Parabolic fitting method for quality factor estimation

Abstract

The quality factor [Formula: see text] has a wide application range in seismic 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 [Formula: see text] values estimated using this method are still unstable under the influence 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 [Formula: see text] and area difference curve of the logarithmic amplitude spectra. Using the logarithmic area difference of multiple frequency bands to fit the parabola, we improve the accuracy and stability of [Formula: see text] estimation. In addition, the PF method does not require special assumptions regarding the source wavelet. We test the PF method in the presence 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 [Formula: see text] value of the formation.