Modern Techniques in Seismic Tomography

  • Alexander A. Boukhgueim
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 7)


This chapter is focussed on two local inverse kinematic problems of seismology, concerning reflected rays and refracted rays. Both model problems are reduced to a sequence of 2D problems, where theoretical and numerical results are offered. In the case of reflected rays, it is shown how to select a stable problem of recovering a velocity distribution in a layer, by using travel time measurements along rays with one reflection on the boundary. This way, a simple inversion algorithm is obtained for the linearized near a constant velocity case. In the case of refracted rays, a Newton-type algorithm for finding the 3D velocity distribution from 3D travel time measurements is constructed for the local inverse kinematic problem. To this end, a sound velocity that increases linearly with depth is chosen as a first approximation. With this particular choice for the linearization, the underlying problem reduces to a sequence of 2D Radon transforms in discs.


Travel Time Sound Velocity Inversion Formula Seismic Tomography Inversion Algorithm 
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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© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Alexander A. Boukhgueim
    • 1
  1. 1.Department of MathematicsUniversity of ViennaAustria

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