Izvestiya, Physics of the Solid Earth

, Volume 54, Issue 2, pp 193–200 | Cite as

Effect of a Starting Model on the Solution of a Travel Time Seismic Tomography Problem

  • T. B. Yanovskaya
  • S. V. Medvedev
  • V. S. Gobarenko
Article
  • 6 Downloads

Abstract

In the problems of three-dimensional (3D) travel time seismic tomography where the data are travel times of diving waves and the starting model is a system of plane layers where the velocity is a function of depth alone, the solution turns out to strongly depend on the selection of the starting model. This is due to the fact that in the different starting models, the rays between the same points can intersect different layers, which makes the tomography problem fundamentally nonlinear. This effect is demonstrated by the model example. Based on the same example, it is shown how the starting model should be selected to ensure a solution close to the true velocity distribution. The starting model (the average dependence of the seismic velocity on depth) should be determined by the method of successive iterations at each step of which the horizontal velocity variations in the layers are determined by solving the two-dimensional tomography problem. An example illustrating the application of this technique to the P-wave travel time data in the region of the Black Sea basin is presented.

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References

  1. Abers, G. and Roecker, S., Deep structure of an arc-continent collision: Earthquake relocation and inversion for upper mantle P and S wave velocities beneath Papua New Guinea, J. Geophys. Res., 1991, vol. 96, pp. 6370–6401.CrossRefGoogle Scholar
  2. Aki, K., Christofferson, A., and Husebye, E.S., Determination of the three-dimensional seismic structure of the lithosphere, J. Geophys. Res., 1977, vol. 82, pp. 277–296.CrossRefGoogle Scholar
  3. Bishop, T., Bube, K., Cutler, R., Langan, R., Love, P., Resnick, J., Shuey, R., Spindler, D., and Wyld, H., Tomographic determination of velocity and depth in laterally varying media, Geophysics, 1985, vol. 50, pp. 903–923.CrossRefGoogle Scholar
  4. Hole, J., Nonlinear high-resolution three-dimensional seismic travel time tomography, J. Geophys. Res., 1992, vol. 97, pp. 6553–6562.CrossRefGoogle Scholar
  5. Nolet, G., Seismic wave propagation and seismic tomography, in Seismic Tomography with Applications in Global Seismology and Exploration Geophysics, Nolet, G., Ed., Dordrecht: Reidel, 1987, pp. 1–23.Google Scholar
  6. Nowack, P.L., and Li, C., Seismic tomography, in Handbook of Signal Processing in Acoustics, Havelock, D., Kuwano, S., and Vorlander, M., Eds., New York: Springer, 2009, chapter 91, pp. 1635–1653.Google Scholar
  7. Phillips, W.S. and Fehler, M.C., Traveltime tomography: a comparison of popular methods, Geophysics, 1991, vol. 56, no. 16, pp. 1639–1649.CrossRefGoogle Scholar
  8. Podvin, P., and Lecomte, I., Finite difference computation of traveltimes in very contrasted velocity model: a massively parallel approach and its associated tools, Geophys. J. Int., 1991, vol. 105, pp. 271–284.CrossRefGoogle Scholar
  9. Rawlinson, N. and Sambridge, M., Seismic traveltime tomography of the crust and lithosphere, Adv. Geophys., 2003, vol. 46, pp.81–197.CrossRefGoogle Scholar
  10. Spakman, W. and Bijwaard, H., Optimization of cell parameterization for tomographic inverse problems, Pure Appl. Geophys., 2001, vol. 158, pp. 1401–1423.CrossRefGoogle Scholar
  11. Thurber, C. and Ritsema, J., Theory and observations–seismic tomography and inverse methods, in Treatise on Geophysics, vol. 1, Schubert, G., Ed., Amsterdam: Elsevier, 2007, pp. 323–360.CrossRefGoogle Scholar
  12. Tikhonov, A.N. and Arsenin, V.Ya., Metody resheniya nekorrektnykh zadach (Methods for Solving the Ill-Posed Problems), Moscow: Nauka, 1986.Google Scholar
  13. Tikhotskii, S.A., Fokin, I.V., and Shur, D.Yu., Traveltime seismic tomography with adaptive wavelet parameterization, Izv., Phys Solid Earth, 2011, vol. 47, no. 4, pp. 326–344.CrossRefGoogle Scholar
  14. Weber, Z., Seismic traveltime tomography: a simulated annealing approach, Phys. Earth Planet. Inter., 2000, vol. 119, nos. 1–2, pp. 149–159.CrossRefGoogle Scholar
  15. Yanovskaya, T.B., The method for three-dimensional traveltime tomography based on smoothness of lateral velocity variations, Izv., Phys Solid Earth, 2012, vol. 48, no. 5, pp. 363–374.CrossRefGoogle Scholar
  16. Yanovskaya, T.B. and Ditmar, P.G., Smoothness criteria in surface wave tomography, Geophys. J. Int., 1990, vol. 102, no. 1, pp. 63–72.CrossRefGoogle Scholar
  17. Yanovskaya, T.B., Gobarenko, V.S., and Yegorova, T.P., Subcrustal structure of the Black Sea basin from seismological data, Izv., Phys Solid Earth, 2016, vol. 52, no. 1, pp. 14–28.CrossRefGoogle Scholar
  18. Zhang, J.M. and Toksoz, M.N., Nonlinear refraction travel time tomography, Geophysics, 1998, vol. 63, no. 5, pp. 1726–1737.CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • T. B. Yanovskaya
    • 1
  • S. V. Medvedev
    • 1
  • V. S. Gobarenko
    • 2
  1. 1.St. Petersburg State UniversitySt. PetersburgRussia
  2. 2.Vernadsky Crimean Federal UniversitySimferopol, Republic of CrimeaRussia

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