🤖 machine learning

Learning Earthquake Wave Arrival Time Picking from Labels with Inaccuracies

This paper introduces LaNCoR, a novel approach that aligns input waveform and label distributions in feature space to effectively mitigate the impact of inaccurate labels on seismic P-phase arrival-time picking, achieving up to a 28.8% performance improvement without requiring large-scale datasets.

Original authors: Sen Li, Xu Yang, S. Mostafa Mousavi, Anye Cao, Keting Fan, Yaoqi Liu, Changbin Wang, Qiang Niu

Published 2026-06-16

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Sen Li, Xu Yang, S. Mostafa Mousavi, Anye Cao, Keting Fan, Yaoqi Liu, Changbin Wang, Qiang Niu

Original paper licensed under CC BY 4.0 (http://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 Big Problem: Learning from a Confused Teacher

Imagine you are trying to learn how to identify a specific sound, like a bird chirping, by listening to recordings. However, the teacher giving you the answers (the "labels") is often tired, distracted, or has bad hearing. Sometimes they point to the chirp, but other times they point to a leaf rustling or a car passing by, claiming, "That's the bird!"

In the world of earthquake science, this is exactly what happens. Scientists use computers (Deep Learning) to find the exact moment an earthquake starts (the "P-wave arrival"). But the "teachers" are human experts who manually mark these start times on thousands of recordings. Humans make mistakes due to fatigue, bias, or instrument glitches. These mistakes are called "label noise."

If you train a computer to learn from these confused teachers, the computer will memorize the mistakes. It will learn that "leaf rustling" is actually an earthquake, leading to poor performance when it tries to find real earthquakes later.

The Solution: LaNCoR (The Smart Detective)

The authors of this paper created a new training method called LaNCoR (Label Noise-Contrastive Robust Learning). Think of LaNCoR not as a student who blindly obeys the teacher, but as a smart detective who checks the evidence before accepting an answer.

Here is how LaNCoR works, broken down into three simple steps:

1. The "Two Views" Strategy

Imagine you are looking at a crime scene. You have two pieces of evidence:

View A: The actual physical evidence (the seismic waveform—the squiggly line on the screen). This never lies; the energy spike is real.
View B: The witness statement (the human label). This might be wrong.

Standard training methods blindly trust the witness. LaNCoR, however, treats both views as important but checks if they match. It asks: "Does the physical energy spike in the wave actually line up with where the human said the earthquake started?"

2. The "Error Learner" (The Correction Mechanism)

This is the paper's secret weapon. LaNCoR has a special module called the Error Learner.

Analogy: Imagine a translator who notices the witness is stuttering or pointing in the wrong direction. The translator doesn't fire the witness; instead, they gently nudge the witness's statement to match the physical reality of the scene.
How it works: The model compares the "squiggly line" (the wave) with the "mark" (the label). If the mark is far off from the actual energy spike, the Error Learner calculates the "shift" or the mistake. It then creates a corrected version of the label internally. It essentially says, "The human said 2:00, but the wave clearly shows the energy started at 2:05. Let's use 2:05 for training."

3. The "Alignment" (Forcing Agreement)

Once the model has a corrected label, it uses a technique called Contrastive Learning.

Analogy: Imagine you are trying to get two different maps of the same city to overlap perfectly. One map is drawn by a local (the wave features), and the other is drawn by a tourist (the labels). If the tourist's map is skewed, you stretch and rotate it until it matches the local's map perfectly.
The Result: The model forces the "shape" of the label to align with the "shape" of the wave. This ensures the computer learns the physics of the earthquake, not the mistakes of the human.

The Results: Why It Matters

The researchers tested this method on real data from coal mines in China. They intentionally added extra "noise" (fake mistakes) to the training data to see if the model would break.

The Baseline: Standard models (and even models that just used "data augmentation," which is like giving the student more practice tests) failed miserably when the mistakes got too frequent. They started memorizing the errors.
LaNCoR's Performance: LaNCoR stayed calm and accurate. Even when the training data was full of bad labels, it improved performance by up to 28.8% compared to other methods.
The "Cross-Region" Test: They trained the model on data from one set of mines and tested it on a completely different mine with different geology. LaNCoR still worked better than the others, proving it learned the true signal, not just the specific quirks of the training data.

Visual Proof

The paper includes images showing that when a human label was way off (pointing to silence), LaNCoR ignored the human and correctly pointed to the actual energy spike in the wave. It successfully "unlearned" the bad habits of the human annotators.

Summary

LaNCoR is a training method that teaches computers to be skeptical of human mistakes. Instead of blindly copying incorrect labels, it uses the physical reality of the earthquake wave to correct the labels during training. This allows the computer to learn the true patterns of earthquakes, even when the data it was trained on is messy and full of errors.

Technical Summary: Learning Earthquake Wave Arrival Time Picking from Labels with Inaccuracies

Problem Statement
Supervised machine learning models in seismology, particularly for microseismic monitoring and phase picking, are highly susceptible to "label noise." This noise arises from human subjectivity, analyst fatigue, instrument timing errors, or systematic biases in automated picking. When models are trained on datasets containing these inaccurate labels, they learn erroneous mappings between seismic waveform features and arrival times. This leads to poor generalization, reduced accuracy on validation data, and a tendency to overfit by memorizing incorrect examples rather than capturing the underlying physical signal distribution. While traditional regularization techniques like data augmentation exist, they are often insufficient to mitigate the adverse effects of significant label noise, especially when high-quality, large-scale training datasets are unavailable or costly to produce.

Methodology: Label Noise-Contrastive Robust Learning (LaNCoR)
The authors propose LaNCoR (Label Noise-Contrastive Robust Learning), a framework designed to handle noisy labels in seismic signal processing without requiring massive, perfectly labeled datasets. The core philosophy of LaNCoR is to treat the input waveform and the provided label as two different "views" of the same physical event. Instead of blindly trusting the noisy label, the model enforces statistical consistency between the stable physical features of the waveform and the target label representation.

The LaNCoR architecture operates through the following key mechanisms:

Dual-Space Alignment: The model maps input seismograms and their associated noisy labels into separate latent spaces. It then aligns the distribution of the feature representation with the distribution of the label representation. The goal is to correct the "distributional shift" caused by label errors, forcing the label representation to align with the robust physical features of the waveform.
Error Learner (EL): A critical component is the Error Learner, which utilizes a multi-head self-attention mechanism. It compares the waveform feature representation ( $\mathcal{Z}_x$ ) against the noisy label representation ( $\mathcal{Z}_y$ ) to estimate the "shift" or error ( $\delta$ ) introduced by the noise. The EL produces a corrected label representation ( $\mathcal{Z}'_y$ ) that is mathematically closer to the ground truth. Crucially, the gradient flow from the Error Learner back to the feature encoder is truncated (detached) to prevent the noisy label space from corrupting the core feature learning process.
Reparameterization: To prevent the model from overfitting to specific noisy values (overconfidence), LaNCoR employs a reparameterization trick. Instead of mapping inputs to fixed points, it treats feature and label representations as probability distributions (Gaussian clouds) defined by a mean ( $\mu$ ) and variance ( $\sigma$ ). This introduces controlled uncertainty, smoothing the learning landscape.
Random Fourier Features (RFF): To capture complex, non-linear relationships that a single low-dimensional space might miss, the model projects representations into a high-dimensional space using Random Fourier Features. This approximates a Gaussian kernel, ensuring alignment of fine-grained structural details between waveforms and labels.
Contrastive Learning: The framework utilizes contrastive learning to enforce alignment across the two modalities (waveform and label). It constructs similarity matrices for both the feature space and the corrected label space. The loss function minimizes the difference between these similarity matrices, ensuring that if two waveforms are similar, their corresponding labels (even if originally noisy) are adjusted to reflect that similarity.

The total optimization objective combines reconstruction losses, KL-divergence for distribution alignment, and contrastive losses, weighted by balancing coefficients ( $\lambda$ ).

Key Contributions

Novel Framework: Introduction of LaNCoR, which integrates robust learning strategies specifically tailored for seismic phase picking under small-scale training regimes with noisy labels.
Mechanism for Noise Correction: Development of the Error Learner module that explicitly estimates and corrects label distribution shifts by leveraging the consistency between waveform features and labels.
Distributional Alignment: A multi-stage alignment strategy combining latent space consistency, reparameterization (variational inference), and Random Fourier Features to robustly handle non-Gaussian and systematic label errors.
Empirical Validation: Demonstration of the method's efficacy on real microseismic data from multiple coal mines in China, including cross-region generalization tests.

Results
The authors evaluated LaNCoR using two baseline models, SeisT and PhaseNet, on datasets from three Chinese coal mines (Chaoyang, Mengcun, Xingcun) and a cross-region test set from the Yingpanhao mine.

Performance Gains: LaNCoR significantly outperformed baseline methods (supervised learning with/without data augmentation) across various noise levels. For SeisT, average F1-score improvements ranged from 5.7% to 16.3% over baselines, with maximum improvements reaching 28.8%. For PhaseNet, average F1-score improvements were even higher, reaching up to 54.7% in specific high-noise scenarios.
Robustness to Noise: While standard data augmentation methods showed performance collapse as noise levels increased (specifically when noise $\sigma_E > 150$ ms), LaNCoR maintained stable performance curves. It effectively ignored grossly incorrect training labels and prioritized the physical signal onset.
Cross-Region Generalization: When applied to the unseen Yingpanhao dataset (which exhibited a measured feature-distribution shift and higher SNR ranges), LaNCoR consistently outperformed other methods, demonstrating superior adaptability to new geographical regions and varying signal conditions.
Qualitative Analysis: Visual inspection of results confirmed that LaNCoR could recover arrival times in low-SNR samples and identify missing phases that human analysts had missed. In cases of intentionally incorrect labels, the model successfully predicted the true physical arrival time rather than the erroneous annotation.

Significance and Claims
The paper claims that LaNCoR offers a promising direction for enhancing the robustness of deep-learning models in seismology and geosciences. By addressing the critical challenge of label noise without relying on labor-intensive data cleaning or massive datasets, the approach enables the training of high-performance models even with imperfect supervision. The authors emphasize that the method's ability to decouple physical feature learning from noisy supervision allows for stable training and reliable generalization, which is essential for applications like induced seismicity monitoring, reservoir characterization, and hazard assessment. The study concludes that LaNCoR effectively mitigates the impact of label noise through feature alignment, making it a versatile tool for seismic signal processing tasks beyond just phase picking.