Reflection and transmission of plane waves by a layer of compact inhomogeneities

J. D. Achenbach*, M. Kitahara, Y. Mikata, D. A. Sotiropoulos

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


Reflection and transmission of elastic wave motion by a layer of compact inhomogeneities has been analyzed. For identical inhomogeneities whose geometrical centers are periodically spaced, the problem has been formulated and solved rigorously. The reflected and transmitted longitudinal and transverse wave motions have been expressed as superpositions of wavemodes, where each wavemode has its own cut-off frequency. At its cut-off frequency a mode converts from a standing into a propagating wavemode. The standing wavemodes decay exponentially with distance to the plane of the centers of the inhomogeneities. At small frequencies only the lowest order modes of longitudinal and transverse wave motion are propagating. Reflection and transmission coefficients have been defined in terms of the coefficients of the zeroth-order scattered wavemodes. These coefficients have been computed by a novel application of the Betti-Rayleigh reciprocal theorem. They are expressed as integrals over the surface of a single inhomogeneity, in terms of the displacements and tractions on the surface of the inhomogeneity. The system of singular integral equations for the surface fields has been solved numerically by the boundary integral equation method. Curves show the reflection and transmission coefficients for the reflected and transmitted longitudinal and transverse waves as functions of the frequency. Some results are also presented for planar distributions of cracks whose spacing and size are random variables. Finally, dispersion relations are discussed for solids which are completely filled with periodically spaced inhomogeneities.

Original languageEnglish (US)
Pages (from-to)101-118
Number of pages18
JournalPure and Applied Geophysics PAGEOPH
Issue number1-2
StatePublished - Mar 1 1988


  • Reflection
  • compact inhomogeneities
  • cracks
  • plane waves
  • transmission

ASJC Scopus subject areas

  • Geophysics
  • Geochemistry and Petrology


Dive into the research topics of 'Reflection and transmission of plane waves by a layer of compact inhomogeneities'. Together they form a unique fingerprint.

Cite this