# Microseismic Data-Direct Velocity Modeling Method Based on a Modified Attention U-Net Architecture
## 2 Methods
### Modified Attention U-Net Neuron Network  
The overall architecture of the modified Attention U-Net for velocity modeling in this paper is shown in Figure 1. In a classical Attention U-Net used for image recognition tasks, AGs are typically not applied at the first skip connection due to the argument that they do not capture the characteristics of high-dimensional input data [36]. However, in the context of velocity modeling for seismic data, each layer of feature maps at different scales implicitly contains information and patterns related to the waveforms and velocities. Attention mechanisms can capture the interrelationships between different positions in the input data, aiding in establishing a mapping from the time-domain seismic records to the depth-domain velocity model. Therefore, in this paper, AGs are incorporated into each decoder layer to filter the features propagated through skip connections, thus enhancing the accuracy of velocity modeling. Furthermore, since U-Net's skip connections directly concatenate some of the input with the output, it may add microseismic waveform information into the final velocity model, which can negatively impact the modeling accuracy. Through experiments, it has been observed that the inclusion of AGs alone does not entirely eliminate this influence. As a result, a decision was made to perform weighted concatenation in the final layer. This involves using convolutional operations to automatically learn appropriate weights for the model, followed by weighted concatenation based on the learned weights, as described in Formula (6):  
\[ \begin{array}{l}\lambda_{1}=W_{a}att\\ \lambda_{2}=W_{c}convt\\ concat=concatenate(\frac{\lambda_{1}}{\lambda_{1}+\lambda_{2}}att,\frac{ \lambda_{2}}{\lambda_{1}+\lambda_{2}}convt])\end{array}  \tag{6}\]  
where \(\lambda_{1}\) and \(\lambda_{2}\) represent the computed weight coefficients, \(W_{a}\) and \(W_{c}\) as convolution operations, \(att\) represents the features after AG filtering, \(convt\) represents the up-sampling features, and \(concat\) represents the concatenated features. Training was conducted on a multi-layer random-stratified model dataset using U-Net networks, both with and without the inclusion of attention mechanisms. Experimental testing was performed on test dataset, and the results, including the root mean square error (RMSE) and structural similarity (SSIM), are presented in Table 1. SSIM is designed to simulate human visual perception of image quality by comprehensively assessing the similarity between two images based on brightness, contrast, and structural factors. It provides ranging values [0, 1], with higher values indicating greater similarity. As shown in Table 1, the accuracy of the modified Attention U-Net has improved. The network ingests microseismic records as input and generates corresponding two-dimensional velocity models as output. Before the network training phase, data preprocessing is conducted. Initially, the microseismic data undergoes normalization. In this paper, maximum value normalization is used to scale all microseismic records within the [\(-\)1, 1] range. This normalization process aims to mitigate variations in size among different features, enhance the model's stability during the learning process, improve its resilience to data transformations and perturbations, and expedite convergence. Seismic records typically possess high sampling rates, leading to significant storage requirements for the dataset and increased demands on computational resources. Moreover, the discrep \begin{table}
\begin{tabular}{c c c} \hline \hline
**Neural Network** & **SSIM** & **MSE** \\ \hline U-Net & 0.9355 & \(1\times 10^{-3}\) \\ Modified Attention U-Net & 0.9729 & \(2\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The difference between the predictive models before/after adding AGs and the true model. ancy in size between inputs and outputs leads to augmented computational complexity.