SeisTailFlow: Tail-Aware Conditional Flow Modeling for Reliable Seismic Phase Picking

Seismic phase picking is fundamental to automated earthquake monitoring, yet existing deep learning pickers still exhibit heavy-tailed error distributions, where a small fraction of large arrival-time errors can compromise the reliability of downstream phase association and event localization. We propose SeisTailFlow, a tail-aware conditional flow model for reliable phase picking. Rather than treating large prediction errors merely as residual uncertainty, SeisTailFlow uses out-of-sample residuals to identify waveform conditions associated with elevated error risk and explicitly models their conditional residual structure alongside dominant arrival-time patterns. Technically, SeisTailFlow builds parallel Main and Tail Flows and integrates residual-based tail supervision, background-referenced spectral enhancement, extreme-value regularization, and adaptive vector-field routing to jointly capture dominant conditional structure and high-error-related residual behavior. This design preserves accurate modeling of dominant arrival-time patterns while providing additional capacity for scarce high-error regimes and large arrival-time deviations. Experiments on synthetic data and the STEAD dataset show that SeisTailFlow improves overall picking accuracy and probabilistic prediction quality while substantially reducing tail errors and large-error events, with particularly robust performance under low-SNR conditions.