Tube Wave Generation At A Layer Boundary For An Incident Compressional Plane Wave

Abstract

An approximate theory for the scattering of an incident plane P wave into tube waves in a fluid-filled borehole drilled through two homogeneous half-spaces is proposed in this paper. This theory is in excellent agreement with the zero frequency formulation (White, 1983) for frequencies below hundreds of Hertz (in the range of conventional crosshole or VSP experiments) and finite difference simulation at high frequencies. At low frequency the excited tube wave is found to be independent of the borehole radius and shows stronger sensitivity to the formation shear velocity contrast across the layer boundary. The sensitivity towards the compressional velocity perturbation is opposite to that of the shear wave and density such that little tube wave can be generated if the compressional and shear velocities are both increased or decreased accordingly. Unlike the tube wave excited in the borehole when an incident plane wave hits a fracture, the reflected and transmitted tube waves generated at a layer boundary show opposite polarities.