A note on the dynamic and static displacements from a point source in multilayered media

2002/03/27 by Lupei Zhu, Luis Rivera, Luis A. Rivera · 5 citations
Computer Science · Engineering · #Advanced Fiber Optic Sensors #Optical measurement and interference techniques #Ultrasonics and Acoustic Wave Propagation

paper · doi:10.1046/j.1365-246x.2002.01610.x

openalex publication_date 2002/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

A simple and unified approach is presented to solve both the elasto-dynamic and elasto-static problems of point sources in a multi-layered half-space by using the Thompson-Haskell propagator matrix technique. It is shown that the apparent incompatibility between the two is associated with the degeneracy of the dynamic problem when ω = 0 and both can be handled uniformly using the Jordan canonical forms of matrices. We re-derive the propagator matrices for both the dynamic and static cases. We then show that the dynamic propagator matrix and the solution converge to their static counterparts as ω → 0. Satisfactory static deformation can be obtained numerically using the dynamic solution at near-zero frequency.

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