Far-field displacement fields have been derived for an impulsive point force acting on a fluid-filled borehole wall under the assumption that the borehole diameter is small compared to the wavelength involved. The displacements due to an arbitrary source can be computed easily by combining the solutions for the impulsive sources.
In general, the borehole source generates not only longitudinal and vertically polarized shear waves, but also horizontally polarized shear waves. This study also indicates that only the axisymmetric motion around the borehole due to normal stress is affected by the fluid in the borehole. In the long-wavelength limit, the presence of the fluid does not affect the radiation from tangential sources into the surrounding medium.