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.

中文翻译：

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随钻声波测井中的反射信号和井筒散射波

在随钻声波测井（LWD）中，由于波场非常复杂，因此难以提取反射信号以实现地质导向。在考虑到井眼末端的介质不连续性的同时，基于真实LWD模型的合成声信号来分析反射和散射效应非常重要。我们数值研究了随钻声波对井眼反射边界的响应。为了模拟接收到的信号，实现了时域3D有限差分法。显示了项圈和斯通利波之间的模式转换。井底会产生强烈的反射，这可能等同于其他散射源（即视点源）。井筒底部的散射波通常比来自地层的层界面的反射要强得多。通过将模型与具有相反倾斜方向的分层界面进行比较，除了LWD模型中的传统体波反射（P和S波）之外，还揭示了两个新识别的反射波的传播机制。颈圈波的能量辐射到井眼外部，然后在地层边界反射。同时，来自井底的散射波也会产生反射。这些反射到达分别与射线理论预测的时间匹配。最后，