# Early Earthquake Detection Using Batch Normalization Graph Convolutional Neural Network (BNGCNN)
## 5 Results and Discussion  
In this section, we compare the performance of our proposed model with the GNN model [18] through experiments on the California dataset. Performance is evaluated separately for training and validation datasets. Charts of Figure 6 show the mean training error, mean validation error, and mean square error obtained from the GNN model for longitude, latitude, depth, and magnitude predictions. The mean absolute difference between the predicted values and the actual values in the catalog is less than 13 km for longitude and latitude, 3.3 km for depth, and 0.13 for magnitude. The experimental results for the proposed BNGCNN model are shown in Figure 7. The mean absolute difference between the predicted values and the actual values in the catalog is less than 10 km for longitude and latitude, 2.6 km for depth, and 0.09 for magnitude. It is visible from the comparison of both Figures 6 and 7 that the proposed model with batch normalization significantly reduces the error and improves accuracy. Figure 6: Mean absolute error for training and validation sets obtained from the California dataset. Predicted values by GNN model and the actual values for (**a**) latitude, (**b**) longitude, (**c**) depth, and (**d**) magnitude after inserting geographical information. On the training and validation datasets, we examine the model's performance with and without station position information. The results are shown graphically in Figure 8a-d for the baseline model and Figure 8e-h for the BNGCNN model. The black color line shows the training error, the yellow line for validation error, and the blue line for errors when no station location information is used. The performance of the model when including the geographic locations of the stations is examined separately for both the train data set and the validation data set, and the results demonstrate minimal overfitting. The performance is evaluated using the combined data set even when the station locations are not included in the analysis. The model posterior is calculated by running inference 100 times on each event in the training and validation catalogs and determining the related mean and standard deviation while retaining dropout regularization. For GNN, both data sets produce similar results, indicating that overfitting on the training set is minimal. The mean absolute difference between catalog data and model projections is less than 0.13 for magnitude, 3.3 km for depth, and less than 0.11\({}^{\circ}\) (13 km) for latitude and longitude (which translates to a mean epicentral location error of 18 km). For the proposed BNGCNN model, averaging the latitude and longitude values from the catalog and model predictions, the mean absolute difference is less than 10 km in distance for the latitude and longitude (resulting in a mean epicentral location error of 18 km), 2.6 km in depth, and 0.09 in magnitude. The approach produces a respectable first-order estimate of location and magnitude that can be used as a starting point for further refinement using typical seismological instruments. The magnitude curve in Figure 8h illustrates some prominent peaks than Figure 8d. This is because of the scale and shift operations that a batch normalization layer uses [13]. Unlike the input layer, which requires all normalized values to have a zero mean and unit variance, Batch Norm allows its values to be shifted (to a different mean) and scaled (to a different mean). Figure 7: Mean absolute error for training and validation sets obtained from the California dataset. Predicted values by the BNGCNN model and the actual values for (**a**) latitude, (**b**) longitude, (**c**) depth, and (**d**) magnitude by inserting geographical information. variance). It does this by multiplying the normalized values by a factor, gamma, and adding to them a factor, beta. Therefore, the results in Figure 8b are different than Figure 8h. Figure 9a,b show the difference between the event's actual epicenter and the predicted epicenter of GNN and BNGCNN, respectively.