Finsler geometry of seismic ray path in anisotropic media

Takahiro Yajima, Hiroyuki Nagahama

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


The seismic ray theory in anisotropic inhomogeneous media is studied based on non- Euclidean geometry called Finsler geometry. For a two-dimensional ray path, the seismic wavefront in anisotropic media can be geometrically expressed by Finslerian parameters. By using elasticity constants of a real rock, the Finslerian parameters are estimated from a wavefront propagating in the rock. As a result, the anisotropic parameters indicate that the shape of wavefront is expressed not by a circle but by a convex curve called a superellipse. This deviation from the circle as an isotropic wavefront can be characterized by a roughness of wavefront. The roughness parameter of the real rock shows that the shape of the wavefront is expressed by a fractal curve. From an orthogonality of the wavefront and the ray, the seismic wavefront in anisotropic media relates to a fractal structure of the ray path.

Original languageEnglish
Pages (from-to)1763-1777
Number of pages15
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2106
Publication statusPublished - 2009 Jun 8


  • Anisotropic media
  • Finsler geometry
  • Fractal
  • Mth root metric
  • Seismic ray path
  • Wavefront

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)


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