Parabolic fitting method for quality factor estimation

The quality factor Q has a wide application range in seis-mic data processing and interpretation. Compared with the commonly used methods of Q estimation (e.g., the spectral ratio method and the centroid frequency shift method), the logarithmic spectral area difference (LSAD) method exhibits better noise immunity. However, the LSAD method uses the area difference in one frequency band, and the Q values es-timated using this method are still unstable under the influ-ence of noise. We have developed a new parabolic fitting (PF) method to estimate Q. This method is an extension of the LSAD method. We derive an analytical relationship between Q and area difference curve of the logarithmic am-plitude spectra. Using the logarithmic area difference of multiple frequency bands to fit the parabola, we improve the accuracy and stability of Q estimation. In addition, the PF method does not require special assumptions regard-ing the source wavelet. We test the PF method in the pres-ence of noise and at varying bandwidths and compare the results with those obtained using the LSAD method. The results of the theoretical examples indicate that the PF method is noise resistant and stable. Applying the PF method to real zero-offset vertical seismic profiling records also indicates that the proposed method can reasonably and stably estimate the Q value of the formation.