Pseudo interface waves observed at the fluid/porous-medium interface. A comparison of two methods

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, depending 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.