Autonomous Extraction of Millimeter-scale Deformation in InSAR Time Series Using Deep Learning
Bertrand Rouet-Leduc, Romain Jolivet, Manon Dalaison, Paul A. Johnson, Claudia Hulbert
AAutonomous Extraction of Millimeter-scaleDeformation in InSAR Time Series Using DeepLearning
Bertrand Rouet-Leduc , ∗ , Romain Jolivet , ,Manon Dalaison , Paul A. Johnson , Claudia Hulbert Los Alamos National Laboratory, Geophysics Group, Los Alamos, New Mexico, USA Laboratoire de G´eologie, D´epartement de G´eosciences, ´Ecole normale sup´erieure,PSL University, CNRS UMR 8538, Paris, France Institut Universitaire de France, 1 rue Descartes, 75005 Paris. ∗ To whom correspondence should be addressed; E-mail: [email protected] a r X i v : . [ phy s i c s . g e o - ph ] D ec bstract Systematic characterization of slip behaviours on active faults is key to unraveling thephysics of tectonic faulting and the interplay between slow and fast earthquakes. Interfero-metric Synthetic Aperture Radar (InSAR), by enabling measurement of ground deformationat a global scale every few days, may hold the key to those interactions. However, atmo-spheric propagation delays often exceed ground deformation of interest despite state-of-theart processing, and thus InSAR analysis requires expert interpretation and a priori knowl-edge of fault systems, precluding global investigations of deformation dynamics. Herewe show that a deep auto-encoder architecture tailored to untangle ground deformationfrom noise in InSAR time series autonomously extracts deformation signals, without priorknowledge of a fault’s location or slip behaviour. Applied to InSAR data over the NorthAnatolian Fault, our method reaches 2 mm detection, revealing a slow earthquake twiceas extensive as previously recognized. We further explore the generalization of our ap-proach to inflation/deflation-induced deformation, applying the same methodology to thegeothermal field of Coso, California. Introduction
Faults slip in a variety of modes, from dynamic earthquakes to transient slow earthquakes andaseismic creep.
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The classical picture of faults being either locked and prone to dynamicand damaging earthquakes, or unlocked and quietly creeping to accommodate tectonic stress,is evolving. Growing evidence indicates complex fault behaviours and interactions among andbetween modes of slip. Evidence includes fault segments hosting both slow and dynamicearthquakes, as well as slow earthquake preceding and possibly triggering the nucleation phaseof dynamic earthquakes.
Answering a number of fundamental questions such as what con-trols the slip mode on a fault, whether there exists a continuous spectrum of slip modes onfaults, and what determines the possible evolution of a slow earthquake into a dynamic seismicrupture, requires exhaustive characterization of all slip phenomena. Interferometric SyntheticAperture Radar (InSAR) holds the promise of continuous geodetic monitoring of fault systemsat a global scale, which may well hold the key to address these questions. However, althoughthe data exists, current algorithms are not suited for global monitoring because they requiretime-consuming manual intervention, and the final product requires exhaustive expert interpre-tation.InSAR is routinely used to measure ground deformation due to hydrologic, volcanic, andtectonic processes.
The apparent range change in the satellite Line-Of-Sight (LOS) betweentwo SAR acquisitions is, after corrections from orbital configurations and topography, the com-bination of atmospheric phase delay and ground deformation. Rapid, large-amplitude deforma-tion signals such as coseismic displacement fields often exceed the amplitude of other knownsources of noise. Similarly, slow but steady accumulation of deformation over long periodsof time may be quantified using InSAR either through stacking, e.g., or time series anal-ysis.
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However, detecting low-amplitude deformation related to transient sources such asslow slip events, episodes of volcanic activity or hydrologic related motion remains challengingand requires significant human intervention and interpretation.
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Measuring Earth surfacedeformation is fundamental to characterizing diverse tectonic processes and the impact, as wellas surface and undergound changes induced by human activities.The most pressing issue in InSAR processing for small, mm-scale, deformation monitoringremains the separation between atmospheric propagation delays and ground deformation. Spa-tial and temporal variations in atmospheric pressure, temperature and relative humidity modifythe refraction index of the air, resulting in spatial and temporal delay variations in the two waytravel time of the radar carrier between a SAR imaging satellite and the ground.
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Such delaysdirectly affect the phase of an interferogram, that combines two SAR acquisitions. Atmosphericpropagation delays in a single interferogram can be equivalent to tens of centimeters in apparentrange change. Current correction methods based either on empirical estimations, e.g.
18, 19 oron independent data, e.g. reduce the contribution of the stratified atmosphere – the longwavelength atmospheric perturbation that, to first order, correlates with topography. Nonethe-less, remaining delays, corresponding to the turbulent portion of the troposphere may representcentimeters of apparent range change. Propagation delays in the atmosphere decorrelate after3eriods of 6 to 24 hours, as shown by the temporal structure function of GNSS zenith delays. Therefore, remaining tropospheric delays, which are coherent in space, can be considered ran-dom in time given the time span between SAR acquisitions (e.g. 6 days for Sentinel 1, 46days for ALOS-2). However, it can be shown that, because of potential temporal aliasing andloss of spatial coherence of the radar phase echo, spatio-temporal filtering can lead to biasedresults. Therefore, deciphering a consistent, days- to month-long transient signal in time seriesof InSAR remains a critical challenge, especially when automation is envisioned.Here we describe a deep learning-based method to automatically detect and extract transientground deformation signals from noisy InSAR time series. Our approach, based on a purelyconvolutional auto-encoder, is specifically designed for removing noise in InSAR time series. Inthe following, we consider the evolution of the interferometric phase with time with respect to areference both in space and time. We consider classical Small Baseline (SBAS)-like approachesfor the reconstruction of the time series e.g.
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Approaches include inversion from a sequenceof SAR interferograms previously corrected from orbital and topographic contributions, witha first-order atmospheric correction derived from global atmospheric re-analysis products.
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Convolutional neural networks (CNN) are central to most recent dramatic advances in com-puter vision and natural language processing. Auto-encoders have been developed to createsparse representations of data –the model copies its input to its output through a bottleneckthat forces a reduction of dimension equivalent to a compressed knowledge representation ofthe original input, enabling noise removal. Of note are recent developments applied to classifyInSAR data in order to detect ground uplift and subsidence, and specifically to identify volcanicunrest.
Although promising, these developments do not make use of the different temporalsignatures of signals of interest to reconstruct de-noised deformation patterns. Our auto-encodertakes as input a noisy InSAR time series reconstructed from successive SAR acquisitions, andoutputs accumulated ground deformation taking place during the time series interval, with theatmospheric noise removed.In the following, we first introduce the notion of auto-encoders before describing the archi-tecture of our neural network. We then describe our training set and perform preliminary testson synthetic data. We finally highlight the efficiency of our algorithm on two reconstructed timeseries of ground deformation, the first one derived from COSMO-SkyMed acquisitions and thesecond one derived from Sentinel 1A-B SAR acquisitions.
Auto-encoder architecture
Our goal is to extract ground deformation from noisy InSAR time series. We assume that in-put time series are the combination of three physical contributions: ground deformation, thestratified component of the atmosphere and the turbulent component of the atmosphere. In4ost cases, the stratified component can be corrected for using Global Atmospheric Models(hereafter referred to as GAMs, often corresponding to re-analysis products), e.g., or GlobalNavigation Satellite System (GNSS) data, e.g., for instance. However, such a correction is of-ten incomplete and part of the remaining, often turbulent, atmospheric delays may still correlatewith topography. Attempts have been made to estimate tropospheric delays using multi-spectralradiometric data; however, the acquisition of such independent data must be coincident withthe SAR acquisition and over a terrain with minimal cloud cover for optimal performance,conditions rarely met. In addition, it can be shown that GAMs-derived correction sometimesworsen the situation as the local estimate of the state of atmospheric variables may be incor-rect. Our deep learning model must recognize transient deformation in InSAR time series in thepresence of remaining atmospheric noise. To this end, it must distinguish the spatial and tempo-ral statistical differences between deformation signals and atmospheric patterns. As mentionedabove, the structure of atmospheric delays decorrelates for periods longer than 6 hours. There-fore, as ground deformation related to transient tectonic events might take place over secondsto minutes for dynamic rupture, to weeks or months or even years for slow slip events,
14, 15, 33, 34 and remains until further ground deformation occurs, the temporal signature is very differentfrom that of atmospheric delays. We make use of this different temporal signature to learn ap-propriate filters to remove atmospheric perturbations and extract ground deformation in InSARtime series.Here, we build and train an auto-encoding architecture to directly output the deformationsignal, formulating the problem as a regression task. We rely on the following assumptions:(1) atmospheric delays are random in time, considering two successive SAR acquisitions, (2)ground deformation has a temporal coherence considering the rate at which SAR images areacquired and (3) part of the atmospheric delay correlates with topography. We therefore use asinputs a time series of interferometric phase change and a map of ground elevation to producea time series of cumulative surface displacements.In order to separate deformation from atmospheric delays, we developed the deep learningarchitecture shown in Fig. 1. This architecture consists of 11 purely convolutional layers. Thefirst 6 layers of the model are tasked with encoding signals that are persistent in time, by pro-gressively removing the time dimension of the input. The remaining layers decode the grounddeformation map. In short, we build a model tasked with reconstructing ground deformationgiven input InSAR time series and ground elevation from noisy input.Initially developed for feature extraction by projecting high-dimensional datasets onto alower-dimension manifold by forcing the reconstruction of the data through a bottleneck indeep learning architectures, auto-encoders have also evolved into powerful denoising
36, 37 andimage enhancing techniques.
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In this work we exploit this aspect of deep learning auto-encoding and tailor it to the problem of cleaning InSAR time series, building a deep learningauto-encoder to effectively automate the design of filters in time and space to recover grounddeformation. 5igure 1:
Auto-encoding InSAR time series.
Schematic of our deep learning model. Top row (left to right):a sequence of synthetic InSAR time series on which the model is trained, where ground deformation signal iscorrupted with atmospheric noise, including turbulence and layering of the atmosphere. Second to fourth rows:architecture of our model. Our model is purely convolutional with progressive pooling on the time dimensionduring the encoding. After time is removed, at the 7th layer, ground elevation is added as a secondary input.Fourth row: The last layers of the model are tasked with decoding ground deformation accumulated during theinput time series, here compared with actual deformation that takes place in the synthetic time series shown above.A detailed description of this neural network can be found in the methods section.
Training on synthetic data
Because deep learning models require large amounts of data and there exists no ground truthfor InSAR time series, we rely on synthetic data to train the deep auto-encoder. The syntheticdata are randomly-generated cumulative surface deformation time series mimicking 9 succes-sive ‘acquisitions’. These cumulative deformation maps include surface displacements in theline of sight (LOS) due either to a slipping fault with random latitude and longitude (positionin a virtual box), depth, strike angle, dip angle and width (based on Okada’s model ) or to an6nflating or deflating point source (Mogi’s model ). Deformation onset occurs at a random timewith a random duration within the time series, excluding the first and last acquisitions whichare taken as non-deforming reference by the model. The model is therefore tasked with findingcumulative deformation in the 7 middle acquisitions of the time series arising from a wide va-riety of transient processes. We then corrupt each map of these ground deformation time serieswith different noise signals. At each time step we create both turbulent and stratified syntheticatmospheric delays. Spatially correlated Gaussian noise mimics delays from atmospheric turbu-lence of various length scales
42, 43 (Fig. 1 top row) and a quadratic function of pixels’ elevationmimics the atmospheric delays that correlate with topography.
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Each of the steps of the timeseries results from a random realization of noise built following these assumptions.We train two independent models with the synthetic time series of deformation, one taskedwith recovering point source deformation, the other with recovering deformation on faults. Allother phase delays are identified as noise. Both models are trained to map synthetic noisytime series to the synthetic cumulative displacements. We trained our deep auto-encoder with . × randomly generated time series for which we provide as input the apparent line of sight(LOS) deformation time series, corrupted by the sum of synthetic noise described above. Thetraining includes a LOS with random orientation (30-45 degrees incidence and any azimuth),so that the model is directly trained for various SAR satellite configurations and for any faultazimuth. The output is the target ground deformation accumulated during the time series. All482,185 trainable parameters are adjusted during that training phase with the Adam variation ofstochastic gradient descent. We note that our deep auto-encoder only considers time series of 9 acquisitions, as a goodcompromise between the tractability of the training phase (the time series are long enough forthe model to learn the temporal differences between signal and noise) and a minimum durationof the analysed time series of displacements. When working with longer time series of n acqui-sitions, we apply the algorithm using a sliding window with a width of 9 time steps and obtain n − images of cumulative deformation. In this way, our model acts as a moving integral ofactual deformation. Performance on synthetic data set
Once trained, we test the deep auto-encoder on synthetic realizations of time series that havenot been used to train the model. We randomly generate 3200 time series of 9 time framesusing the same procedure as that described for the training phase. For each of the 3200 timeseries, we evaluate the signal-to-noise ratio (hereafter referred to as SNR) as the ratio of themean absolute ground deformation and the standard deviation of the noise. We then apply thedeep auto-encoder to these time series in order to evaluate the performance of the model. Weevaluate the resulting, cleaned time series using the coefficient of determination R , a standardregression metric, equal to 1 for a perfect reconstruction, 0 for a reconstruction no better thanthe empirical average, and negative for the worst reconstructions (for example reconstructionsanti-correlated with the ground truth). 7igure 2: Performance on synthetic test data.
Left: Performance of the reconstruction of fault deformation byour deep auto-encoder, on synthetic noisy time series, as measured by the coefficient of determination R (a metricof goodness of fit that compares model error with the error of predicting the empirical average) as a function ofsignal to noise ratio (SNR, see Methods). Each point represents the average over 64 synthetic time series withthe same SNR. Right: examples of the data (last frame of the input), the ground truth and its reconstruction,for different signal to noise ratios. Note that the model outperforms the eye, recovering with reasonable fidelity(R > . ) deformation signals with SNRs below 0.1. We find that the deep auto-encoder applied to synthetic data accurately reconstructs defor-mation signals on faults, even in circumstances very challenging to expert interpretation (SNRslower than 1; Fig. 2). For SNRs above 0.1, our algorithm provides a very accurate recon-struction ( . < R < . ) of the cumulative ground deformation. For very low SNRs (0.1and below), no signal can be visually observed, while the goodness of fit is still correct andthe overall deformation signal is recovered down to SNRs of approximately 0.02, below whichour model fails. Therefore, our architecture allows us to exceed the ability of the expert eye todetect signals in noisy time series of deformation, provided their noise structure resembles thetraining set.In the following we show the application of our auto-encoder to two case studies that havebeen independently analyzed by InSAR experts. Extracting deformation from a slow earthquake along the North Anatolian Fault, Turkey
Our deep auto-encoder is trained to isolate and reconstruct cumulative ground deformation sig-nals in 40x40 pixel time series of 9 acquisitions. However, a fundamental property of purelyconvolutional deep learning models is that the filters they learn do not depend on input size.As a result, we can create an auto-encoder with exactly the same architecture as the model de-scribed in Fig. 1, but with an input size matching the number of pixels in the InSAR time series8f interest. Because the parameters of the model do not depend on input size, we can copy everyparameter (i.e. weights and biases of the filters) of the model trained on synthetics to the newmodel, which can then be applied to InSAR data of any size.Here, we apply the model to a time series built from images acquired by the COSMO-SkyMed constellation over the central section of the North Anatolian fault in Turkey (Fig. 3).This major plate boundary fault accommodates the motion of rotation of the Anatolia plate withrespect to Eurasia and has ruptured in large, Mw 7 earthquakes multiple times over the lastcentury. An 80-km-long section of the fault has been slipping aseismically, at least since the1944, Mw 7.3, earthquake located near the small town of Ismetpasa. In situ measurementsbased on creepmeters indicate that this fault experiences transient aseismic slip episodes.
Rousset et al. produced an approximately one year long time series from COSMO-SkyMedSAR acquisitions and detected a significant slow slip episode that lasted one month during 2013with a maximum of 2 cm of fault-parallel slip. Average long-term velocity maps coveringthe whole region derived from InSAR data show aseismic slip over an 80-km-long section ofthe fault. This average relative displacement was found to result from successive transientevents,
14, 49 which were not apparent in data from older constellations of SAR satellites due tothe long time span between acquisitions.In the InSAR time series processed by Rousset et al., large atmospheric delays are appar-ent, despite careful correction of atmospheric delays using ECMWF re-analysis products.
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Therefore, knowledge of the fault location was key in the interpretation of the surface displace-ment field.Here we revisit the same time series in order to assess if our model is able to recover theknown surface slip in real time series of data. We stress that we do not provide the location ofthe fault to the model.With no human intervention and no a priori knowledge of the local tectonics and fault lo-cation, the model automatically isolates and recovers clean deformation signals where expertanalysis previously found signal attributed to tectonic activity (Fig. 3). Importantly, the recov-ered deformation is obtained after training only on synthetic data and with no further fine tuningon real data. Our model finds up to 1.5 cm line of sight relative displacement across the fault,that we interpret as the signature of surface slip, as previously found. Application to real data: the North Anatolian Fault 2013 slow earthquake.
In order to identifyground deformation signals in the noisy COSMO-SkyMed InSAR time series, we create a deep auto-encoder thathas an input size equal to the size of the acquisitions, 200x650 pixels, and the same parameters as the auto-encodertrained on synthetic data, shown in Fig. 1. Inputs are the InSAR time series. The auto-encoder outputs grounddeformation (bottom plot). The ground deformation is manifest as an offset across the fault. The deep auto-encoderfinds a strong slip signal of about 1 cm (in LOS) on the fault, in agreement with previous expert analysis of thetime series, with no a priori knowledge of the fault’s existence. a. Seismic setting of the region of the creepingsection of the North Anatolian Fault. Thick red lines are the main faults of the NAF system, separating the Eurasiaplate from the Anatolia microplate. Thin red lines are other mapped structures. Colored lines indicate the extentof historical ruptures. b. Input raw time series from COSMO-SkyMed data (subset of the data from Rousset etal. 2016). Color is the apparent range change between the ground and the satellite. c. Denoised cumulativedeformation as output by the deep-autoencoder. The color scale shows ground deformation in the direction ofthe LOS. Dark lines are the surface trace of the NAF, shown here for reference. Thin dashed lines indicate thecross-sections shown in figure 4. L O S ( mm ) Western profile
Distance to the NAF (km) L O S ( mm ) Eastern profile
Figure 4:
Application to real data: the North Anatolian Fault 2013 slow earthquake.
LOS deformationalong fault-perpendicular cross sections. Location of the cross-sections are shown in Fig. 3. Black dots are thedifference between phases averaged over acquisitions between September 5th and 21st, 2013 and over acquisitionsbetween August 4th and 28th, 2013, taken along a fault perpendicular line. The main slow slip event detectedby Rousset et al. occurred during this period. Red dots are the output of the model highlighting the cleaneddeformation pattern. The sharp offset in the input InSAR data observed exactly on the fault was interpreted as aslow slip event by Rousset et al., in spite of the very high noise level presumably caused by atmospheric delays.Such interpretation was only made possible owing to knowledge of the location of the fault and knowledge thatthis segment of the North Anatolian Fault slips aseismically. Our model knows neither and automatically extractsactual ground deformation. Our current model interprets wavelengths longer than a kilometer as noise, althoughexperts might interpret those as the signature of slip at depth.
Fault perpendicular cross sections illustrate that even in regions where slip would not havebeen convincingly identified by an expert (Fig. 4), our model recovers 2 mm of slip, extendingthe previous estimate of along-strike length of this slip event. Rousset et al. identified a 10-km-long slow slip event while the deep learning model determines that the portion that slipped was15-20 km in length. Interestingly, the new 2 mm slow slip we find is on a segment adjacent tothe previously identified 1 cm slow slip, and the two segments are separated by a kink on thefault, suggesting an interplay between fault geometry and slip.
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Extracting ground deformation signal at the Coso geothermal system, California
In a second example, we use our deep learning architecture to detect surface deformation causedby underground pressure changes. As above, our model is trained on several million examplesof synthetic noisy InSAR time series. In this case, surface deformation is modeled by a point11ressure source using Mogi’s equation of elastic deformation, corrupted as before by syntheticatmospheric delays. Mogi pressure sources are used extensively for the modeling of volcanicinflation and deflation signals, e.g.
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Further, the combination of multiple sources allows oneto model complex subsidence/uplift patterns.After training exclusively on synthetic data, we apply our model to real data from the Cosogeothermal field (California, USA), again without further training (details on the InSAR pro-cessing are in the Methods section). Because InSAR time series may be very noisy, even aftercorrecting predicted atmospheric effects, analysis of inflation or subsidence of less than a fewcentimeters per year in InSAR have relied to date on deriving long term cumulative deforma-tion, such that random atmospheric delays cancel out. Detecting transient subsidence anduplift signals in SBAS time series below a few centimeter remains challenging, just as it doesfor faulting.As with identifying deformation on faults, our model is able to disentangle actual grounddeformation from atmospheric noise at short time scales, with a resolution of a few millimeters.In Fig. 5 we show the application of our deep denoising model to a time series over Cosoin 2016. Contrary to what could be inferred from long term cumulative deformation, we findthat ground subsidence at Coso is primarily due to transient episodes of deformation. Thecumulative deformation from these transients we detect account for most of the cumulativedeformation observed in the data (see Supplementary for details and for other examples oftransient deformation). Interestingly, we find a number of transient events that are constitutedof well separated pressure sources, in agreement with geochemical observations showing thatthe geothermal field is constituted of isolated reservoirs. igure 5: Application to real data: the Coso Geothermal Field in California.
After training our deep auto-encoder architecture exclusively on synthetic InSAR time series of point sources of deformation corrupted withatmospheric noise, we apply it to the time series obtained from Sentinel 1A-B from 2016-04-14 to 2016-11-16,that spans the Coso Geothermal Field in California. Our model detects a transient episode of subsidence of 5to 7 mm (in line of sight), where the operational wells are located, with no a priori knowledge of the area. a. Geographic setting with the coverage of the subset of the Sentinel 1 track used here. Red and blue dots indicatethe geothermal wells, respectively for injection and production. Background color is the terrain rendering fromStamen (http://maps.stamen.com). b. Input raw time series of 9 successive images from Sentinel 1 data. Color isthe apparent range change between the satellite and the ground along the LOS. c. Denoised cumulative deformationas output by our deep auto-encoder. Color is ground deformation in the LOS. The thin dashed line indicates thelocation of the cross section shown in the Supplementary. Discussion
As the properties of the atmosphere cannot be measured at the same spatial and temporal resolu-tion as InSAR acquisitions, InSAR time series still contain large amplitude atmospheric delays,on the order of centimeters, in spite of recent marked improvements in atmospheric correctionand processing strategies.
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For this reason, expert processing and analysis is required tointerpret InSAR data. Furthermore, since the onset of the Sentinel 1 mission, the amount ofavailable InSAR data has grown at a pace that is already challenging the ability of the commu-nity to process and analyze it, and the upcoming NISAR mission will increase the amount ofavailable InSAR data several fold. Therefore, significant effort has been put into developingstrategies to build time series with such vast data sets, e.g.
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Nonetheless automatic, au-tonomous InSAR interpretation methods are poised to become essential, if just to leverage theincreasing spatial and temporal resolution of the data.We note that several avenues of improvement should improve the ability of our neural net-work to detect finer and finer deformation signals in the future. First, we did not includesources of noise representative of ionospheric perturbations. The total electronic content ofthe ionosphere introduces a differential delay in interferograms that can bias analysis further. Although this effect is more pronounced for L-band SAR satellites,
16, 59 long-wavelength iono-sphere delays can be problematic for large images acquired with C-band SAR systems such asSentinel 1. Although these delays can be corrected for using techniques such as the rangesplit-spectrum method,
60, 61 the structure of the remaining noise associated with imperfect cor-rections must still be evaluated and could then be used in the training of our model. Second, weconsidered atmospheric turbulence to be isotropic and equivalent everywhere in the image (i.e.noise is second-order stationary) while some anisotropy can be observed in the phase delay ofsome interferograms. However, such anisotropy depends on the scale of the image observed,which would involve complex considerations in the construction of an adequate troposphericnoise model to train our model. In general, any improvement in the forward modeling of thenature of noise in InSAR should lead to a significant improvement in the detection capability ofthe models.Finally, the receptive field of the autoencoder and the pixel size of the input InSAR datarestrict the size of the deformation signal that can be deciphered. For instance, interseismic de-formation related to loading of a fault by plate motion extends over 10s of kilometers, e.g.
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Additional developments may be necessary for the detection and cleaning of long wavelengthdeformation patterns.The initial application of our method on InSAR time series enables the direct observationof a slow earthquake, refining previous estimates, autonomously and without prior knowledge.In particular, we expect that the ability to systematically observe fault and pressure sourcedeformation at a global scale will further the understanding of hydrologic, volcanic and tectonicprocesses, and may bring us closer to bridging the observational that exists for transient surfacedeformation. 14 eferences Avouac, J.-P. From Geodetic Imaging of Seismic and Aseismic Fault Slip to DynamicModeling of the Seismic Cycle.
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B. R.L.’s work was funded by Institutional Support (LDRD) at Los Alamos (20200278ER).R. J., M. D., C. H. were supported by the European Research Council (ERC) under the Euro-pean Union’s Horizon 2020 research and innovation program (Geo-4D project, grant agreement758210). C.H. was also supported by the CEA-ENS Yves Rocard LRC (France). P. J. was sup-ported by DOE Office of Science (Geoscience Program, grant 89233218CNA000001).20 uthor contribution
Author order uses the remote sensing convention of author contribution. B. R.L. and R.J. for-mulated the problem as a deep denoising task. B. R.L. created the deep learning model andapplied it on real InSAR data, with help from R. J., M. D. and C. H.; R. J. implemented thesynthetic data used for training the model and processed the COSMO SkyMED InSAR data;M. D. processed the Sentinel 1A-B data. All the authors analyzed the results and wrote thepaper.
Data availability
All the InSAR data used here is freely available from the European Space Agency. The COSMO-SkyMED archives and the Sentinel 1 data can be found at https://earth.esa.int.
Code availability ∼∼