Reciprocal-condition-number-based borehole acoustic dispersion curve prediction

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.