Diagnosing and Breaking Amplitude Suppression in Seismic Phase Picking Through Adversarial Shape Learning

TL;DR

This framework autonomously discovers target geometry without a priori assumptions, offering a generalizable solution for segmentation tasks requiring precise alignment of subtle features near dominant structures.

Abstract

Deep learning has revolutionized seismic phase picking, yet a paradox persists: high signal-to-noise S-wave predictions consistently fail to cross detection thresholds, oscillating at suppressed amplitudes. We identify this previously unexplained phenomenon as amplitude suppression, which we diagnose through analyzing training histories and loss landscapes. Three interacting factors emerge: S-wave onsets exhibit high temporal uncertainty relative to high-amplitude boundaries; CNN's bias toward sharp amplitude changes anchors predictions to these boundaries rather than subtle onsets; and point-wise Binary Cross-Entropy (BCE) loss lacks lateral corrective forces, providing only vertical gradients that suppress amplitude while temporal gaps persist. This geometric trap points to a shape-then-align solution where stable geometric templates must precede temporal alignment. We implement this through a conditional GAN framework by augmenting conventional BCE training with a discriminator that enforces shape constraints. Training for 10,000 steps, this achieves a 64% increase in effective S-phase detections. Our framework autonomously discovers target geometry without a priori assumptions, offering a generalizable solution for segmentation tasks requiring precise alignment of subtle features near dominant structures.

Figures (13)

• Figure 1: The dynamic process of amplitude suppression. Color coding: P-wave (blue), S-wave (orange), Noise (green); light/dark colors show labels/predictions. This figure visualizes key training steps from a conventional supervised model. The model exhibits a specific learning sequence: initially producing right-flanked responses at regions of sharpest amplitude change, then learning left flanks to form half-Gaussian curves with plateaus, and finally attempting to differentiate P/S features and grow peak amplitudes. However, even in late training stages, the S-phase peak remains trapped at $\sim$0.5 amplitude, oscillating in this suboptimal state. This depicts suppression as a dynamic process, not a static outcome. See Supplementary Movie https://youtu.be/rdnCe1mJpA8 (10,000 steps) and Movie https://youtu.be/tNiBvxP69uM (100,000 steps) for extended dynamics.
• Figure 1: Comparative Analysis of P-wave and S-wave Arrival Time Labels. (a) P-wave: The amplitude boundary coincides with true arrival time, providing a distinct marker with low temporal uncertainty. (b) S-wave: Increasing epicentral distance causes waveform broadening and blurred amplitude boundaries. Longer propagation paths produce multiple overlapping waves, reducing amplitude gradients and annotation accuracy. This produces broad temporal uncertainty in S-wave arrivals, which combined with manual annotation errors significantly impairs model convergence.
• Figure 2: Visual diagnosis and correction of amplitude suppression. Color coding: P-wave (blue), S-wave (orange), Noise (green); light/dark colors show labels/predictions. (a) Representative waveform with phase arrival markers: longest line (reference label), upper short line (conventional prediction, panel b), lower short line (our framework, panel c). Note temporal delay between S-wave onset and high-amplitude wave packet. (b) Conventional method exhibits two suppression symptoms: peak amplitude suppressed at 0.5 (below 0.7 threshold) and temporal position shifted rightward toward high-amplitude boundary. (c) Our framework overcomes suppression: peak exceeds 0.7 threshold and temporal position calibrated within ±0.1 s accuracy. See Supplementary Movie https://youtu.be/rdnCe1mJpA8 (10,000 steps) and Movie https://youtu.be/tNiBvxP69uM (100,000 steps) for complete training dynamics.
• Figure 2: The choice of hyperparameter $\lambda$ and its impact on the convergence trajectory. Yellow dots represent temporally accurate predictions (±0.1 s), gray dots fall outside this range. S-wave prediction trajectories under different $\lambda$ settings reveal BCE-GAN loss balance: (a) $\lambda$=5000 (too high): excessive BCE induces rightward bias, overpowering GAN's lateral correction; (b) $\lambda$=4000 (optimal): forces reach equilibrium with stable convergence within accuracy range; (c) $\lambda$=1000 (too low): GAN dominates but temporal localization becomes unstable. This demonstrates the critical role of $\lambda$ in maintaining dynamic equilibrium for the shape-then-align strategy.
• Figure 3: Large-scale quantitative statistics of S-phase predictions: Confirmation and mitigation of suppression. Black Gaussian curves represent reference labels (see Supplementary Fig. \ref{['fig:peak_distribution']} for complete P- and S-wave comparison). (a) Conventional method: dense horizontal suppression band at 0.5 amplitude confirms widespread amplitude suppression. Many predictions within this band are temporally accurate (±0.1 s red lines) but ineffective due to insufficient amplitude. (b) Our framework: suppression band entirely eliminated, replaced by elliptical distribution centered on label apex. This elevates previously sub-threshold accurate predictions into detectable range, achieving 64% increase in effective S-phase detections (peak $>0.7$, time error $<0.1$ s).