Response of two layers overlaying a half-space to a suddenly applied point force

Chunnan Zhou, Nelson N. Hsu, John S. Popovics*, Jan D. Achenbach

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Expressions for the elastodynamic displacements, generated by a normal point force acting on the top layer of two isotropic layers overlaying an isotropic half-space, are derived. Generalized ray theory is used to develop the displacement expressions. In particular, a combinatorial technique for counting the number of wave rays simultaneously arriving at a specific point on the free surface of the top layer is developed. Reflection and transmission coefficients are derived, the different travel paths are analyzed, the products of the reflection and transmission coefficients are generated, and the arrival times of signals traveling along various rays, including head waves, are obtained. A computer program has been developed for efficient numerical implementation of the formulation. Numerical results are shown.

Original languageEnglish (US)
Pages (from-to)255-272
Number of pages18
JournalWave Motion
Issue number3
StatePublished - Apr 2000

ASJC Scopus subject areas

  • Modeling and Simulation
  • Physics and Astronomy(all)
  • Computational Mathematics
  • Applied Mathematics


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