Finsler metric and elastic constants for weak anisotropic media

Takahiro Yajima, Kazuhito Yamasaki, Hiroyuki Nagahama

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

Differential geometric expressions of elastic constants for a seismic ray path are studied based on Finsler geometry. A Finsler function named mth root metric is considered to discuss transverse isotropic media in weak anisotropic case. Finsler parameters in the mth root metric are estimated from phase velocity surfaces. The slight differences from an elliptic wavefront can be expressed by the Finsler parameters. It is found a correlation between the Finsler parameters and the weak anisotropy parameters consisted of elastic constants. Especially, a positivity of weak anisotropy parameter influences on a restriction of Finsler parameter. On the other hand, a geometric condition of Finsler parameter gives a limitation of weak anisotropy parameter. Moreover, the Berwald Gauss curvature of mth root metric induces a relationship between the spreading ray paths and the weak anisotropy parameter. Therefore, the seismic ray paths in weak isotropic media can be expressed by the Finslerian properties of mth root metric.

Original languageEnglish
Pages (from-to)3177-3184
Number of pages8
JournalNonlinear Analysis: Real World Applications
Volume12
Issue number6
DOIs
Publication statusPublished - 2011 Dec

Keywords

  • Berwald Gauss curvature
  • Elastic constants
  • Finsler geometry
  • Seismic ray theory
  • Weak anisotropic media
  • mth root metric

ASJC Scopus subject areas

  • Analysis
  • Engineering(all)
  • Economics, Econometrics and Finance(all)
  • Computational Mathematics
  • Applied Mathematics

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