⚡ electrical engineering

Improving Deep Learning-Based Seismic Phase Picking by Addressing Label Imbalance

To address the performance degradation of deep learning-based seismic phase picking caused by label imbalance, this paper proposes an area-weighted soft cross-entropy loss function that enhances model sensitivity and event recovery in continuous waveform analysis without altering the underlying network architecture.

Original authors: Shinya Katoh, Masaaki Imaizumi, Yoshihisa Iio, Hiromichi Nagao

Published 2026-07-31

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Shinya Katoh, Masaaki Imaizumi, Yoshihisa Iio, Hiromichi Nagao

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Earth's Secret Language and the Missing Notes

Imagine the Earth is a giant, restless drum. When it shifts, cracks, or settles, it sends out ripples—seismic waves—that travel through the ground like sound through air. Seismologists are the listeners who try to hear these ripples to understand what's happening deep underground. For decades, their job was like trying to find a specific whisper in a crowded, noisy room. They had to stare at squiggly lines on a screen, manually spotting the exact moment a "P-wave" (the first, fast arrival) or an "S-wave" (the slower, shaking arrival) showed up. It was slow, exhausting work, and with modern sensors recording the Earth 24/7, there was simply too much data for human eyes to handle.

Enter deep learning, a type of computer brain that can learn to spot patterns faster than any human. These digital detectives have become incredibly good at reading the Earth's drumbeat, finding earthquakes that humans might miss. But there's a catch: when the Earth gets really rowdy—like during a massive earthquake followed by hundreds of smaller aftershocks—the "noise" of the big event drowns out the tiny whispers of the small ones. The computer gets confused, often missing the smaller signals because it's been trained to pay more attention to the silence between the rumbles than the rumbles themselves. This paper asks a simple question: Can we teach the computer to listen harder to the quiet parts without changing the computer itself?

Tuning the Ear: A New Way to Teach the Computer

The researchers behind this study, led by Shinya Katoh and his team from the University of Tokyo and Kyoto University, realized that the problem wasn't the computer's "brain" (its architecture), but how they were teaching it. They compared the training process to a teacher grading a student's homework.

In the standard way of training these models, the computer looks at a 30-second chunk of earthquake data. In that chunk, the "background" (the quiet, boring parts where nothing is happening) takes up about 98% of the time. The actual earthquake signals (the P-waves and S-waves) are tiny, sharp spikes that might only occupy 1% each. When the computer tries to learn, it gets a "score" based on how well it predicts the whole 30 seconds. Because the background is so huge, the computer learns that the easiest way to get a good score is to just guess "background" all the time. It becomes lazy, ignoring the tiny, important spikes because they don't matter much to its overall grade. It's like a student who only studies the boring chapters of a textbook because the test is mostly about those chapters, and they completely miss the exciting, crucial plot twists.

To fix this, the team invented a new "grading system" called area-weighted soft cross-entropy loss. Instead of treating every second of the recording equally, this new method gives the computer a massive bonus for getting the tiny, important spikes right. It's like telling the student, "If you get the boring background right, you get one point. But if you spot the tiny P-wave or S-wave, you get a hundred points!" This forces the computer to pay intense attention to the arrival times of the waves, even though they are rare.

What They Found: Catching More Whispers

The team tested this new "grading system" on two popular earthquake-detecting models, SegPhase and PhaseNet. They didn't change the models' brains; they just changed the rules of the game.

The results were a clear shift in behavior. The models trained with the new, weighted rules became much more sensitive.

Sharper Timing: When the models did predict an arrival time, they were much more precise. The "scatter" or spread of their errors dropped significantly. For the SegPhase model, the error spread for P-waves shrank from 0.20 seconds down to 0.07 seconds, and for S-waves, it dropped from 0.27 seconds to 0.05 seconds.
The Trade-off: However, being more sensitive came with a cost. The models started "seeing" things that weren't quite there. They became better at catching the real earthquakes (higher recall), but they also started flagging some noise as earthquakes (lower precision). It's like a metal detector that is so sensitive it beeps at a soda can as well as a gold coin. The researchers found that the models became "recall-oriented," meaning they were less likely to miss a real event, even if it meant they had to check a few false alarms later.

The Real-World Test: The Ridgecrest Earthquake

To see if this actually worked in the real world, the team applied their new models to the continuous data from the 2019 Ridgecrest earthquake sequence in California. This was a massive event with a main shock and thousands of aftershocks.

The results were impressive. The weighted-loss models detected significantly more earthquakes than the original models:

SegPhase found 34,008 earthquakes with the new method, compared to 26,914 with the old method.
PhaseNet found 32,997 earthquakes with the new method, compared to 23,622 with the old method.

These numbers even beat the counts from two existing catalogs created by other experts using different methods. The new models successfully mapped out the same earthquake zones as the experts but found many more small events in between. This suggests that by making the models less afraid of missing a signal, they can help scientists build a much more complete picture of seismic activity.

The Limits: When the Noise is Too Loud

But the story doesn't end with a perfect solution. The researchers were honest about the limits. They found that while the new method was great at finding small earthquakes in the middle of a sequence, it still struggled immediately after the biggest, loudest earthquakes.

Right after a massive quake, the ground keeps shaking for a long time with "coda waves"—a chaotic, high-energy rumble that drowns out the tiny signals of the next small earthquake. Even with the new "bonus points" for spotting signals, the computer couldn't hear the tiny whispers because the roar of the big earthquake was just too loud and messy. The paper suggests that while changing the training rules helps, it can't solve the problem of signals that are physically buried under each other.

The Takeaway

This paper shows that you don't always need to build a bigger, more complex computer brain to solve a problem. Sometimes, you just need to change how you teach it. By re-weighting the importance of the tiny, crucial moments in the data, the researchers made existing models much better at spotting earthquakes, especially the small ones that are easy to miss. It's a reminder that in the noisy, chaotic world of earthquake science, sometimes the best way to hear the future is to listen a little harder to the quiet parts of the past.

Technical Summary: Improving Deep Learning-Based Seismic Phase Picking by Addressing Label Imbalance

Problem Statement
Deep learning-based phase picking has significantly enhanced the efficiency of seismic waveform analysis, achieving accuracy comparable to human experts. However, a critical limitation persists: detection performance degrades when multiple seismic phases occur within a single waveform trace, a scenario common during intense seismic sequences like aftershocks. The authors hypothesize that this degradation stems from label imbalance inherent in semantic-segmentation-based phase picking. In standard formulations, the target labels for P- and S-phases are represented as narrow Gaussian distributions (occupying ~~1% of the time window each), while the background (N) label occupies the vast majority (~~98%). Under standard cross-entropy loss, the training objective is dominated by the background class, causing the model to become conservative and miss weak or overlapping phase arrivals.

Methodology
To address this imbalance without altering the underlying model architecture, the authors propose an area-weighted soft cross-entropy loss (WCE).

Label Construction: Target labels are constructed using Gaussian functions centered at manually picked arrival times ( $\mu$ ) with a standard deviation of $\sigma = 0.1$ s. The background label is defined as the complement to ensure the sum of class probabilities equals one at every time step.
Weighting Scheme: The proposed loss function calculates the temporal area ( $A_c$ ) of each class label for a given waveform. Weighting coefficients ( $\alpha_P, \alpha_S$ ) are derived based on the ratio of the background area to the phase areas. These coefficients are used to define a time-dependent weight $w(b,t)$ that emphasizes samples near the P- and S-phase arrivals (where the Gaussian label is high) and down-weights background samples.
Loss Formulation: The final loss is a weighted mean of the soft cross-entropy over time, normalized by the sum of weights for each trace to stabilize training.
Models Evaluated: The method was tested on two established architectures: SegPhase and PhaseNet.
Experimental Setup: Models were trained on Japanese seismic data. Evaluation involved:
1. Test Dataset: Analysis of arrival-time residuals and threshold-dependent metrics (Precision, Recall, F1).
2. Continuous Application: Application to continuous waveforms from the 2019 Ridgecrest earthquake sequence (July 4–9, 2019) using 36 stations. Phase association was performed using REAL, and hypocenters were determined using Hypomh. Results were compared against original-loss models and existing catalogs.

Key Results

Residual Reduction: The weighted loss function significantly reduced the scatter of arrival-time residuals. For SegPhase, the standard deviation of P-wave residuals decreased from 0.20 s to 0.07 s, and S-wave residuals from 0.27 s to 0.05 s. Similar improvements were observed for PhaseNet. The mean residuals remained at 0.00 s, indicating no systematic bias.
Precision-Recall Trade-off: The weighted loss shifted model behavior toward a recall-oriented regime. While precision decreased slightly due to an increase in false positives (FP), recall improved significantly as false negatives (FN) were reduced. The models became less conservative, generating probability peaks for weaker or partially overlapping arrivals that the original-loss models missed.
Event Recovery in Ridgecrest: When applied to the Ridgecrest sequence, the weighted-loss models detected substantially more earthquakes than the original-loss models and exceeded the event counts of reference catalogs based on template matching.
- SegPhase: 34,008 events (Weighted) vs. 26,914 (Original).
- PhaseNet: 32,997 events (Weighted) vs. 23,622 (Original).
- The spatial distribution of detected events correctly reproduced the known aftershock zones, and the temporal evolution matched the sequence's characteristics.
Limitations: The improvement was not uniform. While the weighted loss enhanced the detection of small, successive earthquakes (M ~1–2), it did not fully resolve the detection of small events immediately following the largest mainshocks (Mw 7.1). In these periods, phase onsets were likely masked by high-amplitude, long-duration coda waves, a physical limitation of signal separability that loss reweighting alone cannot overcome.

Significance and Claims
The paper claims that loss function design is an effective, architecture-independent approach to improving the sensitivity of deep learning-based phase picking. By redistributing the training objective from the dominant background to the narrow phase-arrival regions, the proposed method:

Enhances the temporal consistency of predicted picks.
Reduces missed arrivals (false negatives), which is critical for downstream event association in continuous monitoring.
Improves event recovery in dense seismic sequences, even when applied to data from regions (California) different from the training data (Japan).

The authors conclude that while the method does not solve the fundamental challenge of overlapping signals in strong coda environments, it provides a meaningful improvement in sensitivity that facilitates the detection of more earthquakes in continuous waveform analysis. The increased sensitivity necessitates appropriate probability thresholding and association constraints to manage the resulting increase in false positives.