Seismic arrival-time picking on distributed acoustic sensing data using semi-supervised learning

Domain: earth_science
Published: 2023-12-11
Editorial outcome: major_revision

Abstract
Distributed Acoustic Sensing (DAS) is an emerging technology for earthquake monitoring and subsurface imaging. However, its distinct characteristics, such as unknown ground coupling and high noise level, pose challenges to signal processing. Existing machine learning models optimized for conventional seismic data struggle with DAS data due to its ultra-dense spatial sampling and limited manual labels. We introduce a semi-supervised learning approach to address the phase-picking task of DAS data. We use the pre-trained PhaseNet model to generate noisy labels of P/S arrivals in DAS data and apply the Gaussian mixture model phase association (GaMMA) method to refine these noisy labels and build training datasets. We develop PhaseNet-DAS, a deep learning model designed to process 2D spatio-temporal DAS data to achieve accurate phase picking and efficient earthquake detection. Our study demonstrates a method to develop deep learning models for DAS data, unlocking the potential of integrating DAS in enhancing earthquake monitoring.

Introduction
Distributed acoustic sensing (DAS) is a rapidly developing technology that can turn a fiber-optic cable of up to one hundred kilometers into an ultra-dense array of seismic sensors spaced only a few meters apart. DAS uses an interrogator unit to send laser pulses into an optical fiber and measure the Rayleigh back-scattering from the internal natural flaws of the optical fiber. By measuring the tiny phase changes between repeated pulses, DAS can infer the longitudinal strain or strain rate over time along a fiber-optic cable1–3. Previous studies have demonstrated that DAS can effectively record seismic waves4–9. Compared with traditional forms of seismic acquisition, DAS has several potential advantages in earthquake monitoring. It provides unprecedented channel spacing of meters compared with tens-of-kilometers spacing of seismic networks. DAS can also take advantage of dark fibers (i.e., unused strands of telecommunication fiber) at a potentially low cost. Furthermore, DAS is suitable for deployment and maintenance in challenging environments, such as boreholes, offshore locations, and glaciers. New DAS interrogator units are becoming capable of longer sensing ranges at a lower cost with the development of high-speed Internet infrastructure1. Thus, DAS is a promising technology for improved earthquake monitoring and is under active research. However, applying DAS to routine earthquake monitoring tasks remains challenging due to the lack of effective algorithms for detecting earthquakes and picking phase arrivals, coupled with the high data volume generated by thousands of channels. The ultra-high spatial resolution of fiber-optic sensing is a significant advantage compared to seismic networks but also presents a challenge for traditional data processing algorithms designed for single- or three-component seismometers. For example, the commonly used STA/LTA (short-term averaging over long-term averaging) method10 is ineffective for DAS because DAS recordings are much noisier than dedicated seismometer data due to factors such as cable-ground coupling and sensitivity to anthropogenic noise. STA/LTA operates on a single DAS trace and therefore does not effectively utilize the dense spatial sampling provided by DAS. Template matching is another effective earthquake detection method, particularly for detecting tiny earthquake signals11–14. However, the requirement of existing templates and high computational demands limit its applicability for routine earthquake monitoring15.

Deep learning, especially deep neural networks, is currently the state-of-the-art machine learning algorithm for many tasks, such as image classification, object detection, speech recognition, machine translation, text/image generation, and medical image segmentation16. Deep learning is also widely used in earthquake detection17–22 for studying dense earthquake sequences23–28 and routine monitoring seismicity29–33. Compared to the STA/LTA method, deep learning is more sensitive to weak signals of small earthquakes and more robust to noisy spikes that cause false positives for STA/LTA. Compared to the template matching method, deep learning generalizes similarity-based search without requiring precise seismic templates and is significantly faster. Neural network models automatically learn to extract common features of earthquake signals from large training datasets and are able to generalize to earthquakes outside the training samples. For example, the PhaseNet model, which is a deep neural network model trained using earthquakes in Northern California, performs well when applied to tectonic24,25, induced23,26, and volcanic earthquakes34,35 globally.

One critical factor in the success of deep learning in earthquake detection and phase picking is the availability of many phase arrival-time measurements manually labeled by human analysts over the past few decades. For example Ross et al.18 collected ~1.5 million pairs of P and S picks from the Southern California Seismic Network. Zhu and Beroza19 employed ~700k P and S picks from the Northern California Seismic Network. Michelini et al.36 built a benchmark dataset of ~1.2 million seismic waveforms from the Italian National Seismic Network. Zhao et al.37 formed a benchmark dataset of ~2.3 million seismic waveforms from the China Earthquake Networks. Mousavi et al.38 created a global benchmark dataset (STEAD) of ~1.2 million seismic waveforms; Several other benchmark datasets are also developed for training deep learning models39,40. Although many DAS datasets have been collected41 and more continue to be collected, most of these datasets have not yet been analyzed by human analysts. Manually labeling a large DAS dataset can be costly and time-consuming. As a result, there are limited applications of deep learning for DAS data. Most works focus on earthquake detection using a small dataset42–44. Accurately picking phase arrivals is an unsolved challenge for DAS data, hindering its applications to earthquake monitoring.

There have been a number of approaches proposed to train deep learning models with little or no manual labeling, such as data augmentation45, simulating synthetic data46–48, fine-tuning and transfer learning49,50, self-supervised learning51, and unsupervised learning52,53. However, those methods have not proven effective in picking phase arrival time on DAS data. One challenge is the difference in the mathematical structures between seismic data and DAS data, i.e., ultra-dense DAS arrays and sparse seismic networks, which complicate implementation of model fine-tuning or transfer learning. Additionally, phase arrival-time picking requires high temporal accuracy, which is difficult to achieve through self-supervised or unsupervised learning without accurate manual picks. Semi-supervised learning provides an alternative approach, which is designed for problems with limited labeled data and abundant unlabeled data54,55. There are several ways to utilize a large amount of unlabeled data as weak supervision to improve model training. One example is the Noisy Student method54, which consists of three main steps: (1) training a teacher model on labeled samples, (2) using the teacher to generate pseudo labels on unlabeled samples, and (3) training a student model on the combination of labeled and pseudolabeled data. Thus, the Noisy Student method can leverage a substantial amount of unlabeled data to improve model accuracy and robustness.

In this work, we present a semi-supervised learning approach for training a deep learning model to pick seismic phase arrivals in DAS data without needing manual labels. Despite the differences in data modalities between DAS data (i.e., spatio-temporal) and seismic data (i.e., time series), the recorded seismic waveforms exhibit similar characteristics. Based on this connection, we investigate using semi-supervised learning to transfer the knowledge learned by PhaseNet for picking P and S phase arrivals from seismic data to DAS data. We develop a new neural network model, PhaseNet-DAS, that utilizes spatial and temporal information to consistently pick seismic phase arrivals across hundreds of DAS channels. We borrow a similar idea of pseudolabeling56 to generate pseudo labels of P and S arrival picks in DAS data in order to train deep learning models using unlabeled DAS data. We extend the semi-supervised learning method to bridge two data modalities of 1D seismic waveforms and 2D DAS recordings so that we can combine the advantages of the abundant manual labels of seismic data and the large volume of DAS data. We demonstrate the semi-supervised learning approach by training two models. The PhaseNet-DAS v1 is trained using pseudo labels generated by PhaseNet to transfer phase picking capability from seismic data to DAS data. The PhaseNet-DAS v2 is trained using pseudo labels generated by PhaseNet-DAS v1 to further improve model performance similar to the Noisy Student method. Unless specified otherwise, we default to using the PhaseNet-DAS v2 model for evaluation in the following sections. We test our method using DAS arrays in Long Valley and Ridgecrest, CA, and evaluate the performance of PhaseNet-DAS in terms of number of phase picks, phase association rate, phase arrival time resolution, and earthquake detection and location.

Results
Phase picking performance
One challenge in picking phase arrivals in DAS data is the presence of strong background noise, as fiber-optic cables are often installed along roads or in urban environments and DAS is highly sensitive to surface waves. The waveforms of traffic signals have certain resemblance to earthquake signals with sharp emergence of first arrivals and strong surface waves, which leads to many false detections by the pre-trained PhaseNet model. Traffic signals are usually locally visible over short distances of a few kilometers without clear body waves. In contrast, earthquake signals tend to be much stronger and recorded by an entire DAS array with both body and surface waves present. PhaseNet-DAS uses both spatial and temporal information across multiple channels of a DAS array, making it more robust to traffic noise. Figure 1 shows four examples of earthquake signals that can be observed in sections of the DAS array. Due to strong background noise, we can see that PhaseNet detects many false P and S arrivals. However, PhaseNet-DAS predictions have fewer false detections and are consistent across channels with reduced variation in the picked arrival times. We apply both models to all events of four DAS cables and compare the number of associated picks, since picks that can be successfully associated are more indicative of true positives. After applying the phase associator GaMMA57, the rates of associated phase picks increase from 59%-69% for PhaseNet to 89%-92% for PhaseNet-DAS (Table S1).

In addition to traffic noise, other factors such as poor ground coupling and instrumental noise make the signal-noise ratio (SNR) of DAS data generally lower than that of seismic data. The low SNR makes it challenging to detect and pick phase arrivals on DAS data. The PhaseNet model pre-trained on seismic data can detect high SNR events, but struggles with low SNR events in DAS data (Fig. 2). After re-training using semi-supervised learning on DAS data, the PhaseNet-DAS model significantly improves detections of low SNR events. PhaseNet-DAS v1 detects 2–5 times more events than PhaseNet across four DAS cables, and PhaseNet-DAS v2 enhances detection sensitivity by an additional 25–50% compared to PhaseNet-DAS v1 (Fig. 2). Moreover, the number of phase picks per events also significantly increases for both high and low SNR events (Fig. S1). This demonstrates that the PhaseNet-DAS model, which is designed to use coherent spatial information, can effectively detect weaker earthquake signals recorded by DAS and pick P and S picks on more DAS channels than the PhaseNet model, which is designed for 3-component seismic waveforms.

The noisy condition of DAS recording could also impact the temporal precision of picked phase arrival-times for both manual labeling and automatic algorithms. Because we lack manual labels of P and S arrivals as benchmarks, we evaluate the temporal accuracy of PhaseNet-DAS’s picks indirectly. First, we compared the automatically picked phase arrival-times with the theoretical phase arrival-times using a 1D velocity model58. For events within ~100 km, the automatic picks have small time residuals within 2s, while the time residuals increase with epicenter distances (Fig. S2). This discrepancy arises not from imprecise automatic picks, but from differences between the true 3D velocity model and the 1D velocity model we used. Then, we conducted a more precise analysis of the automatically picked phase arrival-times by comparing the differential arrival-times between two events measured using waveform cross-correlation. Waveform cross-correlation is commonly used for earthquake detection (known as template matching or match filtering)11–14, measuring differential travel-time59–62 and relative polarity63. Cross-correlation achieves a high temporal resolution of the waveform sampling rate or super-resolution using interpolation techniques. We cut a 4-s time window around the arrival picked by PhaseNet-DAS, applied a band-pass filter between 1 Hz and 10 Hz, and calculated the cross-correlation between event pairs. The differential time was determined from the peak of the cross-correlation profile. Because DAS waveforms are usually much noisier than seismic waveforms and have low cross-correlation coefficients, we further improved the robustness of differential time measurements using multi-channel cross-correlation64,65 to accurately extract the peaks across multiple cross-correlation profiles. We selected 2539 event pairs and ~9 millions differential time measurements for both P and S waves as the reference to evaluate the temporal accuracy of PhaseNet-DAS picks. Figure 3 shows the statistics of these two differential time measurements. If we assume the differential time measurements by waveform cross-correlation are the ground truth, the errors of differential time measurements by PhaseNet-DAS have a mean of 0.001 s and a standard deviation of 0.06 s for P waves and a mean of 0.005 s and a standard deviation of 0.25 s for S waves. For comparison, the absolute arrival-time errors of the pre-trained PhaseNet model compared with manual picks have a mean of 0.002 s and a standard deviation of 0.05 s for P waves and a mean of 0.003 s and a standard deviation of 0.08 s for S waves19. Although the differential time errors and absolute arrival-time errors cannot be directly compared, the similar scales of these errors demonstrate that we can effectively transfer the high picking accuracy of the pre-trained PhaseNet model to DAS data.

Applications to earthquake monitoring
The experiments above demonstrate that PhaseNet-DAS can effectively detect and pick P- and S-phase arrivals with few false positives, high sensitivity, and precise temporal accuracy. These automatic phase arrival-time measurements can be applied to many seismic studies such as earthquake monitoring and seismic tomography. Here, we further applied PhaseNet-DAS to earthquake monitoring. Following a similar workflow of earthquake detection using seismic networks66, we applied PhaseNet-DAS to DAS data of 11,241 earthquakes in the earthquake catalogs of Northern California Seismic Network, Southern California Seismic Network, and Nevada Seismic Network within 5 degrees from two Long Valley DAS arrays (Fig. 5). These events were filtered based on an approximate scaling relation determined by Yin et al.67. Because of different sensor coverages between seismic networks and DAS cables, seismic signals from distant but small magnitude events are expected to be too small to be detected by DAS, the absolute number of earthquakes in the standard catalogs and those detected by DAS can not be directly compared. To evaluate the improvements from semi-supervised learning, we compared the magnitude and distance distributions of earthquakes detected by three models, PhaseNet, PhaseNet-DAS v1, and PhaseNet v2, in Fig. 4 and Fig. S3. PhaseNet-DAS significantly improves detection of both small magnitude events near the DAS array and large magnitude events at greater distances. We also plotted the approximate locations of these detected earthquakes determined by phase association (Fig. 5 and Fig. S4). The locations of events within the Long Valley caldera, which are close to the DAS array, can be well-constrained using these automatic arrival-time measurements, while the earthquake locations become less constrained with increasing epicentral distances due to the limited azimuthal coverage of a single DAS array (Fig. S5). The physical limitation in azimuth and distance coverage could be addressed by combining seismic networks, deploying additional DAS arrays, or designing specific fiber geometries in future research.

Lastly, we evaluated PhaseNet-DAS on continuous data to demonstrate its potential applications in large-scale data mining and real-time earthquake monitoring. We applied PhaseNet-DAS to 180 h of continuous data from 2020/11/17 to 2020/11/25 using a 5000-channel × 200-s window sampled at 100 Hz without overlap. As PhaseNet-DAS is a fully convolutional network (Fig. 7) and the convolution operator is independent of input data size, it can be directly applied to various time lengths and channel numbers subject to the memory limitations of computational servers. The picked phase arrivals were associated using GaMMA in the same manner as above. Fig. S6 shows the detected and associated picks from three models: PhaseNet, PhaseNet-DAS v1, and PhaseNet-DAS v2. The results from these models show a good consistency, while PhaseNet-DAS proves more effective in detecting several times more picks. To assess the potential for false positive events, we compared the associated earthquakes with events in standard earthquake catalogs. The histograms of temporal earthquake frequency in Fig. S7 reveal a good correlation between events detected by the DAS array and seismic networks. In particular, for events within ~0.5 degree of the DAS cable (Fig. S7c), we can observe that earthquake frequencies vary from over 80 events to no events per 6-hour period. Given the background noise generally does not changed dramatically from day to day, this indicates that these detections are less likely to be false detections from noise sources such as traffic. In addition to the high correlation with the standard catalog, PhaseNet-DAS can detect 2–3 times more events using DAS alone, demonstrating the potential of combining fiber-optic networks to enhance the earthquake monitoring capability of conventional seismic networks. The entire processing time of the continuous DAS data (180 hours and 10,000 channels, 1.8 million channel-hours) was ~3.5 h using 8 GPUs (NVIDIA Tesla V100). The model prediction of PhaseNet-DAS is fast considering the substantial size of DAS data. Since the phase-picking task can be embarrassingly parallelized by segmenting DAS data into windows, the model prediction can be further accelerated with additional GPUs for large-scale data mining tasks. The rapid prediction speed of PhaseNet-DAS also demonstrates its potential for real-time earthquake monitoring and earthquake early warning.

Methods
In this section, we discuss three components of applying deep learning to accurately pick phase arrival times in DAS data: the semi-supervised learning approach, the PhaseNet-DAS model, and the training dataset.

Semi-supervised learning
We explore a semi-supervised learning approach to train a deep-learning-based phase picker using unlabeled DAS data. The procedure of the semi-supervised learning approach is summarized in Fig. 6.

First, we train a deep-learning-based phase picker on three-component seismic waveforms using many analyst-labeled manual picks. Given the existence of several widely used deep-learning-based phase pickers18–20, we directly reuse the pre-trained PhaseNet19 model to omit retraining a deep-learning phase picker for conventional seismic data, which is not the focus of this work. Despite PhaseNet being trained on three-component seismic waveforms, it can also be applied to single-component waveforms because channel dropout (i.e., randomly zero-out one or two channels) is added as data augmentation70.

Second, we apply the pre-trained PhaseNet model to pick P and S arrivals on each channel of a DAS array independently to generate noisy pseudo labels of P and S picks. While PhaseNet works well on channels with high signal-to-noise (SNR) ratios in DAS data, its accuracy is limited compared to that in seismic data (Fig. 1). For example, the model could detect many false picks due to strong anthropogenic noise in DAS data. The picked phase arrival times also have large variations between nearby channels, since each channel is processed individually.

Third, we apply the phase association method, Gaussian Mixture Model Associator (GaMMA)57 to filter out false picks and build a DAS training dataset with pseudo labels. GaMMA selects only picks that fall within a narrow window of the theoretical arrival times corresponding to the associated earthquake locations. We set the time window size to 1 s in this study (Table S2). This hyperparameter can be adjusted to balance the trade-off between the quantity and quality of pseudo labels. A small window size results in a small training dataset with high-quality pseudo labels. Conversely, a large window size creates a large training dataset with potentially less accurate arrival times.

Last, we train a new deep-learning-based phase picker designed for DAS data. The model architecture is explained in the following section (Fig. 7). The training labels utilize the same Gaussian-shaped target function as proposed by Zhu and Beroza19:

P P=e-(t-tP)2/2σtP2

P S=e-(t-tS)2/2σtS2

P N=max(0, 1-P P-P S)

where tP and tS are the arrival-times of P and S phase; P P, P S, and P N are the target functions for P-phase, S-phase, and Noise; σ is the width of the Gaussian-shaped target function, which is used to account for uncertainties in phase arrival times similar to label smoothing commonly used in computer vision71. We set σ to 1.5 s in this work.

Because the pseudo labels are mostly picked on high SNR channels, a deep learning picker trained only on high SNR waveforms could generalize poorly to noisy waveforms. Data augmentation, such as superposing noise onto seismic events, can synthesize new training samples with noisy waveforms, significantly expand the training dataset, and improve model generalization on noisy DAS data and weak earthquake signals45,72. In addition to superposing noise, we add augmentations of randomly flipping data along the spatial axis, masking part of data, superimposing double events, and stretching (resampling) along the temporal and spatial axes.

By following these steps, we can automatically generate a large dataset of high-quality pseudo labels and train a deep neural network model on DAS data. We can further use this newly trained model to generate pseudo labels and train an improved model. This procedure can be repeated several times to enhance performance. In this study, we conducted two iterations using pseudo labels generated by PhaseNet and PhaseNet-DAS. We named the two resulting models as PhaseNet-DAS v1 and v2 for clarity. Future work could further optimize the number of iterations to enhance performance.

Neural network model
The pre-trained PhaseNet model is a modified U-Net architecture73 with 1D convolutional layers for processing 1D time series of seismic waveforms. DAS data, on the other hand, are 2D recordings of seismic wavefields with both spatial and temporal information. So the pre-trained PhaseNet model cannot utilize the spatial information from DAS’s ultra-dense channels. In order to exploit both spatial and temporal information of 2D DAS data, we extend the PhaseNet model using 2D convolutional layers. The architecture of the PhaseNet-DAS model is shown in Fig. 7, which is similar to the original U-Net architecture73. In order to consider the high spatial and temporal resolution of DAS data, we use a larger convolutional kernel size (7×7) and a stride step (4×4) to increase the receptive field of PhaseNet-DAS74. We add the transposed convolutional layers for up-sampling75, batch normalization layers76, relu activation functions77, and skip connections to the model. The semi-supervised approach does not require using the same neural network architecture as the pre-trained model, so that we can also use other advanced architectures designed for the semantic segmentation task, such as DeepLab78, deformable ConvNets79, and Swin Transformer80. In this work, we focus on exploring whether we can transfer the knowledge of seismic phase picking from seismic data to DAS data, so we keep a simple U-Net architecture as PhaseNet. The exploration of optimal neural network architectures, e.g., transformer22,80,81, for DAS data could be done in future research.

Training data
We collected a large training dataset using four DAS cables in Long Valley and Ridgecrest, CA (Fig. 8). The Long Valley DAS array consists of two cables, each with a length of 50 km, 5000 channels, and a channel spacing of ~10 m8,82–85, referred to as the Mammoth north and Mammoth south cables for clarity (Fig. 8a). The Ridgecrest DAS array consists of one short cable (10 km and 1250 channels) and one long cable (100 km and 10,000 channels), referred to as the Ridgecrest north and Ridgecrest south cables respectively (Fig. 8b). The cable locations are determined using a GPS-tracked moving vehicle developed by Biondi et al.85. We extracted event-based DAS records based on the standard catalogs of the Northern California Seismic Network, Southern California Seismic Network, and Nevada Seismic Network. Following the semi-supervised learning approach outlined above, we applied the pre-trained PhaseNet model to pick P and S arrivals in these extracted event data, applied the GaMMA model to associate picks, and kept the events with at least 500 P and S picks as the training datasets. In the first iteration using PhaseNet as the pre-trained model, we obtained a dataset of 1056 events and 1116 events from the Mammoth north and Mammoth south cables, and 597 events and 1430 events from the Ridgecrest north and Ridgecrest south cables respectively. In the second iteration using PhaseNet-DAS v1 as the pre-trained model, we obtained a dataset of 3405 events and 3437 events from the Mammoth north and Mammoth south cables, and 3590 events and 3311 events from the Ridgecrest north and Ridgecrest south cables respectively. Because we do not have manual labels as ground truth to evaluate the model performance, we only split each dataset into 90% training and 10% validation sets. We randomly selected training samples of 3072×5120 (temporal samples×spatial channels) and applied a moving window normalization to each channel. The moving window normalization, implemented using a convolutional operation with a window size of 1024 and a stride step of 256, removes the mean and divides by the standard deviation within a fixed window size, making it independent of input data length. Coupled with the fully convolutional network architecture of PhaseNet-DAS, the model can be applied to flexible length of continuous data. We trained PhaseNet-DAS using the AdamW optimizer and a weight decay of 0.186,87, an initial learning rate of 0.01, a cosine decay learning rate with linear warm-up88, a batch size of 8, and 10 training epochs. Future work could further explore optimal hyperparameters to enhance performance.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The paper “Seismic Arrival-fime Picking on Distributed Acousfic Sensing Data using Semi-supervised Learning” by Zhu et al describes a deep learning method for seismic phase arrival fime picking and event detecfion on DAS data. To this end, the authors generalize the PhaseNet approach to DAS data. The key contribufion of the manuscript is a novel, semi-supervised training strategy for the model, combining noisy labels with a phase associafion step for external validafion. This strategy alleviates the problem of missing manually annotated phase arrival labels for DAS.\nWith the quickly growing adopfion of DAS measurements, providing a sensifive and high-performing method for detecfing earthquakes in DAS data is a fimely and important topic. The provided method is sound and well suited for the task and, if published with a sufficiently user-friendly implementafion, will be of great interest to pracfifioners. Nonetheless, I have two larger points of concern about the current manuscript.\nFirst, the metrics for event detecfion seem rather poor to me. At local to regional distances, already an offset of 3 s in origin fime is considerable. At 15 s, it is quesfionable if this is sfill the same event. In addifion, there are 25 % of events not associated with any cataloged event. Are these addifional detecfions or actually false posifives? On the other side, this also implies that there are a substanfial number of events that have not been detected with the DAS. Looking at Figure 4, a lot of these seem to be around the detecfion limit, but there are also several M3.5+ events at distances of around 100 km that were missed and should definitely be visible on the DAS. To understand the usefulness of the model, I think it is essenfial to understand these missed/falsed detecfions. This is crifical for users aiming to build catalogs with the method, as it might distort the catalogs and subsequent analysis on the catalogs. Related to this point, I think to really prove the necessity of the method for catalog generafion, it should be compared to a regular PhaseNet. Looking at the examples in Figure 1, PhaseNet picks are prefty noisy, but the events are sfill clearly idenfifiable. In parficular, selecfing good labels through associafion shows that GaMMA can actually idenfify the events from these picks. Therefore, I suggest to also compare the catalog obtained from directly applying GaMMA to the PhaseNet picks with the GaMMA + PhaseNet-DAS catalog.\nSecond, as indicated in Figure 5, a key advantage of the method is that it can be iterated. However, according to line 280, this is actually not done. Looking at the PhaseNet predicfions in panel 1, this suggests that the model is trained on very noisy labels and that retraining would considerably improve the model. Therefore I think at least one iterafion of this associafion loop starfing with a PhaseNet-DAS model should be conducted.\nAs a last point, I strongly encourage the authors to deposit their data in a data repository with a DOI. Making data available from the authors upon request increases the risk of data becoming inaccessible in the future and is not in line with open science pracfices.\nIn conclusion, I think this manuscript tackles an important and fimely topic and will be a valuable contribufion to the community. However, there are major points that from my perspecfive need to be addressed before publicafion. In addifion, I list a collecfion of minor points below. I encourage the authors to address these points and think this work will be very useful in future studies of DAS data.\nMinor:\n• The references are numbered in-text but sorted alphabefically (and without numbers) in the bibliography. This makes cross-checking of the references for the reviewers almost impossible.\n• Introducfion: I think it should be menfioned that another advantage of DAS is that it can be deployed offshore prefty easily.\n• Line 40ff: There should be a note that the high data volume is also a key limifing factor for DAS processing.\n• Lines 48ff: The reference to template matching seems a bit unrelated to me at this point. While the applicafion of STA/LTA to DAS is prefty straighfforward and this method has been used, I’m not aware that the same has been done with template matching.\n• Line 79f: Can you provide references that these methods are not effecfive for DAS data? I admit, this is likely difficult as null results are rarely published but, if possible, would be a helpful resource for readers.\n• I think the proposed model does not really fit the noisy student method framework. The key part of the training strategy is using the associafion step as an outside validafion signal. Such an outside validafion is not present in the noisy student method. Personally, I’d call this distantly-supervised learning but machine learning terminology is far from unique here.\n• Line 151f: Please provide the number of channels to put the numbers of picks in context.\n• From personal experience, GaMMA runfimes grow strongly with the number of picks in each cluster (of the inifial DBscan step). With the enormous number of picks in this dataset, how does GaMMA perform in terms of runfime?\n• For the generated catalog, was PhaseNet-DAS trained on this sequence or is this an independent training set.\n• Line 169f: Please provide the employed overlap between windows. As pickers are unfortunately not invariant to shifting, I think a certain overlap between windows is necessary and this value can considerably impact runfime.\n• Lines 169 and 213: There are two different sampling rates (100 Hz and 200 Hz) provided. Does this mean that different sampling rates have been used in training and applicafion?\n• Figure 4: As far as I understood from the text, only the DAS events corresponding to a catalog event are shown. Could you please specify this in the capfion. In addifion, it could maybe be indicated visually. At first glance, it seemed like the DAS had detected substanfially more events, including large ones.\n• Please describe if and how hyperparameter tuning has been performed.\n• How are the labels for PhaseNet-DAS encoded? I’d assume the encoding are probability curves similar to PhaseNet but this should be explicitly specified.\n• For applying GaMMA, the locafion of each channel of the DAS is required. However, DAS channel locafions are generally not perfectly known as the cables might not be absolutely straight. Please provide a discussion on how the channel locafions were determined and if the uncertainty has an effect on the model.", "reviewer_2": "This manuscript describes the development of a seismic phase picker based on deep-learning approaches that can be applied to Distributed Acousfic Sensing (DAS) data. There is liftle doubt that such a tool is useful, and it seems indeed that the authors produced a working solufion.\nThe manuscript is well wriften but in a somewhat exuberant language that gives, from the beginning, the impression that the authors may be trying to sell something. The organisafion of the manuscript, with excessive focus on results but rather sparse informafion on the actual developments, further enhances this impression.\nI read this manuscript several fimes, with a few days between, and now see three major classes of concerns:\nINNOVATION:\n------------------\nI do understand that deep learning is currently a big hype and that it is tempfing, especially for young researchers, to become part of this. However, the days where the mere applicafion of some deep-learning model was science, are over. With numerous easily usable programming tools, the training of a neural network (deep or not; this is just somewhat hollow semanfics) has become an easy task for undergraduate students. After all, it is what it is: fifting the coefficients of some funcfional form to a collecfion of data.\nThis said, it is not clear how exactly the authors go significantly beyond just training yet another deep neural network? What is the innovafion that goes beyond the obvious?\nAdmiftedly, I do not find these quesfions easy to answer. The only problem that the authors seem to address is the absence of labelled training datasets for DAS data. For this, they exploit exisfing single-trace phase pickers, the results of which are filtered by a phase associafion algorithm. Essenfially, this ensures that signals without spafial coherence do not end up being used as pseudo-labels for the new network training.\nIn my opinion, the whole innovafion in this work is precisely this filtering step. Nothing more. This is not to say that there is no innovafion! However, its magnitude does not match the grandiose tone of the manuscript, and I also do not think this is sufficient for a high-profile publicafion.\nMETHOD:\n-------------\nLooking at this filtering step from some distance, I think it becomes clear that the rest of the proposed method, i.e., the training of a new network, has actually become redundant! After the filtering, i.e., the coherence-based cleaning of the single-trace picks, the problem of extracfing seismic phases from the DAS data is actually already solved! The output of the filter is already what we need, and there is no obvious need to then build a new interpolafion functon(neural network) on top of that.\nHence, the whole purpose of half the method is actually not clear.\nI must admit that I may not have understood the method 100 %. However, in this case, I strongly suspect that a majority of the readers would not understand it either. Again, this goes hand in hand with the peculiar presentafion style.\nUNCERTAINTIES:\n----------------------\nThe authors' method also seems to produce earthquake locafions. However, it seems like they are merely dots on a map. For many decades, earthquake locafions have been reported with uncertainfies, for obvious reasons.\nHere, it is not clear to me where these uncertainfies are and how the method could actually produce them. In case it can't, the method basically has no value for quanfitafive science. (It sfill makes impressive pictures.) Hence, this part needs some serious work.\nIn summary, I do not think that there is sufficient innovafion and creafivity for a high-profile publicafion, and not enough technical informafion and detail for a more method-oriented journal.", "reviewer_3": "The paper presents a semi-supervised deep learning approach (PhaseNet-DAS) to pick seismic phase arrival fimes in distributed acousfic sensing (DAS) data. The study proposes the use of pre-trained PhaseNet to generate noisy pseudo-labels of P and S picks from individual DAS channels. Next, the study uses a phase associafion method (Gaussian Mixture Model Associator (GaMMA)) to disfinguish noise and seismic arrivals from the pseudo-labels, essenfially clustering respecfive phases into groups. Data augmentafion (random flipping) is also added to increase the diversity of the dataset. By following this methodology, a large number of training datasets can be generated, and the quality of the dataset can be refined by repeafing the procedure several fimes if desired. Consequently, the study proposes PhaseNet-DAS, which takes in two-dimensional (2D) DAS data, and predicts the relevant 2D P and S arrivals.\nThis study presents a major contribufion to the DAS geophysics community. DAS is often clouded with inherent noise due to its highly sensifive and dense sensors. Exisfing machine learning (ML) pickers only work best on individual traces, which is likely to predict inconsistent phase picks when applied on 2D DAS data. As evident in Figure 1, PhaseNet-DAS seems to be able to predict the P and S picks with minimal noise. Furthermore, the semi-supervision nature of this study means that less manual work is needed to label 2D DAS signals. This contribufion is significant because manually labeling 2D DAS signals can be highly laborious at fimes.\nComments/quesfions:\nAs DAS is not only used to monitor earthquakes, is PhaseNet-DAS limited to only detecfing earthquakes? Can PhaseNet-DAS predict non-earthquake signals captured by DAS? Some examples of other seismic signals include vehicular traffic, mining blasts, thunderstorms, and microseismicity. I suggest discussing the limitafions and/or feasibility of PhaseNet-DAS on detecfing non-earthquake signals.\nFor the deep learning training, how are the input 2D datasets (1024x1024) cut? What about cases when a cut dataset contains only S arrivals? Would this affect the training and predicfion?"}, "author_response": "We thank the editor and reviewers for your valuable feedback and constructive suggestions.We performed additional experiments and made revisions to our manuscript, including three major changes: First, we implemented a seconditeration of trainingusing thesemi-supervised learning approach. For clarity, we named the first iteration as PhaseNet-DAs v1, which is trained using noisy labels generated by PhaseNet,and namedthe second iteration asPhaseNet-DASv2,which is trained using noisy labels generated by PhaseNet-DAS v1. Second, we compared the performance of PhaseNet, PhaseNet-DAS v1, and PhaseNet-DAS v2. We associated the picks from each model using the same phase associator GaMMA, and compared the association rate and detected earthquake numbers. Last, we added more metrics to show the improvementsafter semi-supervised learning, such as the number of picks per event, time residuals of picks, and number of events in relation to SNR and distance. Below we describe the changes that were madeinresponseto reviewers’comments.\n\nREVIEWERCOMMENTS\nReviewer#1(Remarksto theAuthor):\nThe paper “Seismic Arrival-time Picking on Distributed Acoustic Sensing Data using Semi-supervised Learning” by Zhu et al describes a deep learning method for seismic phase arrival time picking and event detection on DAS data. To this end, the authors generalize the PhaseNet approach to DAS data. The key contribution of the manuscript is a novel, semi-supervised training strategy for the model, combining noisylabels withaphase association step for external validation. This strategy alleviates the problem of missing manually annotated phasearrival labelsfor DAS.\nA:Thankyoufor recognizing thecontributions of ourwork.\nWith the quickly growing adoption of DAS measurements, providing a sensitive and high-performing method for detecting earthquakes in DAS data is a timely and important topic. The provided method is sound and well suited for the task and, if published with a sufficiently user-friendly implementation, will be of great interest to practitioners. Nonetheless, I have two largerpoints of concernabout thecurrent manuscript.\nA: We will release the source code and the pre-trained model with the paper to makeit easy for applying our model and re-training models for new DAS datasets. We also clarified the implementation detailsmentionedin thefollowing comments.\nFirst, the metrics for event detection seem rather poor to me. At local to regional distances, already an offset of 3 s in origin time is considerable.At15s,it isquestionable if this isstillthe same event. In addition, there are 25 % of events not associated with any cataloged event. Are these additional detections or actually false positives? On the other side, this also implies that there are a substantial number of events that have not been detected with the DAS. Looking at Figure 4, a lot of these seem to be around the detection limit, but there are also several M3.5+ events at distances of around 100 km that were missed and should definitely be visible on the DAS. To understand the usefulness of the model, I think it is essential to understand these missed/falsed detections. This is critical for users aiming tobuild catalogswith themethod, asit might distort thecatalogsand subsequentanalysisonthe catalogs.\nRelated to this point, I think to reallyprove thenecessityof themethod for cataloggeneration, it should be compared to a regular PhaseNet. Lookingat theexamples inFigure 1, PhaseNetpicks are pretty noisy, but the events are still clearly identifiable. In particular, selecting good labels through association shows that GaMMA can actually identify the events from these picks. Therefore, I suggest to also compare the catalogobtainedfromdirectly applying GaMMAtothe PhaseNetpickswith theGaMMA +PhaseNet-DAScatalog.\nA: Thanks for this constructive suggestion. We have added additional results to address these comments.\n1.Wehaveincludedresults ofboth PhaseNetand PhaseNet-DASinour analysis.We updated Figure 4 to include catalogs generated using PhaseNet+GaMMA andPhaseNet-DAS+GaMMA. We added Figure S3 to show the change of detected earthquake number with distance. We also added Figure S4 to show earthquake locations using PhaseNet+GaMMA similar to Figure 5 using PhaseNet-DAS+GaMMA. The comparison helps to demonstrate the improvedearthquake detectionperformance.\n2. The large origin time error results from its trade-offwithearthquake locationand velocity errors. The limited azimuth coverage of DAS leads to poor constraints on earthquake location (Figure S5). If the earthquake locations are inaccurate, the origin time will also have a large error. As a result, it is not easy to directly compare earthquake catalogs generated by a seismic network and DAS. We added more explanation in the revision: L175 “Because of different sensor coverages between seismic networks and DAS cables, seismic signals from distant but small magnitude events are expected to be too small to detect, so the absolute number of earthquakes in the standard catalogs and detected by DAS can not be directly compared. To evaluate the improvements from semi-supervised learning, we compare the magnitude and distance distributions of earthquakesdetected bythreemodels,PhaseNet,PhaseNet-DASv1,and PhaseNet v2 in Figure 4 and Figure S3. PhaseNet-DAS significantly improves the detection of both small magnitude events neartheDAS arrayandlargemagnitude eventsatgreaterdistances.\n”\nWe have also added an analysis of thetime residualsof phasepicks bycomparing themwith thetheoreticalphasearrival timesbased onthetrueearthquake origin timesand locations(Figure S2).Assuggestedbythereviewer,most picks within~100 km havesmalltime residualswithin a few seconds, while the time residuals become muchlarger asthe epicenterdistanceincreasedue to the differencesbetweenthe true3D velocitymodel andthe1D velocitymodel weused.\n3. Most additional detections come from multiple eventsinthesamewindow, andsome may inevitably be false positives. We select an event window of 120s to build our event dataset. For earthquake swarms in Long Valley and aftershock sequences in Ridgecrest, there may include double or more events in one window. We can see several picks with large negative or positive time residualsatsomedistancesinFigure S2.\nThe missed detections are mostly due to the low SNRs. We added Figure 2toshowhow the detectedearthquakenumberchange withSNRs. Becausethe DASrecordingsarenotonly related to distance, they are also affected by wave incident angle, coupling, local structures, and traffic noise level as the fiber-optic cables are mostly deployed along roads. We can see most of the missed events are around SNR = 0dBin Figure2.PhaseNet-DAShasa betterperformance than PhaseNet at low SNR. We have added more discussion about the detection performance: L129 “The PhaseNet model pre-trained on seismic data can detect highSNRevents,butstruggle with low SNR events on DAS (Figure 2). After re-training using semi-supervised learning on DAS data, the PhaseNet-DAS model significantly improves detections of low SNR events. PhaseNet-DAS v1 detects 2-5 times more events than PhaseNet across four DAS arrays, and PhaseNet-DAS v2 enhances detection sensitivity by an additional 25% - 50% compared to PhaseNet-DASv1(Figure 2).”\nSecond, as indicated in Figure 5, a key advantage of the method is that it can be iterated. However, according to line 280, thisis actuallynot done.Lookingatthe PhaseNetpredictionsin panel 1, this suggests that the model is trained on very noisy labels and that retraining would considerably improve the model. Therefore I think at least one iteration of this association loop starting withaPhaseNet-DASmodel shouldbeconducted.\nA: Thanks for the suggestion. We added another iteration and reported both the performance of PhaseNet-DASv1andv2.\nAs a last point, I strongly encourage the authors to deposit their data in a data repositorywith a DOI. Making data available from the authors upon request increases the risk of data becoming inaccessiblein thefuture andis notinline withopenscience practices.\nA: We deposit the extracted event data of the public Ridgecrest (north) DAS dataset under the DOI: https://doi.org/10.57967/hf/0962. The continuous DAS data can be accessed from the SCEDC Earthquake Data AWS Public Dataset (https://scedc.caltech.edu/data/getstarted-pds.html). Because other datasets are being used by undergoing projectsin thegroup, wecannot sharethem publicly atthe currentmoment.\nIn conclusion, I think this manuscript tackles an important and timely topic and will be a valuable contribution to the community. However, there are major points that from my perspective need to be addressed before publication. In addition, I list a collection of minor points below. I encourage the authors to address these points and think this work will be very usefulinfuture studiesof DASdata.\nA: Thank you for recognizing our contribution to the community and helping us improve our manuscript. We will open-source code and model to facilitate more applications of DAS to earthquakestudies.\nMinor:\n• The references are numbered in-text but sorted alphabetically (and without numbers) in the bibliography.Thismakescross-checkingof thereferencesfor the reviewersalmostimpossible.\nA:Corrected.\n• Introduction: I think it should be mentioned that another advantage of DAS is that it can be deployedoffshorepretty easily.\nA: Good point. Added L37 “Furthermore, DAS is suitable for deployment and maintenance in challengingenvironments suchas offshorelocations, glaciers,andboreholes. ”\n• Line 40ff: There should be a note that the high data volume is also a key limiting factor for DASprocessing.\nA: Good point. Added L42 “... due to the lack of effective algorithms for detecting earthquakes and picking phase arrivals, coupled with the high data volume recorded by over thousands of channels.”\n• Lines 48ff: The reference to template matchingseemsabit unrelated tomeat this point.While the application of STA/LTA to DASis prettystraightforwardandthis method hasbeen used,I’m not awarethatthesamehasbeen donewithtemplate matching.\nA:Wehaveaddedtworeferences ofapplicationsof templatematching toDAS:\nLi, Z., & Zhan, Z. (2018). Pushingthelimitofearthquakedetectionwithdistributedacousticsensingand template matching: A case study at the Brady geothermal field. Geophysical Journal International, 215(3),1583-1593.\nLi, Z., Shen, Z., Yang, Y., Williams, E., Wang, X., & Zhan, Z. (2021). Rapid response to the 2019 Ridgecrestearthquakewithdistributedacousticsensing.AGUAdvances,2(2),e2021AV000395.\n• Line 79f: Can you provide references that these methods are not effective for DAS data? I admit, this is likely difficult as null results are rarely published but, if possible, would be a helpful resourcefor readers.\nA: Few studies havebeenconductedonphase picking onDASdata sofar.Wethink thedifferent data formats between seismic and DAS data is achallenge for transferlearning, whileachieving high temporal accuracy is difficult for self-supervised learning. We think another potential solution for future research is to use self-supervised learning to train a large model first and fine-tuneit onasmallsetofmanually labeleddatasetto achieveagoodpicking accuracy.\n• I think the proposed model does not really fit the noisy student method framework. The key part of the training strategy is using the association step as an outsidevalidation signal.Suchan outside validation is not present in the noisy student method. Personally, I’d call this distantly-supervisedlearningbut machinelearningterminology is farfromunique here.\nA: Thanks for this suggestion. We reference the Noisy Student method as an example of semi-supervised learning, since our training approachis similar toit.Our approachisalso atype of semi-supervised learning using pseudo labels. In semi-supervised learning, key steps lie in filtering of pseudo labels, curation and augmentation of unlabeled dataset. For seismic data, phase association is a unique and effective way for filtering (injecting supervision information). For images, the Noisy Student method also applied multiple criteria for filtering: “We then perform data filtering and balancing on this corpus. … We then select images that have confidence of the label higher than 0.3. For each class, weselectat most130K imagesthat have thehighestconfidence.Finally, for classesthathave lessthan130K images,…”\nXie, Q., Luong, M. T., Hovy, E., & Le, Q. V. (2020). Self-training with noisy student improves imagenet classification.InProceedingsoftheIEEE/CVFconferenceoncomputervisionandpatternrecognition\n•Line151f: Pleaseprovidethe numberofchannels toputthe numbersofpicks incontext.\nA: We have added Figure S1 to show the number of picks per event. We can see the numberof pickssignificantly increases for eachdetected event afterre-training.\n• From personal experience, GaMMA runtimes grow strongly with the number of picks in each cluster (of the initial DBscan step).Withthe enormousnumberof picksin thisdataset, how does GaMMAperform intermsof runtime?\nA: The implementation of DBSCAN in scikit-learn is pretty efficient. For associating 15,974 picks,GaMMAtakes9sonour server usingaCPUof 64cores.\n• For the generated catalog, was PhaseNet-DAS trained on this sequence or is this an independenttraining set.\nA: The catalog is generated on the same sequence. Our task is a bit different from supervised training, which has a cleartestdataset for comparison.Asshownin Table1,the numberofpicks (pseudo labels) from PhaseNet is about 4.2M + 5.3M on the two DAS cable in Long Valley, while the model after training detects 35.9M + 40.2 picks. These new picks areoutsideofthose used for training. But there could be a risk of overfitting on our DAS cables, since these new picks come from nearly but noisier channels. We will open source themodel, sothat people can test on other DAS cables. We also further expand this point in discussion: L242 “The current PhaseNet-DAS model was trained and tested using four DAS arrays in Long Valley and Ridgecrest, CA. The datasets are also formatted using a same time sampling of 100 Hz and a similar spatial sampling of ~10 m. These factors may limit the model's generalization to DAS arraysatdifferentlocationsand/orwithvaryingspatial andtemporal samplingrates. ”\n• Line 169f: Please provide the employed overlap between windows. As pickers are unfortunately not invariant to shifting, I think a certain overlap between windows is necessary andthisvaluecanconsiderablyimpact runtime.\nA: Because we are using a fully convolutional network architecture, we do not cut sliding-windows. L337 “We randomly selected training samples of 3072x5120 (temporaltime x spatial size) and applied a moving window normalization to each channel. The moving window normalization, implemented using a convolutional operation with a window size of 1024 and stride step of 256, removes the mean and divides by the standard deviation within a fixed window size, making it independent of input data length. Coupled with the fully convolutional network architecture of PhaseNet-DAS, the model can be applied to flexible lengths of continuousdata.”\n• Lines169and213: Therearetwodifferentsampling rates(100 Hzand200Hz)provided.Does this meanthat differentsampling rateshave beenused intraining andapplication?\nA: The raw DAS is recorded at 200Hz, so we used the raw sampling rate in the speed test.The training andearthquakedetectionperformance arebothdoneat 100Hz\n• Figure 4: As far as I understood from the text,only theDASeventscorrespondingto acatalog event are shown. Could you please specify this in the caption. In addition, it could maybe be indicatedvisually.Atfirstglance,it seemedlike theDAS haddetectedsubstantially moreevents, including largeones.\nA:Thatiscorrect.Wehave updated thecaption.\n•Pleasedescribeif andhow hyperparametertuning hasbeen performed.\nA: We keep a setting similar toPhaseNetanddidnotapply anyhyperparametertuning. Wehave addedthis point intherevision:\nL316 “In this work, we focus on exploring whether we can transfer the knowledge of seismic phase picking from seismic data to DAS data, so we keep a simple U-Net architecture as PhaseNet. The exploration of the best neural network architectures, e.g., transformer , for DAS datacanbedoneinfuture research.”\nL345“Becausethequalityand sizeofthe trainingdatasetshavea greaterimpactonourproblem thanhyperparameters,wedonottune thesetraininghyperparameters.”\n• How arethelabelsfor PhaseNet-DASencoded?I’d assumethe encoding areprobabilitycurves similar to PhaseNetbut thisshould beexplicitly specified.\nA: We have explicitly specified the training labels now: The training labels are the same Gaussian-shapedtargetfunction proposedbyZhu andBeroza (2019):\nwhere t and t are the arrival-times of P and S phase, P , P , and P arethetarget functionsfor P S P S N\nP-phase, S-phase, and Noise, and σ isthe widthof theGaussian-shapedtarget function,whichis used to account for uncertainty in phase arrival times similar to label smoothing used in computervision.\n• For applying GaMMA, the location of each channel of the DAS is required. However, DAS channel locations are generally not perfectly known as the cables might not be absolutely straight. Please provide a discussion on how the channel locations were determined and if the uncertaintyhasaneffecton themodel.\nA: Biondi et al. (2023) developed a method to determine the DAS channel location pretty accurately using a GPS‐Tracked Moving Vehicle. The channels locations of the four DAS arrays used in this study are determined using the proposed method. We have added this information.\nIn general, the channel locations are pretty accurate. The same DAS cable is also used for seismic tomography, currently under review. The earthquake locationuncertaintyis impactedby multiple factors is beyond the scope ofthis study.Thelimited azimuthcoverageof asingleDAS arrayisamajorfactor,asshownin FigureS5.\nBiondi, E., Zhu, W., Li, J., Williams, E., & Zhan, Z. (2022, December). Fiber seismic tomography of the LongValleyCaldera.InAGUFallMeetingAbstracts(Vol.2022,pp.V33A-04).\nBiondi, E., Wang, X., Williams, E. F., & Zhan, Z. (2023). Geolocalization of Large‐Scale DAS Channels UsingaGPS‐TrackedMovingVehicle.SeismologicalSocietyofAmerica,94(1),318-330.\n\nReviewer#2(Remarksto theAuthor):\nThis manuscript describes the development of a seismic phase picker based on deep-learning approaches that can be applied to Distributed Acoustic Sensing (DAS)data. There islittle doubt that suchatool isuseful,andit seemsindeed thatthe authorsproducedaworking solution.\nThe manuscript is well written but in a somewhat exuberant language that gives, from the beginning, the impression that the authors may be trying to sell something. The organisation of the manuscript, with excessive focus on results but rather sparse information on the actual developments,further enhancesthis impression.\nI readthis manuscriptseveraltimes,with afewdays between, andnow seethree majorclassesof concerns:\nA: Thank you for taking the time to read our manuscript carefully. We have added more results basedonyour commentsandrevised themanuscriptaccordingly.\nINNOVATION:\n------------------\nI do understand that deep learning is currently a big hype and that it is tempting, especially for youngresearchers,tobecome part ofthis. However,thedays where themereapplication of some deep-learning model was science, are over. Withnumerouseasilyusableprogramming tools, the training of aneuralnetwork(deepor not;this is justsomewhathollow semantics)has becomean easy task for undergraduate students. After all, it is what it is: fitting the coefficients of some functional form to acollectionof data.\nThis said, it is not clear how exactlytheauthors gosignificantlybeyondjust training yetanother deepneuralnetwork?What isthe innovation thatgoes beyondthe obvious?\nA: Thanks for these critiques. We think there are three major innovations of our work that goes beyond training yet another neural network. First, our work addresses the challenge of lack of manual labels for DASdata.We agreewiththe reviewers’comment, traininganeural networkis now an easy task evenfor undergraduatestudents.But therearenophase picking modelstrained for DAS data so far. The main challenge is not training neural networks but the lack of manual labels for training. The semi-supervised learning approach we proposed is an effective way to transferthephasepicking capabilityfrom seismicdata tothe newDASdata. Second,as theother two reviewers’ have commented, DAS is a rapidly developing technology for earthquake monitoring, but there are no reliable earthquake detection and phase picking algorithm for DAS data. To our knowledge, this is the first phase detecting/picking model developedfor DAS data. The picker already been used in several related studies of tomography, focal mechanism, fault zone imaging, earthquake magnitude estimation in our group. We will also open source our model to be used by the community, as we did in our previous works. Last, PhaseNet-DAS works significantly better thanPhaseNet.BecausePhaseNetis notdesignedfor DASand cannot use spatial information between channels, so we did not include the comparison in our initial draft. We expanded the revision with the comparisonwith PhaseNet.Deep learningmodelssuch as PhaseNet only works on high SNR channels, which is also the basis of the possibility of semi-supervised learning from seismic data to DAS data. After training, PhaseNet-DAS has higher association rate (much fewer false picks) (Table 1), morepicks per events(pickingphase on noisy channels) (Figure S1), more detected events (sensitive to low SNR events) (Figure 2, FigureS3andS4).\nAdmittedly, I do not find these questionseasy toanswer. Theonlyproblemthat theauthors seem to addressistheabsenceof labelledtraining datasetsfor DAS data.For this,they exploit existing single-trace phase pickers, the results of which are filtered by a phase association algorithm. Essentially, this ensures that signals without spatial coherence do not end up being used as pseudo-labelsfor thenew network training.\nIn my opinion, the whole innovation in this work is precisely this filtering step. Nothing more. This is not to say that there is no innovation! However, its magnitude does not match the grandiose tone of the manuscript, and I also do not think this is sufficient for a high-profile publication.\nA: Thanks for recognizing our innovation in addressing theabsenceof labeledtraining datasets for DAS data using semi-supervised learning. Lack of training labels for DAS is a major block for applying machine learning to DAS data. Although many papers on applications of DAS to earthquake studies are published, the applications of machine learning to DAS are limited. The semi-supervised learning approach we develop makes it possible to re-use many manual labels on seismic data and train machine learning models for DAS data. This approach can also be applied to other seismic tasks on DAS data such as picking first-motion polarity. We revised several sentences to avoid a grandiose tone. Weemphasizedseveral limitationsofour method in discussion.Wewouldappreciateany further suggestionsfor improvement fromthe reviewer.\nWe also think it is incorrect to say that innovation liessolelyinthefiltering step.Otherwise, the performance of PhaseNet-DAS will be similar to PhaseNet given the same filtering step.\nPhaseNet-DAS differs from single-channel phase pickers like PhaseNet, because it utilizes information from nearby channels to detect weak signals and prevent false picks. In the added results (Table S1, Figure 2, 4, S1-S4), we have compared the performance of PhaseNet and PhaseNet-DAS. PhaseNet-DAS’s performanceis significantlybetter thanPhaseNet.Specifically, Figure S1 clearly shows that PhaseNet-DAS can pick phases on many more channels where PhaseNetcannot.\nMETHOD:\n-------------\nLooking at this filtering step from some distance, I think it becomes clear that the rest of the proposed method, i.e., the training of a new network, has actually become redundant! After the filtering, i.e., the coherence-based cleaning of the single-trace picks, the problem of extracting seismic phases from the DAS data is actually already solved! The output of the filter is already what we need, and there is no obvious need to then build a new interpolation functon (neural network) ontopof that.\nHence,thewholepurposeof halfthemethod is actuallynotclear.\nA: Because PhaseNet is not designed for DAS data and the performance of PhaseNet-DAS is significantly better than PhaseNet, so we did not include the comparison in our initial draft.We added new results in the revision to address the reviewer’s concern that training of a new network based on the filtered labels are redundant. We can see improvements in both the first iteration training from PhaseNet to PhaseNet-DASand thesecond iteration fromPhaseNet-DAS v1 to PhaseNet-DAS v2 in association rate (Table 1), picked phases per event (Figure S1), and detected earthquakes (Figure 4, S3, S4). Given the same filtering using the phase associator GaMMA, the improvements demonstrate that the training is not redundant. Moreover, we can alsoseethat theimprovementsfromPhaseNettoPhaseNet-DASaremoresignificantinreducing false positive picks (higher associated rates), increasing phase picks per event (picking onmore channels), and detecting more events (sensitive to lower SNR events). This is because PhaseNet-DAS uses multi-channel information to pick P/S phase, which can reduce false picks on a few channels and increase the detection of coherent but weak signals across channels. Although PhaseNet is trainedonmany moreseismicwaveforms, it cannotuse themulti-channel information, thushaslimited performance onDAS.\nUNCERTAINTIES:\n----------------------\nThe authors' method alsoseemsto produceearthquakelocations. However,itseems likethey are merely dots on a map. For many decades, earthquake locations have been reported with uncertainties,for obviousreasons.\nHere, it is not clear to me where these uncertainties are and how the method could actually produce them. In case it can't, the method basically hasnovalue for quantitative science. (Itstill makesimpressivepictures.) Hence,this partneeds someserious work.\nA: We agree that location uncertainty is an important issue, but this is beyond the focus of this work. The method does not directly produce earthquake locations. The earthquake locationsare the associated location based on the picked phase arrival times, which are similar to earthquake location based on phase arrivals. The earthquake location uncertainty depends on multiple factors, including phase picking uncertainty, velocity model uncertainty, cable geometries and azimuthal coverages, and optimization methods. We have analyzed the temporal accuracy of these automatic phase picks in Figure 3 using waveform cross-correlation. The otherfactorsare independentof thephasepicking model.\nBecause we only use one DAS array to constrain earthquake locations, the location uncertainty mainly comes from the limited azimuth coverage from the geometry of DAS. To provide more information about the location uncertainly, we added a grid-search result by plotting the whole loss surface using synthetic phases picks and velocity models in order to consider the effect of DAS geometry. From the loss surfaces in Figure S5, we can see that: (1) earthquake depths are hard to constrain using a single DAS array; (2) Events along the parallel line of the DAS array have alargelocation uncertainty(FigureS7a); (3) Eventsperpendicular to the DAS array have better constrained horizontal locations, though ambiguitymay ariserelative to which side of the DAS array (Figure S7c and d). The uncertainty also explains the location errors in Figure 5, especially the poor depth locations and the dispersion of events in the North-Westcorner.\nI must admit that I maynothave understoodthe method100%. However,inthis case,Istrongly suspect that a majority of the readers would not understand it either. Again, this goes hand in handwiththepeculiarpresentationstyle.\nIn summary, I do not think that there is sufficient innovation and creativity for a high-profile publication, andnotenoughtechnical informationand detailfor amoremethod-oriented journal.\nA: We hope our point-by-point responses and revisions can addressthe raisedconcerns. Wewill release our code and model for testingthe improvementsof theretrainedmodels.Themodel has already been used in several research projects in our group. We believe this can become beneficialtothecommunitytoo.\nReviewer#3(Remarksto theAuthor):\nThe paper presents a semi-supervised deep learning approach (PhaseNet-DAS) to pick seismic phase arrival times in distributed acoustic sensing (DAS) data. The study proposes the use of pre-trained PhaseNet to generate noisy pseudo-labels of P and S picks from individual DAS channels. Next, the study uses a phase association method (Gaussian MixtureModel Associator (GaMMA)) to distinguish noise and seismic arrivals from the pseudo-labels, essentially clustering respective phases into groups. Data augmentation (random flipping) is also added to increase the diversity of the dataset. By following this methodology, a large number of training datasets can be generated, and the quality of the dataset can be refined by repeating the procedureseveraltimes if desired.Consequently, thestudy proposesPhaseNet-DAS,which takes in two-dimensional (2D) DAS data,and predictsthe relevant 2DP andS arrivals.\nThis study presents a major contribution to the DAS geophysics community. DAS is often clouded with inherent noise due to its highly sensitive and dense sensors. Existing machine learning (ML) pickers only work bestonindividual traces,which islikely topredict inconsistent phase picks when applied on 2D DAS data. As evident in Figure 1, PhaseNet-DAS seemstobe abletopredictthePandS picks withminimalnoise. Furthermore,the semi-supervisionnatureof this study means that less manual work is needed to label 2D DAS signals. This contribution is significant becausemanually labeling2D DASsignalscan behighly laboriousat times.\nA: Thank you for recognizing the challenges in picking seismic phases on DAS and the innovation of our methods.\nComments/questions:\nAs DAS is not only used to monitor earthquakes, is PhaseNet-DAS limited to only detecting earthquakes? Can PhaseNet-DAS predict non-earthquake signals captured by DAS? Some examples of other seismic signals include vehicular traffic, mining blasts, thunderstorms, and microseismicity. I suggest discussing the limitations and/or feasibility of PhaseNet-DAS on detectingnon-earthquakesignals.\nA: The current model is trained to detect only earthquake signals. This is because the PhaseNet model is trained to detect only earthquakes, the generated noisy labels are mostly earthquake signals, and we further applied phase association to filter out onlyearthquake signals.However, the semi-supervised learning approach could also be applied to other non-earthquake signals. The semi-supervised learning approach is effective in utilizing large unlabeled DAS data. The limitation is that we need a pre-trained model on either seismic data or a small labeled DAS dataset for other non-earthquake signals.Here aresome thoughtsabout developingdeeplearning modelsfor non-earthquakesignals thereviewer mentioned:\nFor vehicular traffic: since PhaseNet also picks many false picks ontrafficsignals,wecould design some filtering criteria to select only picks from traffic, for example, setting the velocity model of phase associationtocommon vehiclevelocity.Thenwecan trainanewPhaseNet-DAS model topickthetrafficsignals.\nFor mining blasts: there are some manual labels on seismic data. We can retrain a PhaseNet model for detecting mining blasts, then follow the same semi-supervised approach to develop a PhaseNet-DASmodel formining blasts.\nFor thunderstorms: I am not familiar with thunderstorms signals on DAS. I am happy to discussmore aboutpotentialways todevelop modelsfor detectingthunderstorms onDAS.\nFor microseismicity: There areseveral studiesshowingthat PhaseNetworksgoodonpicking P and S phases of microseismicity. So we can directly apply PhaseNet and semi-supervised learning to train a PhaseNet-DAS model for microseismicity. I think the currently trained PhaseNet-DAS should also work for microseismicity, but maybe with reducedperformance. We will releasethemodel withthe paperfor testingonmicroseismicity.\nFor the deeplearningtraining,how arethe input2D datasets(1024x1024) cut?What about cases whenacutdatasetcontains onlyS arrivals?Would thisaffect the trainingandprediction?\nA: In training, we randomly sample a window from DAS data to generate many training samples. In inference, if the data can fit into GPU memory, wedonotneedto cutanywindows. If the data can not fit into GPU memory, we will cut the whole DAS data into consecutive windows. The training includes samples containing only P or S arrivals, since we are randomly sampling the DAS data.Thiscan makethe model stillworkinprediction withonly Por S phase, but performancewill reduce duetolimited contextofwaveforms information."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The paper “Seismic Arrival-fime Picking on Distributed Acousfic Sensing Data using Semi-supervised Learning” by Zhu et al describes a deep learning method for seismic phase arrival fime picking and event detecfion on DAS data. The revision is very comprehensive and addresses the crifical comments I provided in my first review. I only have one larger point and a few minor comments remaining.\nAs far as I understand the experiments, all tests were performed on cataloged events, i.e., tesfing the sensifivity of the proposed models. However, for a full picture of the performance it would also be essenfial to quanfify to which degree the models produce false posifives. Without such an analysis, it is not clear whether the befter detecfion performance only comes at the cost of a higher false posifive rate. To clarify this, I’d suggest to add an analysis on confinuous waveforms or a similar test addressing the quesfion.\nUpon reading the second review, I also want to clarify that in my opinion the contribufions of this paper, in parficular, the developed novel training scheme are far from trivial. In contrast to simple supervised learning, the proposed semi-supervised scheme is non-standard and the use of a single-stafion model together with a phase associator is an innovafive approach. In addifion, the work is of a high technical standard. While I agree with reviewer 2 regarding the language being exuberant in places, I think this revision of the manuscript has appropriately toned down the claims.\nGiven the comprehensive revisions to the manuscript, I recommend acceptance once the remaining points have been addressed.\nLine numbers refer to the version with change highlighfing.\n• The manuscript states that as the model is fully convolufional, it can be applied to any input size. While technically correct, in pracfice U-Nets expose clear boundary arfifacts that make applicafions to window sizes the model was not trained on not advisable. I’d suggest to add a comment to the manuscript whether such arfifacts occur.\n• L345: The statement that data quality and size mafter more than hyperparameter tuning seems none-obvious to me. I’d suggest either providing a reference or removing the statement.\n• Line 70: “million of pairs” → “million pairs”\n• Lines 242 – 244: I’d recommend phrasing the sentence slightly more speculafive as it’s not clear whether the same approach would work for the suggested tasks.\n• Please add a table with the parameters chosen for GaMMA.\n• Please specify the value of sigma used for the labels.\n• Please clarify how overlaps on P and S waves are labeled, i.e., if Ps + Pp > 1.\n• The link to the implementafion currently (8th September) does not work."}, "author_response": "We appreciate the constructive comments from the reviewer that helped us improve the manuscript. Based on the major comment about false positives, we have added a new test using one week’s continuous data and updated the manuscript (Figures S6 and S7). Below, we provide a detailed point-by-point response.\nReviewer #1\nThe paper “Seismic Arrival-time Picking on Distributed Acoustic Sensing Data using Semi-supervised Learning” by Zhu et al describes a deep learning method for seismic phase arrival time picking and event detection on DAS data. The revision is very comprehensive and addresses the critical comments I provided in my first review. I only have one larger point and a few minor comments remaining.\nAs far as I understand the experiments, all tests were performed on cataloged events, i.e., testing the sensitivity of the proposed models. However, for a full picture of the performance it would also be essential to quantify to which degree the models produce false positives. Without such an analysis, it is not clear whether the better detection performance only comes at the cost of a higher false positive rate. To clarify this, I’d suggest to add an analysis on continuous waveforms or a similar test addressing the question.\nA: Thank you for this suggestion. We have added a case using continuous data and updated the last paragraph of the section of earthquake monitoring (L188-L211). We note that due to the lack of ground truth for the number of earthquakes in real data, it is challenging to conduct a quantitative analysis. There are two indirect pieces of evidence showing the better detection performance does not come at the cost of a higher false positive rate.\nFirst, the event data window (120s) contains a lot of noise. The association results in Table S1 gives an approximate estimation of false positive picks. The association ratio shows that the rate of false positive picks are not high (<10%), and PhaseNet-DAS has significantly fewer false positive picks compared to PhaseNet. Meanwhile, we also need to be cautious that the unassociated picks can be from true events (and, vice versa, the associated picks could also contain false positives), because GaMMA is not perfect especially when many events exist in one event sample, and we have to choose some thresholds, for example, a minimum of 500 picks per event.\nSecond, the rate of false positive events should be much lower after association filtering out false positive picks. From the example of the continuous data results. We can see well correlation with the routine seismic catalog in Figure S7. We added the discussion in the revision: “To assess the potential for false positive events, we compared the associated earthquakes with events in routine earthquake catalogs. The histograms of temporal earthquake frequency in Figure S7 reveal a good correlation between events detected by the DAS array and seismic networks. Specifically, for events within ~0.5 degree of the DAS cable (Figure S7c), we can observe that earthquake frequencies vary from over 80 events to no events per six hours. Given the background noise generally does not change dramatically from day to day, this indicates that these new detections are less likely to be false detections from noise sources such as traffic.”\nEvaluating false positives is a common challenge both for seismic data and DAS data, as deep learning models are generally more sensitive to weak signals and detect several times more events than the routine catalog. Comprehensively and qualitatively evaluating earthquake detection performance on real continuous data would require a well-designed benchmark dataset, which could be one direction of future research.\nUpon reading the second review, I also want to clarify that in my opinion the contributions of this paper, in particular, the developed novel training scheme are far from trivial. In contrast to simple supervised learning, the proposed semi-supervised scheme is non-standard and the use of a single-station model together with a phase associator is an innovative approach. In addition, the work is of a high technical standard. While I agree with reviewer 2 regarding the language being exuberant in places, I think this revision of the manuscript has appropriately toned down the claims.\nA: Thank you very much for recognizing the contribution of our work.\nGiven the comprehensive revisions to the manuscript, I recommend acceptance once the remaining points have been addressed.\nLine numbers refer to the version with change highlighting.\n• The manuscript states that as the model is fully convolutional, it can be applied to any input size. While technically correct, in practice U-Nets expose clear boundary artifacts that make applications to window sizes the model was not trained on not advisable. I’d suggest to add a comment to the manuscript whether such artifacts occur.\nA: We agree that U-Nets could use boundary information to improve the prediction. For example, Figure 1 of Perk et al. (2023)’s work show that only two events near the two edges are picked. But this failed case is primary because we do not have closely space events (~5s) in the training dataset. If we up-sample the waveform by a factor 2 or more, which is similar to doubling the event intervals, all events can be picked well.\nOn the other hand, using a long window size should prevent the model from to using the boundary information. Although the model may use the boundary information to improve performance, we think a robust model should not deteriorate too much without using the edge information when using a long time window, since the edge information are not true information of waveforms. In the test of continuous data, we use a window of 200s (20,000 points) limited by GPU memory. The performance using a long window size looks good in Figure S6 and S7.\n• L345: The statement that data quality and size matter more than hyperparameter tuning seems none-obvious to me. I’d suggest either providing a reference or removing the statement.\nA: Thank you for the suggestion. That conclusion is based more on our empirical experience. We have removed this sentence.\n• Line 70: “million of pairs” → “million pairs”\nA: Corrected.\n• Lines 242 – 244: I’d recommend phrasing the sentence slightly more speculative as it’s not clear whether the same approach would work for the suggested tasks.\nA: We have modified the sentence. “It would be promising to explore whether the semi-supervised approach could also serve in the development of deep learning models for other seismic signals on DAS data, including the detection of tremors and the picking of first motion polarities, where significant seismic archives are available”\n• Please add a table with the parameters chosen for GaMMA.\nA: We have added Table S2 of GaMMA parameters used.\n• Please specify the value of sigma used for the labels.\nA: We have added that: “We set sigma to 1.5 seconds in this work.”\n• Please clarify how overlaps on P and S waves are labeled, i.e., if Ps + Pp > 1.\nA: We updated Eq 3: Pn = max(0, 1 - Ps - Pp), which is how we implement in the code. Ps and Pn stay the same.\n• The link to the implementation currently (8th September) does not work.\nA: We are cleaning the code and will soon make the repo public under the same link.\nReferences:\nPark, Y., Beroza, G. C., & Ellsworth, W. L. (2023). A mitigation strategy for the prediction inconsistency of neural phase pickers. Seismological Society of America, 94(3), 1603-1612."}, {"round": 3, "reviewer_comments": {"reviewer_1": "The paper “Seismic Arrival-fime Picking on Distributed Acousfic Sensing Data using Semi-supervised Learning” by Zhu et al describes a deep learning method for seismic phase arrival fime picking and event detecfion on DAS data. As the first revision, the second revision comprehensively addresses the points raised in the review. The analysis of false posifives is well-done and shows that indeed the sensifivity increases without substanfial false detecfions. I want to point out that even the discussed false posifive rate around 10 % is rather low in comparison to my own experience with broadband data.\nGiven the results, I now recommend the manuscript for publicafion in Nature Communicafion. This is a well-executed work and a well-wriften manuscript. It fills an important method gap, because automafic catalog generafion from DAS data is currently not easily achievable with ready-made tools."}, "author_response": "Response: Thank you for your posifive comments. In terms of the false posifive rate, it's important to note that this is based on an approximafion using the associafion result as reference, because we do not have manual labels to calculate the true false posifive rate. There are two factors that may affect the estimafion of false posifive rate. The first factor is the associafion algorithm is not perfect, which could associate some false picks as true picks or mis-assocated true picks. We've set a minimum threshold of 500 picks to declare a true posifive event in order to mifigate this issue. The second factor is PhaseNet-DAS already considers mulfi-channel informafion, which has a similar effect as associafion. This makes PhaseNet-DAS unlikely to predict false picks on just a few channels. For example, PhaseNet-DAS can effecfively handle traffic noise which only exists within a small spafial range."}]

Decision letter