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Procedure of reduction of travel-time curves ofP andS waves at the focal surface


A method for the calculation of seismic waves velocities at focal depth is here proposed. A stratified earth model with spherical symmetry and the analytical relationship between the epicentral distance and the travel times of seismic waves are used.

This method, applied to the southern Tyrrhenian region and to the Japanese islands, allows to reduce the observed travel times to the focal depth independently of a particular velocity model.

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  1. Barberi, F., Gasparini, P., Innocenti, F., andVillari, L. (1973),Volcanism of the Southern Tyrrhenian Sea and its Geodynamics Implications. J. Geophys. Res.78, 5221–5232.

  2. Bottari, A., andLo Giudice, E. (1975),On the P-wave Velocity and Plate Tectonics Implications for the Tyrrhenian Deep Earthquake Zone, Tectonophys.25, 187–200.

  3. Bottari, A., andFederico, B. (1979),Estimate of the Focal Depth of Deep Earthquakes and Some Structural Implications for the Deep Seismic Activity in the Tyrrhenian Region. Bull. Seismol. Soc. Am.69, 1193–1208.

  4. Bullen, K. E.,An Introduction to the Theory of Seismology (University Press, Cambridge 1953).

  5. Caputo, M., Panza, G. F., andPostpishl, D. (1972),New Evidences about the Deep Structure Lipari Arc, Tectonophysics,15, 219–231.

  6. Engdahl, R. E., Taggart, J., Lobdell, J., Arnold, E. P., andClawson, G. E. (1968),Computational Methods, Bull. Seismol. Soc. Am.58, 1339–1344.

  7. Federico, B. (1975),Onde longitudinali riflesse sulla discontinuita’ 20°, Ann. Geof.XXVIII (1), 45–63.

  8. Gutenberg, B. (1953),Wave Velocities at Depths between 50 and 600 Kilometers, Bull. Seismol. Soc. Am.43, 223–232.

  9. Herrin, E. (1968),Introduction to Seismological Tables for P Phases, Bull. Seismol. Soc. Am.58, 1193–1241.

  10. Jeffreys, H., andBullen, K. E. (1948),Seismological Tables, British Association for the Advancement of Science.

  11. Kaila, K. L. (1969),A New Analytical Method for Finding the Upper Mantle Velocity Structure from P and S Wave Travel-time of Deep Earthquakes, Bull. Seismol. Soc. Am.61, 1549–1570.

  12. Kaila, K. L., Krishna, V. G., andHari, Narrain (1969),Upper Mantle Velocity Structure in the Hindukush Region from Travel-time Studies of Deep Earthquakes Using a New Analytical method. Bull. Seismol. Soc. Am.59 (5), 1949–1967.

  13. Mohorovičić, S. (1914),Die reduzierte Laufzeitkurve und die Abhängigkeit der Herdtiefe eines Bebens von der Entfernung des Inflexionspunktes der primären Laufzeitkurve, G. Gerlands Beiträge zur GeophysikIX, 217–240.

  14. Ritsema, A. R. (1971),Notes on Plate Tectonics and Arc Movements in the Mediterranean Region, Proc. European Seism. Comm., 22–26, L1970.

  15. Ritsema, A. R. (1972),Deep Earthquakes of the Tyrrhenian Sea, Geol. Mijmbouw51, 541–545.

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Bottari, A., Federico, B., Pietrafesa, M. et al. Procedure of reduction of travel-time curves ofP andS waves at the focal surface. PAGEOPH 140, 641–653 (1993).

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Key words

  • Seismic waves
  • travel time
  • hypocentral surface
  • southern Tyrrhenian
  • Japanese islands