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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
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.
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.
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.
Hole, J., Nonlinear high-resolution three-dimensional seismic travel time tomography, J. Geophys. Res., 1992, vol. 97, pp. 6553–6562.
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.
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.
Phillips, W.S. and Fehler, M.C., Traveltime tomography: a comparison of popular methods, Geophysics, 1991, vol. 56, no. 16, pp. 1639–1649.
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.
Rawlinson, N. and Sambridge, M., Seismic traveltime tomography of the crust and lithosphere, Adv. Geophys., 2003, vol. 46, pp.81–197.
Spakman, W. and Bijwaard, H., Optimization of cell parameterization for tomographic inverse problems, Pure Appl. Geophys., 2001, vol. 158, pp. 1401–1423.
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.
Tikhonov, A.N. and Arsenin, V.Ya., Metody resheniya nekorrektnykh zadach (Methods for Solving the Ill-Posed Problems), Moscow: Nauka, 1986.
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.
Weber, Z., Seismic traveltime tomography: a simulated annealing approach, Phys. Earth Planet. Inter., 2000, vol. 119, nos. 1–2, pp. 149–159.
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.
Yanovskaya, T.B. and Ditmar, P.G., Smoothness criteria in surface wave tomography, Geophys. J. Int., 1990, vol. 102, no. 1, pp. 63–72.
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.
Zhang, J.M. and Toksoz, M.N., Nonlinear refraction travel time tomography, Geophysics, 1998, vol. 63, no. 5, pp. 1726–1737.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © T.B. Yanovskaya, S.V. Medvedev, V.S. Gobarenko, 2018, published in Fizika Zemli, 2018, No. 2, pp. 3–11.
Supplementary materials are available for this article at DOI: 10.1134/S1069351318020167 and are accessible for authorized users.
Electronic supplementary material
Rights and permissions
About this article
Cite this article
Yanovskaya, T.B., Medvedev, S.V. & Gobarenko, V.S. Effect of a Starting Model on the Solution of a Travel Time Seismic Tomography Problem. Izv., Phys. Solid Earth 54, 193–200 (2018). https://doi.org/10.1134/S1069351318020167
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1069351318020167