Evanescent Acoustic Waves

Abstract

A theoretical study of “geometric” SP-evanescent (head) waves propagating in an isotropic homogeneous half-space or half-plane with a free boundary shows that these waves can satisfy the condition of absence of effort on the boundary plane if and only if the Lamé parameter λ is vanishingly small, which makes the existence of head waves of this type practically impossible. The analysis is based on the Helmholtz representation for the displacement field in combination with the decomposition of the stress and strain tensor into spherical and deviatoric parts. The obtained result about the non-existence of this type of evanescent waves can find application in theoretical geophysics in the study of seismic wave fields in the vicinity of earthquake epicenters, as well as in non-destructive acoustic diagnostic methods.