Wavelet-Lifting Fourier transformer with Capsule-based Temporal Deformable Convolution embedded multi-decoder for Earthquake Early warning

In this research, a new framework of multi-task deep learning is proposed for earthquake magnitude, epicentral distance, and focal depth prediction based on the seismic waveforms simultaneously. The study relies on 3 channel seismic recordings from the Stanford Earthquake Dataset (STEAD) that contain a large amount of waveform data and exhibit various characteristics, providing a robust training set for the model. The first step in pre-processing the raw seismic signals is to apply a Butterworth band-pass filter to remove noise and improve the quality of the signals. Then, a Wavelet-Lifting Fourier Transformer (WL-FT) is used to identify meaningful features from the seismic data through multi-resolution characteristics, frequency-domain information, and crosschannel dependency. This allows the model to acquire powerful and noise-tolerant representations. Then the extracted feature vectors are fed to the Capsule-based Temporal Deformable Convolution embedded multi-decoder (CT-DCMD) module. The capsule network is able to capture the hierarchical relationships between features, and the temporal deformable convolution dynamically learns the important time regions with adaptive changes of the receptive field. This has been beneficial for the model to capture complex temporal and structural features of seismic signals. The refined features are then passed through batch normalization, GELU activation, and dropout to stabilize training, enhance non-linearity, and generalize. Last, a multi-decoder structure is employed to simultaneously predict magnitude, epicentral distance, and focal depth. The proposed model is assessed with the help of a number of performance metrics like MAE, MSE, RMSE, and R 2 . The proposed model scored MAE and MSE values of 0.126 and 0.025, respectively. The experimental results show that the model can predict the seismic data with high accuracy and reliability, which is suitable for prediction and early warning of seismic data in the real world.