Kevin Feghoul
email: kevin.feghoul@univ-lille.fr

Mondher Bouazizi
email: mondher.bouazizi@keio.jp

Deise Santana
email: deise.santanamaia@univ-lille.fr....

Santana Deise

Action Unit Detection using Facial

Facial Action Unit Detection using 3D Face Landmarks for Pain Detection

Keywords: Fully-connected neural network 1, Anonymizer 2, AUs detector model

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Facial Action Unit Detection using 3D Face Landmarks for Pain Detection

Kevin Feghoul 1 , Mondher Bouazizi 2 and Deise Santana Maia 3

Abstract-Automatic detection of facial action units (AUs) has recently gained attention for its applications in facial expression analysis. However, using AUs in research can be challenging since they are typically manually annotated, which can be time-consuming, repetitive, and error-prone. Advancements in automated AU detection can greatly reduce the time required for this task and improve the reliability of annotations for downstream tasks, such as pain detection. In this study, we present an efficient method for detecting AUs using only 3D face landmarks. Using the detected AUs, we trained state-ofthe-art deep learning models to detect pain, which validates the effectiveness of the AU detection model. Our study also establishes a new benchmark for pain detection on the BP4D+ dataset, demonstrating an 11.13% improvement in F1-score and a 3.09% improvement in accuracy using a Transformer model compared to existing studies. Our results show that utilizing only eight predicted AUs still achieves competitive results when compared to using all 34 ground-truth AUs.

I. INTRODUCTION

The Facial Action Coding System (FACS) [START_REF] Ekman | Facial action coding system[END_REF] is a comprehensive taxonomy that objectively describes anatomical movements of the face. This coding system is composed of 32 non-overlapping fundamental actions of individual muscles or groups of muscles, known as action units (AUs). By combining AUs, any facial expression can potentially be encoded, allowing inference of an individual's emotional state. Each AU is identified by an ID and can characterize several emotions. For example, AU number 9, which represents nose wrinkle, can indicate emotions such as disgust or pain. Table I show different emotions and their corresponding AUs [START_REF] Cordaro | Universals and cultural variations in expression in five cultures[END_REF].

Automatic pain detection is of high interest due to its potential impact in various fields, such as medical diagnosis, remote monitoring, and robotics. With the recent advances in machine learning techniques, deep learning [START_REF] Lecun | Deep learning[END_REF] is now the de facto choice for dealing with unstructured data, leading to significant breakthrough in computer vision [START_REF] Krizhevsky | Imagenet classification with deep convolutional neural networks[END_REF], speech recognition [START_REF] Chiu | State-of-the-art speech recognition with sequence-to-sequence models[END_REF], and natural language processing [START_REF] Devlin | BERT: Pre-training of deep bidirectional transformers for language understanding[END_REF]. As such, deep learning is of great significance for the task of pain detection, as it enables the recognition of human pain through facial expressions and physiological data [START_REF] Hinduja | Multimodal fusion of physiological signals and facial action units for pain recognition[END_REF].

Privacy concerns are one of the main challenges faced by researchers conducting experiments on human subjects.

The inability to share valuable and well-constructed datasets impedes progress in various fields, including pain and emotion recognition. In this study, we propose a novel approach to anonymize data specifically for pain detection. Our aim is to remove confidential information related to human faces from the dataset, while preserving critical features that enable the research community to utilize the dataset with minimal information loss.

In this study, we propose a novel method for extracting AUs from 3D face landmarks. To evaluate the effectiveness of our approach, we conducted experiments on the pain detection task using the extracted AUs to train Transformer [START_REF] Vaswani | Attention is all you need[END_REF] and LSTM [START_REF] Hochreiter | Long short-term memory[END_REF] models. We assessed the performance of these models by comparing their results with the benchmark obtained from ground-truth AUs. All experiments were conducted on the BP4D+ [START_REF] Zhang | Multimodal spontaneous emotion corpus for human behavior analysis[END_REF] dataset.

The contributions of this work are fourfold and can be summarized as follows: (1) a method to extract AUs from 3D face landmarks; (2) the use of the extracted AUs for the task of pain detection; (3) the demonstration that the bare minimum number of AUs (i.e. 8 among 34 ground-truth AUs) extracted from the 3D face landmarks can be used for pain detection; (4) to the best of our knowledge, this is the first work to propose the utilization of a Transformer model for pain detection using AUs.

II. RELATED WORK

Our proposed framework is mainly related to the detection of AUs and their uses for facial expression analysis, thus we separated this section in two parts.

A. AUs detection

Traditional methods for AUs detection rely heavily on handcrafted features. For example, Valstar et al. [START_REF] Valstar | Fully automatic facial action unit detection and temporal analysis[END_REF] used a Support Vector Machine to recognize AUs and analyze their temporal behavior from face videos, utilizing a set of spatiotemporal features calculated from 20 facial fiducial points. Baltrušaitis et al. in [START_REF] Baltrušaitis | Cross-dataset learning and person-specific normalisation for automatic action unit detection[END_REF] presents a real-time facial AUs intensity estimation and occurrence detection framework based on the combination of appearance features (Histogram of Oriented Gradients) and geometry features (shape parameters and landmark locations).

Recent advancements in deep learning have yielded impressive results in detecting AUs. Li et al. [START_REF] Li | Semantic relationships guided representation learning for facial action unit recognition[END_REF] utilized a Gated Graph Neural Network (GGNN) in a multi-scale CNN framework to integrate semantic relationships among AUs. In [START_REF] Zhang | Multi-modal learning for au detection based on multi-head fused transformers[END_REF], Zhang et al. proposed a model called Multi-Head Fused Transformer that uses both RGB and depth images to learn discriminative AUs features representations. In their work, Jacob et al. [START_REF] Jacob | Facial action unit detection with transformers[END_REF] utilized image features and attention maps to feed different action unit branches, where discriminative feature embeddings were extracted using a novel loss function. Next, to capture the complex relationships between the different AUs, a Transformer encoder is employed.

Unlike deep learning models that preprocess entire images, our approach employs a straightforward fully-connected neural network to map 478 facial landmarks to 8 AUs. Our method stands out for its efficiency in terms of computational complexity and time.

B. AUs for facial expression analysis

FACS has been widely used for facial expression analysis in various applications. Darzi et al. [START_REF] Darzi | Facial action units and head dynamics in longitudinal interviews reveal ocd and depression severity and dbs energy[END_REF] used AUs to evaluate the intensity of symptoms of OCD and depression in individuals undergoing deep brain stimulation. Other studies have explored the use of AUs for detecting stress [START_REF] Giannakakis | Automatic stress analysis from facial videos based on deep facial action units recognition[END_REF] and pain. Hinduja et al. [START_REF] Hinduja | Multimodal fusion of physiological signals and facial action units for pain recognition[END_REF] trained a Random Forest model to recognize pain by combining AUs with physiological data. In [START_REF] Meawad | Automatic detection of pain from spontaneous facial expressions[END_REF], Meawad et al. proposed an approach for detecting pain in sequences of spontaneous facial expressions, based on extracted landmarks from a mobile device. For comprehensive surveys on automatic pain detection from facial expressions, the readers may refer to [START_REF] Chen | Automated pain detection from facial expressions using facs: A review[END_REF], [START_REF] Hassan | Automatic detection of pain from facial expressions: a survey[END_REF].

As we could see, creating effective tools for detecting AUs can have a wide range of benefits in fields such as medicine, psychology, and affective computing.

III. PROPOSED APPROACH

Before presenting our proposed approach, we will introduce the method we used to extract the 3D face landmarks, as well as the dataset on which we conducted our experiments.

A. Face mesh

The face mesh is a 3D model of the human face. This type of model is commonly used in applications involving 3D modeling or augmented reality [START_REF] Kitanovski | 3d tracking of facial features for augmented reality applications[END_REF]. In our current work, we will be using a pre-trained neural network (NN) to extract the face mesh [START_REF] Kartynnik | Real-time facial surface geometry from monocular video on mobile gpus[END_REF]. This NN has been trained to identify the x and y coordinates of the different landmarks as well as to estimate the z coordinate. The model is designed to predict the positions of 468 landmarks spread out across the facial surface, with an additional 10 landmarks allocated for the iris. Overall, the face mesh consists of 478 points, as illustrated in Fig. 2.

By reducing a face image to its face mesh, we can significantly decrease the size of the information while preserving most of the information, as we will demonstrate later. Additionally, converting a face image into a face mesh can help safeguard the privacy of the individuals participating in any study in which their faces are visible. In the present work, we only used the 3D face landmarks from the face mesh.

B. Dataset

The BP4D+ dataset includes a collection of data for each frame, including a 3D facial model, an RGB image, a thermal image, and eight physiological signals. For our study, we focused on analyzing the 2D RGB image data. From this data, we extracted the 3D face landmarks as described previously. The BP4D+ dataset consists of 140 participants, including 82 females and 58 males, with ages ranging from 18 to 66 years old. The dataset was designed to elicit a wide range of authentic emotions, with each participant performing a set of 10 activities. However, FACS experts annotated AUs for occurrence and intensity for four emotion elicitation tasks (happiness, embarrassment, fear, and pain). Nevertheless, regarding these four emotions, only the most expressive segments were annotated (roughly 20 seconds on average). We have defined a binary classification task for pain by considering pain sequences as the positive class and the remaining three emotion sequences as the negative class.

C. Overall system description

In Fig. 1 and2, we show the flowchart of our proposed system. Our system is composed of three main parts:

1) An anonymizer: this component refers to the transformation of images in our dataset into 3D face landmarks. In brief, it generates a set of 478 landmark coordinates over time. Such point coordinates are very useful in extracting information allowing for pain detection, as we will demonstrate, yet, they do not allow identifying the identity of the subjects. 2) An AU detector: this component simply allows extracting the main AUs from a given set of 3D face landmarks. Conventionally, NNs are trained to identify face meshes from full images, making use of all embedded information. By creating NNs that extract the AUs from the 3D face landmarks, we demonstrate the usefulness of the first component, and that it is still possible to derive relevant information from a condensed and small-size vector such as the set of 3D landmarks.

3) A pain detector: this component relies on the detected

AUs to identify the pain expressed by the subjects. While the accuracy of the AU detection is nowhere near perfect, we show that it is still possible to identify pain with an accuracy nearly similar to that when using the ground-truth AUs. We also demonstrate that for the pain detection task, very few AUs are required to achieve an accuracy relatively close to that when using all the AUs.

D. Detailed system description

1) The AUs detector: Conventionally, AUs are extracted from the images of human faces (as shown in Fig 2). However, the transformations we have applied that allowed us to remove the identify-related information of the participants led to a transformation of the input format itself. In the current work, we use a neural network that follows the structure of a typical fully connected neural network. In Fig. 1, we show the structure of the proposed network. The network is composed of one dense layer with 128 neurons. The input layer's shape follows the size of the input vector generated for the face landmarks, i.e. a shape of 3 × N s , with N s referencing to the number of landmarks (478 in our case). The results of the detection will be shown later in Section IV.

2) The pain detector: In this study, we propose using advanced deep learning models to detect pain by utilizing the AUs extracted from our AU detector approach as well as all ground-truth AUs. We believe that tailored neural networks will enhance performance and enable real-time operation. Deep learning is particularly well-suited for processing sequential data and eliminates the need for feature engineering, which is often required in traditional machine learning algorithms. We employed both Transformer and LSTM and compared their performance.

LSTM is a type of recurrent neural network (RNN) that handles sequential data by storing and retrieving information over time. It uses a series of gates to selectively update and forget information at each time step, allowing it to capture long-term dependencies in the input sequence. On the other hand, the Transformer is a type of neural network model that has become the go-to method for handling natural language processing tasks. Unlike LSTMs, it does not use recurrent connections, but instead uses self-attention mechanisms to model the relationships between different positions in the input sequence. This allows it to capture dependencies between distant positions in the sequence, which can be difficult for LSTMs. In this work, we utilize only the encoder component of the Transformer model, as shown in Fig. 2.

IV. RESULTS AND DISCUSSION

A. Evaluation framework 1) AUs detection: To validate our AU detection approach, we employed a subject-independent 3-fold cross-validation strategy. Each fold consisted of extracted 3D face landmarks from distinct subjects, which ensured that the model was trained on one set of subjects and evaluated on another set of subjects to ensure generalizability. In terms of performance metrics, we utilized the F1-score to account for imbalanced class distribution.

2) Pain detection: Following prior works [START_REF] Hinduja | Multimodal fusion of physiological signals and facial action units for pain recognition[END_REF], we utilized a subject-independent 10-fold cross-validation strategy, where each fold comprised distinct subjects whose AUs were extracted using the AUs detection model. For evaluation, we used the accuracy and F1-score.

B. Implementation details 1) AUs detection: A total of 197,782 frames have been used for the training and testing. More precisely, we have used approximately 66% of the frames for training and the remaining ones for testing. The FCN model is composed of one hidden layer with 128 neurons. As for hyperparameters, we fixed the batch size to 64, the maximum number of epochs to 500, and the learning rate was set to 0.01.

2) Pain detection: During the training process, we used a fixed timestamp of 350 frames, which corresponds to approximately 14 seconds of data. To determine the optimal parameters for our models, we employed a grid-search strategy. For the Transformer model, we set the dimension of the linear projection layer to 1024, the number of multi-head attention to four, the number of encoder layers to two, and the learning rate to 10 -5 . Regarding the LSTM model which is composed of two layers, we fixed the hidden dimension to 512, and the learning rate to 10 -3 . Both models were trained with a batch size of 16 and a maximum number of epochs of 150.

All models (for AUs and pain detection) were trained using the Adam optimizer [START_REF] Kingma | Adam: A method for stochastic optimization[END_REF], with an exponential decay rate for the first and second-moment estimates fixed at 0.9 and 0.999, respectively. The whole pipeline was implemented using the PyTorch framework [START_REF] Paszke | Pytorch: An imperative style, high-performance deep learning library[END_REF].

C. Results

1) Action units detection:

In Table II, we show the performance of our proposed method for AUs detection. As previously stated, since numerous AUs are absent in the majority of the frames, most of the 34 AUs has not been detected. However, since those infrequent AUs represent only a very small portion of the ground-truth, it has not impacted the overall performance of the downstream detection task, as we demonstrate later on. Therefore, we present in Table II the 8 most present AUs, which also happens to be the most useful in our study. The detection accuracy ranges from 55.13% for AU18 to 89.1% for AU8, with an overall average F1-score equal to 79.25%. The main reason behind the poor detection accuracy of AU18 is its low presence in the dataset. As opposed to the other 7 AUs identified here, AU18 is present in only 14.76% of the frames in our dataset. That being said, the performance is overall good for our method which relies on a limited number of face landmarks, as opposed to other deep learning models which process the whole images. More importantly, as we will demonstrate, the detected AUs from the human face landmarks can be used to perform Lip pucker classification tasks such as pain detection. We will present the performance of the pain detection task using three different settings, which are:

• 8 predicted AUs (8AUP), in which the top 8 predicted AUs (see Table III) are used for pain detection • 8 ground-truth AUs (8AUG), in which the ground truth of the same 8AUP are used for pain detection • All ground-truth AUs (All-AUG), in which all the 34 ground truth AUs are used for pain detection

D. Pain detection

In Table IV, we show the performance for the task of pain detection. We report the overall accuracy and F1-score for each of the three experiments. As we can see, the results of training Transformer and LSTM models with 8AUP and 8AUG show a marginal difference. For Transformer and LSTM models, the difference in F1-score is 0.26% and 0.09% in favor of 8AUG, respectively. When comparing 8AUP with All-AUG, we can see a small difference of 2.43% and 1.13% in terms of F1-score, and 1.30% and 0.58% in terms of accuracy in favor of All-AUG for Transformer and LSTM, respectively.

In addition, 8AUP outperforms the Random Forest (RF) model proposed in [START_REF] Hinduja | Multimodal fusion of physiological signals and facial action units for pain recognition[END_REF], who is the only direct comparison to our work. Our approach results in a significant improvement in F1-score and accuracy, by 8.7% and 1.79% when using Transformer, and by 8.1% and 2.14% when using LSTM, compared to the Random Forest model. When using all-AUG, the F1-score and accuracy are improved by 11.13% and 2.72% when using Transformer, and by 9.23% and 2.14% when using LSTM, compared to the Random Forest model.

The confusion matrix as shown in Table V summarizes the classification performance for the pain detection task using 8AUP. Overall, we can see that we have a well-balanced confusion matrix indicating that the pain detection model is performing well for both classes (pain vs no pain), and is not biased towards one class or the other.

V. CONCLUSIONS AND FUTURE WORK

In this paper, we first proposed an approach for AUs detection using only 3D face landmarks. We achieved an overall F1-score of 79.25% when using 8 among all the ground truth AUs. Then, to further demonstrate the effectiveness of our method, we trained a Transformer and LSTM models for the task of pain detection using solely the 8 extracted AUs from our AUs detection model. Those results are then compared to the ones obtained from ground-truth AUs. The results from the 8 predicted AUs are similar to the ones from the 8 ground truth AUs, which confirms the relevance of our AUs detection model. Nevertheless, we observe an acceptable drop in performance when compared to results from all the available AUs. Moreover, the experimental results show that our framework, even only using the 8 predicted AUs, outperforms the state-of-the-art existing approach for the task of pain detection on the challenging BP4D+ dataset.

In a future study, we will work toward (1) the estimation of AUs intensity using 3D face landmarks, and; (2) on the design of a more sophisticated model for both AUs detection and AUs intensity estimation in a multi-task setting, to reach higher performance and efficiency.

Fig. 1 .

 1 Fig. 1. A flowchart of the AUs detector: upon generating the 3D face landmarks, a fully-connected neural network with multiple outputs is used to detect the AUs.

Fig. 2 .

 2 Fig. 2. A flowchart of the pain detector: the AUs detected from the face mesh (on the left) is processed through a Transformer encoder to identify the class (pain).

TABLE II THE

 II INDIVIDUAL AND AVERAGE F1-SCORE OF THE DETECTED ACTION UNIT.

	Method	AU5	AU6	AU8	AU9	AU10 AU12 AU14 AU18	AVG
	FCN	82.87 86.27 89.10 77.43	87.83	80.10	75.27	55.13	79.25

TABLE IV PAIN

 IV DETECTION PERFORMANCE USING 8AUP AS WELL AS THE GROUND TRUTH ONES.

			8AUP		8AUG	All-AUG
	Method	F1	Acc	F1	Acc	F1	Acc
	RF [7]	-	-	-	-	73.40 89.02
	LSTM	81.50 91.16 81.59 91.03 82.63 91.74
	Transformer 82.10 90.81 82.36 90.89 84.53 92.11

TABLE V SUM

 V OF ALL THE CONFUSION MATRICES FOR THE TASK OF PAIN DETECTION OVER THE 10-FOLDS USING THE 8 PREDICTED AUS (8AUP).

	Class	Classified as Others Pain
	Others	387	22
	Pain	29	117


Espín Bedón

M-P Doin

V Pinel

Unrest at Cayambe Volcano revealed by SAR imagery and seismic activity after the Pedernales subduction earthquake, Ecuador (2016)

Keywords: Cayambe, volcanic unrest, InSAR time series, seismic swarm, volcano-tectonic interactions

For the first time in decades, a sudden increase in seismicity has been observed and monitored at Cayambe volcano in Ecuador, in 2016. This seismic unrest, which occurred a few months after the April 2016, Mw 7.8 Pedernales subduction earthquake, has raised many questions, especially as there is no record of recent eruptions at Cayambe volcano. Here we analyze a time series of 104 images from Sentinel 1 (SAR) data spanning the period 2014-2018 using the NSBAS processing chain in order to quantify surface deformation around this potentially explosive and ice-covered volcano. We evidence a large-scale uplift reaching a maximum mean displacement rate of about 0.44 cm/yr in Line of Sight. This uplift is mainly due to a significant and sudden acceleration of the deformation pattern, focused on the SE flank starting in November 2016. We model this signal as related to magma emplacement at around 6 km depth below the summit, with a sudden volume influx of about 2.6 million m 3 . The inflation and surface deformation pattern is concomitant in time with two Mw 3 seismic events recorded at Cayambe volcano in November 2016 1 and is consistent with the location at the summit of the volcano-tectonic (VT) seismic swarm from September 2016 onwards. This VT swarm follows an earlier swarm in June 2016 located on the northern side of the volcano and closer to a western branch of the Chingual-Cosanga-Pallatanga-Puna (CCPP) fault system, that plays a major role in accommodating plate tectonic processes in South America. We thus propose that static stress changes from the Pedernales megathrust earthquake triggered magma ascent below the Cayambe volcano, through reactivation of the CCPP fault system.

Finally, volcanic hazards around Cayambe ice-capped volcano, previously dormant for the last 300 years, should be reassessed in light of this recent unrest.

Introduction

With the launch of Sentinel satellites initiated in 2014 as part of the Copernicus Program led by the European Space Agency (ESA) remote sensing has entered a new era with data systematically acquired and provided free of charge, thus offering new opportunities for the study of volcanoes and their monitoring (Pinel et al. 2014, Biggs and[START_REF] Biggs | Global volcano monitoring : What does it mean when volcanoes deform ?[END_REF][START_REF] Ebmeier | Synthesis of global satellite observations of magmatic and volcanic deformation: Implications for Volcano monitoring & the lateral extent of magmatic domains[END_REF][START_REF] Valade | Towards global volcano monitoring using multisensor sentinel missions and artificial intelligence: the MOUNTS monitoring system[END_REF][START_REF] Biggs | How satellite InSAR has grown from opportunistic science to routine monitoring over the last decade[END_REF].

In particular, InSAR which combines the Satellite Aperture Radar (SAR) signal acquired from different orbital positions and/or at different times is a wellestablished and efficient technique to monitor large scale deformation of the Earth's surface at multiple times [START_REF] Simons | Interferometric Synthetic Aperture Radar Geodesy[END_REF][START_REF] Biggs | The lateral extent of volcanic interactions during unrest and eruption[END_REF]Pepe and Calo, 2017). A few processing chains have been implemented to fully take advantage of these new datasets, among them the "New Small Baseline Subset (NSBAS)" processing chain [START_REF] Doin | Presentation of the small baseline NSBAS processing chain on a case example: The Etna deformation monitoring from 2003 to 2010 using Envisat data[END_REF]) dedicated to retrieving the temporal evolution of surface displacement for SAR time series. The combination of an increasing amount of SAR data and improved processing methods is expected to favor subtle signal detection and analysis particularly in such vegetated and topographically active areas as the Andes. Here, we test this new potential by studying surface deformation patterns at Cayambe volcano, in northern Ecuador, which experienced a recent seismic crisis [START_REF] Butcher | Evolution of Seismicity During a Stalled Episode of Reawakening at Cayambe Volcano, Ecuador[END_REF]).

For regional studies, InSAR is indeed a perfect tool to be applied to the Andes volcanic arc where volcano-tectonic activity mostly induces low magnitude (M<4) local earthquakes and moderate surface deformation, but significant volcanic hazards. This technique will improve the monitoring of broad volcanic areas where a scarce number of field instruments are deployed on volcanoes identified as active with the risk of missing the sudden reactivation of a dormant edifice. It has thus already been applied widely in Latin America allowing detection of surface deformation at 26 volcanic edifices between 2013 and 2017 [START_REF] Pritchard | Towards coordinated regional multi-satellite InSAR volcano observations : results from the latin america pilot project[END_REF]. No surface displacement had been detected at Cayambe volcano neither during this time period nor between 2006 and 2008, reported in an ALOS data-based survey of Latin American volcanoes (Fournier et al. 2010). However, to our knowledge, no detailed study has been performed mainly because the last known eruption occurred more than two hundred years ago.

The Northern Andes of Ecuador displays one of the most active volcanic areas in the word. The geodynamic setting of the active volcanic arc in Ecuador is characterized by intense activity since the Pleistocene, with at least 21 active volcanoes during the Holocene (e.g., Hall and Beate, 1991;Hall et al., 2018;[START_REF] Bernard | Volcanes cuaternarios del Ecuador continental[END_REF][START_REF] Bablon | Interactions between volcanism and geodynamics in the southern termination of the Ecuadorian arc[END_REF]. Eight of these volcanic edifices have erupted in the last 500 years, and some of which have been active and erupting in recent years: Guagua Pichincha (1999[START_REF] Samaniego | Transition entre magmatismes calcoalcalinet adakitique dans le cas d'une subduction impliquant une ride oceánique: Le volcan Cayambe (Equateur)[END_REF]), Tungurahua (1999[START_REF]Global Volcanism Program[END_REF] (https://www.igepn.edu.ec/red-de-observatorios-vulcanologicos-rovig). For the last 10 years, seismic and GPS networks have been deployed over the main hazardous volcanoes in Ecuador [START_REF] Mothes | Monitoring the Earthquake Cycle in the Northern Andes from the Ecuadorian cGPS Network[END_REF][START_REF] Mothes | Monitoring the Earthquake Cycle in the Northern Andes from the Ecuadorian cGPS Network[END_REF] as seismicity, in particular Volcano-Tectonic (VT) and Low-Period (LP) events, remains the clearest geophysical signal provided by field instruments of an impending eruption (White andMcCausland, 2016, 2019). However the interpretation of seismic swarms during volcanic unrest, despite its huge potential for eruption forecasting, is significantly improved by using additional geodetic datasets [START_REF] Champenois | Large-scale inflation of Tungurahua volcano (Ecuador) revealed by Persistent Scatterers SAR interferometry[END_REF][START_REF] Biggs | The lateral extent of volcanic interactions during unrest and eruption[END_REF]. Surface displacements induced by magma emplacement at depth have been observed at long-lived volcanic edifices in Ecuador, such as Tungurahua, whether during eruptions or inter-eruptive periods [START_REF] Biggs | Stratovolcano growth by co-eruptive intrusion: The 2008 eruption of Tungurahua Ecuador[END_REF][START_REF] Champenois | Large-scale inflation of Tungurahua volcano (Ecuador) revealed by Persistent Scatterers SAR interferometry[END_REF]. But, short-term transient deformation signals limited to the area proximal to the summit remain difficult to detect with infrequent satellite observations, or distal ground based monitoring instruments [START_REF] Ebmeier | Applicability of InSAR to tropical volcanoes: insights from Central America[END_REF].

-
Cayambe volcano is located at to the northern part of the Eastern Cordillera and its construction has been probably controlled by regional N35° major fault systems that connect to the Chingual-Cosanga-Pallatanga-Puna (CCPP, dextral transcurrent, with compressive components) limit of the North Andean Sliver (Alvarado et al., 2017;[START_REF] Bablon | Interactions between volcanism and geodynamics in the southern termination of the Ecuadorian arc[END_REF]). Significant seismic activity was recorded in the volcano: between 2000 and 2004 [START_REF] Samaniego | Los peligros volcánicos asociados con el Cayambe[END_REF] characterised by an increase in VT-type event activity. Also, increase of seismic activity in 2016-2017 as well as new cracks on the ice cap at the end of 2016 have been reported on Cayambe volcano by Instituto Geofísico -Escuela Politécnica Nacional (IGEPN). Here we analyze the Sentinel 1 descending time series recorded between 2014 and 2018 and compare the surface deformation observed at Cayambe volcano with the seismic activity. We then invert for the magma volume perturbation at depth causing the displacement field recorded at the surface. Based on this particular example, we further discuss both the triggering of volcanic unrest by subduction earthquakes and the potential of systematic processing of Sentinel-1 data to complement field measurements and improve the monitoring of large scale volcanic areas.

Cayambe volcano tecto-volcanic context and recent eruptive activity

In Ecuador, volcanoes are distributed within a ~70-120 km-wide area in the high Andes encompassing the volcanic front in the Western Cordillera, the main arc in the Eastern Cordillera, and the back-arc region in the Eastern foothills (Fig. 1). In the northern part of the Eastern Cordillera, the construction of the Cayambe Volcanic Complex (CVC) was controlled by the major CCPP fault system and its related subsidiary NNE faults, which bound the North Andean Sliver (NAS) (Fig. 1, [START_REF] Alvarado | Partitioning of oblique convergence in the northern Andes subduction zone : migration history and present-day boundary of the North Andean Sliver in Ecuador[END_REF]Yepes et al., 2016). The Cayambe volcanic complex (CVC) is located at 0.023º latitude, -77.98º longitude, 60 km northeast of Quito (Ecuador's capital) and 15 km west of Cayambe city (Fig. 1). CVC is composed of an old, extinct western edifice called the 'Viejo Cayambe' and a younger, still active eastern Nevado Cayambe volcano [START_REF] Samaniego | Temporal Evolution of Magmatism in the Northern Volcanic Zone of the Andes: The Geology and Petrology of Cayambe Volcanic Complex (Ecuador)[END_REF]. Nevado Cayambe Volcano is an explosive stratovolcano (Fig.

2

) emitting andesitic and dacitic lavas and composed of several domes and summits;

the maximum height is 5790 m.a.s.l. [START_REF] Samaniego | Late Holocene eruptive activity at Nevado Cayambe Volcano, Ecuador[END_REF][START_REF] Samaniego | Temporal Evolution of Magmatism in the Northern Volcanic Zone of the Andes: The Geology and Petrology of Cayambe Volcanic Complex (Ecuador)[END_REF].

Above 4800 meters elevation a.s.l., the volcano is covered by an important ice cap with an area of approximately 22 km2 and which reaches a thickness of 30 to 50 m at the summit (Caceres, 2010). Nevado Cayambe (NC) is considered an active volcano, whose eruptive activity was characterized by lava dome extrusions, dome collapses, and pyroclastic currents.

Based on tephocronologic studies at least 21 eruptive events have been reported

during the last 4000 years, of which the most recent took place between 1785 and 1786 CE [START_REF] Samaniego | Late Holocene eruptive activity at Nevado Cayambe Volcano, Ecuador[END_REF] During the last 20 years, Instituto Geofísico -Escuela Politécnica Nacional (IG-EPN) reported punctual increases in seismic activity related to volcano tectonic events (VT). Such a seismicity increase occurred between 2001 and 2005 (in 2002 ~ 1310 VT events), but quickly returned to the background level without producing surface manifestations or eruptions (Global Volcanism Program, 2006, Report on Cayambe).

In 2016 the increase in VT seismic events was stronger in amplitude than previous events, thus motivating the installation of a temporary seismological network to monitor the crisis evolution in case of an upcoming eruption. Additionally, an increase in sulphur emissions in the upper parts of the volcano and the appearance of In April 2016, a large subduction earthquake struck the Manabi coast, offshore Pedernales (Figure 1). With a magnitude Mw = 7.8, a general westward displacement centimeters was observed in many GPS stations, including those at Cayambe (Mothes et al., 2019) located 232 km away from the epicenter. This shaking could also have provoked movement on faults and volcanic systems [START_REF] Alvarado | Partitioning of oblique convergence in the northern Andes subduction zone : migration history and present-day boundary of the North Andean Sliver in Ecuador[END_REF]Mothes et al., 2018;[START_REF] Hernandez | Earthquake-Volcano Conversations at Volcan Guagua Pichincha, Ecuador[END_REF]. Since June 6 th , 2016, a new increase in seismicity corresponding to fracture VT events has been observed in the Cayambe area (Fig. 3).

This new increase reached an important peak in June 12-13; and produced a much higher energy release than that observed in 2001-2002. In this period, 2300 earthquakes were recorded, the highest number of events recorded at Cayambe since seismic monitoring began in the late 1980s. According to [START_REF] Butcher | Evolution of Seismicity During a Stalled Episode of Reawakening at Cayambe Volcano, Ecuador[END_REF], the June swarm was associated with a reactivation of the regional Chingual fault system.

Over a few weeks this activity progressively decreased, returning to background level in August, 2016. Shortly afterwards, in September, a new increase in activity was recorded, with the presence of short-duration seismic swarms (VT earthquakes). The location of the September events was beneath Nevado Cayambe central cone, more particularly beneath the southern and western flanks. Two significant VT events, larger than usual, with a magnitude above 3, were recorded on November 14th (M3.3) and 27th (M3.6), respectively. In the last weeks of December 2016, the energy release of events and number of seismic events remained above the normal (average 68 events/day, Fig. 5 in Supplementary Material ) for this volcano (Instituto Geofísico -EPN, 2016d; [START_REF] Butcher | Evolution of Seismicity During a Stalled Episode of Reawakening at Cayambe Volcano, Ecuador[END_REF].

At the beginning of 2017, seismic activity continued similar to the last 6

months of 2016 and since May 2017 a decrease in the number of events was observed.

Another swarm occurred in September 2017 with fewer events compared to the beginning of this year. The month with the greatest activity was March with a total of 2723 earthquakes, while the month with the lowest activity was December with 179 earthquakes, for a total of 13140 events registered in 2017. Overall, that year's activity was considered moderately high, especially in February and March.

Hypocenter depths reach approximately 10 km, while earthquakes that pertain to local tectonic activity reached depths close to 30 km below the summit (Instituto Geofísico -EPN, 2017a,b; [START_REF] Butcher | Evolution of Seismicity During a Stalled Episode of Reawakening at Cayambe Volcano, Ecuador[END_REF].

Concerning 2018, a total of 5696 seismic events were recorded, marking a decrease compared to the number of events in 2017. November was the month with the greatest activity for a total of 834 earthquakes, while the month with the least activity was January with 203 earthquakes. Most of the events were concentrated in the central zone of the volcano and depths did not exceed 20 km below the surface (Instituto Geofísico -EPN, 2018).

SAR data description and processing method a. Interferogram computation

In order to study surface deformation patterns at Cayambe volcano area, we use an implementation of the Small Baseline Subset (SBAS) strategy, the "New Small Baseline Subset (NSBAS)" processing chain package [START_REF] Doin | Presentation of the small baseline NSBAS processing chain on a case example: The Etna deformation monitoring from 2003 to 2010 using Envisat data[END_REF], to process the Synthetic Aperture Radar (SAR) dataset provided by Sentinel-1 (C band, wavelength = 5.6 cm). The NSBAS chain ingests Single Look Complex (SLC) radar scenes to obtain interferograms and finally time series of the line of sight (LOS) surface displacement [START_REF] Doin | Presentation of the small baseline NSBAS processing chain on a case example: The Etna deformation monitoring from 2003 to 2010 using Envisat data[END_REF][START_REF] Doin | InSAR measurement of the deformation around Siling Co Lake: Inferences on the lower crust viscosity in Central Tibet[END_REF][START_REF] Grandin | Interferometric Processing of SLC Sentinel-1 TOPS Data, processing of the 2015 ESA Fringe workshop[END_REF]. NSBAS has been especially optimized for monitoring transient ground motion of small amplitude, taking place over large areas and in natural settings [START_REF] Doin | InSAR measurement of the deformation around Siling Co Lake: Inferences on the lower crust viscosity in Central Tibet[END_REF].

The Sentinel-1 archive on the descending track with relative orbit number 142 (see footprint on Fig. 1, white square) consists of 104 acquisition dates between October 2014 and November 2018. Continuous SLC images along subswath iw3 have been obtained by cutting burst overlaps in the middle of the overlap region, by stitching the bursts, and by correcting the phase from the effect of antenna azimuth steering within each burst. The combined use of precise orbital data [START_REF] Peter | Sentinel-1A-First precise orbit determination results[END_REF], of the digital elevation model from the Shuttle Radar Topographic mission [START_REF] Farr | The shuttle radar topography mission[END_REF], and of SLC image correlation, allowed co-registering of all images to a reference image geometry. Differential interferograms are generated with 8 looks in range and 2 looks in azimuth. The enhanced spectral diversity technique [START_REF] Scheiber | Coregistration of interferometric SAR images using spectral diversity[END_REF] was applied on each interferogram to extract a parameterization of phase jumps across burst boundaries. This parameterization has been inverted into a time series to obtain stable values, before being used to correct differential interferograms. We then correct all interferograms for stratified atmospheric delays using the ERA5 meteorological model from European Centre for Medium-Range

Weather Forecast [START_REF] Hersbach | The ERA5 global reanalysis[END_REF], as described in [START_REF] Doin | Corrections of stratified tropospheric delays in SAR interferometry: Validation with global atmospheric models[END_REF] and in [START_REF] Jolivet | Systematic InSAR tropospheric phase delay corrections from global meteorological reanalysis data[END_REF]. After this correction, interferograms are filtered to enhance the signal to noise ratio and decrease the impact of decorrelation. Different filter combinations and filter strength have been tested. We found that the optimal combination was to : (1) compute phase colinearity (Pinel-Puyssegur et al., 2012), replace interferogram amplitude by the colinearity (as in [START_REF] Daout | Large-scale InSAR monitoring of permafrost freeze-thaw cycles on the Tibetan Plateau[END_REF], before further multilooking by a factor of 2;

(2) repeat step ( 1) to obtain interferograms with 8 looks in azimuth and 32 looks in range;

(3) apply a sliding window with a gaussian weight on the wrapped interferogram, and keep, besides the phase, the coherence associated with the gaussian convolution. Then, the unwrapping process begins in the sub-region of the interferogram where the coherence is maximum and propagates to the contiguous areas where coherence is above the threshold, while choosing an optimal path maintaining the coherence as high as possible [START_REF] Grandin | Long-term growth of the Himalaya inferred from interseismic InSAR measurement[END_REF].

b. Transforming the interferogram combination into time series

The inversion of the interferogram network into time series allows us to compute discrepancies between original and reconstructed interferograms, for each pixel and each interferometric couple [START_REF] Lopez-Quiroz | Time series analysis of Mexico city subsidence constrained by radar Interferometry[END_REF]. This led us to identify the main unwrapping errors and to correct them manually wherever possible.

A few interferograms were discarded when a proper correction of unwrapping errors was unsuccessful. Remaining unwrapping errors of small spatial extent were automatically corrected as explained in [START_REF] Doin | Presentation of the small baseline NSBAS processing chain on a case example: The Etna deformation monitoring from 2003 to 2010 using Envisat data[END_REF]. The root mean square average of the misclosure maps then serves as a proxy for the time series quality and is used, with a threshold of 1 rad, to mask some low-quality pixels.

The choice of the interferogram network is particularly crucial, as it has been shown recently that "fading" signals associated with vegetation can bias the reconstructed time series [START_REF] Ansari | Study of Systematic Bias in Measuring Surface Deformation With SAR Interferometry[END_REF]. A first network of 264 short temporal baseline interferograms (≤ 3 months, Fig. 1a and Fig. 1d in Supplementary Material) was constructed to limit the impact of temporal decorrelation, on top of which 74 oneyear and 12 six months interferograms have been added (Fig. 1b and Fig. 1e in Supplementary Material). Several tests have been conducted in order to choose the best interferogram network. Including only small temporal baseline interferograms (≤ 3 months) resulted in strong apparent subsidence in mostly crop areas (Fig. 1g in Supplementary Material). This effect almost completely disappears when one year interferograms are added (Fig. 1h in Supplementary Material). To further assess whether adding one year vintage interferograms was sufficient to remove the bias, we also removed interferograms shorter than one month while keeping long duration interferograms (Fig. 1c, Fig. 1f and Fig. 1i in Supplementary material). The obtained Line Of Sight (LOS) velocity map was then in very good agreement with the preceding one. Note that, on the NC complex itself, the three solutions show consistent LOS velocity patterns, probably because the volcanic complex is characterized by relatively limited temporal decorrelation and the absence of agricultural fields. However, including one year vintage interferogram slightly decreases the amplitude of the velocity pattern on the volcano. In this paper, we choose to present results with the third network, that should be devoid of phase bias.

The last steps have been to estimate the North-South and East-West ramps of all interferograms, to invert them into time series, and then to correct the interferograms from the ramps to obtain "flattened" interferograms. Finally, all interferograms have been referenced in a small and coherent area located close to NC.

This finally allows the generation of the LOS velocity map shown in Fig. 2 of Supplementary Material and the time series in the Cayambe Volcano area, shown in Fig. 3 of Supplementary Material.

c. SAR time series post-processing

The phase time series includes mainly two contributions that we aim to separate, the displacement and the residual atmospheric delay. Although interferograms were corrected from the predicted delay using the ERA5 model, and

d. Modeling of the displacement field

We modeled the displacement field retrieved from SAR data analysis using the analytical solution for a point source volume change applied in a homogeneous halfspace as defined by [START_REF] Mogi | Relations between the eruptions of various volcanoes and the deformations of the ground surfaces around them[END_REF]. This four parameters model, which is the simplest and the most widely used in volcanology, provides a robust first order estimation of the 3-D coordinates (position and depth) as well as the strength of the deep perturbation responsible for surface displacement. The model does not take into account the topography of the volcano. A classical Bayesian inversion was performed on the subsampled displacement map following [START_REF] Bagnardi | Inversion of surface deformation data for rapid estimates of source parameters and uncertainties: A Bayesian approach[END_REF] and using the Geodetic Bayesian Inversion Software (GBIS), written in Matlab. During the inversion a constant offset in the line-of-sight direction was estimated, increasing the number of unknown parameters to five.

Results a. Deformation signal

The mean velocity map derived from the SAR time series analysis (Fig. 2 However, in the following, we will focus on the sudden displacement recorded during November 2016 as it is the most significant of all. As detailed previously (section 4.b), we performed a linear decomposition of the signal using a Heaviside function with a step defined at 2016.85 corresponding to the 6th November 2016. Figure 5 shows the amplitude of the displacement associated with the step recorded in November 2016.

The southeastern part of the edifice shows an important displacement signal. This deformation is also seen around the entire volcano, but in the SE flank the signal is clearer due to the acquisition geometry. For the descending track here considered, horizontal and vertical components of the displacement field induced by an inflating volcano are added on the southeastern flank whereas they are subtracted on the northwestern one. This discrepancy between both flanks appears clearly on both profiles displayed (A-A' and B-B'). The inflation signal reaches 2.5 cm in LOS. ∼

b. Mogi source modeling

We inverted the displacement field corresponding to the step of the linear decomposition (displayed in Fig. 5) for a volume change at depth using a Mogi model as described in section 4.c. The subsampled displacement field was composed of 339 data points. The optimal (maximum a posteriori probability) model derived from the Bayesian inversion was obtained at 0.0148°N, 77.9613°W located 6133 m beneath the surface, with a volume change of 2.63 million m 3 (see Fig. 6 and Table 1 for 1: Inversion parameters and results. Positions (X and Y) are expressed in distance from the grid center located at 0.0193 °N, 77.98°W (m).

. Discussion and Conclusions

The NSBAS processing chain developed at ISTerre for time series analysis of SAR data has proven efficient to evidence a previously undetected uplift event taking place at Cayambe volcano possibly through the whole studied period, 2014-2018, but mostly in November 2016, about 7 months after the Pedernales subduction earthquake. Such large-scale (around 10 km in radius) inflation had never been documented at Cayambe volcano which hasn't erupted for more than two centuries.

We attribute this local uplift to pressure increase around 6 km beneath the surface. Magma emplacement at this depth seems consistent both with the petrological data reported by [START_REF] Samaniego | Transition entre magmatismes calcoalcalinet adakitique dans le cas d'une subduction impliquant une ride oceánique: Le volcan Cayambe (Equateur)[END_REF] and [START_REF] Samaniego | Temporal Evolution of Magmatism in the Northern Volcanic Zone of the Andes: The Geology and Petrology of Cayambe Volcanic Complex (Ecuador)[END_REF], who suggests that amphibole crystallization pressures occurred at 18 MPa (6.6 ± 1.5 km below the summit); and with relocation of seismic swarm [START_REF] Butcher | Evolution of Seismicity During a Stalled Episode of Reawakening at Cayambe Volcano, Ecuador[END_REF] that point out to VT hypocenters at >6 km below the summit.

SAR data are particularly useful in this case where the sparse GPS and tiltmeters network was not able to evidence significant surface deformation. Our study confirms the interpretation of [START_REF] Butcher | Evolution of Seismicity During a Stalled Episode of Reawakening at Cayambe Volcano, Ecuador[END_REF] of the late seismic part of the VT seismic swarm located on the flank of the Cayambe volcano edifice being induced by magma ascent. The decrease in seismic activity and deformation after the end of 2017 could indicate that the limited volume of magma emplaced prevented any further ascent towards the surface, but a new inflow in the coming years could build on this event and promote an eruption in the future.

The NSBAS processing chain thus allows studying the surface deformation patterns of the Cayambe volcanic complex, despite its highly variable geomorphic features, ice cap, different vegetation type (on the eastern Amazonian side compared with the western interandean side), varying size of watersheds with different atmospheric effects. These results obtained in a volcanic, vegetated and compressional setting are promising and should promote the generalization of the use of Sentinel-1 data set for operational volcanoes monitoring, especially in the Andes.

The relationship between megathrust tectonic earthquakes and volcanic activity in the far field overriding crust remains a striking question in Earth sciences, mainly due to the lack of observational data. Large earthquakes can affect volcanic areas within the continental region located at hundreds of kilometers away from the epicenter, inducing swarms of earthquakes, ground deformation, migration of magmatic gasses, excitation of geothermal activity and even possibly triggering eruptions (e. g. Linde & Sacks, 1998;[START_REF] Hill | Earthquake-Volcano Interactions[END_REF]Watt et al., 2009;Walter and Amelung, 2007;[START_REF] Namiki | Volcanic activities triggered or inhibited by resonance of volcanic edifices to large earthquakes[END_REF]. Recent illustrations of the susceptibility of volcanic zones, characterized by the presence of fluids at depth, to be influenced and/or destabilized by large subduction earthquakes include the Maule 2010, Chile earthquake [START_REF] Pritchard | Subsidence at southern Andes volcanoes induced by the 2010 Maule, Chile earthquake[END_REF][START_REF] Li | Postseismic uplift of the Andes following the 2010 Maule earthquake: Implications for mantle rheology[END_REF] and Tohoku 2011 earthquake in Japan [START_REF] Takada | Volcanic subsidence triggered by the 2011 Tohoku earthquake in japan[END_REF]Brenguier et al., 2014;[START_REF] Ishitsuka | Ground uplift related to permeability enhancement following the 2011 Tohoku earthquake in the Kanto Plain, Japan[END_REF]. As triggering can occur either through dynamic or static stress variations, or through cascading events and/or results from fluid migration, the induced volcanic unrest can be either almost instantaneous or delayed by several months, the wide range of timescale involved making it more difficult to identify and characterize the phenomenon.

The geophysical observations recorded at Cayambe volcano in Ecuador

provide new insight into the potential influence of regional tectonics on volcanoes behavior. The Pedernales earthquake on April 16, 2016 (Mw 7.6) caused tectonic strain changes in volcanic centers within the NAS, in the inter-Andean valley as evidenced for instance at Guagua Pichincha volcano [START_REF] Hernandez | Earthquake-Volcano Conversations at Volcan Guagua Pichincha, Ecuador[END_REF]. Seismic activity at Guagua Pichincha located at 12 km distance from Quito city, is typically characterized by recurrent, short duration seismic swarms recorded by a network of short-period and broad-band seismometers. A reactivation of seismic swarms was observed as a result of the Pedernales earthquake and interpreted as due to a widespread volumetric expansion within the NAS induced by the subduction earthquake [START_REF] Hernandez | Earthquake-Volcano Conversations at Volcan Guagua Pichincha, Ecuador[END_REF]. A significant increase in seismic activity also occurred in the vicinity of Cayambe Volcano. It started in June with distal seismicity located north of Cayambe Volcanic Complex. This June swarm was interpreted as resulting from stress perturbations and displacements induced on the CCPP by the Pedernales earthquake [START_REF] Butcher | Evolution of Seismicity During a Stalled Episode of Reawakening at Cayambe Volcano, Ecuador[END_REF]. This first phase of seismic unrest was followed by a second one starting in September on the volcano flanks and culminating in two M>3 events in November 2016. The uplift recorded in November 2016 proves that magma emplacement 6 km below the surface was probably causing this second VT swarm.

The triggered unrest of the Cayambe volcano is probably directly linked to its location near/on to the CCPP NAS tectonic boundary, expected to accommodate partitioning of the oblique convergence and strain within the South American upper plate with respect to the subducting Nazca/Cocos plates. This process has been invoked, for instance, in Chile for the Chiloe forearc sliver (Wang et al., 2007) or Central America (La Femina et al., 2009) where the major fault system accommodating the oblique convergence runs along the active volcanic arc. Most of the active volcanic arc in Ecuador lies west of the narrow CCPP tectonic limit but the Cayambe volcano lies the closest to the northern CCPP Chingual segment.

It seems that the location of Cayambe Volcano in proximity to the CCPP fault system at the boundary of the NAS makes it prone to be strongly influenced by subduction earthquakes. Being active, potentially explosive and covered by an ice cap, its high-sensibility to large earthquakes should be taken into account in local hazard assessment as a large eruption near the summit would melt ice and snow, resulting in lahars, which might be directed toward the town of Cayambe and adjacent inhabited areas, potentially impacting more than 30000 people and Ecuador's largest hydroelectric plant situated along Cayambe's eastern drainage network.

Supplementary Material

Figure 1 .

 1 Figure 1. Location of Cayambe Volcano: A) Map of the current Ecuadorian volcanic arc (yellow dashed lines) with recently active volcanoes (last eruption < 20 years, blue circles) and Cayambe Volcano area (red square), b) Inactive volcanoes of the eastern cordillera in the vicinity of Cayambe volcano (from www.igepn.edu.ec) shown on the shaded DEM (Digital Elevation Model). The bold red contour line is for the young Cayambe whereas the surrounding blue contour line is for the older Cayambe volcanic complex. The Chingual-Cosanga-Pallatanga-Puna ( CCPP) active faults that limit the North Andean Sliver are shown as solid lines with dashed lines for inherited sutures, partly hidden by the Quaternary volcanic layers.

  new cracks in the ice cap on the highest summit were reported by climbers (Instituto Geofísico -EPN, 2016a, b, c, d and e; Instituto Geofísico -EPN, 2017a and b).

Figure 2 .

 2 Figure 2. Cayambe volcano. View from the northeast (Photo: Matthieu Perrault, May 2nd, 2015)

Figure 3

 3 Figure 3. a, b) Top-Locations of seismic events from 10 January 2015 to December 2018.Most events are concentrated between 3 and 10 km below sea level(778 earthquakes between 2015-01-10 -2018-12-06 with magnitudes between 0.1 -3.6). c) Cayambe Volcano Seismic activity record from December 2014 to December 2018, VT: volcano tectonic events, LP: low period events and HB: Hybrid events.(Source: Instituto Geofísico -EPN) The red star represent the subduction Pedernales earthquake in April 16, 2016. The box black line in Figure3a) outlines the area over which principal component analysis (PCA) has been conducted.

  despite the high elevation of the volcanic structure, residual atmospheric patterns still affect the phase delay maps at each time step. Therefore, in order to extract the most significant deformation pattern on Cayambe volcano, we perform a Principal Component Analysis of the time series on the area of interest. The first component in time is characterized by a linear trend and a step in November 2016, and a spatial component with displacement towards the satellite on the eastern flank of the volcano. This led us to perform a linear decomposition of the phase delay time series as: Phi(t_i) = a * t_i + b * H(t_i-2016.85) + c where t_i is the decimal year of each acquisition i, a is the pluri-annual LOS velocity, b is the displacement step occurring in November 2016, H is the Heaviside function and c is a constant. The parameters a, b, and c are obtained by least square inversion for each pixel, with an iteration to downweight acquisitions i with large averaged dispersion around the adjusted function Phi(t_i).

  in Supp Mat.) evidences a significant displacement of the ground surface reaching 0.44 cm/yr in LOS and directed towards the satellite. This displacement is located on the southeastern part of the Cayambe volcano flanks and is interpreted as an uplift induced by magma emplacement at depth. From the temporal evolution of the surface displacement field (see Fig.3of Supp. Mat.), this uplift may have started in August 2016 and became significant in November 2016. Figure 4 presents the temporal evolution of the amplitude of the first component resulting from the Principal Component Analysis of the SAR time series, this principal component explaining 58% of the signal. It clearly shows that most of the uplift is focused in time and occurs around November 2016, being concomitant with the two M>3 VT events recorded in the seismic swarm about 7 months after the Pedernales earthquake (Fig. 4). From Fig 4b, an uplift trend is probably observed before an observed step and possibly after.

Figure 4 .

 4 Figure 4. Comparison between the first PCA component in time (bottom panel) and the number of volcanic events between 2014 and 2018 (top panel, as in Figure 3). The orange and black dashed lines, sketched by hand, underline the significant signal increase between mid-2016 and mid-2017 related to the seismic activity increase. The star shows the date of the Pedernales Subduction Earthquake. The green triangle shows the main VT events occurring at the volcano in November 2016 (M>3).

Figure 5 .

 5 Figure 5. LOS displacement field of Cayambe Volcano corresponding to the step amplitude (parameter b in equation (1)) of the linear decomposition and occurring in November 2016. On the right panel, elevation and LOS displacement are displayed for two profiles located by dashed blue lines on the displacement field map.

  inversion input parameters and results). Note that the uncertainty on the depth remains relatively large and the volume change of magma is expected to increase with the depth of emplacement (see Fig 4 of Supp. Mat.). The offset in LOS is estimated around 6 mm.

Figure 6 .

 6 Figure 6. Displacement field recorded at Cayambe volcano in November 2016 (in LOS) from (left), (middle) optimal Mogi model, and (right) residuals between data and model (black dashed line corresponds to the Cayambe volcano area). The model corresponds to a Mogi source located 6133 m beneath the surface (red cross), inflating with the en try of 2.63 millions of m 3 .

Figure 1 .

 1 Figure 1. Effect of the chosen interferogram network on the final velocity field. Panels (a-c): Interferometric networks. Each black line represents an interferogram calculated between two SAR images acquired at different dates (dots). Panels (d-f): Distribution of the temporal baseline of the selected interferograms. Panels (g-i): Resulting LOS velocity maps, positive towards satellite. The contours of the volcanoes in the area are shown as black lines. Left column (a,d,g): with only short temporal baseline interferograms. Middle column (b,e,h): with added long duration interferograms. Right column (c,f,i): excluding the shortest temporal baselines.

Figure 2 .

 2 Figure 2. Mean velocity map in the Line of Sight for the entire area, after removal of eastwest and north-south ramps. The velocity is expressed in cm/year and positive for surface displacements towards the satellite. The contours of the volcanoes in the area are shown as black dotted lines.

Figure 3 .

 3 Figure 3. Cumulative line-of-sight displacement over Cayambe volcano, from October 2014 to November 2018. Displacements are relative to the first image (in centimeters) and plotted on 30 meters shadow DEM. The red star and the purple triangle mark the timing of, respectively, the Pedernales earthquake and the two M>3 seismic events located on the volcano flank.

Figure 4

 4 Figure 4. a) Joint probabilities of the Mogi model parameters for Cayambe Volcano, scatter plots are contoured according to frequency (cold colors for low frequency, warm colors for high frequency) and b) Histograms showing the posterior density functions for all source model parameters (blue bars) are plotted together with the optimal values (red lines). Results presented are obtained setting the burning time to 5000.

Acknowledgments

This research was supported by SENECYT (Secretaría de Educación Superior, Ciencia, Tecnología e Innovación, Programa de Becas Internacionales de Posgrado 2018, Ecuador), IDEX (Initiatives-Science -Innovation -Territoires -Economie), IRD (the French National Research Institute for Sustainable Development), the Instituto Geofísico de la Escuela Politécnica Nacional (IG-EPN, Ecuador) through the Laboratoire Mixte International "Séismes et Volcans dans les Andes du Nord". This work is also supported by the Centre National d'Etude Spatiale (CNES) of France through the program APR CNES and was part of P. A. Espín Bedón master studies at Grenoble Alpes University.

We thank the Programme National de Teledétection Spatiale (PNTS) of French CNRS for its support through the "TRIPLETS" project (PI Doin). This was carried out at ISTerre, which is part of Labex International efforts @ OSUG and benefited from CIMENT computing center facilities. We thank the "Seismic cycle and transient deformations" staff from ISTerre and Instituto Geofísico -EPN staff for helping with the data and for providing useful comments. Sentinel-1 data from the Copernicus Sentinel program were provided by the European Space Agency and have

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