## 3 Data and Methods
### Mixed-Phase Wavelet Frequency Broadening  
The predominant frequency of the seismic profile in the study area is 35.5 Hz. The P-wave velocity for typical glutenite is approximately 3800 m/s, and the vertical resolution of the seismic data measures 26 m. However, the thickness of the sand body drilled in  
Figure 2: Stratigraphic column chart of the study area (Well 1601, modified after Qin, 2020).  
the S3 sand group is primarily distributed between 6 and 25 m. As a result, it becomes imperative to achieve high-frequency signal amplification through frequency extension. By effectively widening the frequency band, enhancing high-frequency energy, and improving the resolution of the seismic data, these goals can be accomplished [54; 55].  
In this study, seismic data processing is conducted using mixed-phase wavelet frequency extension technology. This technology can expand the bandwidth and enhance the dominant frequency to a certain extent while achieving phase seismic profile. The definition of wavelet extraction and the determination of the \"expected output\" are crucial factors in assessing the quality and rationality of frequency extension [56; 57]. The vertical resolution of seismic data is influenced by wavelets. According to [PERSON] classical definition of wavelet resolution, a wider wavelet frequency band leads to higher resolution (Equation (1)). Additionally, based on the calculation formula for wavelet period number, a smaller period number (jitter or side lobe) corresponds to higher resolution; thus, a low-cut frequency results in high resolution (Equation (2)). To achieve a broadband wavelet, it is essential to have a narrow main lobe and minimal side-lobe jitter. Hence, [PERSON]'s wavelet is selected as the desired output in this study. The desired output spectrum clearly indicates an increase in the seismic main frequency from 35.5 to 47 Hz (Figure 3). Simultaneously, the effect of broadening the frequency band is evident (Figure 3).  
\[p=2(\mathrm{f}_{2}-\mathrm{f}_{1}) \tag{1}\]  
where \(p\) is the resolution of wavelets, \(\mathrm{f}_{2}\) is the high-cut frequency, and \(\mathrm{f}_{1}\) is the low-cut frequency.  
\[\mathrm{NC}=1+(2\mathrm{f}_{1})/(\mathrm{f}_{2}-\mathrm{f}_{1}) \tag{2}\]  
where NC represents period number of wavelets, \(\mathrm{f}_{2}\) represents high-cut frequency, and \(\mathrm{f}_{1}\) represents low-cut frequency  
Well-side trace analysis revealed that seismic data have improved the ability to detect a thin layer of \(\sim\)10 m. Furthermore, the relative amplitude relationship between different lithology combinations has been effectively preserved before and after data processing. However, for thick sand bodies (<8 m thick), the original seismic data cannot be directly identified due to the limitation of resolution, which makes it difficult to identify single-phase fans and single sand bodies. Therefore, the identification of thin sand bodies needs to be combined with subsequent seismic sedimentology methods to solve this problem.  
Figure 3: Seismic profiles and spectrum analysis before and after frequency extension. (**a**) Seismic profile before frequency extension. (**b**) Seismic profile after frequency extension.