Propagation of elastic waves in a cylindrical bore in a liquidsaturated porous solid

Abstract

SUMMARY The propagation of the elastic waves in a cylindrical bore through a liquid-saturated porous solid of infinite extent is discussed. The velocity dispersion equation appropriate to the surface wave propagation in a liquid-filled porous solid containing an empty bore is derived. The surface wave which is analogous to a Rayleigh wave at a plane boundary of liquid-saturated porous solid will be dispersive. The case of a liquid-filled bore is also discussed. Study of seismic waves is also concerned with the waves near cylindrical boreholes, since any measurement below the Earth's surface requires the drilling of a hole. Biot (1952) presented an analysis of the problem of propagation of elastic waves in a fluid-filled cylindrical bore hole in an elastic solid of infinite extent. The elastic solid considered was isotropic and homogeneous, and no account was taken of porosity, permeability and viscosity. Keeping in view the presence of porous solids, permeated by groundwater or oil in the Earth, the study of the problem of boreholes in liquid-saturated porous solids is more important. Biot (1956) established a systematic theory for the propagation of elastic waves in a porous solid containing a compressible viscous fluid. Constitutive equations and equations of motion for such solids were also formulated. We discuss here the probleni of propagation of elastic waves in a circular borehole through a liquid-saturated porous solid of infinite extent. Only harmonic waves with axial symmetry are considered here. The problem of propagation of surface waves is treated. Biot's (1952) results are obtained as special case of those presented here. The effects of presence of liquid in the borehole on the phase velocity are examined for a particular model.