Wave propagation along a cylindrical borehole in an anisotropic poroelastic solid

Abstract

This paper deals with the propagation of elastic waves along a cylindrical borehole embedded in an anisotropic fluid-saturated porous solid of infinite extent. Biot's theory is used to derive the Christoffel equation for the propagation of cylindrical waves in an anisotropic fluid-saturated porous material. The saturated fluid is viscous. Waves of axial symmetry are considered here. The frequency equations of surface waves corresponding to the empty and liquid-filled borehole are obtained. The effects of transverse isotropy on the phase velocity of surface waves are studied. The phase velocity of surface waves increases with anisotropy. Surface modes in empty and liquid-filled boreholes in an isotropic poroelastic solid and Rayleigh waves propagating on the free surface of a transversely isotropic fluid-saturated porous solid are obtained as particular cases. The presence or absence of fluid in the borehole affects the phase velocity considerably. The phase velocity increases when the empty borehole is filled with liquid.