Technique

Technology Evolution: InSAR, DInSAR and PSInSAR™

From radar image to deformation map.

This section describes the theory behind interferograms and the evolution of the algorithms that led to the advanced algorithm PSInSAR™ - an algorithm capable of extracting the temporal evolution of ground deformation.

The latest SqueeSAR™ algorithm has superseded these techniques is described in the following section.

InSAR: Interferometric Synthetic Aperture Radar

Interferometry

Interferometric Synthetic Aperture Radar (InSAR), also referred to as SAR Interferometry, is the measurement of signal phase change, or interference, over time.

When a point on the ground moves, the distance between the sensor and the point on the ground also changes and so the phase value recorded by a SAR sensor flying along a fixed orbit will be affected, too. Figure 1 shows the relationship between that ground movement and the corresponding shift in signal phase between two SAR signals acquired over the same area.

The change in signal phase (Δφ) can be expressed in the form of the following simple equation:

Where λ is the wavelength, ΔR is the displacement and a is a phase shift due to different atmospheric conditions at the time of the two radar acquisitions. As a consequence, any displacement of a radar target along the satellite line of sight creates a phase shift in the radar signal that can be detected by comparing the phase values of two SAR images acquired at different times.

Apart from decorrelation effects, to be discussed in the next sections, SAR interferometry can only be applied in the following circumstances:

Images have to be acquired by the same satellite using the same acquisition mode and properties (beam, polarization, off-nadir angle, etc).
Images have to be acquired with the satellite in the same nominal orbit.
The baseline separation between the master scene and any of the slave scenes must be no more than the ‘critical baseline’ (a parameter that varies with the SAR sensor in use); the baseline being the distance between the satellite paths.

Figure 1

Interferograms

An interferogram is the difference of the phase values corresponding to a certain area, i.e. it is a digital representation of change in surface characterization. It is a matrix of numerical values ranging from –π to +π (as they correspond to phase variations) and it can be converted to a map – the easiest way to observe whether or not motion has occurred over a certain area.

Figure 2 is an interferogram of the L’Aquila earthquake that occurred in Italy, in April 2009. The colored bands, referred to as fringes, indicate areas where movement can be measured. The highly speckled areas indicate where some form of decorrelation arose. Here the noise level (mostly due to vegetation) prevents the application of InSAR and no useful information can be extracted. Data were acquired by the Envisat satellite for which one phase cycle corresponds to 28mm of ground deformation along the line of sight (neglecting atmospheric effects).

The analysis of a SAR interferogram is not a trivial task to perform for non-specialists. Apart from noise and decorrelation effects, interferometric phase values are a blend of different signal contributions, as will be discussed in the next section.

Figure 2

Phase Signal Contributions

Interferometric phase (Δφ) is impacted by four contributions:

topographic distortions arising from slightly different viewing angles of the two satellite passes (t)
atmospheric effects (α) arising from the wavelength distortion that occurs when signals enter and leave a moisture-bearing layer
any range (distance between the sensor and the target) displacement of the radar target (∆R)
noise

These factors, expressed more precisely, are given in the equation below:

It is clear that the difficulties related to the estimation of surface deformation signals from a single SAR interferogram are essentially due to the presence of decorrelation effects (contributing to the noise level), the impact of local topography on phase values and the presence of atmospheric phase components superimposed on the signal of interest. In Figure 2, most of the fringes visible in the interferogram are due to co-seismic deformation induced by the earthquake: in fact, the impact of the local topography has been removed and atmospheric disturbances are not evident in this image.

Coherence

Interferometric fringes can only be observed where image coherence prevails. When an area on the ground appears to have the same surface characterization in all images under analysis, the images are said to be coherent. If the land surface is disturbed between two acquisitions (e.g. an agricultural field has been ploughed, tree leaves have moved positions, etc.), those sub-areas will decorrelate in an InSAR analysis, resulting in noise and no information being obtainable. Coherence and correlation have the same meaning in this context. The term ‘noise’ is frequently used in this context and it is another word for non-coherence, or decorrelation. The fringes visible in Figure 2 reveal areas with high coherence while the speckled areas represent very low coherence and noise.

The coherence of an interferogram is affected by several factors, including:

Topographic slope angle and orientation (steep slopes lead to low coherence)
Terrain properties
The time between image acquisitions (the longer the time interval the lower the coherence)
The distance between the satellite tracks during the first and second acquisitions, also referred to as the baseline (larger baselines lead to lower coherence)

Typical sources of decorrelation are:

Vegetation: leaves grow and die and they also move. From one scene to the next, these changes are sufficient to change the appearance of the surface characterization. This is a particular problem for X-band and C-band sensors. L-band sensors can overcome this limitation in many situations, because their significantly longer wavelength is able to ‘see’ through foliage and reflect off objects beneath the vegetation and back through the foliage.
Construction: at a construction site, the appearance of the land surface is changing constantly. This can a problem that is common to X-band, C-band, and L-band sensors.
Erosion: whether prompted by rain, snowmelt or wind, surface erosion will also change the surface characterization of land and, thereby, can decorrelate those areas where erosion is prevalent.
Rapid movement: landslides and earthquakes precipitate rapid motion of an area of land. Quite often, the rapid motion causes destruction and, with it, a total change in the land surface appearance. With earthquakes, it is sometimes possible for rapid motion to occur without changes to surface characterization and, in those situations, interferometry can be successful. If the total movement occurring between successive image acquisitions exceeds one-half of the signal wavelength, decorrelation is likely to occur.

Coherence is measured by an index ranging from 0 to 1. When an area is completely coherent, it has a coherence value of 1. Correspondingly, if an area completely decorrelates, its coherence index is 0. In general, interferometry is successful and accurate deformation is measurable when the coherence index lies between 0.5 and 1.0. Interferometry can still produce meaningful results with coherence levels below 0.5 but as the index gets lower, so the results will display increasing levels of noise and may show erratic deformation patterns from scene to scene, although movement trends are visible and generally reliable.

Wherever fringes occur, it is possible to calculate deformation by calculating the number of fringes and multiplying them by half of the wavelength. In the case of L’Aquila, C-band SAR was used and therefore each fringe should be multiplied by 28mm (one-half of the wavelength) to calculate the total apparent displacement.

DInSAR: Differential InSAR

Analyzing a Pair of SAR Images

When a pair of images is subject to interferometric analysis with a view to identifying movement and, thereafter, quantifying that movement, the process is referred to as Differential InSAR (or DInSAR). Since change detection is the goal, topographic effects are compensated for by using a Digital Elevation Model (DEM) of the area of interest, creating what is referred to as a differential interferogram (the word ‘differential’ here refers to the subtraction of the topographic phase contribution from the SAR interferogram). This can be expressed as:

Where ε is the contribution to phase arising from possible errors in the DEM that was used to remove the topographic effects.

Whenever noise levels are low (i.e. decorrelation effects are negligible) and the phase contribution due to the local topography is accurately compensated for (i.e. ε is also negligible), the interferometric phase can be simplified as follows:

Where Δφ is the differential interferometric phase, ΔR is the incremental distance the signal travels from the sensor to the ground and back and α is the atmospheric contribution to phase shift.

Once a differential interferogram has been prepared, a deformation map can be created for all areas that are coherent, as shown in Figure 3.

In the mid-90’s, after extensive application of the DInSAR technology, the atmospheric contribution to phase shift was found to be significant, particularly in tropical and temperate areas. Unfortunately, with differential interferometry, it is not possible to removing the α component and users should be aware of their effects.

Thus, DInSAR should only be used on the understanding that deformation measurements are prone to errors arising from atmospheric circumstances. However, although DInSAR may not be the tool for accurate displacement measurements, it is still useful in identifying footprints of progressing movement. It can only measure total displacement between two points in time. Accordingly, it cannot distinguish between linear and non-linear motion.

Figure 3

Interferogram Stacking

Following the realization that atmospheric effects on signal phase values were significant, a method emerged in the late 1990’s that sought to mitigate this effect by ‘averaging’ data within multiple interferograms. This process was referred to as Interferogram Stacking.

By averaging the data in a stack of interferograms, the signal to noise ratio (SNR) values are enhanced and, theoretically, it is easier to extract information on displacement over longer periods of time than are realistic for single interferogram DInSAR.

However, for this process to be successful, certain assumptions are made:

Although different versions of this technique exist, the displacement rate of the area of interest is assumed to be constant in time. In reality, such an assumption has limited validity. Multiple interferograms usually describe ground movement over time lines measured in years. Apart from tectonic deformation, linear movement over such time periods is not common.
The data are heavily filtered, spatially, before the stacking procedure is implemented. Not only does this reduce the resolution but also prompts the loss of potentially valuable data contained in ‘isolated’ pixels with high SNR values, and it also smoothes out abrupt changes in displacement, e.g. seismic faults.
The atmospheric contribution to signal phase is not estimated. Thereby, no assessment is possible on the quality of the filtering procedure. Atmospheric disturbances are characterized by specific statistical features, and the separation of motion and atmospheric phase components should take into account the peculiarities of the ‘noise’ to be filtered out.
Typically, stacking procedures are only applied using interferograms with an orbital baseline less than 300m, because of the spatial filtering. As a result, substantial quantities of information that can be found from within interferograms whose baselines are as high as 1300m are overlooked, the latter being a common baseline upper limit for PSI technologies.

While interferogram stacking provides the user with better information than can be obtained from single differential interferograms (DInSAR) the approach is far from optimal, particularly because deformation cannot be considered constant in time. Moreover, for the estimation of atmospheric noise, the procedure usually adopted to produce a weighted average, i.e. to assign different importance to different interferograms, is based on visual inspection of multiple interferograms.

Finally, as already mentioned, the estimation of errors is usually not performed.

PSInSAR™: Permanent Scatterer InSAR Technique

General Concept

Persistent Scatterer Interferometry (PSI) is the collective term used within the InSAR community to distinguish between single interferogram DInSAR and the second generation of InSAR technologies, of which there are but a few. The first of these to appear, in 1999, was the PS Technique™, the base algorithm of which is PSInSAR™. It is proprietary to the Politecnico di Milano (Polimi) and licensed exclusively to TRE for commercial development. TRE has no specific knowledge of the competing algorithms; however, in concept they are all likely to be similar in approach, although probably different in their analytical capability. The following description of PSI technology is based on the PSInSAR™ model.

All PSI technologies are advanced forms of DInSAR. In other words, the interferogram is at the core of PSI. The fundamental difference is that PSI technologies develop multiple interferograms from a stack of radar images. As a minimum, 15 radar scenes are usually required for PSI methods, including PSInSAR™, even though there are circumstances when an analysis can be conducted with fewer images (typically in urban areas). However, it should be noted that the more there are radar scenes available, the more accurate will be the results of PSInSAR™, and the same holds true for other PSI methods.

The main driver for the development of PSInSAR™ was the need to overcome the errors introduced into signal phase values by atmospheric artifacts. By examining multiple images, usually a minimum of 15 scenes, many interferograms (in this case 14 interferograms) are generated by selecting one of the scenes as a master to which the other 14 scenes become slaves.

The process by which removal of atmospheric effects is achieved involves searching the imagery and interferograms for pixels that display stable amplitude and coherent phase throughout every image of the data set. They are referred to as Permanent, or Persistent, Scatterers. Thus a sparse grid of point-like targets characterized by high signal to noise ratios (SNR) is identified across an area of interest on which the atmospheric correction procedure can be performed. Once these errors are removed, a history of motion can be created for each target.

Having removed the atmospheric artifacts, the interferometric data that remain are displacement values (resolved along the satellite LOS) plus noise, dependent on the quality (SNR) of the reflector.

Permanent Scatterers

A Permanent Scatterer (PS) is defined as a radar target, within a resolution cell, that displays stable amplitude properties and coherent signal phase, throughout all of the images within a data stack.

Sometimes a target may behave with a stable amplitude characteristic but its phase is erratic, or non-coherent. Further, some targets behave as if they are PS but only within a portion of the images within the data stack. Such targets are not PS.

Objects that make good PS are varied and can be natural or man-made. Among the natural forms are: rock outcrops, hard un-vegetated Earth surfaces and boulders. Among the man-made objects are: buildings, street lights, transmission towers, bridge parapets, above-ground pipelines, appurtenances on dams and roof structures, and any rectilinear structure that can create a dihedral signal reflection back to the satellite.

Figure 4 shows the results of a PSInSAR™ analysis over a landslide, Italy. The colored dots represent the location of a PS, the color reflecting the displacement rate measured at that point.

Figure 4

Calculating Displacement

All measurements are made in the satellite’s LOS radar beam and are relative to a point that is pre-selected as being stable and not moving (P0). The selection of the reference point is best made conjunctively with the client, the latter having better local knowledge on which sub-areas are stable within an area of interest (AOI).

Once the data have been analyzed, it is possible to develop the history of movement across the AOI. This is achieved by sequentially calculating the relative displacement between an individual radar target and the reference point, throughout the entire period of the analysis. Thus, the deformation is relative in time and space. A typical time series of movement of a single PS is shown in Figure 5.

It should be noted that the PSInSAR™ algorithm generates a standard deviation map for the AOI, as well as providing error bar data for each PS, within the data base.

A priori information is always helpful before commencing a PS analysis. If an area is known to be subsiding, then measurement can be satisfactorily made using a single viewing geometry, also referred to as ‘acquisition mode’. However, if the hazard is a landslide, where significant horizontal movement might occur, the use of data acquired by satellites in both the ascending and descending orbits will enable true vertical movement and the east-west component of horizontal movement to be computed.

At the present time, it is not possible to determine the horizontal component of movement in the north-south direction. However, research is underway to try to resolve this problem. Such computations will require the use of at least 3 data sets with differing viewing geometries and look angles.

Figure 5

Precision

Error bars of measurement of a PS are calculated as the deformation pattern is developed. However, precision of the displacement calculations is an important element in validating PS data. The most important factors impacting on data quality are:

Spatial density of the PS (the lower the density, the higher the error bar)
Quality of the radar targets (signal-to-noise ratio levels)
Climatic conditions at the time of the acquisitions
Distance between the measurement point (P) and the reference (P₀)

Comparable values for the satellites launched during 2007/8 are not yet available since the volume of data from these satellites that has been processed to date is still quite low. However, it is expected that precision will be improved because a) the sensors on the newer satellites are more sophisticated, and b) the resolution cell sizes are smaller than those of the earlier satellites.

The table below describes the precision values obtained from many analyses of data from the ERS, Envisat, and Radarsat-1 satellites. Typical values of precision (1σ) for a point less than 1 km from the reference point (P₀), considering a multi-year dataset of radar images.

Displacement (LOS)	Average Displacement Rate	Single Measurement
Precision (1σ)	< 1 mm / year	5 mm

Positioning	East-West	North-South	Height
Precision (1σ)	6 m	2 m	1.5 m