## 3 Field Data Application
Figures 7a-c and 8a-c show the multivariate intrinsic mode functions (MIMFs) from the MVMD method, geological structural changes are more consistent and reasonable, which improves seismic interpretation. Figure 4: The location of wellbore and the through-well seismic profiles. (**a**) The time slice at t = 1650 ms; (**b**) the vertical seismic profile extracted at Crossline No. 98520; (**c**) the vertical seismic profile extracted at Crossline No. 11272. The dotted lines indicate the location of the through-well seismic profiles. For extracting the appropriate frequency bands, the dominant frequency of seismic data is considered, which is approximately 45 Hz on average with the effective bandwidth ranging from 10 to 81 Hz. Accordingly, three frequency bands of the RMS amplitude are chosen, including 10-33 Hz, 34-57 Hz, and 58-81 Hz, by the STFT method (Figure 9a-c). Consequently, three decomposed components are calculated by the VMD and MTVMD methods, as shown in Figures 10 and 11, respectively. Based on the VMD methods, channels of the fluvial-delta depositional system in the Shawan Formation are complete, verifying the results of the proposed method. Figure 5: The well log recording of Well C1 in Figure 4. The dashed circle indicates the location of the seismic geological channel. Figure 6: The RMS amplitude slices at t = 1650 ms calculated by full bandwidth seismic dataset. that both the VMD and MTVMD methods are valid for enhancing the geological features' discrimination. However, details of the geological features, especially for the subtle seismic geological channel features, are dissimilar. Figure 8: The decomposed components of the seismic vertical profile BB’ by using the MTVMD and the VMD methods. (**a–c**) are the components from the MTVMD method; (**d–f**) are the components from the VMD method. Black arrows indicate the lateral inconsistency in seismic profile. Figure 7: The decomposed components of the seismic vertical profile AA’ by using the MTVMD and the VMD methods. (**a–c**) are the components from the MTVMD method; (**d–f**) are the components from the VMD method. Black arrows indicate the lateral inconsistency in seismic profile. Recognized channels in fluvial-delta depositions are noted as red arrows in Figures 9-12. The presence of gaps and \"jumps\" in Figure 10a,c, marked as the black arrows, are evident due to the inconsistent center frequency. Overall, it is noticed that the high-frequency data (e.g., Figures 9c, 10c and 11c) are all presenting more sedimentary details compared to those of a low and medium frequency. However, it is always difficult to identify the spatial location, width, and flow direction of the narrow channels by using traditional time-frequency analysis methods. Although the high-frequency results are not as clear as the intermediate-frequency results in some locations, it is evident that the high-frequency spectrum is better described. For instance, some narrow channels (shown as the red arrow in Figure 11) in slices by the VMD method (Figures 10a and 11b) are expected but unrecognizable, however, these characteristics are significantly improved using the MTVMD based algorithm (Figure 11c,d). Figure 10: The RMS amplitude slices at t = 1650 ms. (**a**–**c**) show three decomposed components from the VMD method: (**a**) IMF1; (**b**) IMF2; (**c**) IMF3. Figure 9: The RMS amplitude slices at t = 1650 ms. (**a**–**c**) show the RMS amplitude from the three frequency bands: (**a**) 10–33 Hz; (**b**) 34–57 Hz; (**c**) 58–81 Hz calculated by STFT method. Specifically, spatial spreading of the narrower branched channels is differentiated (Figure 10c, marked with a red arrow), except for the main stream of wide channels (Figure 9c). Subtle channels in lateral distributions are more distinct with the MTVMD method (Figure 11c, red dash lines). As estimated by scales, the resolution of channels by  
Figure 6.0 The RMS amplitude slices at t = 1650 ms. (**a–c**) shows three decomposed components from the MTVMD method: (**a**) IMF1; (**b**) IMF2; (**c**) IMF3.