The interaction between borehole and elastic waves: theory, method and application

This paper elaborates the theory and method for solving the classic problem of the elastic-wave interaction with a borehole, emphasizing the recent important developments and applications. The use of the cylindrical-wave expansion method to solve both the borehole wave radiation and reception (and scattering) problems avoids the plane-wave incidence approximation commonly used in the latter problem, allowing for correctly modeling the spherical-wave propagation characteristics of the wavefield. By employing the far field asymptotic solution and the reciprocity of borehole radiation and reception, a fast and effective analysis method is obtained. Applying the analysis method to single-well acoustic imaging, one can accurately model and analyze the complex wave phenomena in the borehole wave radiation, scattering/reflection, and reception process. This method can also be used to simulate the azimuthal characteristics of the wavefield from a directional acoustic source (such as borehole dipole source), enabling the determination of the reflector azimuth using the four-component measurement. The analysis results not only laid a solid theoretical foundation for the single-well imaging technology, but also achieved good results in practical applications.