# Microseismic Data-Direct Velocity Modeling Method Based on a Modified Attention U-Net Architecture
## 3 Numerical Tests and Results
### Results
#### 3.3.1 Multi-Layer Random Stratigraphic Models  
The descent of the loss function during the training process for the multi-layer random stratigraphic models is shown in Figures 8 and 9. Figure 8 shows the loss for the single-event microseismic dataset, while Figure 9 shows the loss for the multi-event microseismic dataset. Comparing the loss descent curves of the two models reveals distinct patterns for the single-event and multi-event microseismic datasets. The single-event dataset displayed notable oscillations in the early stages of validation during training, gradually stabilizing after approximately 200 iterations and ultimately converging to the optimal solution at around 400 iterations. In contrast, the loss for the multi-event dataset maintained overall stability throughout training, showing smoother descent and reaching the optimal solution after approximately 200 iterations. This disparity can be attributed to the inherent limitations of single-event datasets, which are constrained by the number and positions of seismic sources. These constraints make it challenging to capture all the features of underground velocity structures accurately. As a result, the single-event dataset experiences more pronounced early fluctuations and sharper gradient changes, necessitating a greater number of iterations to find the best parameter configuration compared to multi-event datasets. Figure 7: (**a**) An original multi-event microseismic record. (**b**) Corresponding velocity model. In the single-event test dataset, we selected one velocity model each with two, three, and four layers for presentation in Figure 10. Additionally, we have plotted the corresponding velocity profiles at the chosen model locations, as shown in Figure 11. This visual representation provides a more intuitive evaluation of the accuracy of the modeling approach proposed. Figure 8: Loss decreases during the training process for single-event dataset of multi-layer random stratigraphic models. Figure 9: Loss decreases during the training process for multi-event dataset of multi-layer random stratigraphic models. The comparison of microseismic modeling results with different numbers of layers reveals that for models with fewer layers, such as two or three (Figure 10a,b), the neural network's outputs closely resemble the real models. However, in the case of the four-layer model (Figure 10c), there are discrepancies in depicting the topography and larger errors occur at the model's edges. The profile plots indicate that the modeling results provide reasonably accurate predictions for velocity magnitudes, although there may be some deviations in the positions of the geological layers (Figure 11a,c). Overall, the predictions are reasonably accurate. Figure 11: Velocity profile comparisons for single-event test dataset of multi-layer random stratigraphic models: (**a**) at a horizontal distance of 0.96 km; (**b**) at a horizontal distance of 0.6 km; (**c**) at a horizontal distance of 1.1 km. Figure 10: The modeling results for single-event test dataset of multi-layer random stratigraphic models. (**a**–**c**): DL predicted results; (**d**–**f**): real velocity models. Similarly, in the multi-event test dataset, we selected one velocity model each with two, three, and four layers for presentation in Figure 12. The corresponding velocity profiles are shown in Figure 13.  
Similar to the results obtained using single-event microseismic records as the labeled dataset, the multi-event microseismic modeling results are most accurate when dealing with fewer layers (Figure 12a,b). However, when faced with undulating four-layer geological structures (Figure 12c), there are minor inaccuracies in edge characterization. Nevertheless, the overall modeling results remain reliable. Figure 12: The modeling results for multi-event test dataset of multi-layer random stratigraphic models. (**a–c**): DL predicted results; (**d–f**): real velocity models.