## 3 Field Data Application  
We evaluate the performance of the proposed method by a 3D field seismic data. The dataset here is derived from the Chepaizi uplift in the western Junggar Basin, China. The Chepaizi Uplift was formed during the deposition of the Neogene Shawan Formation as a large-scale terrestrial slope with fluvial-delta sedimentation in the western basin, and it currently offers a potential exploratory perspective [27, 28]. These data contain the sedimentary transition from the braided channel to the curved channel and the near-end delta, with frequent vertical superposition of sand bodies and continuous channel migration in the Shawan Formation. Discriminating subtle geological features of sedimentary channels from seismic data is difficult, due to the complicated patterns of the fluvial-delta deposition. Figure 3 shows the 3D field dataset, and time slices and vertical profiles are extracted from the seismic volume. The exacted time slice at t = 1665 ms (Figure 4a), the vertical profiles at inline No. 98520 (Figure 4b), and crossline No. 11272 (Figure 4c) are used as cases. As seen in the vertical profiles, pinch out on both sides of the seismic reflections are characteristic of the fluvial seismic facies (noted by the black arrows), however, hardly seen features of an entire channel in the horizontal time slice. We can use the through-well seismic profiles to analyze more precisely the properties of the seismic geological channels. Figure 5 depicts the location of Well C1 on the southeastern channel of the selected real data. Through the lithological characteristics of the channel of Well C1, the grain size gradually becomes finer, the grains are coarser, and the lithology is gravel-bearing fine sandstone with a thickness of 2-9 m. The logging facies at the black ellipse dotted line is a zigzag box shape, which is in line with the logging facies type characteristics of the channel. On the well-passing seismic section, it can be seen that the seismic facies at the location of the black ellipse dotted line are continuous-moderately strong amplitude, which is consistent with the characteristics of the seismic facies type of the channel, and has a channel shape in the lateral direction. Figure 3: The 3D view of the field seismic dataset. AA\({}^{\prime}\) and BB\({}^{\prime}\) are through-well seismic profiles. We use the full bandwidth dataset to calculate the Root Mean Square amplitude to analyze the seismic geological channels in this dataset, as shown in Figure 6. The figure shows that the extension direction and detailed description of the subtle channel facies are not clear. Apparently, spectral decomposition on the frequency bands is necessary in this case. We evaluate the performance of the proposed method by 3D field seismic data. To compare the performance on the resolution, we extracted band range frequency profiles and applied VMD- and MTVMD-based methods for comparison. Otherwise, RMS amplitude is else calculated. We demonstrate the superiority of MVMD over VMD using the through-well seismic profiles extracted from the seismic data. The input parameters \(K\), \(\alpha\), \(\tau\) and \(\varepsilon\) equal to 3, 2000, 0, and \(10^{-4}\), respectively. Figures 7 and 8 depict the decomposed components by using the MTVMD and VMD methods on the vertical seismic profile AA' and BB', respectively. The center frequencies of the decomposed components are from low frequency to high frequency. In Figures 7d-f and 8d-f, we can observe that the lateral consistency of the 2D data cannot be guaranteed, because the processing is calculated trace by trace. Even a slight oscillation can completely alter the outcome of the breakdown, indicated by the black arrows. Instabilities such as these are a common drawback of the mode decomposition methods, which make it harder to control noise and cause structural abnormalities.