Single-well acoustic imaging using a dipole tool has been applied in anisotropic formations. For this application, the effect of anisotropy on the radiation and reception of acoustic waves in the borehole needs to be analyzed and a proper analysis method needs to be developed. We use the far-field asymptotic solution of the wavefield to calculate the radiation pattern of the dipole source in a borehole penetrating vertically transverse isotropic (VTI) formation. We model the spherical wave propagation characteristics of the radiated and reflected waves in the VTI formation and the receiving of the waves in the borehole for the on- and off-axis positions. Based on the developed analytical modeling methods, we study systematically the effects of the formation anisotropy on the radiation pattern and borehole response characteristics. Our modeling result demonstrates that due to the coupling between the longitudinal and the transverse particle motions, quasi-P-(qP-) and quasi-SV-(qSV-) wave radiation patterns contain two components. The result also indicates that the anisotropy causes the arrival time of the SH-reflection wave to differ from that of the qSV wave, and the misposition of the imaged targets would occur if the velocity measured along the borehole is used for migration. The azimuth sensitivity of the off-axis data can be used to help eliminate the 180° ambiguity for the dipole acoustic imaging in the VTI formation. Understanding the effects of anisotropy on borehole acoustic imaging can help improve the accuracy of the imaging result in anisotropic formations.

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