Radiation of an acoustic dipole source in open and cased borehole with application to single-well shear-wave imaging

Single-well shear-wave imaging using borehole dipole source has recently emerged as an important geophysical well-logging technology to detect formation geologic structures outside an open or cased borehole.Using an integral formulation of the elastic wave-field and solving it using an asymptotic solution,we analyze and compare the radiation of a borehole dipole source in open and cased boreholes.We report,for the first time,the dipole radiation characteristics in fast and slow formations for the frequency range used in the single-well shear-wave imaging.In particular,we analyze the radiation characteristics of SH waves from a cased borehole for the bonded and no-bonding conditions and compare the results with those for the open-hole condition.Our results demonstrate that the dipole radiation characteristics are significantly influenced by formation elastic parameters and source frequency.For a cased borehole,the casing reduces the shear-wave radiation to some extent.However,the radiated wave energy is still significant to allow for applying dipole-shear wave imaging in cased boreholes.Our analysis results provideatheoretical support for the application of the dipole shear-wave imaging technology.