Pseudo Interface Waves Observed at the Fluid/Porous-Medium Interface: A Comparison of Two Methods

Abstract

At the fluid/porous-medium interface the pseudo-Rayleigh (pR) and pseudo-Stoneley ($pSt$) waves exist. The relation with the corresponding poles in the slowness plane is not unambiguous but depends on the choice of branch cuts. For a point-force excitation, the far-field Green’s functions are computed using vertical branch cuts (method I) implying that the $pR$- and $pSt$-poles obey the radiation condition. Then, a separate pseudo interface wave is entirely captured by the corresponding pole residue because the loop integral along a branch cut contributes to a body wave only. When hyperbolic branch cuts are used (method II) the poles lie on the “principal” Riemann sheet. Then, also the loop integrals necessarily contribute to the $pR$-wave because the $pR$-pole is different from that in method I. They do not contribute to the $pSt$-wave when the $pSt$-pole lies on the principal Riemann sheet because the pole is identical to that in method I. When the $pSt$-pole has migrated to another Riemann sheet, however, the $pSt$-wave is fully captured by the loop integrals. In conclusion, the phase velocity and attenuation of a separate pseudo interface wave can be computed from the pole location in method I, but should be extracted from the full response in method II.

This chapter has been published as a journal paper in J. Acoust. Soc. Am. 129 (5), 2912–2922 (van Dalen et al. 2011) and is reproduced with permission. Note that minor changes have been introduced to make the text consistent with the other chapters of this thesis.