Reflection signals and wellbore scattering waves in acoustic logging while drilling

In sonic logging while drilling (LWD), it is difficult to extract reflection signals for the goal of geo-steering as the wave fields are so complicated. It is important to analyse the reflection and scattering effects based on the synthetic acoustic signals of the real LWD models, while considering the medium discontinuity at the end of the borehole. We numerically investigate the acoustic LWD responses to reflective boundaries out of the borehole. To simulate the received signals, the 3D finite difference in time domain method is implemented. Mode conversions between the collar and the Stoneley waves are revealed. Strong reflections are generated at the bottom of the well, which can be equivalent to an additional scattering source (i.e. an apparent point source). The scattering waves by the wellbore bottom are generally much stronger than the reflections from the layer interfaces of formations. By comparing the models with stratified interfaces of opposite inclination directions, the propagation mechanisms of two newly recognised reflection waves are revealed in addition to the traditional body wave reflections (P and S waves) in LWD models. The energy of the collar wave radiates outside the borehole and then reflects at the bedding boundaries; meanwhile, the scattering waves from the well bottom can generate reflections too. These reflection arrivals match well with the time predicted by ray theories, respectively. Finally, we propose a possible means to estimate the dipping directions of geological interfaces by reflection waves emitted from both LWD transmitters and the apparent source at the well bottom.