Spectral analysis approaches have been shown to be useful for the purpose of analyzing dispersion characteristics from borehole acoustical measurements [M. P. Ekstrom and C. J. Randall, J. Acoust. Soc. Am. 98, 2867 (1995)]. In this approach, the receiver wave fields are processed using a hybrid spectral estimator, with the space-time array first being transformed into the space-frequency domain, and a high-resolution estimator based on the matrix pencil used to estimate the wave numbers at each frequency of interest. In the frequency-wave-number domain, the spectral estimates are of sufficient quality to allow the decomposition of the spectral description into its constitutive parts. The frequency-wave-number plane is segmented to capture the loci of poles for an individual mode or headwave, and the spectral components within this segment extracted from the spectral descriptor matrices. This allows an individual mode to be isolated from the multicomponent wave fields, and the subsequent detailed analysis of its slowness and attenuation. Furthermore, the extracted spectral information can be used to reconstruct the space-time description for the individual mode, thereby providing the complete duality of viewing the individual components in both the space-time and frequency-wave-number domains. This procedure will be demonstrated using both model [C. J. Randall, J. Acoust. Soc. Am. 90, 1620--1631 (1991)] and field data sets.