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**SAR Interferometry (InSAR): principles**

INGV SAR Interferometry (InSAR): principles Salvatore Stramondo Antonio Montuori Istituto Nazionale di Geofisica e Vulcanologia Corso presso Univ. della Calabria 10/04/2017

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**Summary Interferometry SAR Interferometry (InSAR) technique: theory.**

Differential InSAR (DInSAR): general aspects. Multi-Temporal DInSAR techniques: SBAS & PSI Corso presso Univ. della Calabria 10/04/2017

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Interferometry Interferometry refers to a family of techniques in which electromagnetic waves are coherently combined in order to extract information about the waves. An instrument used to interfere waves is called an interferometer. Interferometry is an important investigative technique in the fields of astronomy, fiber optics, engineering metrology, optical metrology, oceanography, seismology, quantum mechanics, nuclear and particle physics, plasma physics, remote sensing and biomolecular interactions. Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR)**

InSAR technique is a powerful tool to retrieve the position and/or the displacement of surface point scatterers through the pixel-to-pixel phase difference processing of couple SAR images acquired over the same scene viewed from comparable well-known acquisition geometries. We call interferogram the image of the pixel to pixel phase differences. An interferogram is a complex image with (a) magnitude given by the product of the SAR amplitudes and (b) phase (the InSAR phase) given by the path length difference, as well as variations of the scattering properties and the medium conditions. Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR)**

The recorded phase is composed by two terms: the propagation phase, relevant to the sensor-to-target distance the backscattered phase, due to the surface backscattering The backscattered phase is obtained as the sum of the phase contribution of each scatterer within the resolution cell on the plane perpendicular to the satellite LOS Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR)**

baseline Bn Bp Two radar antennas mounted on board of two satellite-based SARs (1 and 2) observe a target with a slight separation in space (the interferometric spatial baseline). Bp is the parallel spatial baseline Bn is the parallel spatial baseline If the two images are acquired simultaneously single-pass interferometry If the two images are acquired at different times repeat-pass interferometry Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR)**

Along-track InSAR mode: The two SAR antennas are along-track aligned and acquire the scattered electromagnetic field at slightly different times. This mode is exploited to estimate the sea surface spectrum. This mode is obviously operated in a single-pass. Across-track InSAR mode: The two SAR antennas are aligned across-track. This mode can be operated both in single-pass and multi-pass configurations. This mode is used to estimate the Digital Elevation Model (DEM). Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR)**

SAR vs InSAR

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**SAR Interferometry (InSAR)**

Whenever the surface backscattering is unchanged (high coherence degree), the signal (S) received by the SAR from a target at distance R has an amplitude (A) related to the scattering strength of the target and a phase () related to the two-way traveling wave path between the radar and the target:

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**SAR Interferometry (InSAR)**

Be S1 and S2 the received signals at two satellite positions: The interferogram is the map of the pixel-to-pixel phase differences between S1 and S2: baseline Bn Bp Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR)**

The two complex SAR images must be coregistered by interpolating one image (the slave image) to generate imagery at the same pixel locations as the second (the master image). After registration, the two complex SAR images are multiplied, and the interferometric phase is obtained. Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR)**

The interferometric phase contains some distinct contributions: flat Earth topographic phase deformation phase atmospheric phase noise (error phase) Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR)**

Flat Earth Raw interferogram includes a quasi-linear phase trend caused by tilt of terrain surface relative to the baseline Flattening removes interferometric phase component using a sphere with radius of curvature derived from the ellipsoid. Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR) Flat Earth**

Unflattened interferogram Flattened interferogram Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR) Flat Earth**

Unflattened interferogram Flattened interferogram

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**SAR Interferometry (InSAR)**

Topographic phase The topographic phase contains the information relative to the relief. The spacing between the fringes depends on the perpendicular baseline: the longer the perpendicular baseline, the narrower the fringes B=174 m B=40 m Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR)**

Topographic phase Baseline doubling Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR)**

Topographic phase The ambiguity height is the elevation difference corresponding to a full phase cycle (2): ERS satellites: Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR)**

Phase ambiguity The interferometric phase is generally modulus 2p. A phase unwrapping method can be then applied to calculate the exact phase value in order to extract correct information about the scene (the elevation). Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR)**

Phase ambiguity The interferometric phase component is known save for 2Np: Phase unwrapping algorithms can be applied to retrieve from the “wrapped phase” : Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR)**

Phase ambiguity Branch-cut region growing algorithm: it is based on the identification of branches linking the areas with phase continuities. It is typically applied to the filtered interferograms. Critical areas, such as areas of very low coherence or residues, are identified and avoided in the phase unwrapping. Minimum Cost Flow (MCF) techniques and Triangular Irregular Network (TIN): global optimization technique to the phase unwrapping problem (for example at locations of very low coherence) which provides high density of unwrapped points together with an efficient and robust unwrapping Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR)**

Phase ambiguity Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR) From SAR raw data to Interferogram**

Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR)**

Atmospheric phase Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR)**

Atmospheric phase The phase due to atmospheric artifacts does not depend on the baseline and its sensitivity to the atmosphere is related to the wavelength (Longer wavelengths are less sensitive to atmospheric distortions). A propagation delay (Dl) of 2cm would result in an additional phase of an almost full fringe at C-band but only of 1/6th of a fringe at L-band. In case of stronger delays, the spatial phase variations might be so large that at higher frequencies phase unwrapping could fail because of more cycles being wrapped. Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR)**

Tropospheric effects Interferogram B perp. =5 m B temp.=55gg SAR ERS intensity image of the Apennine Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR)**

Complex coherence The degree of correlation between two SAR images is measured by the coherence parameter. The amplitude is the degree of coherence, the phase is the interferometric phase. Coherence is a measure of the phase noise or fringe visibility Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR)**

Complex coherence Interferometric phase Coherence Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR)**

Complex coherence The spatial coherence can be filtered out. A part remains if we have a volume (forest, snow, city). This is called volume decorrelation and increases with the spatial baseline. The temporal coherence can NOT be filtered out, it is a property of the image. This is also referred to as temporal decorrelation term and depends on the stability of the objects between the two acquisitions. Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR)**

Complex coherence Geometric decorrelation: it relies on the sight angle differences of the two SAR scenes part of the interferogram. The critical value of the baseline at which complete decorrelation occurs is given by: For ERS and ENVISAT the critical baseline is about 1100 m (R=850 km, =23º, Lc=25m, =5.6 cm). For JERS-1 and PALSAR the critical baseline is about 4 km (R=730 km, =35º, Lc=25m, =23 cm). Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR)**

Complex coherence Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR)**

Complex coherence The two SAR antennas see the scene under slightly different angles, hence they record different parts of the image spectrum shifted by an amount f. Spectrum1 Spectrum2 If the spectrum shif is equal to the critical one (see the formula above), they automatically loose part of the correlation they have (spatial decorrelation). Spectral shift filtering removes the effect of spatial decorrelation for level surfaces. There is a proportional loss of range resolution. Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR)**

Complex coherence In the repeat-pass configuration the scatterers may move (e.g. water surfaces and tree canopies) or their dielectric properties may change (e.g. snow, wet soils) between observations. The two SAR images are only partially correlated because of the temporal interval between the acquisitions. In general it is likely that the longer the time interval between acquisitions, the stronger the temporal decorrelation. Taking into account that typically temporally unstable scatterers have dimensions of the order of a few centimeters or less (e.g. leaves, grass, snow grains etc.), temporal decorrelation is more pronounced at shorter wavelengths (e.g. at X- and C-band). Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR) Spatial decorrelation effects**

06/02/ /05/ Baseline ort. = 330 m 22/05/ /12/1997 Baseline ort. = 40 m Corso presso Univ. della Calabria 10/04/2017

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**SAR Interferometry (InSAR) Temporal decorrelation effects**

07/05/ /05/ Baseline temp. = 1 day 02/06/ /02/2002 Baseline temp. = 980 days Baseline ort. = 3 m Corso presso Univ. della Calabria 10/04/2017

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**Differential SAR Interferometry (DInSAR)**

Differential SAR Interferometry (DInSAR) is an InSAR technique addressed to measure the Earth surface displacements with centimetric accuracy. DInSAR is used in seismology, for instance, when an earthquake takes place. Two SAR images, one pre-seismic and one post-seismic, are acquired. The interferometric phase is computed. Using a DEM, the topographic phase is canceled. The residual phase contains also the eventual surface deformation effect (differential interferogram). Each differential fringe corresponds to a full phase cycle (2p) and represents a sensor-to-target distance change (LOS change) of l/2. For C-Band sensors it is about 2.8 cm. Corso presso Univ. della Calabria 10/04/2017

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**Differential SAR Interferometry (DInSAR)**

Be S1 and S2 two SAR satellites. The interferometric phase is: The residual phase contains, besides atmosphere and Noise phase component, the displacement projected onto the LOS. Corso presso Univ. della Calabria 10/04/2017

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**Differential SAR Interferometry (DInSAR)**

Objective of DInSAR: Separation of topo from total phase to determine displ 2-pass: Simulate topo based on existing DEM. Phase unwrapping not required for the simulated interferogram. High accuracy of DEM required. 3- and 4-pass: Derive topo from independent interferogram, no existing DEM is required but phase unwrapping required. The combination of complex interferograms may be of interest to do a kind of differential interferometry without phase unwrapping and geocoding requirement to improve the sensitivity to topography. Corso presso Univ. della Calabria 10/04/2017

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**Differential SAR Interferometry (DInSAR)**

Consider a standard deviation on phase and displacement: For ERS: Corso presso Univ. della Calabria 10/04/2017

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**Differential SAR Interferometry (DInSAR) Multi-Temporal DInSAR**

In conclusion... InSAR Configurations Along-Track InSAR (∆t = ms to s) Across-Track InSAR (∆θ) DInSAR (∆t = giorni - anni) Multi-Temporal DInSAR Field of Application Oceanic current & Target detection Digital Elevation Model (DEM) Surface deformation velocity maps Surface time-series and deformation velocity maps Corso presso Univ. della Calabria 10/04/2017

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**Principi di base – Interferometria SAR**

Evolution of Satellite-based DInSAR: Multi-temporal DInSAR Time series and deformation velocity maps of observed surface. Main Multi-Temporal DInSAR Techniques “Small BAseline Subset (SBAS)” Super-Master reference SAR image Different subsets of SAR images “Small” spatial and temporal baselines “Linking” among SAR subsets Reference Scatter points with high interferometric coherence values Poor spatial resolution

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**Principi di base – Interferometria SAR**

Evolution of Satellite-based DInSAR: Multi-temporal DInSAR Time series and deformation velocity maps of observed surface. Main Multi-Temporal DInSAR Techniques “Persistent Scatterers Interferometry (PSI)” Unique “Reference master” SAR “Large” spatial and temporal baselines Scatter points smaller than resolution cell dimensions Persistent scatter points (stability in terms of SAR amplitude) High spatial resolution

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