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

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

Mar 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002geoji.148..619z&link_type=abstract

Geophysical Journal International, Volume 148, Issue 3, pp. 619-627.

Astronomy and Astrophysics

Astronomy

34

: Deformation, Elastic Wave Theory, Seismic Wave Propagation

Scientific paper

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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