Polarizations of split shear waves and flexural borehole waves are most commonly estimated from four-component data using the rotation technique of Alford (1986). Thismethod is limited to the case of the two polarizations being orthogonal to each other.We present a method that is able to handle the case of nonorthogonally polarized wavesand, moreover, is computationally more efficient than Alford's technique. Our methodis based on the eigenvalue decomposition of an asymmetric matrix and a least-squaresminimization of its off-diagonal components. In the case of orthogonally polarized waves,our method will yield exactly the same results as the Alford rotation. We apply ourmethod to a cross-dipole shear-wave logging data set from the Powder River Basin inWyoming and find that independently rotated source-receiver sets are very consistentwith each other in anisotropic sections. After the rotation we compare two methodsfor estimating the phase velocities of fast and slow waves-a semblance method andhomomorphic processing (Ellefsen et al., 1993). We find homomorphic processing to bemore reliable due to the dispersive nature of flexural waves.
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机译：分裂切变波和弯曲钻孔波的极化最常使用Alford（1986）的旋转技术根据四分量数据估算。该方法仅限于两个极化彼此正交的情况。我们提出了一种能够处理非正交极化波情况的方法，而且该方法比Alford技术的计算效率更高。我们的方法基于不对称矩阵的特征值分解及其非对角线分量的最小二乘最小化。对于正交极化波，我们的方法将产生与Alford旋转完全相同的结果。我们将该方法应用于怀俄明州粉河盆地的跨偶极横波测井数据集，发现独立旋转的震源-接收器在各向异性剖面上非常一致。旋转后，我们比较了两种估计快波和慢波相位速度的方法-相似法和同态处理（Ellefsen et al。，1993）。由于弯曲波的分散性，我们发现同态处理更加可靠。
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