Wave propagation in porous solid containing liquid filled bound pores and two-phase fluid in connected pores

A mathematical model is considered for wave motion in a porous solid containing liquid-filled bound pores and a connected pore-space saturated by two-phase fluid. For the propagation of harmonic plane waves, the model is solved into a modified form of Christoffel equations, which are solved further to define the complex velocities of four attenuated waves in the medium. Three of these waves are longitudinal waves and the one is a transverse wave. Inhomogeneous propagation is considered with a complex specification of slowness vector involving a finite non-dimensional inhomogeneity parameter. The phase velocities and attenuation coefficients are calculated for the inhomogeneous propagation of each of the four attenuated waves in the porous aggregate. A numerical example is studied to analyse the effects of bound liquid film, sharing of connected pore-space, wave frequency, miscibility of pore-fluids and capillary pressure on the phase velocity and attenuation. The incidence of an acoustic wave at the plane boundary of the ocean bottom is studied to calculate energy partition among the acoustic wave reflected in water and the four waves refracted to oceanic crust. The effects of bound liquid film, sharing of connected pore-space between gas and liquid, wave frequency and capillary pressure on energy partition at the interface are studied in the numerical example. (C) 2012 Elsevier Masson SAS. All rights reserved.