## 4 Discussion  
The multitrace reflectivity inversion method based on geological sparsity criteria proposed in this paper demonstrates significant advantages in improving inversion accuracy and stability. By integrating geological guidance information into the sparse matrix, this method not only optimizes the inversion results but also achieves promising outcomes in practical data applications.  
The inversion method proposed in this paper differs from conventional geological structural constraint methods. Conventional methods primarily derive structural information through mathematical or physical formulas, such as calculating total variation regularization [16; 34] or using dip attributes [35; 36]. And the extracted structural constraints are directly applied to the inversion objective function. Therefore, the structural information above may not align with the actual subsurface conditions. Moreover, as variables during the iterative process, the structural constraints are computationally unstable. In contrast, our geological-guided approach introduces prior geological knowledge and geological interpretation, providing guidance information. The prior geological information is directly incorporated into the inversion matrix. Here, known geological insights are quantitative, and they influence the iterative process but do not change during the process. This ensures greater stability of the prior geological information.  
Despite these advantages, several limitations should be noted. First, the effectiveness of the geologically guided inversion largely depends on the availability, accuracy, and completeness of the prior geological knowledge (**Geo** matrix). In regions where geological interpretation is incomplete, uncertain, or incorrect, the inversion results may still be affected by artifacts or misinterpretations. Moreover, acquiring high-quality geological  
Figure 14: Comparison of C3 coherence attribute slices of the target reservoir original data and inversion data: (**a**) C3 coherence attribute slice from original data; (**b**) C3 coherence attribute slice from inversion data. The figure demonstrates the enhanced reservoir characterization from inversion: the original coherence slice (**a**) shows obscured features under coal-seam interference, while the inversion result (**b**) clearly reveals fault and karst systems, validating the method’s effectiveness.  
information requires extensive analysis and expertise, which may not always be feasible in every field area. Secondly, although the sparse matrix construction enhances seismic resolution, the performance of the inversion remains inherently limited by the choice of the initial sparse basis \(\mathbf{Q}\), particularly in highly heterogeneous geological environments. This is because the static sparse basis may not fully capture local complexity. Future work should focus on developing adaptive sparse representations and dynamically updated geological constraints to further improve the robustness and generalization of the inversion process.  
In addition, for specific geological targets such as coal seam characterization, integrating targeted predictive techniques developed by other scholars [37, 38] could provide more accurate geological priors. Combining such targeted geological prediction with the proposed geologically guided inversion framework represents a promising avenue for further improving inversion precision. Furthermore, the current study focuses solely on seismic data. Future research will prioritize multi-physics data integration, such as coupling seismic, electromagnetic, and gravity data within a joint inversion framework, to achieve more comprehensive and accurate characterization of complex geological structures and subtle hydrocarbon reservoirs.