Studia Geophysica et Geodaetica

, Volume 38, Issue 2, pp 140–156 | Cite as

Kinematic hypocentre determination using the paraxial ray approximation

  • Luděk Klimeš


The robust nonlinear approach by Tarantola and Valette, consisting in direct evaluation of the "probability" density function, is supplemented with the paraxial ray approximation of the travel time. A sufficiently dense 2-parametric system of rays from each receiver is evaluated only once for all hypocentre determinations. The interpolation formulae for the travel times apply to all travel-time branches. Their derivation is based on the summation of Gaussian packets. The proposed algorithm for determining the hypocentre is able to find all of its possible locations.


Density Function Travel Time Structural Geology Direct Evaluation Interpolation Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    A. Tarantola, B. Valette: Inverse problems=quest for information. J. Geophys.,50 (1982), 159–170.Google Scholar
  2. [2]
    T-J. Moser, T. Van Eck, G. Nolet: Hypocenter determination in strongly heterogeneous Earth models using the shortest path method. J. geophys. Res.,97B (1992), 6563–6572.Google Scholar
  3. [3]
    V. Červený, L. Klimeš, I. Pšenčík: Paraxial ray approximations in the computation of seismic wavefields in inhomogeneous media. Geophys. J. R. astr. Soc.,79 (1984), 89–104.Google Scholar
  4. [4]
    L. Klimeš: The relation between Gaussian beams and Maslov asymptotic theory. Studia geoph. et geod.,28 (1984), 237–247.Google Scholar
  5. [5]
    L. Klimeš: Gaussian packets in the computation of seismic wavefields. Geophys. J. int.,99 (1989), 421–433.Google Scholar
  6. [6]
    V. Červený: The application of ray tracing to the numerical modeling of seismic wavefields in complex structures. In: G. Dohr (Ed.), Seismic Shear Waves, Part A: Theory, (K. Helbig, S. Treitel (Eds.), Handbook of Geophysical Exploration, Section I: Seismic Exploration, Vol. 15A), Geophysical Press, London, 1985, pp.1–124.Google Scholar
  7. [7]
    V. Červený: Gaussian beam synthetic seismograms. J. Geophys.,58 (1985), 44–72.Google Scholar
  8. [8]
    V. Červený, L. Klimeš, I. Pšenčík: Applications of the dynamic ray tracing. Phys. Earth planet. Interiors,51 (1988), 25–35.Google Scholar
  9. [9]
    V. Červený, L. Klimeš, I. Pšenčík: Complete seismic-ray tracing in three-dimensional structures. In: D. J. Doornbos (Ed.), Seismological Algorithms, Academic Press, New York 1988, pp. 89–168.Google Scholar
  10. [10]
    V. Červený, J. Pleinerová, L. Klimeš, I. Pšenčík: High-frequency radiation from earthquake sources in laterally varying layered structures. Geophys. J. R. astr. Soc.,88 (1987), 43–79.Google Scholar
  11. [11]
    L. Klimeš: Discretization error for the superposition of Gaussian beams. Geophys. J. R. astr. Soc.,86 (1986), 531–551.Google Scholar
  12. [12]
    L. Klimeš: Expansion of a high-frequency time-harmonic wavefield given on an initial surface into Gaussian beams. Geophys. J. R. astr. Soc.,79 (1984), 105–118.Google Scholar
  13. [13]
    L. Klimeš: Kinematic location of a seismic hypocentre. Acta montana, No. 75, Instit. Geol. Geotechn. Czechosl. Acad. Sci., Praha 1987, pp.51–64 (in Czech).Google Scholar

Copyright information

© StudiaGeo 1994

Authors and Affiliations

  • Luděk Klimeš
    • 1
  1. 1.Department of GeophysicsCharles UniversityPrague

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