## 1 Introduction
Q estimation methods based on time frequency domain mainly use wavelet transform, S transform, and the generalized S transform and other time frequency analysis methods, including wavelet envelope peak frequency offset method. Constant Q can be estimated via Gabor Analysis (CVG) based on Gabor spectrum, etc. [PERSON] et al. (2009) [35] compared four time-frequency analysis methods, namely the short time Fourier transform (STFT), the Gabor transform, the S transform, and the continuous wavelet transform, and pointed out that different transforms have different time frequency characterization capabilities. A time frequency characterization method has also been proposed using least square inversion and regularization constraint algorithms for seismic data sand detection, noise suppression, and Q value estimation of post stack seismic data. Based on the wavelet envelope peak frequency migration method, [PERSON] and [PERSON] (2013) [36] proposed the EPIFO method to calculate the quality factor of pre-stack CMP data by using horizon information, which provides an effective basis for reservoir prediction. Based on the generalized S transform, [PERSON] and [PERSON] et al. (2018) [37] proposed the continuous spectral ratio slope method to calculate the Q value of the pre-stack CMP channel set based on the linear relationship between Q value and offset distance and the Dix formula, which improves the resolution of the Q profile and correctly characterizes the absorption characteristics of seismic wave energy by the formation. [PERSON] and [PERSON] (2020) [38] proposed a Q estimation method based on the mutual correlation function and S transform to calculate the Q value based on the linear relationship between the spectral ratio and frequency, which can reduce the error caused by the Gaussian window function. [PERSON] and [PERSON] (2022) [39] proposed a method to extract the quality factor Q based on the S transform and variational method to address the problems of insufficient noise immunity and over dependence on the seismic wavelet type of the traditional method. Each of these methods has its own advantages and disadvantages, and none of them is universally applicable. The effectiveness depends on the quality of the records. In earthquake seismology, the attenuated travel time tomography is first applied for attenuation calculation in the shallow crustal [40]. In seismic exploration, the approach is modified and used for seismic data attenuation calculation [41; 42; 43]. The Q volume can be calculated by this method and its resolution is controlled by the size of the grid. By comparing the estimated and real attenuated travel time, the Q volume can be inverted [44]. The key of the method is the accuracy of attenuation travel time. The conventional method calculates it by choosing frequency components with high S/N ratio and always introduce bias of the results. To overcome this disadvantage, the proposed method uses spectral ratio of seismic data in simultaneous inversion. The method can calculate multiple attenuated travel times simultaneously. The error from frequency component selection can be avoided by taking into account the different ray paths in the overburden and thus give more accurate Q results.