# Microseismic Data-Direct Velocity Modeling Method Based on a Modified Attention U-Net Architecture
## 3 Numerical Tests and Results
### Results
#### 3.3.2 Local Marmousi Models  
The descent of the loss function during the training process for the local Marmousi models is shown in Figures 14 and 15. Figure 14 shows the loss for the single-event microseismic dataset, while Figure 15 shows the loss for the multi-event microseismic dataset. Similar to the loss curves observed in the multi-layer random stratigraphic models, training with the multi-event dataset results in a smoother descent and faster convergence of the model's loss function compared to the single-event dataset. However, it typically  
Figure 14: Loss decreases during the training process for single-event dataset of local Marmousi models. Figure 15: Loss decreases during the training process for multi-event dataset of local Marmousi models. requires more iterations than the multi-layer random stratigraphic models. This is due to the diverse nature of the extracted Marmousi velocity models in terms of the number of layers, velocity distributions, and angle variations, unlike the linear velocity variations in the former case. Consequently, finding the optimal configuration necessitates additional iterations. Three randomly selected modeling results from the single-event test set are shown in Figure 16. The velocity model obtained from using single-event microseismic records as the input generally yields accurate results. However, there are discrepancies observed in predicting the locations of geological layer boundaries (Figure 16c) and the magnitude of velocity within these layers (Figure 16a,b). These deviations indicate that although the overall modeling captures the characteristics of the velocity structure, there may be limitations in accurately predicting specific details at geological boundaries and within the layers. This may still be related to the limited ability to capture features in single-event microseismic records. Three randomly selected modeling results from the multi-event test set are shown in Figure 17. The velocity models obtained using multi-event microseismic records as input demonstrate increased reliability. Whether dealing with simpler models that include low-velocity layers (Figure 17a) or more complex models with nonlinear velocity variations across multiple layers (Figure 17b,c), these velocity models accurately depict the angles and distributions of geological layers. This indicates that using multi-event microseismic records as input enhances the modeling capabilities for capturing intricate geological structures and velocity variations. Figure 16: The modeling results for single-event test dataset of local Marmousi models. **(a–c)**: DL predicted results; **(d–f)**: real velocity models. Figure 17: The modeling results for multi-event test dataset of local Marmousi models. **(a–c)**: DL predicted results; **(d–f)**: corresponding real velocity models. FWI is currently considered the most accurate technique for seismic velocity modeling. This approach minimizes the discrepancies between simulated and observed data through gradient optimization techniques, ultimately producing precise velocity models. In this numerical test, a linear initial model was chosen for FWI, with a velocity model (Figure 17f) serving as the true model. Using 17b as the initial model for FWI, the inversion results are shown in Figure 18.  
The results demonstrate that, in the absence of a reliable initial model and when the sub-wavelet frequency is excessively high, FWI can only reconstruct the geological interfaces of high-velocity layers, leading to lower modeling accuracy. In comparison, the modeling results obtained using the method proposed in this paper closely resemble the true model. By using this method as an initial model for FWI, it becomes possible to achieve a more precise characterization of geological interfaces and inter-layer velocities. Compared to the microseismic inversion research by [PERSON] et al. [19], they used a single network to simultaneously tackle source localization and velocity model updating tasks, while our focus lies solely on microseismic velocity modeling.