Italy) plutonic clasts and their relation to the Campanian ignimbrite. Contrib. Mineral. Petrol., 167: 953, doi: 10.1007/s00410-013-0953-7.
  34. Gephart, J., and Forsyth, D. (1984), An improved method for determining the regional stress tensor using earthquake focal mechanisms data: application to the San Fernando earthquake sequence. J. Geophy. Res., 89, 9305–9320.Google Scholar
  35. Hippolyte, J.C., Bergerat, F., Gordon, M., Bellier, O., Espurt, N. (2012), Keys and pitfalls in mesoscale fault analysis and paleostress reconstructions, the use of Angelier’s methods. Tectonophysics, doi: 10.1016/j.tecto.2012.01.012.
  36. Lee, W.H.K., and Stewart, S.W. (1981), Principles and applications of microearthquake networks. In: Advances in Geophysics, Supplement 2, Academic Press, New York, 293 pp.Google Scholar
  37. Macedonio G., Giudicepietro F., D’Auria L. and Martini M. (2014), Sill intrusion as a source mechanism of unrest at volcanic calderas. J. Geophys. Res. Solid Earth, 119, doi: 10.1002/2013JB010868.
  38. McKenzie, D. P. (1969), The relation between fault plane solutions for earthquakes and the directions of the principal stresses, Bull. Seismol. Soc. Am. 59, 591–601.Google Scholar
  39. McTigue, D. F. (1987), Elastic stress and deformation near a finite spherical magma body: Resolution of the point source paradox. Journal of Geophysical Research: Solid Earth (1978–2012), 92(B12), 12931–12940.Google Scholar
  40. Michael, A. J. (1984), Determination of stress from slip data: faults and folds. J. Geophys. Res., 89, 11517–11526.Google Scholar
  41. Michael, A.J. (1987), Use of Focal Mechanisms to Determine Stress: A Control Study. J. Geoph. Res., 92, 357–368.Google Scholar
  42. Mogi, K. (1958), Relations between the eruptions of various volcanoes and the deformations of the ground surfaces around them. Bulletin of the Earthquake Research Institute 36, 99–134.Google Scholar
  43. Nelder, J.A. and Mead, R. (1965), A simplex method for function minimization, Comput. J., 7, pp. 308–313.Google Scholar
  44. Okada, Y. (1985), Surface deformation due to shear and tensile faults in a half-space. Bulletin of the seismological society of America, 75(4), 1135–1154.Google Scholar
  45. Okada, Y. (1992), Internal deformation due to shear and tensile faults in a half-space. Bulletin of the Seismological Society of America, 82(2), 1018–1040.Google Scholar
  46. Orsi, G., Civetta, L., Del Gaudio, C., De Vita, S., Di Vito, M. A., Isaia, R., S.M. Petrazzuoli, G.P. Ricciardi and Ricco, C. (1999), Short-term ground deformations and seismicity in the resurgent Campi Flegrei caldera (Italy): an example of active block-resurgence in a densely populated area. Journal of Volcanology and Geothermal Research, 91(2), 415–451.Google Scholar
  47. Orsi, G., De Vita, S., and Di Vito, M. (1996), The restless, resurgent Campi Flegrei nested caldera (Italy): constraints on its evolution and configuration. Journal of Volcanology and Geothermal Research, 74(3), 179–214.Google Scholar
  48. Orsi, G., Di Vito, M. A., and Isaia, R. (2004), Volcanic hazard assessment at the restless Campi Flegrei caldera. Bulletin of Volcanology, 66(6), 514–530.Google Scholar
  49. Otsubo, M., A. Yamaji, and A. Kubo (2008), Determination of stresses from heterogeneous focal mechanism data: An adaptation of the multiple inverse method, Tectonophysics, 457, 150–160.Google Scholar
  50. Otsubo, M., Sato, K., Yamaji, A. (2006), Computerized identification of stress tensors determined from heterogeneous fault-slip data by combining multiple inverse method and k-means clustering. Journal of Structural Geology, 28, 991–997, doi: 10.10106/j.jsg.2006.03.008.
  51. Patanè, D., Privitera, E., Gresta, S., Akinci, A., Alparone, S., Barberi, G., Chiaraluce, L., Cocina, O., D’amico, S., De Gori, P., Di Grazia, G., Falsaperla, S., Ferrari, F., Gambino, S., Giampiccolo, E., Langer, H., Maiolino, V., Moretti, M., Mostaccio, A., Musumeci, C., Piccinini, D., Reitano, D., Scarfì, L., Spampinato, S., Ursino, A., and Zuccarello, L. (2003), Seismological constraints for the dike emplacement of July–August 2001 lateral eruption at Mt. Etna volcano, Italy. Annals of geophysics, 46(4), 599–608.Google Scholar
  52. Pedersen, R., and Sigmundsson, F. (2004), InSAR based sill model links spatially offset areas of deformation and seismicity for the 1994 unrest episode at Eyjafjallajökull volcano, Iceland. Geophys. Res. Lett., 31(14), doi: 10.1029/2004GL020368.
  53. Ramsay J., Lisle R. (2000), Applications of continuum mechanics in structural geology (Techniques of modern structural geology. Vol.3), 701–1061.Google Scholar
  54. Reasenberg, P. and Oppenheimer D. (1985), FPFIT, FPPLOT and FPPAGE: Fortran computer programs for calculating and displaying earthquake fault-plane solutions, US Geol. Surv., Open-File Rept, 85–739.Google Scholar
  55. Rivera, L. and Cisternas, A. (1990), Stress tensor and fault plane solutions for a population of earthquakes. Bull. Seismol. Soc. Am., 80(3): 600–614.Google Scholar
  56. Rubin, A.M., Gillard, D., and Got, J.L. (1998), A reinterpretation of seismicity associated with the January 1983 dike intrusion at Kilauea volcano, Hawaii. J. geophys. Res., 103, 10003–10015.Google Scholar
  57. Segall, P. (2013), Volcano deformation and eruption forecasting. Geological Society, London, Special Publications, 380, doi: 10.1144/SP380.4.
  58. Segall, P. (2010), Earthquake and volcano deformation. Princeton University Press.Google Scholar
  59. Segall, P., Llenos, A. L., Yun, S. H., Bradley, A. M., and Syracuse, E. M. (2013), Time‐dependent dike propagation from joint inversion of seismicity and deformation data. Journal of Geophysical Research: Solid Earth 118(11), 5785–5804.Google Scholar
  60. Sen, M. K., and Stoffa, P. L. (1995), Global optimization methods in geophysical inversion. Elsevier.Google Scholar
  61. Toda, S., Stein, R. S., and Sagiya, T. (2002), Evidence from the ad 2000 Izu islands earthquake swarm that stressing rate governs seismicity. Nature, 419, 58–61.Google Scholar
  62. Tramelli, A., Troise, C., De Natale, G., and Orazi, M. (2013), A New Method for Optimization and Testing of Microseismic Networks: An Application to Campi Flegrei (Southern Italy). Bulletin of the Seismological Society of America, 103(3), 1679–1691, doi: 10.1785/0120120211.
  63. Troise, C., F. Pingue, and G. De Natale (2003), Coulomb stress changes at calderas: Modeling the seismicity of Campi Flegrei (southern Italy), J. Geophys. Res., 108, 2292, doi: 10.1029/2002JB002006, B6.
  64. Umakoshi, K., Shimizu, H., and Matsuwo N. (2001), Volcano-tectonic seismicity at Unzen Volcano, Japan, 1985-1999. Journal of Volcanology and Geothermal Research, 112, 117–131.Google Scholar
  65. Vitale, S., and Isaia, R. (2013), Fractures and faults in volcanic rocks (Campi Flegrei, southern Italy): insight into volcano-tectonic processes. International Journal of Earth Sciences, 1–19.Google Scholar
  66. Wallace, R. E. (1951), Geometry of shearing stress and relationship to faulting, J.Geol., 59, 111–130.Google Scholar
  67. Woo, J. Y., and Kilburn, C. R. (2010), Intrusion and deformation at Campi Flegrei, southern Italy: sills, dikes, and regional extension. Journal of Geophysical Research: Solid Earth (1978–2012), 115(B12).Google Scholar
  68. Yamaji, A. (2000), The multiple inverse method: a new technique to separate stresses from heterogeneous fault-slip data. J. Struct. Geol., 22: 441–452.Google Scholar
  69. Yamaji, A. (2007), An Introduction to Tectonophysics: Theoretical Aspects of Structural Geology, 4-88704-135-7, Terrapub, Tokyo.Google Scholar
  70. Yamaji, A., and M. Otsubo (2011), Multiple Inverse Method Software Package User’s Guide, Kyoto, Japan. [Avialable at].
  71. Yang, X. M., Davis, P. M., and Dieterich, J. H. (1988), Deformation from inflation of a dipping finite prolate spheroid in an elastic half‐space as a model for volcanic stressing. Journal of Geophysical Research: Solid Earth (1978–2012), 93(B5), 4249–4257.Google Scholar
  72. Zuppetta, A., and Sava, A. (1991), Stress pattern at Campi Flegrei from focal mechanisms of the 1982–1984 earthquakes (Southern Italy). Journal of Volcanology and Geothermal Research, 48(1), 127–137.Google Scholar

Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Luca D’Auria
    • 1
  • Bruno Massa
    • 1
    • 2
  • Elena Cristiano
    • 1
  • Carlo Del Gaudio
    • 1
  • Flora Giudicepietro
    • 1
  • Giovanni Ricciardi
    • 1
  • Ciro Ricco
    • 1
  1. 1.Istituto Nazionale di Geofisica e Vulcanologia, sezione di NapoliNaplesItaly
  2. 2.Dipartimento di Scienze e TecnologieUniversità degli Studi del SannioBeneventoItaly

Personalised recommendations