## 1 Introduction
[PERSON] and [PERSON] (2003) [20] showed that the automatic selection of available frequency bands is key to the accuracy in the spectral ratio method. [PERSON] and [PERSON] (2004) [21] used reflection coefficients from well logs to correct for the interlayer interference problem of reflected waves. The success of this method depends on the local relation between the well and the seismic data. Further, it needs the time windows long enough to bracket several periods of the peak frequency of the seismic waves. [PERSON] and [PERSON] (2015) [22] analyzed the error in Q value estimation by the spectral ratio method under the assumption that the Q value varies with frequency. [PERSON] et al. (2014) [23] proposed the logarithmic spectral root equation method for Q inversion, which has improved accuracy and noise immunity. [PERSON] et al. (2015) [24] proposed the logarithmic spectral area difference method. When seismic wave propagates through the media with a decrease in amplitude and reduction in bandwidth, it leads to the variation of the logarithmic spectral area of seismic wave, which enhances the stability of the algorithm compared to that of the traditional spectral ratio method. [PERSON] et al. (2018) [25] proposed a Q value estimation method combining Capon2D and weighting strategy to improve noise immunity and suppress wavelet and relate Q value estimation results to reservoir fracture development characteristics to guide shale gas exploration. Compared with the conventional spectral ratio method, the improved method is insensitive to high-frequency noise and has the ability to suppress wavelet interference. Stable Q value estimation results were obtained by [PERSON] et al. (2019) [26] through the nonlinear inverse amplitude spectral ratio method. To address the problem that the pre-stack seismic data have complex ray paths and there are noise and tuned interference effects that make Q calculation difficult, [PERSON] and [PERSON] (2020) [27] used the local information of seismic events combined with spectral ratio method and multi-ray waveform spectrum to jointly invert Q values based on the seismic wave ray propagation principle, and they also verified the validity of the calculation results by predictive mapping technique. Based on the spectral ratio method, [PERSON] and [PERSON] (2022) [28] performed the second-order Taylor series expansion of the seismic wave amplitude decay term, established the equation related to Q value by the difference of amplitude spectrum at different moments, and proposed a Taylor series expansion-based amplitude spectrum integral difference method, which effectively improved the noise immunity of Q value estimation. In response to the disadvantages of poor stability and dependence on frequency band selection of the spectral ratio method, [PERSON] and [PERSON] (2022) [29] proposed the weighted spectral ratio method with reference to the idea of the weighted center-of-mass frequency shift method, which effectively enhanced the stability of Q value prediction. [PERSON] and [PERSON] (1997) [30] used the shift of centroid frequency to estimate Q values for VSP data, which is calledthe centroid shift method. [PERSON] (2001) [31] used the centroid frequency shift method to combine the interwell seismic velocity and Q value joint tomography on this basis. [PERSON] and [PERSON] et al. (2016) [32] combined the traditional center of mass frequency shift method and Gaussian weighting coefficients to propose a weighted center of mass frequency shift method, which reduces the influence of band selection and improves the accuracy and robustness of Q value calculation. Based on a similar idea, [PERSON] and [PERSON] (2002) [33] brought up the peak frequency method for Q estimation and assumed the source wavelet is Ricker-like. [PERSON] and [PERSON] (2018) [34] introduced the generalized seismic wavelet function on top of the peak frequency shift method to establish the relationship between the GSW function and the quality factor, which enhances the noise immunity of Q value prediction.