## 4 Principles of Technical Methods
### Technical Workflow for Thin-Bedded Sandbody Boundary Delineation  
For the Lower E3d2 Sub-member, an optimized analysis was conducted by integrating seismic facies characteristics and well logging data. Earthquake attributes insensitive to seismic facies were excluded, and those with similar data features were evaluated using correlation and clustering analysis to select optimal seismic attributes. Three types of seismic attributes capable of characterizing the distribution of thin sand bodies were extracted: envelope attributes, main peak attributes, and amplitude energy (Figure 9a). By examining individual attributes, boundaries were delineated using artificial intelligence-based SOM (Self-Organizing Map) clustering to group data with consistent features. Subsequently, well-seismic calibration was employed to determine the threshold for sand body distribution (Figure 9b). After hollowing out non-sand bodies, the spatial distribution of the Lower Member of the Second East Sandstone Formation was sculpted (Figure 9(c-1)). This approach enhances the visibility of beach-bar sand body distribution and provides clearer identification and delineation of sand body edges compared to using single attributes alone. Figure 9: Detailed characterization of Beach-bar Sedimentary Microfacies in the Lower E3d2 Sub-member, HHK Depression, via SOM Multi-Attribute Optimization and Seismic Waveform Inversion Fusion. The attribute following-out map of the Lower E\({}_{3}\)d\({}_{2}\) Sub-member (Figure 9(c-1)) reveals that the study area can be primarily divided into three regions: red, yellow, and green. The number of colors corresponds to the identified clustering types. Based on potential sedimentary environments, green is defined as areas with thin sand bodies near the sandstone pinch-out boundaries, red represents thicker sand bodies marking the main body of the beach-bar, and yellow indicates a transition zone where sand body thickness gradually decreases. Sandstones are concentrated in the southern part of the central strike-slip zone, the central uplift zone, and the development of the northwestern sub-sag, exhibiting sheet-like and domal distributions overall. SOM-based seismic multi-attribute clustering and waveform inversion analysis reveal significant amplitude anomalies on both the east and west sides of the key area, with the anomalies extending in a north-south direction. The central and northern parts exhibit weak amplitudes. Inversion slices show high-resistance anomaly features in the northern parts of well areas C3-1-a and C4-3-a, as well as in the northern part of well area C4-3-a, with irregular dome-shaped boundaries of the anomaly zones. Combining single-well data and geological understanding, waveform inversion was used to predict the cumulative thickness of the Lower E\({}_{3}\)d\({}_{2}\) Sub-member, resulting in a thickness map of sandbody distribution (Figure 9(c-2)). Sandstone layers have developed in the southern part of the central strike-slip zone, the central uplift zone, and the northwestern sub-sag, with thicknesses ranging from 4 m to 12 m. Thick sandbodies are concentrated near wells B8-2-a and C4-4-b in the eastern part of the study area, extending in a near NE-SW direction, while the southwestern part has a large sandbody distribution area with thinner thicknesses (4-8 m) and a sheet-dome shape. The sandbody distribution range is consistent with the structural highs on the top surface map of the Lower E\({}_{3}\)d\({}_{2}\) Sub-member, indicating the potential for oil and gas exploration in the target area. The inversion thickness map shows that the sandbody thicknesses in well areas C3-1-a, C4-3-a, and B8-2-a are relatively thick and gradually thin out toward the surrounding areas. The pinch-out lines of the sandstone thickness and the boundaries of the high-amplitude anomaly regions of the attributes show a high degree of coincidence.