###### Abstract
Building on the pseudo-depth conversion, [PERSON] (2012) and [PERSON] et al. (2019) developed deterministic seismic inversion workflows for rock properties [15; 16]. [PERSON] et al. (2018) used pseudo-depth conversion to invert depth-domain fluid factors [17]. In addition, [PERSON] et al. (2018) extracted the wavelet from depth-domain seismic data using pseudo-depth conversion and the Gibbs sampling algorithm [18]. Moreover, according to the pseudo-depth conversion, [PERSON] et al. (2022) searched for the wavelet that minimizes the residual difference between the synthetic record and the field data as the estimated constant wavelet in the pseudo-depth domain [19]. In short, domain conversion is time-consuming and introduces additional uncertainty to the geophysical workflow [20]. To reduce the accumulation of resampling errors caused by repeated domain conversion, [PERSON] et al. (2022) derived an analytic formula for the depth-domain forward process from the time-domain wavelet and the depth-domain model and attained direct acoustic impedance (AI) by the least-squares method in the depth domain [2]. The last group of methods uses depth-domain seismic wavelets to accommodate the non-stationarity of depth-domain seismic data. And then it directly carries out seismic inversion in the depth domain. The approaches used for estimating depth-domain seismic wavelets mainly include point spread functions [21; 22] and depth-wavenumber spectral decomposition [20; 23; 24]. [PERSON] et al. (2012, 2016) replaced the 1D wavelet in conventional time-depth inversion with the point spread functions of depth imaging processing, attaining direct seismic inversion in the depth domain [21; 22]. Then this idea was applied to complex subsalt environments [25; 26; 27; 28], depth-domain \(Q\) compensation [29], depth-domain deghosting [30], pre-stack depth-domain elastic inversion [31; 32; 33], 4D inversion in the depth domain [34], and enhanced quantitative interpretation [35]. However, solving the point spread function requires a long computation time and large storage space, and the accuracy of the solution is highly dependent on the accuracy of the built depth-domain velocity model. [PERSON] and [PERSON] (2018) performed depth-wavenumber spectral decomposition on the depth-domain seismic data and estimated depth-variant wavelets from the depth-wavenumber spectrum [23]. They could then carry out the inversion of the depth-domain seismic data directly through a non-stationary convolutional model. Based on this idea, [PERSON] et al. (2021) also extracted depth- and angular-variant wavelets to predict depth-domain elastic parameters through linear Bayesian inversion [20]. The spectral decomposition method avoids error accumulation caused by repeated domain conversion and makes full use of the high-frequency information of logging data, which is conducive to the prediction of thin reservoirs. However, the extracted depth-variant wavelets based on the spectral decomposition method may change too sharply with the depth, affecting the accuracy of inversion results. In brief, the last group of methods mainly addresses the issues of depth-domain wavelet extraction and establishing a convolutional model for inversion. In summary, the optimal approach uses depth-domain wavelets to characterize the non-stationarity of depth-domain seismic data. This enables direct seismic inversion based on the non-stationary convolutional model in the depth domain. However, these depth-domain seismic wavelet extraction methods do not consider attenuation. Amplitude decrease and frequency dispersion occur when the source wavelet propagates in the actual medium, and the degree of variation is related to the propagation distance and attenuation strength. The generalized seismic wavelet is a compact and flexible model, which describes the actual seismic wavelet well. The generalized seismic wavelet is defined by the fractional derivative and reference frequency.