Open AccessOn extending Biot's theory of multiple scattering at low frequencies from acoustic to elastic media
Author(s) -
Menke William
Publication year - 1982
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1982.tb02776.x
Subject(s) - biot number , boundary value problem , displacement (psychology) , scattering , discontinuity (linguistics) , displacement field , plane wave , boundary (topology) , physics , plane (geometry) , wavelength , mathematical analysis , mathematics , geometry , optics , mechanics , finite element method , thermodynamics , psychology , psychotherapist
Summary We derive a linear, inhomogeneous boundary condition that approximately describes long‐wavelength multiple scatter about a plane of spherical inclusions embedded in an elastic wholespace. This boundary condition relates the discontinuity in the displacement—stress vector to a description of the material properties of the inclusions and to spatial derivatives up to fourth order of the average displacement field across the plane. The boundary condition is an elastic medium analogue to Biot's boundary condition for scattering in an acoustic medium. While the acoustic theory predicts that a plane of rigid, fixed inclusions can support a boundary wave, our results suggest that in elastic media analogous modes are leaky.