Cylindrical waves in transversely isotropic media

Abstract

Because of fine layering, many sedimentary rocks can be characterized as transversely isotropic, possessing an axis of symmetry perpendicular to the layering. The many kinds of measurements made in fluid-filled holes drilled parallel to this axis prompted this study of axisymmetric cylindrical waves. The literature shows how such waves in an isotropic solid can be expressed in terms of a compressional potential or a shear potential. This paper shows that in a transversely isotropic medium, particular combinations of these potentials are needed simultaneously, yielding either a quasi-compressional wave or a quasi-shear wave. The expressions are used to compute the transient response of an acoustic logging tool. The speeds of refracted compressional and shear waves agree with the speeds of plane waves traveling along the axis of symmetry. Dispersive waves in the fluid annulus yield further information about the elastic constants of the solid. The potentials also portray the radiation of elastic waves from a point force or from a transducer on the surface.