⚡ electrical engineering

Estimating Earthquake Magnitude in Sentinel-1 Imagery via Ranking

This article proposes a metric learning approach that integrates pairwise rankings to improve the estimation of earthquake magnitudes from Sentinel-1 satellite images, achieving a reduction in mean absolute error of over 30% compared to conventional pure regression methods, particularly in models based on Transformer architectures.

Original authors: Daniele Rege Cambrin, Isaac Corley, Paolo Garza, Peyman Najafirad

Published 2026-05-08

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CC BY 4.0

Original authors: Daniele Rege Cambrin, Isaac Corley, Paolo Garza, Peyman Najafirad

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: Too Few Earthquakes to Learn From

Imagine you are trying to teach a student to guess the strength of an earthquake solely based on satellite photos of the ground before and after the event.

The problem is that large earthquakes are rare. It is like trying to teach someone to recognize different types of rare birds, but you only have 3,000 photos of them in the entire library. Because there is so little data, conventional machine learning methods (which usually just try to guess the exact number) often get confused and make mistakes. They struggle to learn the "rules" because they haven't seen enough examples.

The Old Way: Guessing Only the Number

Traditionally, researchers tried to build a model that works like a calculator. You feed it an image, and it spits out a number (e.g., "Magnitude 5.2").

The Analogy: This is like asking a student to memorize a specific answer for every single exam question. If they see a question they haven't practiced, they might just guess wildly.

The New Idea: Learning by Ranking (The "Taste Test")

The authors of this paper developed a clever trick. Instead of just having the computer guess the exact number, they also taught it to compare two earthquakes.

The Analogy: Imagine teaching a child to judge the spiciness of chili peppers.
- Old Way: You show them one pepper and ask: "How many Scoville units does this have?" (Hard to guess without a reference).
- New Way: You show them two peppers and ask: "Which one is hotter?" The child can easily say, "The red one is hotter than the green one," even if they cannot say exactly how hot each individual pepper is.

By training the computer to do both—guess the number AND correctly rank which earthquake was stronger—the model learns the "shape" of the data much better. It learns that "Earthquake A looks more like a 6.0 than Earthquake B," which helps it determine the actual numbers correctly.

What They Did

The Data: They used satellite images from the Sentinel-1 satellite. These are special radar images that can see through clouds and at night. They looked at pairs of images: one before an earthquake and one after.
The Models: They tested various types of "brains" (computer algorithms) to find out which worked best. They tried out:
- Convolutional Neural Networks (CNNs): Like traditional pattern-recognition machines.
- Transformers: The same type of powerful AI used in modern chatbots and image generators.
The Test: They compared the "old way" (guessing only numbers) with their "new way" (guessing numbers + ranking).

The Results

The results were impressive. By adding the "ranking" task to the training:

Accuracy Improvement: The models became significantly better at guessing the strength. In the best cases, they improved their accuracy by over 30% compared to the old methods.
Best Performer: A model named ConvNeXt (a type of pattern-recognition machine) worked best overall.
Efficiency: Interestingly, the largest, most complex models (like the Transformers) did not necessarily win. They consumed a lot of computing power but were not always the most accurate. A smaller, lighter model named MobileNet actually did an excellent job with very little computing power.

The Conclusion

The paper proves that if you do not have enough data to teach a computer a difficult mathematical problem, you can help it by teaching it to compare things. By letting the AI play a game: "Which earthquake was bigger?" alongside "What is the exact number?", it learns to recognize the differences in the satellite images much more effectively.

This approach requires no new data or expensive sensors; it only changes how the computer learns from the data already available.

Technical Conclusion: Estimating Earthquake Magnitude in Sentinel-1 Images via Ranking

Problem Definition
Earthquake magnitude estimation traditionally relies on physical seismic stations. However, the high costs and logistical challenges associated with installing and maintaining these stations limit global coverage, hindering the monitoring of seismic activity in remote or underserved regions. Although Earth Observation (EO) satellite data, particularly Synthetic Aperture Radar (SAR) from Sentinel-1, offers a promising alternative for global monitoring, the application of machine learning in this field faces the problem of a "low-data regime." The scarcity of historically recorded earthquakes combined with satellite imagery limits the performance of conventional regression models, which struggle to generalize effectively with such small datasets.

Methodology
To address the challenge of data scarcity, the authors propose redefining earthquake magnitude estimation not solely as a regression task, but as a metric learning problem. The core innovation involves a training strategy with two objectives:

Regression Objective: The model predicts the absolute magnitude ( $G_t$ ) from Sentinel-1 image pairs (before and after the event).
Ranking Objective: The model is trained to rank image pairs based on their relative magnitude.

The overall loss function ( $L$ ) combines the standard Mean Squared Error (MSE) ( $L_{MSE}$ ) with a Margin Ranking Loss ( $L_{MR}$ ):
$L = L_{MSE} + L_{MR}$

The Margin Ranking Loss is defined as:
$L_{MR}(x_1, x_2, y) = \max(0, -y \cdot (x_1 - x_2) + m)$
Where $x_1$ and $x_2$ are the predicted magnitudes for two samples, $y$ is a label indicating the relative order (1 if $x_1 \geq x_2$ , otherwise -1), and $m$ is a margin hyperparameter (set to 0.02 in the experiments). This approach encourages the model to learn the relative distance between samples of different magnitudes without requiring additional labeled data beyond the existing magnitude values.

Experimental Setup
The study utilized the QuakeSet dataset, comprising 3,327 pairs of 2-channel Sentinel-1 images (VV and VH polarizations) with a resolution of 512 × 512 pixels, captured before and after seismic events. The authors evaluated a variety of architectures to determine the influence of model size and type:

Convolutional Neural Networks (CNNs): ConvNeXt v2 (Atto variant) and MobileNet (Small and Large variants).
Transformers: MobileViT v2 and ViT-tiny.

All models were initialized with ImageNet-pretrained weights and trained for 10 epochs using the AdamW optimizer. Performance was measured using Mean Absolute Error (MAE) and computational cost (FLOPS).

Key Results
The experiments demonstrated that incorporating the ranking objective significantly improved performance across all tested architectures.

Performance Improvement: The proposed method achieved an MAE improvement of over 30% compared to pure regression baselines.
Architecture Comparison:
- ConvNeXt v2 (Atto) achieved the best overall results, reducing the MAE from 0.2577 to 0.2287 when using the ranking loss.
- ViT-tiny also showed significant improvement, dropping from 0.3150 to 0.2613.
- MobileNet-Small proved to be a highly efficient solution, achieving a low MAE (0.3678 with ranking) at the lowest computational cost (44.10 MFLOPs).
- MobileNet-Large exhibited tendencies toward overfitting, resulting in the poorest performance.
Efficiency: While Transformer-based models (ViT) demonstrated high accuracy, they incurred higher computational costs compared to CNNs. MobileViT offered a middle ground but remained less competitive than convolutional solutions for this specific task.

Significance and Claims
The work claims that redefining magnitude estimation as a metric learning problem enables models to generalize better from limited data by leveraging the relative order of samples within a batch. A key significance of this work is that no additional data beyond the existing magnitude labels is required to implement the ranking objective. By simply utilizing the relationships between samples already present in the training dataset, the method enhances the model's ability to distinguish between different magnitude levels, thereby increasing accuracy and robustness in a low-data regime. The authors conclude that this approach is effective for both CNN and Transformer architectures, offering a practical pathway for more accurate, global earthquake monitoring via satellite imagery.