Reflection and refraction of acoustic waves at poroelastic ocean bed

Abstract

Ocean bottom is considered as a plane interface between non-viscous liquid and anisotropic dissipative poroelastic solid. The dissipation comes from the viscosity of pore-fluid as well as the anelasticity of the porous frame. Biot's theory is used to derive a system of modified Christoffel equations for the propagation of plane harmonic waves in a porous medium. The non-trivial solution of this system is ensured by a determinantal equation. This equation is solved into a polynomial equation of degree eight, whose roots represent the vertical slowness values for the waves propagating upward and downward in a porous medium. The eight, numerically obtained, slowness values are identified with the four waves propagating towards (or away from) the boundary in the porous medium. Incidence of acoustic wave through the liquid at the interface results in its reflection and the refraction of four attenuating waves in the poroelastic medium. The energy partition among the reflected and refracted waves is calculated at the interface. Conservation of energy is obtained except in the case of partially opened surface pores of the porous medium. Energy refracted to the dissipative porous medium is expressed through an energy matrix. The four diagonal elements of this matrix represent the energy shares of the four inhomogeneous waves and the sum of all the off-diagonal elements of this matrix represents the interaction energy. Few significant results are extracted from the observations in the numerical examples studied. These results represent the effect of anisotropic symmetries, anelasticity, wave-frequency, opening, configuration and flow-impedance of pores, on the energy shares of reflected and refracted waves.

Anisotropic poroviscoelastic medium: reflection of inhomogeneous waves at the plane boundary with restricted seepage of pore fluid

“…In the order of the descending real parts, let denote the four complex roots of (). Then, for , the four waves with complex velocities and V 4 are identified as qP1, qS1, qS2 and qP2 waves, respectively (Vashishth and Sharma, 2009). The prefix ‘q’ with P (S) indicates the particle motion deviated a bit from the longitudinal (transverse) wave.…”

“…Later, Sharma (2008a) explained a general procedure to calculate the slowness surfaces for inhomogeneous propagation of four waves in a bounded anisotropic poroelastic medium. Refraction at the boundary of anisotropic porous solid has been discussed for the incidence of acoustic waves through a fluid (Vashishth and Sharma, 2009). But, reflection at the stress‐free boundary of dissipative poroelastic medium is available for isotropic propagation only (Sharma, 1991b).…”

Wave-induced fluid flow and reflection/transmission of seismic waves at a fluid/double-porosity thermoelastic medium interface

“…However, they did not consider the attenuation of mesoscopic flow. Vashishth and Sharma [17] examined plane waves' reflection and transmission properties at a solid-fluid interface that is anisotropic and poro-viscoelastic. Using acoustoelastic theory, Liu et al [18] investigated the reflection and refraction of plane waves at the interface between fluid and rock, taking into account elastic deformations.…”