Generate earthquake catalog using the VAE method

The earthquake catalog is essential for seismic activity analysis and earthquake forecasting. Researchers would like to use a complete catalog for further study. In this study, we use a machine learning method to derive a double-variable model to learn the latent rules of catalogs and generate the synthetic ones from a historical catalog. In the first step, we obtain an individual cluster from the catalog by the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm. Then we take the envelope of the magnitude-time curve of the clusters. In the end, we apply the Variational AutoEncoder (VAE) method to learn the inherent feature and produce the latent magnitude-time curves. We use the earthquakes in Southern California from 2016 January 1 to 2022 December 18 to train the VAE model. After training, the model can generate abundant magnitude-time curves and the result shows that the magnitude-time curves during this period can be divided into single-peak, double-peak, and treble-peak patterns. Furthermore, we can use this method to generate more clusters for swarm identification and analysis of regional seismic activity.