dataesr/scientific-paragraphs-categorization huggingface dataset:
Electromagnetic modelling For simulating our M-GPR data, we used the open-source software GprMax2D  (Warren et al. , 2016) , in two dimensions, as presented in  Léger et al. (2020). The EM model was set to 1. 2 m wide and 0. 6 m high, larger than the real model to avoid side effects, filled up to 0. 47 m with saturated sand following the simplistic permittivity distribution presented in Sect. 2. 3. The cell size was 5 × 5 mm 2. A perfect electrical conductor (PEC) layer was set at the bottom of the sand layer and the model domain sides were padded with 10-cell-thick absorbing boundaries. The freezing layer was modelled using the dielectric permittivity distribution (derived from Eq. 3), corresponding to a frozen layer increasing from 0. 02 m up to 0. 3 m with 2 cm step. The GPR antenna was modelled by a Hertzian dipole polarised in the direction perpendicular to the two-dimensional plane model, emithttps://doi.
The difficulty in interpreting the origin of reflections is illustrated by the difference in the modelling and the experimental radargram. As presented, the M-GPR system, is fully autonomous and can monitor during 2 months at 30 min intervals with a 12 V, 60 Ah car battery without any recharge. The field deployment is about to start, having been delayed due to international tensions. That being said, coupled with a set of temperature and volumetric water content, the method holds a strong potential for bringing valuable thermo-hydro-dynamical information and refines the various processes taking place during melting and freezing. Financial support. This research has been supported by the Institut national des sciences de l'Univers (In situ extreme conditions instrumentation grant). Review statement.
Code availability. For GPR modelling we used gprmax, which can be found at https://github. com/gprMax/gprMax (last access: 9 March 2023) and Zenodo (https://doi. org/10. 5281/zenodo. 7727092, Léger, 2023). All the codes we used here were developed in Python and are available from the corresponding authors upon reasonable request. Data availability. All datasets are available from the corresponding author upon reasonable request. Supplement. The supplement related to this article is available online at: https://doi. org/10. 5194/tc-17-1271-2023-supplement.
The continuous monitoring of ground displacement with Global Navigation Satellite System allowed, at the beginning of the 2000s, the discovery of slow earthquakes-a transient slow slippage of tectonic faults that releases stress without generating seismic waves. Nevertheless, the detection of small events is still a challenge, because they are hidden in the noise. Most of the methods which are traditionally employed are able to extract the deformation down to a certain signal-to-noise level. However, one can ask if deep learning can be a more efficient and powerful alternative. To this end, we address the problem by using deep learning, as it stands as a powerful way to automatize and possibly overcome traditional methods. We use and compare three data representations, that is time series, images, and image time series of deformation, which account for the temporal, spatial, and spatio-temporal variability, respectively.
Introduction Global Navigation Satellite System (GNSS) is one of the reference sources of information in geodesy. Geodetic data can help analyze the ground displacement with millimeter precision as well as monitor its evolution through time  (Blewitt et al. , 2018). Such data is commonly used to monitor the ground displacement as a response to environmental (e. g. , tides, snowpacks, or hydrology), tectonic, or seismic forcing, and to characterize the mechanical response of the Earth to these forcings. Notably, GNSS data has been widely used to study the deformation associated with the different phases of the earthquake cycle. This leads to a better understanding of the loading of faults between earthquakes, of the seismic ruptures studied with either static or kinematic approaches, and of the processes driving the post-seismic relaxation  (Bock & Melgar, 2016; Bürgmann, 2018, and references therein).
In this study, we address the problem of seismic source characterization using deep learning from raw GNSS Abstract The detection of deformation in Global Navigation Satellite System (GNSS) time series associated with (a)seismic events down to a low magnitude is still a challenging issue. The presence of a considerable amount of noise in the data makes it difficult to reveal patterns of small ground deformation. Traditional analyses and methodologies are able to effectively retrieve the deformation associated with medium to large magnitude events. However, the automatic detection and characterization of such events is still a complex task, because traditionally employed methods often separate the time series analysis from the source characterization. Here we propose a first end-to-end framework to characterize seismic sources using geodetic data by means of deep learning, which can be an efficient alternative to the traditional workflow, possibly overcoming its performance.
We exploit three different geodetic data representations in order to leverage the intrinsic spatio-temporal structure of the GNSS noise and the target signal associated with (slow) earthquake deformation. We employ time series, images, and image time series to account for the temporal, spatial, and spatio-temporal domain, respectively. Thereafter, we design and develop a specific deep learning model for each dataset. We analyze the performance of the tested models both on synthetic and real data from North Japan, showing that image time series of geodetic deformation can be an effective data representation to embed the spatio-temporal evolution, with the associated deep learning method outperforming the other two. Therefore, jointly accounting for the spatial and temporal evolution may be the key to effectively detect and characterize fast or slow earthquakes.
position time series. Seismic source characterization consists of the inversion of the location, magnitude, and depth (and focal mechanism when possible) of seismic events. This is usually performed by employing seismic recordings because the data has a high signal-to-noise ratio (SNR) and contains the information needed to estimate the earthquake parameters  (Dziewonski et al. , 1981). Thus, catalogs having low magnitudes of completeness can be obtained. Thus, catalogs having low magnitudes of completeness can be obtained. Because they directly measure the ground displacement associated with seismic events (and not the acceleration or the velocity) and because they do not saturate in near-field (unlike velocimeters), GNSS data provides interesting measurements in near-field that complement seismic data to constrain the earthquake source.
Therefore, several studies carried out the source parameter characterization with GNSS data. They usually focus on one particular event or tectonic area, involving visual inspection of the data and dedicated modeling methods with a fine-tuning of the parameters  (Blewitt et al. , 2009; Feng et al. , 2015; Guo et al. , 2015; Lin et al. , 2019; Page et al. , 2009; Riquelme et al. , 2016; Weston et al. , 2012). Indeed, GNSS data presents several challenges associated with a lower SNR than seismological records. In other words, GNSS data has an intrinsic detection threshold, meaning that the signature of a seismic event (or any phenomena producing ground displacement) can be perceived in GNSS time series down to a certain magnitude, which is much higher than the completeness magnitude of catalogs obtained from seismic recordings.
This makes it difficult to automatically estimate the seismic source parameters based on the ground displacement recorded on the surface. Here, we want to explore the effectiveness of deep learning methods to automatically characterize the seismic source. To this end, as the static deformation associated with regular earthquakes can be approximated with a similar simple dislocation model  (Okada, 1985) , we use GNSS data to characterize the static deformation signature of earthquakes. Catalogs listing the source of all M w earthquakes are made available by the routine analysis of seismic recordings by seismological agencies, allowing for a benchmark with real GNSS data against an independent ground truth. Machine learning and deep learning methodologies have recently been successfully applied to geosciences.
(2019 Hulbert et al. ( , 2020)) , and  He et al. (2020) , with notable applications to InSAR data by  Rouet-Leduc et al. (2021)  and  Anantrasirichai et al. (2019). As we can remark from the literature, seismic recordings are still the main source of information for the analysis of surface ground movements, linked to either slow or regular earthquakes. Thus, this is another motivation to explore the potential of machine learning to analyze GNSS times series. We want to explore and test recent developments in machine learning applied to time series or image analysis, to be able to mine the geodetic data and characterize the events with a physics-based approach. In this paper, we address the problem of the fast seismic source characterization, that is, estimating the location and magnitude of a "regular" seismic event, based on deep learning applied to GNSS position time series.
To the best of our knowledge, this is the first attempt at using machine learning-based techniques in such a direction. We solve our problem as a regression in the framework of supervised learning, meaning that the input data used during the training are labeled. The data ground truth comes from seismic catalogs, serving as a benchmark for our analyses. We explore three different ways to represent GNSS data (time series, images, image time series) taking into account both the spatial coherency and the temporal variability of GNSS data. We associate a customized deep learning model to each data representation either by re-adapting already existing methods or by designing it afresh. Training and testing of the different methods are first made on synthetics. The performance of our methods is then evaluated against real GNSS data using an independent benchmark coming from actual earthquake catalogs.
Followed Approach An overview of the proposed methodology is shown in Figure  1. The employed pipeline consists of a training and an inference phase. During the training process, a model is provided with data to learn from. In the case of supervised learning, a couple 〈 input, desired output 〉 is presented to the model, which learns by minimizing a certain error metric between the estimated output and the desired output, which serves as a reference. We use the epicenter position (fault centroid) and the magnitude of the event as a target output for the characterization, with GNSS data as input. In the inference phase, the trained model is used to make predictions on new data. We will test our methods both against synthetic and real data. We provide new input data to the trained model and we compare the outcomes with the reference outputs, that is, the epicenter position and the event magnitude associated with this new input data.
In general, the more the parameters, the more the trade-off. This is why we decided to assess the location and magnitude only. We make use of synthetic data to train and validate our deep learning models and we test on synthetic and real data afterward. Japan is probably one of the best-instrumented regions in the world, with GNSS data among the cleanest and the densest ones. Yet, we did not train our models with real data for the following two main reasons. 1. GNSS data suffers from the presence of data gaps and missing stations. They can be associated with station inactivity (e. g. , electricity blackouts) or to inconsistent daily measurements, for example, due to large earthquakes. Moreover, the number of GNSS stations may evolve over time, due to the installation of new receivers or the temporary unavailability of certain ones.
It can moreover make it hard to collect regular and well-formatted subsets of data to train on. This drastically reduces the number of exploitable training samples, which is indeed a key issue when training deep learning models  (LeCun et al. , 2015). 2. Real data is not uniformly distributed in terms of source parameters, most notably position and magnitude. Since we are dealing with subduction events, most of the actual epicenters will be located on the subduction interface. This can constitute a limitation since a deep learning model trained on such a configuration might not generalize well for events that would be located inshore or sufficiently far from the training area. In addition, the magnitude distribution follows the Gutenberg-Richter scaling law  (Gutenberg, 1956). As a consequence, the deep learning methods would be biased because of the small magnitude events, which will be more numerous, thus possibly resulting in worse performance on the larger ones.
To this end, we generate synthetic ruptures whose source parameters are assumed to be random variables drawn from a uniform distribution. By employing synthetic data, it is possible to generate as many samples as needed, overcoming the lack of data and exploiting the features of deep models. Nonetheless, the resemblance between the synthetic data and the real one plays a critical role, since it will have an impact on how well the deep learning model will perform on real data: we need to generate ultra-realistic time series. To this end, we add realistic noise computed from actual GNSS data, as it will be detailed in Section 2. 2.
Generation and Representation of Synthetic Data We generate synthetic data samples as the sum of a modeled displacement signal and a realistic noise sample. We rely on three data representations both for synthetic and for real samples and we associate each of them with a different deep learning model. More formally, the synthetic dataset is represented as a set of N couples  {, Θ}  =1 , with Θ a set of source parameters (epicenter position, magnitude, focal mechanism, etc. ) and x being the data following an additive model: 𝐱𝐱 = 𝐬𝐬 + 𝜺𝜺 (1) with s the synthetic signal (cf. Section 2. 2. 1) and ɛ the noise term (cf. Section 2. 2. 2). Here we use Global Navigation Satellite System (GNSS) data as input and a triple consisting of fault centroid latitude, fault centroid longitude, and magnitude as desired output for each event.
Moreover, although we randomly generate events in a 3D space, we do not let them have a random focal mechanism. This choice is motivated by two reasons: (a) allowing for a complete variety of focal mechanisms would dramatically increase the size of the training database and (b) we can effectively assess the performance of the methods in locating the events, since no a priori has been made on the location, allowing us to more objectively test the performance of the models. This also allows the model to characterize events offset from the subduction interface (which is important when testing on real data, since the number of characterizable events is limited and includes both thrust subduction events and thrust crustal events, as we see in Figure  10 ). It is worth remarking that the input of the deep learning models is driven by synthetic dislocations and the outputs are expressed in terms of point sources (cf.
Section 2. 1. 2 and Figure  1 ). Here we estimate the magnitude of seismic events and their location, assumed as the position of the fault centroid. This does not represent an issue, since the approximation of the rupture as a dislocation in the synthetic database takes into account an extended fault, that allows a satisfactory first-order fit also for shallow sources beneath the GNSS network. Therefore, our approach should be able to characterize earthquakes even at shallow depths. Finally, we also choose to fix the aspect ratio of the synthetic dislocations. Deep learning models are able to generalize the samples presented during the training phase through nonlinear combinations of the features computed within the network. Therefore, the combination of those features acts as if the aspect ratio was variable.
Results on Synthetic Data and Discussion We first evaluate the performance of the three models on a synthetic test set, independent of the training and validation ones. In order to concretely compare the three methods, the synthetic and real datasets under consideration are the same for all the models and differ only in their input representation. Table  1  shows the position and magnitude error in terms of median and median absolute deviation for the three models with respect to the synthetic test set. The position error is assumed as the Euclidean distance and is computed for each sample as: 𝐸𝐸 𝑖𝑖 𝑝𝑝 = √ ( 𝑋𝑋𝑖𝑖 -X𝑋𝑖𝑖 ) 2 + ( 𝑌𝑌𝑖𝑖 -Ŷ𝑌𝑖𝑖 ) 2 (7) where X i and Y i represent the actual fault centroid longitude and latitude and  X and  Ŷ the predicted fault centroid longitude and latitude, respectively.
This may not happen in correspondence with the smallest and largest magnitude bins because the models have rather a random behavior at small magnitudes or because the error at high magnitudes does not depend on the distance to the GNSS network anymore. Since the depth has been taken into account when computing the distance to the nearest GNSS station, the offset in the large magnitude prediction associated with TS (cf. Figure  5 ) affects very shallow and near events, leading to the conclusion that image-based data representation can bring more exploitable information about the deformation field. Therefore, more low-magnitude events are captured.
Magnitude Threshold Estimation From ITS Localization Error Since we will test the deep learning models on real data (cf. Section 4), we define here a criterion to assess whether a characterization coming from a learning model is reliable. Figure  8  shows the position error for the ITS method, computed for each test sample, as a function of the magnitude, with each subplot corresponding to a different range of hypocenter-station distances and hypocentral depths. The general idea is to get an estimation of the magnitude limit (the magnitude down to which the models provide acceptable estimations) for different settings, that is, for different values of depth and distance to the GNSS network. Based on the magnitude limit, the event location, and depth, we assign it a hard threshold (characterizable, non-characterizable) that can be used, when testing on real data, to filter out all those events which would necessarily be incorrectly characterized.
Testing of the Models on Data Affected by a Post-Seismic Signal The data that we use to train the deep learning models does not contain any post-seismic signal following the co-seismic rupture. Nevertheless, we test the models on real data, which is affected by the post-seismic relaxation signals. Therefore, we generate a synthetic test set made of noise, co-seismic signals, and post-seismic signals. We model the post-seismic signals p s (t) at each station s as: 𝑝𝑝𝑠𝑠(𝑡𝑡) = 𝐻𝐻log 10 ( 1 + 𝑡𝑡 -𝑡𝑡𝑐𝑐 𝜏𝜏 ) (9) where t c is the time of the earthquake (co-seismic). The amplitude H is assumed as a uniform random variable: for the three models (columns) as a function of the distance range (cf. Figure  7 ) with respect to the Global Navigation Satellite System (GNSS) network (rows) and for different magnitude ranges (color).
Vertical lines individuate the zero. 𝐻𝐻 ∼  (0. 5𝑐𝑐𝑐 1. 5𝑐𝑐) (10) where c is the amplitude of the synthetic co-seismic displacement at the station s. The relaxation time is assumed as a uniform random variable as well: 𝜏𝜏 ∼  (1, 50) days. ( 11 ) The results are shown in Figures  S1-S5  in Supporting Information S1. The performance of the models degrades when testing (without retraining) on data having a quite strong post-seismic signal following the co-seismic offset. The magnitude and latitude predictions do not significantly differ from the ones in Figure  5 , while the longitude estimation is degraded, for all the models. This result is not surprising, since the data is different from the training one and since the longitude was already a difficult parameter to retrieve, notably for events occurring offshore.
Application to Real GNSS Data After testing the models and extracting some statistics on synthetic data, we use the trained models to make further inference on real data. For each cataloged earthquake, we run our processing pipeline (details in Section 4. 1) to obtain the estimated fault centroid location and magnitude, which we compare with the cataloged ones, in order to analyze the performance of the tested deep learning models in presence of raw noisy GNSS data. 2 , focal mechanisms are colored as follows: green indicates the characterizable events having a thrust focal mechanism, blue for the characterizable events having any focal mechanism but thrust, while red indicates all the events that cannot be characterized. because of the Precise Point Positioning solution, which is slightly noisier with respect to the DD approach, which has been used in the noise generation phase.
From these results, it seems that analyzing longer time periods (time-series-based approaches) may help reduce the error on noisier data. However, Figure  11  shows that, on average, the predictions of the image-based models, that is, IMG and ITS, are less scattered with respect to the perfect prediction line and have less variability. Thus, their performance is globally more accurate than the TS model on both datasets, in line with the results obtained on synthetic data (cf. Section 3). The presence of a larger amount of location and magnitude error in the case of TS may be probably linked to data gaps and missing stations in the real data, which worsen its resemblance to synthetic data. This also can introduce potential artifacts via the interpolation in the time domain, thus deteriorating the performance of TS, notably for the (11 March 2011) in the NGL/PPP dataset, where the co-seismic offset may have been masked.
As a result, image-based models can better deal with data gaps thanks to spatial interpolation. Hence, the amount and continuity of the data play an essential role in the final prediction accuracy, which is mitigated by the image and image time series representations. Since the models have been trained on a synthetic dataset obtained from a DD approach, we will focus on the ISTerre/DD dataset henceforward, which also has more data samples to analyze. The events in Figure  11  have been marked with a full-colored symbol if their rupture has a thrust focal mechanism (ϕ S = 200 ± 40°, δ = 35 ± 30°, λ = 90 ± 45°). Differentiating thrust and non-thrust events is interesting to assess if the shape of the associated deformation field plays a key role in the characterization performed by image-based models, given that the model was trained on thrust events only.
The results shown in Figure  11  seem to suggest that the shape of the displacement field might be a relevant feature in the characterization of the location and the magnitude for IMG and ITS, since their predictions seem to depend on the nature of the focal mechanism. However, all the models have been trained on a dataset made of events having thrust focal mechanisms, thus they might not be able to generalize well in a setting that is different from the training one. Interestingly, IMG and ITS models seem to be complementary on some events, as shown in Figures  12d, 12g  and 12h. The ITS model is unable to separate the source of displacement in the 19 July 2008 event (Figure  12d ) because of an outlier in the displacement field, whose influence is better mitigated by the differential approach used for IMG (cf.