Methodology and Techniques - DInSAR

By providing spatial continuous measurements at relatively large scale and low cost, in recent decades Interferometric Synthetic Aperture Radar (InSAR) has grown up to be a powerful technique in monitoring surface displacements caused by the fluxes of subsurface fluid such as groundwater variation, oil and gas exploration, geothermal production, and magmatic activity. Especially since the multi-temporal InSAR (MT-InSAR) algorithms (e.g., Persistent Scatterer (PS), Small Baseline Subsets (SBAS), and Temporarily Coherent Point (TCP)) was developed, the slow and subtle displacement signals due to the subsurface fluid fluxes can be better expected by suppressing the InSAR inherent errors like decorrelation noises and atmospheric artifacts. However, the InSAR measurements only correspond to the projection of actual surface displacements onto the Line-Of-Sight (LOS) direction. Since the subsurface fluid fluxes generally give rise to surface displacements in the U-D, E-W and N-S directions, simultaneously, the one-dimensional (1-D) InSAR LOS measurements are generally insufficient to provide comprehensive information for preventing the geo-hazards related to the variations of subsurface fluid, and can even promote misjudgment in the extreme case.

Complete three-dimensional (3-D) displacements can theoretical be recovered by integrating three or more InSAR LOS measurements with similar covering periods but remarkable differences among their imaging geometries. In fact, due to the Sun-synchronous orbit and side-looking radar of the current Synthetic Aperture Radar (SAR) satellites, only two distinguishable InSAR LOS measurements dominated by the U-D and E-W displacement components can be provided by the cross-heading tracks (i.e., the ascending and descending orbits). In other words, the InSAR LOS measurements are almost blind to the N-S displacement component. Note that there are little exceptions for the SAR data acquired in the polar region, but they are only meaningful for the glacier research. Therefore, a simplified geometry is always adopted to ignore the contribution of the N-S displacement component in the InSAR LOS measurements, which can only produce the quasi U-D and E-W displacement components with satisfying accuracies. 

In order to compensate the insensitivity of InSAR LOS measurements to the N-S component, Offset-Tracking and multi-aperture InSAR (MAI) techniques had been proposed to estimate the displacement measurements along the azimuth direction (nearly parallel to the N-S direction) from the InSAR pair. Complete 3-D displacements can thus be constructed by adjusting InSAR derived LOS measurements and Offset-Tracking/MAI derived azimuth measurements from two cross-heading InSAR pairs with a weighted least squares (WLS) algorithm. Nevertheless, this method is limited in the investigation of significant surface displacements such as earthquake, volcano eruption and glacier movement due to the inferior accuracies of azimuth measurements derived by Offset-Tracking or MAI. High precision GPS observations provide another option to aid InSAR in resolving reliable 3-D and particularly N-S displacements. In order to integrate the InSAR and GPS measurements, the sparse GPS observations need to be interpolated into the same lattice of InSAR measurements, or linked to the stress-strain based on the theory of elasticity. Obviously, this method requires an amount of GPS stations, which however cannot always be guaranteed in the areas affected by the subsurface fluid fluxes. Therefore, it is concluded that the existing methods of estimating 3-D displacements based on InSAR are not applicable in monitoring ground movements associated with subsurface fluid fluxes.

In this paper, we propose a novel InSAR-based approach to infer the complete 3-D surface displacements caused by the fluxes of subsurface fluid. Based on the elastic half-space theory, the algorithm exploits the relationship between the deformations of the Earth’s surface and the variations of fluid within subsurface space to construct a joint model with InSAR LOS measurement, from which the 3-D surface displacements as well as the volume change of the subsurface fluid can be estimated, simultaneously. More importantly, the InSAR LOS measurement acquired in a single track is adequate for the algorithm to resolve accurate U-D, E-W and N-S displacement components, and the Offset-Tracking/MAI or GPS measurements are not required. The performance of the proposed approach is firstly verified by a series of simulation experiments. It is found that the appearances of all the three estimation components agree with the simulated ones very well, by providing the InSAR LOS measurements with different levels of noises (i.e., 0, 1, 2, 5, 10 and 20 mm STDs). Subsequently, the proposed approach is applied to monitor the ground deformation associated with the eruption of the Kilauea Volcano, Hawaii on June 17, 2007. With a pair of ascending ALOS PALSAR images, completely 3-D deformation field of the Kilauea Volcano is recovered in this study. Comparing with the conventional WLS method, an improvement of about 54%, 73%, and 28% has been achieved for the E-W, N-S and U-D components, respectively, revealing by the GPS observations.

The last step in the SBAS processing chain is the estimation of a deformation time-series from a stack of unwrapped differential interferograms. This step includes two subsequent filtering operations in order to remove the atmospheric phase component. It is assumed that the atmospheric signal is highly correlated in space but nearly uncorrelated in time. Therefore a two-dimensional spatial lowpass filter, followed by a temporal highpass filter is applied to the image stack.
We present an integrated spatio-temporal technique for deformation time-series estimation based on three-dimensional polynomial base functions with finite support (Splines). For this approach we assume that the deformation in every pixel (with respect to a temporal reference) can be described by an at least once continuously differentiable function. Through the length of the finite support in direction of the temporal axis, it is possible to introduce certain assumption about the temporal behavior of the deformation, e.g. annual or semiannual amplitudes.
This temporal model is directly linked to the spatial spline model. In consequence, every spatial spline can separately change in time while the estimated function has to satisfy predefined continuity conditions in the spatial domain. Thus, the deformation signal is fully described through a spatio-temporal model without  specifying an explicit parametric deformation model.
We estimate the deformation signal by an integrated least squares data fitting approach using the whole stack of unwrapped differential interferograms. Under the assumption that the atmospheric phase component is nearly uncorrelated in time, this part cannot be absorbed by the model and will be  contained in the residuals together with the noise component.

(Please refer to the attached paper for the full abstract)

Deformation monitoring by multi-baseline repeat-pass synthetic aperture radar (SAR) interferometry is so far the only imaging-based method to assess millimeter-level deformation over large areas from space. Past research mostly focused on the optimal deformation parameters retrieval on a pixel-basis. Only until recently, the first demonstration of object-based urban infrastructures monitoring by fusing SAR interferometry (InSAR) and the semantic classification labels derived from optical images was presented in [1]–[3]. This paper demonstrates a general framework for object-based InSAR parameters retrieval where the estimation of the parameters is achieved in an object-level instead of pixel-wisely. Furthermore, to handle outliers in real data, a robust phase recovery step in prior to the parameters inversion is also introduced. The proposed method outperforms the current pixel-wised estimators, e.g. periodogram, by a factor of as much as several dozens (40~100) in the accuracy of the linear deformation estimates.

This framework is one promising development of multibaseline InSAR, as it moves parameters retrieval on single-pixel to an object-level which explores the geometric information as a nature in any kind of images besides the interferometric phase measurement observed at each pixel. This framework can greatly help the application of deformation monitoring, 3-D city model reconstruction from InSAR point cloud, and so on.

[1]        Y. Wang and X. X. Zhu, “Fusing Meter-Resolution 4-D InSAR Point Clouds and Optical Images for Semantic Urban Infrastructure Monitoring,” IEEE Trans. Geosci. Remote Sens., 2016.

[2]        Y. Wang and X. X. Zhu, “InSAR Forensics: Tracing InSAR Scatterers in High Resolution Optical Image,” presented at the Fringe 2015, 2015.

[3]        Y. Wang and X. X. Zhu, “Semantic Fusion of SAR Interferometry and Optical Image with Application to Urban Infrastructure Monitoring,” presented at the CMRT, France, La Grande Motte, France, 2015.

The launch of Sentinel-1 A/B as well as the planning of the future wide swath satellite missions with low revisit cycle, such as NASA’s NISAR and DLR’s Tandem-L, opens a new era in the capabilities of InSAR for global and systematic monitoring of the earth deformation. The combination of wide swath and high temporal resolution of such missions will soon give birth to an unprecedented wealth of interferometric data. The processing of the emerging Big-Data with the state-of-the-art InSAR time series analysis techniques will however pose new challenges. As one of such techniques, the maximum-likelihood estimator (MLE) retrieves high precision phase-series from the InSAR time series with precision closest to the theoretical lower bound for phase estimation. The estimated phase-series are the input for deformation retrieval. The MLE however exploits all possible interferometric pairs in the time series, thus is computationally demanding.

We propose a recursive estimation scheme in the realm of the maximum-likelihood estimator, which enables efficient processing of the InSAR time series with reduced computational burden. The proposed estimator is shown to achieve a performance with acceptable degradation compared to the expensive MLE scheme. Coined Sequential Estimator, the algorithm is based on the processing of small batches of data at each its sequences; and compressing the interferometric content to substitute the small data batch with its compressed version. Exploitation of the compressed data at each successive data batch and formation of new artificial interferograms between the compressed and acquired data are the backbones of the scheme for preventing performance loss compared to the theoretical lower bound for the estimation.

The proposed sequential processing of the time series both decreases the computational burden and provides a recursive solution for the inherently non-parallel problem of phase-estimation in the temporal direction. The proposed scheme therefore may be adapted for near-real-time processing of InSAR time series with the objective of high precision deformation monitoring of even small crustal changes. The latter capability introduces new geodetic applications for InSAR.

For demonstration purposes both simulation and real-data experiments are performed: two ideal simulation scenarios are considered for validation. The performance of the estimator is compared against the computationally-expensive state-of-the-art approaches such as MLE as well as probable alternative computationally-cheap processing schemes. The application of the Sequential Estimator is demonstrated using a 1.5 year archive of Sentinel-1 data; an overview of the result is presented in figure 1.

We analyze the methods for measuring azimuth deformation with L-band ALOS-2 ScanSAR interferometry. To implement the methods, we extract focused bursts from the ALOS-2 full-aperture product, which is the only product available for ScanSAR interferometry at present. The extracted bursts are properly processed to measure azimuth deformation using interferometric phase. We apply the range split-spectrum method to ScanSAR to estimate the ionospheric phase of the interferogram, and take the azimuth derivative of the estimated ionospheric phase to mitigate the relative azimuth shift caused by ionosphere. We then present the following results:
1. We present the first ALOS-2 ScanSAR interferogram processed using a burstby-burst approach. We also compare the result with the result processed by full-aperture approach which is the main approach used to process JAXA ALOS-2 full-aperture ScanSAR product at present.
2. We present the large-scale ionospheric correction results for both ScanSAR regular and double-difference interferograms.
3. For the first time, azimuth deformation of a large earthquake is nearly completely measured by L-band ScanSAR interferometry with moderate precision. The result is validated by azimuth deformation measured by incoherent cross correlation using a pair of high-resolution RADARSAT-2 images.

Besides measuring the deformation caused by earthquakes, other possible applications of this research include measuring the movement of glaciers.
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1 The authors are with the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109 USA

A comparison of interferograms processed using burst-by-burst and full-aperture approaches. (a) Interferogram processed using burst-by-burst approach. (b) Interferogram processed using full-aperture approach. (c) Difference of the two interferograms. (d) Amplitude image of master from burst-by-burst processing. Data: subswath 5, Feb. 22, 2015 and May 3, 2015.

Ionospheric correction result of regular ALOS-2 ScanSAR interferogram for September 16, 2015 Mw8.3 Chile earthquake. (a) Original interferogram. (b) Estimated differential ionospheric phase. (c) Corrected interferogram. (d) C-band Sentinel-1A TOPS interferogram after filtering, phase unwrapping and scaled according to the ratio of ALOS-2 and Sentinel-1A wavelengths. ALOS-2 ScanSAR data acquired on Jul. 30, 2015 and Sep. 24, 2015. Sentinel-1A TOPS data acquired on Aug. 24, 2015 and Sep. 17, 2015. Background image copyright Google Earth. Azimuth deformation of Nepal earthquake measured by ALOS-2 ScanSAR interferometry. Background image copyright Google Earth.  Azimuth deformation of New Zealand earthquake measured by ALOS-2 ScanSAR interferometry.
Background image copyright Google Earth.