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Transformation ray method: controlling high frequency elastic waves (L).

Zheng Chang1, Xiaoning Liu, Gengkai Hu

  • 1Key Laboratory of Dynamics and Control of Flight Vehicle, Ministry of Education, School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, People's Republic of China.

The Journal of the Acoustical Society of America
|October 9, 2012
PubMed
Summary
This summary is machine-generated.

Elastic ray theory, used in seismology, allows exact control of seismic wave paths via transformation methods. However, controlling energy distribution along these paths is only an approximation.

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Area of Science:

  • Geophysics
  • Seismology
  • Wave propagation

Background:

  • Elastic ray theory is a high-frequency approximation for elastodynamic equations, crucial in seismology.
  • Understanding wave control and form invariance is essential for seismic wave analysis.

Purpose of the Study:

  • To examine form invariance and high-frequency wave control under general spatial mapping using transformation methods.
  • To investigate the exactness of elastic ray path control versus energy distribution control.

Main Methods:

  • Application of transformation methods to elastic ray theory.
  • Analysis of the eikonal and transport equations under spatial mapping.
  • Development of an elastic rotator model based on ray tracing.

Main Results:

  • The eikonal equation retains its form under general mapping with a symmetric elastic tensor.
  • The transport equation's form invariance is limited to conformal mappings.
  • Elastic ray paths are exactly controllable, but energy distribution is only approximately controllable.

Conclusions:

  • Transformation methods offer exact control over elastic ray paths.
  • Approximation in energy distribution control necessitates further research for precise applications.