Seismic waves often are strongly attenuated in the near surface. The measurement and compensation for attenuation are crucial for high-resolution seismic imaging. The quality factor (), as a measure of attenuation, is usually estimated by frequency-based methods. We have extended the centroid frequency-shift (CFS) method for estimation to high loss media without the usual assumption of . The adaptability of this approach for an unknown source wavelet also is demonstrated. Skewness and kurtosis have been used for analyzing the spectral shape change during attenuated wave propagation. Synthetic data tests show a strong relationship between skewness and factor estimation accuracy for the conventional CFS method. Surprisingly, our extended CFS approach shows frequency band insensitivity and accuracy for strongly attenuating media. The relative insensitivity of the method to the selected or available frequency bandwidth is shown to be the theoretical basis for its good noise immunity. Finally, a layered medium inversion method is derived, which is appropriate to vertical seismic profile (VSP) surveying and is applied to a multioffset field VSP data set to obtain a reliable and stable internal value depth distribution.