## 3 Results
### Physical Modeling Data Example
Colored circles indicate the locations of fracture clusters associated with different faults. The northern region contains eight systematically arranged fracture sets (marked as the black numbers 1–8), with controlled variations in density, spacing, and orientation. To compare the structural interpretation capabilities of different methods, a horizon slice from the target layer was selected to evaluate the original seismic amplitude, instantaneous phase, traditional C3 coherence, and the proposed OOCA coherence, as shown in Figure 7. The original amplitude slice (Figure 7a) exhibits continuous reflectors but lacks structural contrast in fault- and fracture-rich areas, particularly in the northern and central parts of the section, making it difficult to identify discontinuity boundaries. The instantaneous phase attribute (Figure 7b) exhibits certain structural responses to the southern fault and northern fracture sets; however, the overall imaging remains blurred, with poorly defined boundaries. The traditional C3 coherence slice (Figure 7c) improves lateral discontinuity contrast compared to amplitude and phase attributes and delineates some fault and fracture boundaries. However, the overall fault continuity remains blurry, and responses to small-scale structures are weak, especially in the densely fractured northern region (blue box). In contrast, the OOCA coherence slice (Figure 7d) demonstrates superior performance in structural imaging. It provides clear and continuous boundaries of southern reverse faults (indicated by red arrows), accurately delineates multiple fracture sets in the north (blue and  
Figure 6: OOCA coherence slices at different Gabor frequencies: (**a**) 10 Hz, (**b**) 30 Hz, (**c**) 45 Hz, and (**d**) fused result. Green arrows in (**a**) indicate southern faults; red arrows in (**a**–**c**) highlight northern fractures and southern clusters. Blue dashed boxes show frequency-dependent visibility. The fused result (**d**) enhances continuity but introduces slight blurring near high-frequency zones. red boxes), and enhances both structural continuity and spatial resolution. Furthermore, the method preserves background reflector consistency while effectively suppressing noise, offering improved interpretability in complex areas such as fracture-fault intersections. In addition to enhancing structural imaging, the proposed OOCA method offers a practical balance between resolution and computational efficiency. Benchmark evaluation on a 3D seismic model with dimensions of 1500 \(\times\) 625 \(\times\) 625 under parallel computation showed that OOCA completed in 21 min, compared to 16 min for C3 coherence and 13 min for the instantaneous phase method. These results demonstrate that the method improves imaging performance without incurring excessive computational cost, making it feasible for practical applications. To further quantify the performance differences among various methods, we conducted a comparative analysis from two perspectives: overall detection accuracy in the northern fracture zone and the minimum resolvable scale for localized discontinuities. As illustrated in Figure 5b, the northern region contains eight designed fracture sets, totaling 95 individual fractures. The proposed OOCA method successfully identifies 88 fractures, achieving a detection accuracy of 92.6%, whereas C3 coherence and instantaneous phase  
Figure 7: Vertical slices of amplitude (**a**), instantaneous phase (**b**), C3 coherence (**c**), and OOCA coherence (**d**). The OOCA result in (**d**) shows enhanced structural clarity compared to other attributes. The red arrows indicate the superior continuity and delineation of southern reverse faults achieved by the proposed method. The blue and red boxes in the northern section highlight a dense fracture zone, where the OOCA method better captures fine-scale discontinuities compared to the C3 and phase attributes. attributes identify 71 and 76 fractures, yielding detection rates of 74.7% and 80.0%, respectively (Table 1).