An end-to-end deep learning approach for epicentral distance and magnitude determination from single station waveforms

Conventional single-station earthquake parameter estimation relies heavily on precise P- and S-wave arrival picking, a dependency that often compromises speed and robustness in real-time scenarios. To overcome these limitations, we propose a Deep Fully Convolutional Encoder-Decoder Network designed for the simultaneous estimation of magnitude and epicentral distance directly from three-component waveform time series. Addressing the conflict between neural network input normalization and the loss of amplitude information required for magnitude scaling, we introduce a pseudo-normalization strategy. This approach normalizes the input waveform to facilitate training while preserving the normalization factor, allowing the network to decouple waveform shape features from amplitude scaling to achieve high-precision magnitude recovery. The normalized waveforms are utilized as neural network’s input to predict the epicentral distance and magnitude contribution excluding the absolute amplitude. The architecture employs stacked convolutional and pooling layers to automatically extract waveform features, culminating in a probabilistic output layer that models predictions as one-dimensional Gaussian distributions, thereby quantifying estimation uncertainty. Trained on the comprehensive INSTANCE dataset from Italy, the model utilizes a multi-time-window strategy to simulate real-time data streaming. This enables the system to generate immediate estimates upon station triggering and progressively refine predictions as the waveform evolves. Evaluation on the test set yields a Mean Absolute Error (MAE) of 0.1977 for magnitude and 1.67 km for epicentral distance. These results demonstrate that our end-to-end framework achieves rapid, reliable estimation without the need for auxiliary phase picking, offering significant potential for enhancing Earthquake Early Warning (EEW) systems.