A theoretical analysis of the logging-while-drilling dipole acoustic reflection measurement

Post-drilling wireline acoustic single-well imaging technology can now detect geological structures tens of meters away from boreholes. Further development of this single-well imaging technology in the logging-while-drilling (LWD) environment will have significant values in real-time applications such as geosteering and reservoir navigation. Based on the wireline imaging application, we propose a new method for the LWD application. In wireline imaging, the four-component (4C) dipole acoustic data are azimuthally rotated to scan the reflectors around the borehole. In LWD, azimuthal scanning is achieved by drilling rotation such that the 4C dipole system in the wireline is replaced by a one-dipole-source and two-receiver LWD system, where the two receivers are mounted on opposite sides of the drill collar. For the LWD application, we first developed the theory for LWD dipole shear-wave reflection imaging and validated the theory using 3D finite-difference waveform modeling. Using the analytical solution, we analyzed the far-field radiation directivity of an acoustic LWD dipole source and the effect of drilling rotation on the shear-wave reflection imaging using the LWD acoustic system. The LWD analysis results show that, for fast formations, the SH-wave is the dominant component for imaging, whereas for slow formations, the P-wave becomes important and can be used for imaging. Our results also indicate that the reflection data acquired by the system are affected by the speed of drilling rotation. The take-off azimuth at the wave radiation may be different from the incident azimuth at the wave reception. Knowing the rotation speed, this azimuth difference can be corrected. A further advantage of using the oppositely mounted receivers is that the reflected wave arrives earlier (later) at the front (back)-side receiver; thus, the arrival time difference between the receivers can be used to eliminate the 180°-azimuth ambiguity of dipole acoustic imaging. For reflection imaging, using the proposed LWD system configuration, we tested its azimuth sensitivity and validated its 180°-ambiguity solution using synthetic LWD and field wireline dipole data. The results of this work, therefore, provide a theoretical foundation for the development of the LWD acoustic reflection imaging system.