# Microseismic Velocity Inversion Based on Deep Learning and Data Augmentation
## 5 Discussion and Conclusions  
We attempt to directly invert the velocity models from microseismic waveforms in this study. The testing results with purely synthetic data demonstrate the Unet model can predict the layered velocity model quite well and in an efficient manner. Since the predicted velocity models are almost the same as the real ones and thus do not contain much information, we do not show those simple results in this manuscript. [PERSON] et al. [29] demonstrated the effectiveness of a modified Attention Unet in predicting complex synthetic velocity models with microseismic records. They did not consider field microseismic data and adopted Gaussian noise to evaluate the robustness of the model, while we used field data to enhance the synthetic data by data augmentation operations. We also investigate and test many other scenarios by considering different SNRs, source locations, source mechanisms, and model numbers and sizes to mimic the field cases. Specially, the number and coverage of real microseismic events largely determine the features and constraints that can be extracted by the network model. However, these cases just introduce more complicated features which require a larger training dataset and computation expense. Further investigation of the influential factors on deep learning-based microseismic velocity inversion is out of the scope of the current study. The disadvantage of most current deep learning algorithms is the heavy dependence on the training dataset and weak generalization capability. The introduced data augmentation method and hybrid training strategy proved to be effective in alleviating the feature gap in data domains and improving the generalization ability of the network model, which may provide guidance for other deep learning-based seismic inversion tasks. Transfer learning is also helpful to fill the feature gap, but also relies on the scale of the training data. Another feasible approach to realize seismic inversion with a limited training dataset is combing data-driven algorithms with the physical laws of seismic wave propagation, to provide more physical constraints and optimize the learning performance. In this work, we only consider a horizontally layered model, which is the most-commonly used model in microseismic processing. We will investigate the performance of the proposed method on \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Training Dataset** & **Phase** & **PSNR** & **SSIM** & _MAE_ \\ \hline \multirow{2}{*}{Synthetic} & P & 18.75 & 0.7094 & 314.843 \\  & S & 19.16 & 0.7209 & 155.461 \\ \hline \multirow{2}{*}{Augmented} & P & 21.50 & 0.7030 & 228.985 \\  & S & 17.89 & 0.6759 & 152.441 \\ \hline \multirow{2}{*}{Hybrid} & P & 22.24 & 0.7478 & 221.382 \\  & S & 18.46 & 0.6369 & 165.114 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The mean values of quantitative metrics for multi-stage examples. Figure 10: The loss curves for three different training strategies. heterogeneous models and compare it with conventional velocity inversion methods (e.g., FWI method). One of the advantages of deep learning methods is the weak dependence on the raypath coverage since we can train the model with a large and complete dataset. In this paper, we propose an improved deep learning method for microseismic velocity inversion. The synthetic data are augmented to incorporate the features of the real data, and a hybrid training strategy that integrates the synthetic and augmented data is introduced. The Unet model can directly predict the layered velocity model from microseismic waveforms. Training the synthetic data involves first learning the low-frequency information in the data, and then it can provide an initial velocity model. Then, the augmented data are trained to learn the high-frequency information, which can improve the precision of the predicted velocity model. The hybrid training strategy makes better use of the data and enables the model to learn more imbedded connections between the waveforms and velocity models.