The algorithm for solving the direct kinematic problem of seismics in three-dimensional heterogeneous isotropic media

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Abstract

The solution of the direct kinematic problem of seismics is an important stage of the seismic data processing in seismology and seismic explorations, e.g., while solving the inverse kinematic problem of seismics by the method of nonlinear seismic tomography, in the method of the space-time Kirchhoff’s migration, etc. There are several approaches now to the solution of this problem: 1) methods based on the solution of two-point boundary value problems; 2) the wavefront construction method; 3) finite-difference methods for solving eikonal differential equations, etc. [2-3]. The method proposed in this paper relates to ray tracing methods and overcomes some of the limitations inherent in the above methods. The basis of the approach is the iterative Newton’s method. The algorithm of three- dimensional shooting is simple to implement and allows “almost” linear speedup from parallelization. Questions of convergence of the Newton method applied to this problem are not considered in this paper. In addition, we do not consider the applicability of the method in the presence of caustics, shadow zones, and diffraction.

Original languageEnglish
Pages (from-to)53-68
Number of pages16
JournalMathematical Notes of NEFU
Volume27
Issue number1
DOIs
Publication statusPublished - 1 Jan 2020

Keywords

  • 3d shooting
  • Ray tracing
  • Ray-based method

OECD FOS+WOS

  • 1.02 COMPUTER AND INFORMATION SCIENCES
  • 1.01 MATHEMATICS

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