Asymptotic analysis of surface waves at vacuum/porous medium and liquid/porous medium interfaces

Multi-Component Acoustic Characterization of Porous Media

“…In the first method (see also Feng & Johnson (1983a); Edelman & Wilmanski (2002); Gubaidullin et al (2004)) we compose the Green's functions using branch cuts for the square roots q α along vertical half-lines departing from the corresponding branch points being the body-wave slownesses s α , as shown in Figure 5.2. In this figure also the closed integration contour is displayed, which is formed by the entire real axis, Table 5.1).…”

“…Obviously, the loop integrals along the branch cuts can not only affect the waveform but also the spatial decay of a pseudo interface wave. Sometimes, a residue of a pole is (implicitly) considered to represent the corresponding interface-wave part of the spectrum of the Green's function (see e.g., Feng & Johnson (1983a); Edelman & Wilmanski (2002); Gubaidullin et al (2004); Albers (2006);Markov (2009)) while the loop integrals are considered to constitute the part related to body waves and head waves (if present). This can be true but we emphasize that the choice of branch cuts is not unique.…”

“…Several theoretical studies were performed on interface waves propagating along the boundary of a porous medium. Most of them were carried out in the context of Biot's theory for wave propagation in fluid-saturated poroelastic solids and discuss the fluid/porous-medium configuration (Rosenbaum, 1974;Feng & Johnson, 1983a,b;Edelman & Wilmanski, 2002;Allard et al, 2003Allard et al, , 2004Gubaidullin et al, 2004;Albers, 2006;van Dalen et al, 2010b). In general, three types of interface wavemodes can exist at such an interface: the pseudo-Rayleigh (pR) wave, the pseudo-Stoneley (pSt) wave and the true interface wave.…”

“…Physical constraints for the involved square roots were derived using the radiation condition, defining the Riemann sheets where the zeroes lie on. A similar approach was adopted by Edelman & Wilmanski (2002) and Gubaidullin et al (2004).…”

“…Method I is representative of Feng & Johnson (1983a), Edelman & Wilmanski (2002) and Gubaidullin et al (2004), and method II of Allard et al (2004) and van Dalen et al (2010b). In method I we use vertical branch cuts for the involved square roots, which implies that the contributing poles are formed exactly by the zeroes found using the squareroot restrictions of Feng & Johnson (1983a).…”