Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Response of Two Layers Overlaying a Half-Space to a Suddenly Applied Point Force



Nelson N. Hsu


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.
Wave Motion


Dynamic Green's Tensor, layered elastic media, point force, transient electric wave, wave form


Hsu, N. (1999), Response of Two Layers Overlaying a Half-Space to a Suddenly Applied Point Force, Wave Motion (Accessed July 15, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created April 1, 1999, Updated February 19, 2017