# Development of a Deep Neural Network Model for the
## 4 Results and Discussion  
### Linearly Distributed Events  
We have developed four models (designated as Model I to Model IV) capable of inversely predicting velocity models and the locations and times of earthquakes that are spatially distributed linearly (generated using event generation method I). Using an iterative training approach, we conducted tests to evaluate the efficacy of these models in earthquake relocation. Our evaluation involved generating new datasets using the same methods employed for training data generation, then utilizing our trained models to predict earthquake source relocations The primary focus of this assessment was comparing the predicted source locations against the actual source locations to assess the performance of our DNN models. It is important to emphasize that the true data used in the testing phase is generated independently and is not related to the true data used during training. Firstly, we examined linearly distributed earthquake locations to simulate scenarios where earthquakes occur along a linear faulting plane (Figure 6). We also preformed analysis on the discrepancies between the actual source locations and our predicted locations of earthquakes, using models I-IV (Figure 7), and we found the following:  
Figure 6: Performance test of the first four models with linear data. Panels (**a–d**) correspond to models I–IV, respectively, where the crosses represent the true data and triangles denote predicted coordinates. * Model I: Average distance error in earthquake source location is approximately 20 m. The trend in predicted locations for the first 50 events varied widely, showing a lack of linear trend in most cases. However, the vertical velocity model achieved a close fit of 99%. * Model II: Average distance error in earthquake source location is around 18 m. There was some linear trend observed in the first 50 events, although the coordinates clustered together. Later events showed a clearer linear trend, with the vertical velocity model also achieving a 99% match. * Model III: Average distance error in earthquake source location ranges from 12 to 16 m. A majority of the events exhibited a linear trend. * Model IV: Distance errors mostly ranged between 5 to 10 m, indicating the closest proximity between predicted and actual earthquake coordinates. These findings highlight Model IV as the most accurate in predicting earthquake source locations, demonstrating significant improvement in localization precision compared to the other models. Also, for the sake of comparison and assessing our model's performance against traditional relocation techniques, we made a comparison with the results obtained from a genetic algorithm. The genetic algorithm starts with a pre-assumed earthquake location at (x, y, z) and a velocity model similar to the one used for generation training data in this study. Each iteration of the genetic mutation allows the (x, y, z) and parameters that describe the velocity model (30 layers with no account for horizontal variation) to vary by a certain percentage (10% in this study). The seismic wave arrival times are calculated with these parameters and compared with station recorded arrival times. L2 norm is used as the metric to determine if this mutation yields better results; if the L2 norm is smaller than the previous iteration, these mutated parameters are kept and allowed to further mutate in the next iteration. The iterative process stops when the L2 norm stops improving/decreasing. Figure 7: Performances of models I–IV. (**a**) Error in predicted coordinates compared to actual source coordinates, and (**b**) histogram showing the distribution of errors. Figure 7 shows that the results produced by this traditional genetic algorithm is less accurate than our models, even the initial model I. Considering that our model can be further improved with more iterations and the input of more field 'true' data, the accuracy disparities between our model and the genetic algorithm will only be greater.