However, since the proportionality holds on the phases and not on their principal values apart from the special case of an integer ratio between the baselines , the fringes obtained from the couple must be first unwrapped and then scaled. Other very important results on the use of this technique for studies of volcano deflation Etna or glacier motion can be found in [ 11 , 8 ]. Atmospheric Effects In repeated pass SAR interferometry from satellite, different propagation velocities along the scene due to atmospheric changes at the time of the two surveys could be responsible of interferometric phase variations that cannot be related either to the topography or to relative terrain motions[ 25 , 20 ].
Multibaseline techniques can be usefully exploited to get a DEM that is less affected by artifacts by averaging the uncorrelated atmospheric contributions coming from the single interferograms [ 3 ]. When the ML DEM is generated it is possible to get the phase difference with respect to each interferogram. These phase residues are proportional to atmospheric changes.
Vesuvius [ 3 ]. Orbits number, dates and normal baselines are summarized in Table 2. As an example the phase residues obtained by subtracting the combined DEM from the April, July and August interferograms of the Vesuvius data set are shown in Figure 6 , Figure 7 and Figure 8.
Figure 6: Vesuvius. Differential interferogram generated subtracting the estimated DEM from the April Tandem interferogram. The normal baseline is m. Figure 7: Vesuvius. Differential interferogram generated subtracting the estimated DEM from the July Tandem interferogram. The normal baseline is 39 m. Figure 8: Vesuvius. Differential interferogram generated subtracting the estimated DEM from the August Tandem interferogram.
The normal baseline is 57 m. The phase variations about one fringe peak to peak with very low spatial frequency more than one kilometer in both directions visible in the figure are generated by atmosphere changes within the surveys.
These effects appear to be the major limitation to the use of SAR interferometry as a technique for generating highly accurate Digital Elevation Models and for detecting small surface deformations. However, the interferometric phase depends on the relative elevation through a coefficient that is directly proportional to the baseline see equation 0.
On the other hand, the phase variations due to atmospheric changes are independent of the baseline. Thus, the higher is the baseline of the interferometric pair the smaller is the topographic error due to parasitic effects. Moreover, if many interferometric pairs of the same area are available, ''outliers'' can be identified and eliminated from the database.
The remaining results can be combined to ''filter out'' the effects of atmospheric changes. An example of outliers identification is shown in Figure 9. Figure 9: Example of atmospheric outliers. Low-pass filtering the differential interferogram that contains low frequency signal plus white spectrum noise, allows us to extract useful information. An example is shown in Figure Figure Etna 36 days interferogram. The topographic contribution has been compensated for and low frequency phase distortions are visible.
Coherence The quality of the interferometric phase depends on the amount of noise that, in general, comes from distinct sources [ 14 , 18 ]: i- system noise; ii- terrain change non simultaneous acquisitions ; iii- images misregistration; iv- approximate and unequal focusing of the two passes; v- decorrelation due to the baseline ''geometric'' decorrelation.
It is obvious that there is no way to avoid the first two sources of noise. On the other hand, as far as the last three sources are concerned, they can be taken under control. In other words, since in most cases the system noise is quite small compared with the usually sensed signals, and the processor noise is well under control if it is designed to be phase preserving [ 14 ], it can be seen that the fringes quality is degraded by scattering change in time and volumetric effects only.
The coherence of two complex SAR images and , is defined as follows [ 16 ]: where E[. The absolute value of is a fundamental information on the exploitability of SAR interferograms.
The signal usable fringes to noise ratio can be usefully expressed as a function of the coherence: Thus, it is clear that every effort should be dedicated to avoid coherence loss during the interferogram generation process.
The statistical confidence of the estimated coherence sampled coherence and of the derived measurements, depends on the number of independent samples n that can be combined for the computation. As a first approximation, the standard deviation of the estimator is proportional to. Thus, whenever uniform areas in the statistical sense are identified, the sampled coherence can be computed as: In fact, since the coherence is estimated from the combination of the phases of a few pixels at the very least, the topography effects on the interferometric phase proportional to the known terrain changes have to be removed from the result.
Thus, in order to compensate this unwanted effect, the vectors at the numerator of equation 0. It is also clear that, in order to generate an interferogram, the pixels of the images gathered in the two different images must be registered accurately, so that the random variates corresponding to the reflectivity are properly aligned. A single pixel shift, if the focusing processor is a good one, is enough to practically zero the correlation. In the following we will not consider the effects due to misregistration and system noise, since they can be avoided with a good system or with a proper processing.
The elevation error of maps generated by means of SAR interferometry will follow the value of as: As an example, the coherence map of the area of Mt. Figure Coherence map of Mt. Multi-Interferogram Coherence Maps A multi-interferogram approach can be usefully exploited to estimate the coherence using an ensemble average instead of a space one. When a good DEM is available with the same resolution of the SAR images, it is in fact possible to combine all the data to compute a multi-baseline coherence map of the area of interest on a fine spatial resolution: the increased number of freedom degrees due to multiple interferograms allows to get high resolution products say 20 20 m.
First the topographic contribution on the phases of each interferogram is compensated for using the DEM. Then the phases are high-pass filtered to eliminate local distortions due to atmospheric effects. Finally the mean phase value is subtracted in each interferogram so that all the data can be considered phase aligned.
The estimation is then straightforward: where is the standard space average on the i - th interferogram this time using a small estimation window. The achieved coherence map highlights what remains unchanged during the time interval between the first and the last acquisition and could be exploited for image segmentation and classification; it gives a measure of SNR on a fine spatial resolution.
Applications to image segmentation SAR coherence is an additional source of information with noticeable diagnostic power. In the following we shall enumerate some of the most relevant applications.
In [ 12 ] it was first observed that forests, that appeared with variable reflectivity in the ERS - 1 detected images, appeared almost black in the coherence images: this effect is due to the scarce penetration of C band radiation in the vegetated canopy, so that small variations of the positions of leaves and smaller branches were enough to change the disposition of the scatterers and therefore practically annihilate coherence; likewise happens for water bodies, that appear always with negligible coherence.
In [ 17 , 23 , 22 ] it was also observed that cultivated field changed their coherence after plowing, harvesting etc. In general, the combination of multitemporal observation both of detected images and coherence allows a very good segmentation of agricultural areas; it is thus possible to identify cultures potatoes are harvested in that month, whereas corn matures in that other..
Other authors [ 21 ] observe that from the phase of the interferometric takes the height of the trees and therefore the biomass can be estimated. Conclusions In this overview, we have seen that interferometry is speckle free, since its effect disappears from the differential phase. Oil spills are much easier to detect and definitions of nature such as the above Volcano Fagradalsfjall with its fissures and sculpted cones come up brilliantly.
Road systems, buildings and boats are very easy to identify with SAR. To put it simply, it is a type of mapping technique for ground movement through the use of SAR. The technique requires two or more precise SAR images taken at different times. If there has been any surface movement, then what is known as a phase shift occurs, where these are measured and recorded via an interferogram.
Lets take it back to the volcano and look at this image below to see what we mean by interferogram. This image sure is colourful, but this is how InSAR data is displayed. Each of the colours represent a value of depth to reveal surface movement resulting from the phase shifts. InSAR is a highly accurate land deformation detection technique and is great for many applications. Imagine monitoring urban developments. I mean… Leaning Tower of Pisa much? Construction, town planning, transportation, mining, oil and gas industries can all benefit from the brilliance of InSAR.
Natural occurrences like detecting landslides or identifying tectonic deformations are core founding use cases of InSAR. The technology is advancing all the time with new imaging equipment.
The satellite is side-looking, orbits the Earth at an altitude of approximately miles kilometers , and has day repeat cycles. Illustration by the European Space Agency. InSAR is ideally suited to measure the spatial extent and magnitude of surface deformation associated with fluid extraction and natural hazards earthquakes, volcanoes, landslides. It is often less expensive than obtaining sparse point measurements from labor-intensive spirit-leveling and global positioning system GPS surveys, and can provide millions of data points in a region about 10, square kilometers.
By identifying specific areas of deformation within broader regions of interest, InSAR imagery can also be used to better position specialized instrumentation such as extensometers, GPS networks, and leveling lines designed to precisely measure and monitor surface deformation over limited areas.
Satellites are an integral part of InSAR. In March , the European Space Agency ESA launched Envisat, an advanced polar-orbiting Earth observation satellite which provides measurements of the atmosphere, ocean, land, and ice.
The Envisat satellite has an ambitious and innovative payload that will ensure the continuity of the data measurements of its predecessor, the ESA European Remote Sensing ERS satellites. Envisat data supports earth science research and allows monitoring of the evolution of environmental and climatic changes. Furthermore, the data will facilitate the development of operational and commercial applications.
Description and illustration courtesy of the European Space Agency. Interferograms are maps of relative ground-surface change that are constructed from InSAR data to help scientists understand how tectonic or human activities, such as groundwater pumping and hydrocarbon production, cause the land surface to uplift or subside.
Interferograms require 2 images taken at intervals in time to determine if there has been any shift in land surface levels. If the ground has moved away from subsidence or towards uplift the satellite between the times of the two SAR images, a slightly different portion of the wavelength is reflected back to the satellite resulting in a measurable phase shift that is proportional to displacement. The map of phase shifts, or interferogram, is depicted with a repeating color scale that shows relative displacement between the first and the second acquisitions.
The direction of displacement - subsidence or uplift - is indicated by sequence of the color progression of the fringe s toward the center of a deforming feature. Reading an interferogram isn't as complicated as it might seem. The process can be broken down into a few steps:. In this illustration, two InSAR fringes are equal to 56 mm of deformation.
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