The prediction of dispersion curves is an essential part of understanding borehole acoustic modes. Traditional dispersion curve calculation requires finding zeros of the determinant of the characteristic matrix of a borehole system. This approach is subject to interpretational ambiguity because the determinant can be scaled arbitrarily. We have developed an alternative approach based on the reciprocal condition number (RCN) of the characteristic matrix. The RCN quantifies the singularity of a matrix on a fixed scale between zero and unity; thus, it represents wave modal strengths. We find that our method and traditional methods give identical dispersion-curve locations for simple models and that our method provides more insights on the wave modal amplitudes of complicated models with multiple layers, such as those incorporating logging tools and casing strings. Finally, we determine how our method can be used as the basis of sensitivity analysis to indicate how the dispersion curves are dependent on the model parameters.

中文翻译：

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基于互易条件数的钻孔声波频散曲线预测

色散曲线的预测是理解井眼声模的重要部分。传统的色散曲线计算需要找到井眼系统特征矩阵行列式的零。由于行列式可以任意缩放，因此该方法易受歧义解释的影响。我们已经基于特征矩阵的倒数条件数（RCN）开发了一种替代方法。RCN以零到一之间的固定比例量化矩阵的奇异性；因此，它代表了波模态强度。我们发现我们的方法和传统方法为简单模型提供了相同的色散曲线位置，并且我们的方法提供了对具有多层的复杂模型的波模态振幅的更多见解，例如那些结合了测井工具和套管柱的工具。最后，我们确定如何将我们的方法用作灵敏度分析的基础，以指示色散曲线如何依赖于模型参数。