DASFormer: Self-supervised Pretraining for Earthquake Monitoring

Q1: The evaluation scheme mainly demonstrates the usefulness of SSL pretraining with a large amount of data, but it is unclear why the extensive pretraining technique is necessary compared to more standard SSL methods in CV.

A1: Thanks for your valuable suggestion. We have indeed considered representing DAS data as images, but drawing an analogy between DAS data and images can also be misleading. Image data does not inherently consider the causal information along the time axis that is present in DAS data. Adapting image-based methods to a causal-related forecasting-based approach would require additional design considerations. We will explore the possibilities like adapting ViT-based image methods in the future.

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Q2: The comparison table shows that the "traditional" aggregation baseline performs on par with or better than the deep learning models, suggesting the potential for simpler modeling approaches. There is literature showing that simple models can outperform deep learning methods on time-series tasks like Random Forest.

A2: Thanks for pointing out this. Aggregation-0 in Table 1 is a variant of well-known traditional method "STA/LTA" for DAS data.

The traditional time-series methods like Random Forest and ARIMA-family are not applicable to our task, as they are designed for stationary time series. However, DAS data is characterized by dynamic and evolving patterns, making it challenging to model using traditional stationary time series methods

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Q3: The paper does not include a comparison to a baseline that does not use the point-wise loss, despite mentioning its weakness in the baseline models.

A3: Thanks for pointing out this. To alleviate the drawback of point-wise loss, DASFormer utilizes an extra pretrained VGG-based on intermediate features (it's a features-to-features autoencoder, not on the final predictions) in DASFormer to extract the high-level features, and use the feature-wise loss as the metric. This feature extractor is not universal for other methods, so we have to design feature extractors/encoders to suit the specific architecture and characteristics of each baseline model. Therefore, we only use the point-wise loss for other baselines.

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Q4: The paper lacks a discussion of uncertainty, which is important for earthquake monitoring given the stochastic noise in DAS data.

A4: Thanks for your suggestion. We show the confidence intervals of the results in Table 4 in Appendix, where we can observe that the results are stable and reliable with small variance. Due to the limitations of time and computation, we will explore and add more uncertainty analysis in the future work.

We also conduct comparison experiments for different magnitude (different noise levels) of earthquakes. The results are shown in the following tables:

Distribution of the magnitude of the 45 earthquakes in the training set:

Distribution of the magnitude of the 45 earthquakes in the evaluation set and the performance:

For the earthquakes in the range of M2 ~ M3 and M3 ~ M4, we can see that the performance is becoming better for larger magnitude earthquakes. In each level, the performance of DASFormer is better than Aggregation-0. For the earthquakes in the range of M0 ~ M2 and M4 ~ M5, the number of samples is too small to draw a conclusion.

Q1: Lacks a comparison with other DAS earthquake detectors like PhaseNet-DAS.

A1: To the best of our knowledge, the existing DAS earthquake detectors like PhaseNet-DAS are for P/S phase pickup tasks, which are different from seismic detection tasks we did. Please refer to the Answer to A6.

P/S phase pickup refers to the identification and classification of seismic wave phases, specifically the arrival times of the P (primary) and S (secondary) waves, which focuses on accurately detecting and labeling these specific phases point-wise in DAS data. On the other hand, seismic detection task (in Table 1) involves identifying and classifying anomalies or abnormal patterns in DAS data. The main differences between P/S phase pickup and seismic detection tasks can be summarized in the following aspects:

(1) Wave identification: In P/S phase pickup, the method needs to accurately distinguish between P and S waves in seismic data. But seismic detection tasks do not require this specific wave identification, only with earthquake events. Most of the existing P/S phase pickup methods like PhaseNet-DAS learn on the context of P/S phases, while our method is a forecasting-based method which is easier and more suitable for real-time systems.

(2) Data representation: P/S phase pickup typically provides point-wise results, indicating the exact arrival times of P and S waves. In contrast, seismic detection tasks focus on determining whether there is an event or anomaly within a specific time span, without the need for precise point-wise results. Moreover, our training/valid/testing splits are different from PhaseNet/PhaseNet-DAS.

(3) Learning setting: P/S phase pickup methods are typically implemented in a supervised learning setting, where labeled data with ground-truth P/S wave information is required for training. However, our seismic detection task is addressed in an unsupervised learning setting like anomaly detection, as obtaining labeled data for anomalies can be challenging.

As a self-supervised learning model, DASFomer can be adapted to the P/S phase pickup tasks and we've done some preliminary experiments shown in the paper. However, considering the above points and the limited ground-truth annotations of P/S phases of our data, we hardly find a fair evaluation metric to compare with PhaseNet-DAS. We will explore more in the future work.

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Q2: The generalizability of the method to other DAS sensors is not addressed, and it is unclear if the self-training needs to be performed again for different DAS setups.

A2: Our method is applicable to any other DAS site. In the preprocessing stage, we downsample and resize the DAS data to match the resolution required by the model. By downsampling the data to the same resolution, our method can be easily transferred and applied to new DAS sensors. This approach is similar to computer vision models trained on ImageNet, where they are designed to be applicable to various image resolutions.

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Q3: The method's suitability for other tasks and its performance in predictable scenarios, such as aftershocks, is not discussed.

A3: The effectiveness of our model for unpredictable earthquakes is derived from its good capabilities for other predictable events.

In this work, we primarily showcase the usage of DASFormer as a forecasting-based earthquake monitor. For tasks that are predictable, we can remove the masking and directly employ DASFormer as a feature extractor. We demonstrate its capability as a feature extractor in detecting malfunctioning sensors in Figure 4. Additionally, Figure 3 also illustrates its ability to detect predictable events such as traffic signals.

Regarding your concern about the assumption that "earthquakes are unpredictable" may potentially confuse the model, it is important to note that our look-back window is only around 13 seconds, with a prediction window of approximately 1 second. At this time scale, the level of predictability is nearly indistinguishable for relatively predictable events like aftershocks. Thus, we can treat each aftershock as a separate earthquake event, considering them as individual instances rather than relying on their predictability.

Q1: It is unclear how the method performs for smaller earthquakes and whether there are many false positives.

A1: For performance on smaller earthquakes, we visualized several cases ranging from M2.0 to M3.66 in Figure 9 in Appendix. And we show the performance for different magnitudes in answer A3. The false positive rate (FPR) and true positive rate (TPR) for DASFormer are shown as follows:

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Q2: It would be beneficial to conduct a sensitivity analysis of the method concerning the choice of hyperparameters since this application is associated with hazards to public safety

A2: Thanks for your suggestion. We have the results with confidence intervals in Table 4 in Appendix. Actually we didn't careflly tune these hyperparameters due to the time and computation limitation. The training time of DASFormer is about 3~4 days on 4 NVIDIA RTX A5000 GPUs. We list all the 7 hyperparameters and the empirical setup in Table 7 in Appendix, where we think only $\alpha$ and $\beta$ are sensitive to the performance. For the resolution $V$ and $L$, they are larger is better, and are set to $128$ which is the maximum under our computation. For the number of heads $h$, it is empirically set as in multi-head attention mechanism. For the dimension of kernels $K$, it is less is better, and $2$ is the minimum value that we can use. For $\alpha$ and $\beta$, they are the trade-off between the reconstruction loss and the normalization tricks, which are empirically set to $1$ and $0.1$. We will conduct a sensitivity analysis of the method concerning the choice of hyperparameters once we have the results in the future. Thanks!

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Q3: What is the distribution (histogram) of the metric as a function of earthquake magnitude? How does it compare to the baseline? How about traditional signal processing techniques?

A3: We provide the magnitude distribution of our datasets with performance here:

Distribution of the magnitude of the 45 earthquakes in the training set:

Distribution of the magnitude of the 45 earthquakes in the evaluation set and the performance on DASFormer and Aggregation-0(STA/LTA baseline):

For the earthquakes in the range of M2 ~ M3 and M3 ~ M4, we can see that the performance is becoming better for larger magnitude earthquakes. In each level, the performance of DASFormer is better than Aggregation-0 (STA/LTA baseline). For the earthquakes in the range of M0 ~ M2 and M4 ~ M5, the number of samples is too small to draw a conclusion.

Q10: The paper emphasizes the limitations of existing time series models in incorporating spatial information, but does not include network structures that can effectively integrate both spatial and temporal analyses.

A10: Thanks for the suggestion. There are many existing spatio-temporal time series methods aim to capture and integrate spatial information for multi-variate time series data. We select three representative methods (Autoformer, GDN, and Crossformer) and compare them with DASFormer. The results are shown in Table 1 and Table 6. Autoformer and Crossformer are two Transformer-based methods utilizing spatial dependency in multi-variate time series. GDN is a graph-based method that uses a graph neural network to capture the spatial dependency of the multi-variate time series.

There are many existing spatio-temporal time series methods aim to capture and integrate spatial information for multi-variate time series data. However, to the best of our knowledge, all of them are order-agnostic models (with GNNs or Transformers) to capture spatial dependency, which typically do not consider the order or sequence of the variates in the data. This can be problematic in the context of DAS data, where the order of variates is crucial as it represents the location of stations along the fiber optic cable.

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Q11: The paper emphasizes the role of the coarse and fine steps in its approach, but it does not include ablation experiments to demonstrate the individual contributions and effectiveness of these two components.

A11: Thanks for the suggestion. We conduct ablation studies on the three steps (Coarse, Coarse-to-Fine, Coarse-to-Fine with Discriminator). The results are shown in the following table:

The results demonstrate the effectiveness of the coarse-to-fine framework and the discriminator. We will add these results to the revision.

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Q12: Figure 3 exclusively compares the earthquake detection effects of different prediction methods, with DASFormer being the only one shown to predict effective information, lacking a comprehensive assessment of the capabilities of different methods.

A12: In fact, all samples of baselines are like "not capable of prediction", we didn't select the worse ones. We suggest to consider the results of both aggregation-0 (sta/lta) and aggregation-inf in Table 1 together with Figure 3. Note that if an algorithm consistently predicts 0 as the predicted future DAS signals, which corresponds to a completely white region in the forecasting region of Figure 3, it can be seen as a special case of the sta/lta algorithm. This means that the expected long-term average is 0, and the difference between the real value and 0 (LTA) is kind of equivalent to the sta/lta value (assuming the expected average of lta remains constant). Given this context, we can observe that almost all methods (except FEDformer) perform similarly to aggregation-0 (sta/lta) in Table 1. And in Figure 3, we can see that most of the baselines (except FEDformer) output values close to white (close to 0 in values) , resulting in similar results to aggregation-0.

Q6: The paper fails to make a clear distinction between P/S phase pickup and seismic detection tasks, causing confusion in the results presented in Table 1.

A6: P/S phase pickup refers to the identification and classification of seismic wave phases, specifically the arrival times of the P (primary) and S (secondary) waves, which focuses on accurately detecting and labeling these specific phases point-wise in DAS data. On the other hand, seismic detection task (in Table 1) involves identifying and classifying anomalies or abnormal patterns in DAS data. The main differences between P/S phase pickup and seismic detection tasks can be summarized in the following aspects:

(1) Wave identification: In P/S phase pickup, the method needs to accurately distinguish between P and S waves in seismic data. But seismic detection tasks do not require this specific wave identification, only with earthquake events.

(2) Data representation: P/S phase pickup typically provides point-wise results, indicating the exact arrival times of P and S waves. In contrast, seismic detection tasks focus on determining whether there is an event or anomaly within a specific time span, without the need for precise point-wise results. Moreover, our training/valid/testing splits are different from PhaseNet/PhaseNet-DAS

(3) Learning setting: P/S phase pickup methods are typically implemented in a supervised learning setting, where labeled data with ground-truth P/S wave information is required for training. However, our seismic detection task is addressed in an unsupervised learning setting like anomaly detection, as obtaining labeled data for anomalies can be challenging.

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Q7:: The paper lacks a detailed description of the dataset and evaluation metrics for the downstream task of accurate seismic phase-on-arrival pickup.

A7:: We will update more description of the dataset, including the distribution of the magnitude of the earthquakes and the SNR analysis of the training data. Actually, we don't have evaluation metrics for the downstream task of accurate seismic phase-on-arrival pickup. We just visually show the results. It is worth mentioning that while resampling the frequency to 10Hz is sufficient for earthquake detection and monitoring, it may not be adequate for tasks like P/S phase pickup that require original-resolution (250Hz) data. We acknowledge that generalizability for original-resolution data is an area we plan to explore in the future.

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Q8: The paper lacks ablation experiments to elucidate the quantity of training data necessary for effective seismic monitoring.

A8: We agree that ablation studies on the quantity of training data can investigate the performance especially the scalability of DASFormer. The results of this ablation study is shown in following table:

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Q9: The "Deep Learning on DAS Data" section of the RELATED WORKS lacks sufficient relevance to DAS data, apart from PhaseNet-DAS and j-DAS.

A9: In the revision, we will make sure to include more relevant works that are related to DAS data. It would be better if you can give some suggestions on the related works. Thanks!

Q1: The 'Aggregation-0' and 'Aggregation-inf’ lack description.

A1: (1) "Aggregation-0" is a multi-variate version of STA/LTA method. It calculates the average of the absolute values of the STA/LTA scores across all variables, which is used as our anomaly score.

(2) "Aggregation-inf" functions as a ransdom detector with no detection ability. It randomly assigns labels of 0 or 1 with a 50% probability for each sample.

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Q2: The use of the j-DAS method for seismic detection comparison is considered unfair and may not yield equitable results.

A2: We understand the reviewer's concern that j-DAS seems more focused on denoising tasks. To the best of our knowledge, j-DAS is the only existing model that the authors claim to be a foundational model on DAS data. Therefore, considering the claimed potential capabilities of j-DAS, we decided to conduct comparison experiments with it.

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Q3: The paper does not effectively compare with established DAS seismic detection methods, diminishing its ability to demonstrate the effectiveness of its proposed approach.

A3: Please refer to the Answer to A6.

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Q4: The resampling of the dataset from 2000-4000Hz to 10Hz for pre-training lacks a comparative verification of its impact on downstream tasks.

A4: As you mentioned, the original sampling of our DAS data is 250Hz. Resampling the data from 250Hz to 10Hz allows us to retain the important features and characteristics of the seismic signals while reducing the data size and computational complexity. ****For seismic detection tasks, the lasting time of P waves typically spans a few seconds, while S waves can last even longer, up to several minutes. Given this context, a sampling frequency of 10Hz is sufficient to capture the necessary temporal information required for accurate seismic detection.

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Q5: The model's ability to detect earthquakes below a certain magnitude or signal-to-noise ratio.

A5: Thanks for your suggestion. We provide magnitude distribution of our datasets here:

We provide magnitude distribution of our datasets here:

Distribution of the magnitude of the 45 earthquakes in the training set:

Distribution of the magnitude of the 45 earthquakes in the evaluation set and the performance:

For the earthquakes in the range of M2 ~ M3 and M3 ~ M4, we can see that the performance is becoming better for larger magnitude earthquakes. In each level, the performance of DASFormer is better than Aggregation-0. For the earthquakes in the range of M0 ~ M2 and M4 ~ M5, the number of samples is too small to draw a conclusion.