InSAR Theory

Interferometric Synthetic Aperture Radar (InSAR) methods provide high resolution maps of surface deformation applicable to many scientific, engineering and management studies.  Modern spaceborne satellites, perhaps today best exemplified by Sentinel-1A and B, provide long sequences of observations that we can reduce to many interferograms, which in turn provide the deformation histories of many points on the surface.  InSAR measures mm-cm level surface deformation over large areas at fine resolution, and has been extensively applied in studies such as earthquake and volcano modeling [1-4], glacier mechanics [5,6], hydrology [7,8], and topographic mapping [9,10]. The InSAR technique combines interferometry and conventional synthetic aperture radar (SAR) to compute the phase differences between two single look complex (SLC) SAR images. Since the resulting interferometric phase is proportional to the change in range between the sensor location and a given point on the surface, a single interferogram contains phase signals from i) the local topography due to the spatial separation of the two sensor locations and ii) any radar line of sight displacements of the point occurring between the two SAR acquisition times.

Despite its utility, analyzing InSAR data remains difficult for the non-specialist. First of all, it requires InSAR data users to be considerably familiar with the detailed SAR imaging geometry for each acquisition, and also experienced in InSAR processing techniques.  In addition, differential interferometric SAR techniques for investigating temporal evolution of surface deformation, such as the small baseline subset (SBAS) [11] and persistent scatterers [12,13] approaches are typically based on a large number of SAR acquisitions and an even larger number of interferograms. For example, a sequence of 100 radar acquisitions yields 4950 interferograms, and it is much easier to download the 100 SLCs rather than the huge transfer volume of all of those interferograms.  Recognizing all of these restrictions, applying topographic corrections to all interferograms in a given analysis can require significant computational resources.  Finally, for many users the range-Doppler radar coordinate system is perplexing, so that many users find it hard to ingest even useful products in their own customary analyses.  Our goal here is to make access to InSAR methods and data easy for most users, relieving them of the burden of understanding the processing details and the need for large computational resources.

Here we present a case for delivering semi-reduced SLC data directly to users, so that those who can benefit greatly from the analytical methods can readily use data in well-defined coordinate and reference systems.  We show how raw radar data, or partially processed single look complex images may be precorrected for imaging geometry so that formation of the hundreds of interferograms from an observation sequence is both reliable and efficient.  One approach, most useful when there exist modest errors in orbit knowledge or drifts in instrument performance, is to use motion compensation to precisely coregister the images and a common master orbit. Another approach, most effective when the orbit is very accurately determined, allows resampling of products such as Sentinel-1 TOPS SLCs directly to a latitude/longitude grid with automatic viewpoint and topographic correction.  In both cases we fully compensate for the topographic phase terms so that simple cross multiplication yields the needed interferograms directly in map coordinates. 

In the first method, we make use of motion-compensation techniques to propagate actual radar echoes to a virtual ideal orbit as suggested by Zebker et al. [14]. The advantage of using a common ideal orbit is that the imaging geometry is particularly simple and therefore topographic correction is relatively simple as well. Fine image registration is applied to the motion compensated products so that m-scale errors can be resolved in the reduction.  The motion compensation techniques can equally well be applied to the generation of the SLC radar images, or to the zero-Doppler SLC products produced by many sensors today (e.g., Sentinel, Radarsat-2, COSMO-SkyMed or ALOS-II). We find the topography related phase term for each individual SLC radar image and then remove it to generate topography corrected SLC radar images.

For the case in which the orbit is very well known, we can directly resample the natural-coordinate SLCs to a latitude/longitude grid, simultaneously applying a phase correction that compensates for both the specific viewing geometry and the topographic elevation of the surface.  Since we need to align images to a small fraction of a pixel in order to maintain high InSAR correlation, this method is most effective when the orbit is accurate to a few 10’s of cm.  Many modern systems, including Sentinel 1AB, achieve this regularly.

Sentinel 1 data pose a secondary challenge resulting from the TOPS scanning that minimizes amplitude scalloping in the images.  Users must apply a correction for the scanning phase itself, moreover slight inaccuracies in position knowledge cause additional phase artifacts as the Doppler centroid of pass to pass matched pixels can vary.  This can be partially resolved by cross-correlation of the patches, but the very fine accuracy needed (about 0.001 pixel) often implies the need for a secondary phase compensation generally referred to as an enhanced spectral diversity correction.  Nevertheless, once all of these are applied, regularly gridded SLC images may be generated that facilitate interferogram formation from simple cross multiplication.  As in previously described cases, these products greatly lessen the burden on the user so that one with basic GIS skills can successfully use the InSAR products.

All of the phase correction algorithms described above rely on knowledge of the topography of the Earth’s surface.  Several good digital elevation models (DEMs) with fairly wide coverage exist, including the NASA SRTM DEM valid between +/- 60 degrees latitude, and the Tandem-X DEM that is somewhat more accurate.  The effect of an error in one of these DEMs translates directly into a mispositioning of SLC pixels, and an unwanted elevation-dependent phase error. We calculate the phase error expressed as cm of deformation error as a function of DEM error and InSAR baseline, and show that even the more modest DEM accuracy of SRTM suffices for InSAR reduction if baselines can be maintained within a few hundred meters.  Extreme precision requirements can be met either through use of the higher quality Tandem-X DEM or by better orbit control, or both.

In summary, either motion compensation or direct resampling methods we are able to precisely coregister SLC images corrected for topographic distortions using a master radar orbit to generate a set of radar baselines.  These methods relieve the user of having to understand any of the processing complexities or, in fact, even having to know the spatial baselines involved.  It also allows downloading only of the small set of actual SLC images, rather than requiring the large bandwidth and data storage needs for acquiring perhaps 100’s or 1000’s of interferograms for a given deformation time series.  These innovations greatly increase the number of users who can successfully use InSAR in their applications and investigations.

References

[1] Massonnet, D., Rossi, M., Carmona, C., Adragna, F., Peltzer, G., Feigl, K., & Rabaute, T. (1993). The displacement field of the Landers earthquake mapped by radar interferometry. Nature, 364(6433), 138-142.

 [2] Zebker, H. A., Rosen, P. A., Goldstein, R. M., Gabriel, A., & Werner, C. L. (1994). On the derivation of coseismic displacement fields using differential radar interferometry: The Landers earthquake. Journal of Geophysical Research: Solid Earth (1978–2012), 99(B10), 19617-19634.

 [3] Wicks, C., Thatcher, W., & Dzurisin, D. (1998). Migration of fluids beneath Yellowstone caldera inferred from satellite radar interferometry. Science, 282(5388), 458-462.

 [4] Amelung, F., Jónsson, S., Zebker, H., & Segall, P. (2000). Widespread uplift and ‘trapdoor’faulting on Galapagos volcanoes observed with radar interferometry. Nature, 407(6807), 993-996.

 [5] Goldstein, R. M., Engelhardt, H., Kamb, B., & Frolich, R. M. (1993). Satellite radar interferometry for monitoring ice sheet motion: application to an Antarctic ice stream. Science, 262(5139), 1525-1530.

 [6] Fatland, D. R., & Lingle, C. S. (2002). InSAR observations of the 1993-95 Bering Glacier (Alaska, USA) surge and a surge hypothesis. Journal of Glaciology, 48(162), 439-451.

 [7] Hoffmann, J., Zebker, H. A., Galloway, D. L., & Amelung, F. (2001). Seasonal subsidence and rebound in Las Vegas Valley, Nevada, observed by synthetic aperture radar interferometry. Water Resources Research, 37(6), 1551-1566.

 [8] Galloway, D. L., & Hoffmann, J. (2007). The application of satellite differential SAR interferometry-derived ground displacements in hydrogeology. Hydrogeology Journal, 15(1), 133-154.

[9] Zebker, H. A., & Goldstein, R. M. (1986). Topographic mapping from interferometric synthetic aperture radar observations. Journal of Geophysical Research: Solid Earth (1978–2012), 91(B5), 4993-4999.

[10] Farr, T. G., Rosen, P. A., Caro, E., Crippen, R., Duren, R., Hensley, S., ... & Alsdorf, D. (2007). The shuttle radar topography mission. Reviews of geophysics, 45(2).

[11] Berardino, P., Fornaro, G., Lanari, R., & Sansosti, E. (2002). A new algorithm for surface deformation monitoring based on small baseline differential SAR interferograms. Geoscience and Remote Sensing, IEEE Transactions on,40(11), 2375- 2383.

[12] Ferretti, A., Prati, C., & Rocca, F. (2001). Permanent scatterers in SAR interferometry. Geoscience and Remote Sensing, IEEE Transactions on, 39(1), 8-20.

[13] Hooper, A., Zebker, H., Segall, P., & Kampes, B. (2004). A new method for measuring deformation on volcanoes and other natural terrains using InSAR persistent scatterers. Geophysical research letters, 31(23).

[14] Zebker, H., Hensley, S., Shanker, P., & Wortham, C. (2010). Geodetically accurate InSAR data processor. Geoscience and Remote Sensing, IEEE Transactions on, 48(12), 4309-4321.

Introduction

Closure phase deviations are fundamental phase inconsistencies arising in SAR interferometric stacks when multi-looking is applied to the interferograms. Besides challenging simple interpretation and retrieval of the interferometric phase history, they seem to contain information on the propagation in semi-transparent dielectrics which could find application in moisture monitoring and vegetation growth. In general phase inconsistencies signal the presence of two or more scattering mechanisms with different phase evolutions. Satisfactory and sound physical interpretation of the observation of closure phases remains a research subject.

In order to shed more light into this poorly understood effect, we are currently investigating different datasets at the phenomenological level. In this work, we collect evidence to show possible polarimetric effects, seasonal effects, and wavelength dependencies. ALOS-2 and Sentinel-1 are ideal tools to explore closure-phase effects, in particular to their high coherence over vegetated targets.

Dependencies with polarimetry

Preliminary results demonstrate that changing the polarimetric basis can have a modulatory effect on the closure phase. This is observed in an L-band dataset acquired by ALOS-2 over Japan. These first results indicate that the Pauli 3 component is more subject to closure phase deviations relative to the Pauli 1 component, suggesting an influence of vegetation. Polarimetry shows thus some capability in separating the mechanisms that generate phase inconsistencies, though no polarization will in general yield perfect consistency. The relation with polarimetric entropy is under investigation.

Dependency with season

Seasonal observations are now possible with Sentinel-1 data, since many stacks have now reached two year temporal span. Clear seasonal dependencies are observed in a Sentinel-1 dataset over Mexico, where dry winters and wet summers clearly show up in the average closure phase for consecutive acquisitions. These observations support the idea that water status is the main driver for closure phase, especially in modern datasets where the baseline component is kept under strict control, and rule out pure volumetric-geometric effects.

Analysis of the discrepancy between 12 day and 24 day interferograms reveal that the potential reconstruction drift in the phase history is in the order of >1 cm/year: a relevant limitation to InSAR analyses over distributed targets.

Dependency with wavelength

In general phase closures have been observed at frequencies ranging from P to X-band, but for entirely different datasets. We now plan to compare different frequencies over the same area and time span, by analyzing Sentinel-1 data and ALOS-2 data together. Depending on the coupling between propagation and attenuation of the electromagnetic wave, closure phases are expected to show more or less wavelength dependency.

Modelling closure phase evolution

A key parameter to characterize dielectrics is the tangent loss, i.e. the ratio between the imaginary part and the real part of the dielectric constant. Assuming that the tangent loss is constant while the moisture content of soils or woods varies in time, a small tangent loss allows for large phase evolution with a small change in the power balance between different scattering mechanisms or scattering surfaces. Large tangent losses instead cause a rapid change in the attenuation and consequently fast decorrelation, as different scatterers or surfaces suddenly appear or disappear. Values of the tangent loss appropriate for wood are compatible with the observations, though it has not been possible yet to invert a physical model.

Acknowledgement

The authors acknowledge ESA and JAXA for Sentinel-1 and ALOS-2 data (PI1118 of RA-4 and proposal PI3009 of RA-6)

Additional material and references

Some figures showing sesonal effects and polarimetric effects on closure phases are to be found in the attached pdf.

[1] De Zan, F., Zonno, M. and Lopez-Dekker, P. "Phase inconsistencies and multiple scattering in SAR interferometry", IEEE Trans. Geosci. Remote Sens., vol. 53, no. 12, pp. 6608-6616, Dec. 2015.

[2] S. Zwieback et al., "A Statistical Test of Phase Closure to Detect Influences on DInSAR Deformation Estimates Besides Displacements and Decorrelation Noise: Two Case Studies in High-Latitude Regions," in IEEE Transactions on Geoscience and Remote Sensing, vol. 54, no. 9, pp. 5588-5601, Sept. 2016.

[3] McDonald, K., Zimmermann, R. and Kimball, J., "Diurnal and spatial variation of xylem dielectric constant in Norway Spruce (Picea abies [L.] Karst.) as related to microclimate, xylem sap flow, and xylem chemistry," Transactions on Geoscience and Remote Sensing, vol. 40 (9), pp. 2063-2082, Sep 2002.

[4] De Zan, F., Parizzi A., Prats-Iraola, P. and Lopez-Dekker, P., "A SAR interferometric model for soil moisture", Transactions on Geoscience and Remote Sensing, vol. 52 (1), pp. 418-425, Jan 2014.

Interferometric techniques for the retrieval of surface topography and surface movement are well understood. After appropriate image pre-processing, the interferometric phase is associated only with the parameter to be retrieved from the imagery. Over soils, this phase is classically considered to arise as a return from a fixed surface which can be regarded as impenetrable. Although there may be tacit recognition that the signal may be a combination of surface and sub-surface returns, the relative contributions are considered static.

Recent work, however, has identified a clear sensitivity of interferometric phase to soil moisture. The sensitivity can arise from both physical movement of the soil surface horizon and the dielectric contrast. Clay soils can be expected to show heave and slump in response to varying moisture, whereas sandy soils likely show little shrink or swell. Phase sensitivities from all soil types can be expected to have contributions from both the surface and sub-surface. For moderate moisture contents (>10%) the large dielectric contrast at the air/surface interface leads to a strong surface return. Sub-surface returns are heavily attenuated by the level of moisture in the volume. This phase signature is typically characterised by a dominant surface return slowly varying at a rate of several degrees per percent moisture change. As moisture content lowers, however, there can be an increasing volume return. The size of the sub-surface return depends upon the types of scattering features present in the volume. The source of these scattering centres is still open to question, but is associated with discontinuities in the volume such as rocks, air pockets, and layer boundaries. Subtle differences in the distributions and populations of these scatterers can produce markedly different phase histories.

Thus, at the very least, the moisture-phase sensitivity represents a noise term in conventional interferometric retrievals. In some observation scenarios it seems likely that the soil moisture phase may significantly distort the phase term, leading to erroneous retrievals of scene parameters. The presentation will provide results of laboratory and modelling studies which detail how the phase response of soils to moisture arises, identifying the components of the signal, and understanding how it impacts on conventional interferometric satellite applications.

In time-series InSAR approaches exploiting multi-master stacks of interferograms (targeting mainly distributed scatterers), one of the key steps is a process called phase linking, phase triangulation, or equivalent single master phase estimation. This step is applied in order to estimate, for each pixel, an equivalent single-master (ESM) phase time-series from multi-master interferometric phases, preserving useful information and filtering noise. In principle, this estimation can be applied either after phase unwrapping, or before unwrapping.

A fundamental assumption common to all the existing methodologies is the principle of phase consistency. This means that out of the phases of N(N-1)/2 interferograms that can be formed out of N Single Look Complex (SLC) images, only N-1 are linearly independent. Although phase consistency does not hold for multilooked data, the general assumption made (whether implicit or explicit) is that inconsistencies are purely induced by random noise. In fact, the purpose of applying the ESM-phase estimation is to estimate a set of consistent interferometric phases (i.e. where phase consistency holds for every combination of three interferograms) from a stack of inconsistent multilooked interferograms.

However, recently it has been shown that there are also some mechanisms that can induce systematic phase inconsistencies, for example due to the variation in the soil moisture. The existence of such inconsistencies raises the question regarding the extent to which they affect the phase estimators. In other words, what would happen to the soil moisture effect by postulation/constraining the phase consistency in the estimation process? Is this effect filtered out, or may it leak into the final estimated phases?

Here, we evaluate and compare the sensitivity of different phase estimators (e.g., maximum likelihood estimator, integer least squares estimator, eigendecomposition-based methods, and least circular variance estimator) to the soil moisture inconsistencies via a simple simulation scenario based on an analytical model. We demonstrate the methods over pasture and agricultural areas in the Netherlands, and we discuss the implication of the observed soil moisture effects for applications in deformation monitoring.

2.01.b InSAR Theory