Abstract: Dispersion and attenuation analysis can be used to determine formation anisotropy induced by fractures, or stresses. In this paper, we propose a nonparametric spectrum estimation method to get phase dispersion characteristics and attenuation coefficient. By designing an appropriate vector filter, phase velocity, attenuation coefficient and amplitude can be inverted from the waveform recorded by the receiver array. Performance analysis of this algorithm is compared with Extended Prony Method (EPM) and Forward and Backward Matrix Pencil (FBMP) method. Based on the analysis results, the proposed method is capable of achieving high resolution and precision as the parametric spectrum estimation methods. At the meantime, it also keeps high stability as the other nonparametric spectrum estimation methods. At last, applications to synthetic waveforms modeled using finite difference method and real data show its efficiency. The real data processing results show that the P-wave attenuation log is more sensitive to oil formation compared to S-wave; and the S-wave attenuation log is more sensitive to shale formation compared to P-wave.