Borehole radiation and reception responses for azimuthal shear-wave reflection imaging with an off-centred dipole acoustic tool

Abstract Radiation and reception responses of a dipole acoustic logging tool placed eccentrically in borehole fluid are an interesting and important topic in acoustic reflection imaging. Herein, we present a thorough research study on these responses. We treat the wave incidence from the reflector as the radiation from a virtual source and use the cylindrical-wave expansion method to solve both the wave radiation and reception problems for the off-centred tool, which, by using the steepest-descent method, yields asymptotic solutions for modelling the radiation and reception wavefield characteristics. The modelling results from the analytical solution and the 3D finite-difference method were in good agreement. Specifically, we analysed the radiation directivity of an eccentric dipole source in a fluid-filled borehole. The results revealed that the radiation pattern was asymmetric with respect to the borehole, and the asymmetry was determined by the eccentric distance, source frequency and formation properties. In particular, for the typical 3 kHz dipole logging frequency, the radiation was stronger in the off-centred direction than in the opposite direction. The asymmetry of the eccentric radiation resulted in a significant amplitude difference relative to its centred counterpart, which provided a potential method for addressing the 180° azimuth ambiguity of the dipole source. We used a theoretical waveform modelling example to demonstrate this advantage. Therefore, the results of this study provide a theoretical foundation for the development and application of dipole shear-wave imaging technology.