Ground-Based Interferometric radar systems with fast acquisition capabilities: assessment of their use for the monitoring of deformation processes of geological interest.

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Sistemi radar interferometrici da terra a sintesi elettronica:

definizioni dei vantaggi derivanti dal loro uso per il

monitoraggio di fenomeni deformativi di interesse

geologico.

Ground-‐Based Interferometric radar systems with fast acquisition capabilities: assessment of their use for the monitoring of deformation processes of geological

interest.

Tesi di dottorato di ricerca Dottorato Scienze della Terra

XXVIII Ciclo

Autore: Dario Tarchi

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Abstract

A new class of Radar interferometer, based on an electronically scanned array in MIMO configuration (MIMO-‐SAR) has been assessed for the operational use in the monitoring of phenomena of geological interest, such as landslides and unstable slopes. The new system is able to apply the very well-‐known and proven Ground Based Interferometric technique and may guarantee and unprecedented short refreshing time in comparison with traditional systems based on the mechanical movement of the radar transceiver on a rail or on the mechanical steering of a real antenna. This new feature can allow monitoring a number of phenomena having deformation rates too high to be correctly retreived by traditional systems currently in use. The implementation of a prototype, termed MELISSA, has been finalized and a full validation of the system in a controlled environment has been completed. A framework to assess in general terms all the different measurement parameters of a radar interferometer and how they relate and influence each other has been defined. This allowed identifying the advantages but also the expected limitations of the new system in comparison to existing instruments. Real cases where GB-‐InSAR is currently being applied have been first analysed to evaluate the possible advantages of using a similar system and then real experiments have been conducted on different sites including, the operational monitoring of the stability of the Costa Concordia wreck, the Vetto landslide and the Stromboli Volcano. The experimental results have been combined with the theoretical framework to provide the final assessment of the system and identify possible scenarios for its operational use. A reference design for the MIMO-‐SAR able to ensure about 125 images per second in a maximum range of about 500 m turns out to be fully validated. In this scenario the MIMO-‐SAR may acquire images with an unprecedented high rate while it is equivalent to existing system concerning other relevant measurement parameters. Over larger distances the MIMO-‐SAR system cannot actually maintain similar performances and the second recommended scenario is in support and combination with a traditional system to provide temporary close-‐in view over portions that exhibits an acceleration of the deformation rates. A third scenario concerning the provision of early warning is also defined. This is particularly tailored for situations where a fast evolving phenomenon may suddenly develop whitout clear precursors. Finally possible options to enhance the system are presented.

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Riassunto

Una nuova classe d’interferometri radar, basata su una schiera di antenne in configurazione MIMO (MIMO-‐SAR) e scansionate elettronicamente è stata valutata al fine di un suo uso per il monitoraggio di fenomeni d’interesse geologico quali frane e instabilità di versante. Il nuovo sistema è capace di applicare la ben nota e comprovata tecnica dell’interferometria radar con sensore basato a terra (GB-‐ InSAR) garantendo un tempo di ripresa della singola immagine molto breve in confronto a strumenti tradizionali basati sulla movimentazione meccanica del sensore radar su un binario o sulla scansione meccanica di un’antenna reale. Tale nuova capacità può consentire di monitorare fenomeni con dinamiche veloci che eccedono le possibilità dei sistemi tradizionali correntemente in uso. La realizzazione di un prototipo, denominato MELISSA, è stata completata attraverso l’effettuazione di una serie di test di validazione in laboratorio. In parallelo è stato definito un quadro generale per la valutazione delle prestazioni di un generico interferometro tenendo in conto i diversi parametri di misura e le principali interdipendenze fra essi. Questo ha consentito una valutazione preliminare delle prestazioni e dei possibili vantaggi attesi anche considerando esempi reali di monitoraggio effettuato con sensori GB-‐InSAR tradizionali. Esperimenti con il nuovo strumento sono stati quindi compiuti in una serie di siti con diverse e significative tipologie di fenomeno e che includono il monitoraggio del relitto della Costa Concordia all’isola del Giglio, la frana di Vetto e il vulcano Stromboli. I risultati ottenuti sono stati combinati con il complesso degli elementi precedentemente elaborati per fornire una valutazione finale del nuovo sistema ed identificare possibili scenari per il suo impiego. Utilizzando una configurazione base del sistema, precisamente descritta nel lavoro, è possibile eseguire, entro una distanza di ca. 500 m, monitoraggi operativi con risultati equivalenti a sistemi tradizionali ma con un numero di acquisizioni fino a 125 per secondo. Su distanze superiori il sistema non può, nella configurazione analizzata, mantenere le stesse prestazioni e l’uso suggerito è in combinazione e complemento a sistemi tradizionali allo scopo di monitorare temporaneamente aree specifiche che mostrino una dinamica di deformazione particolarmente rapida. Un terzo scenario è infine specificamente elaborato al fine di ottenere early-‐warning rispetto a fenomeni che insorgono improvvisamente e senza chiari precursori. Possibili attività per migliorare

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Introduction

The Synthetic Aperture Radar (SAR) interferometry is a remote sensing technique well known since decades and offer a number of interesting applications. It may be implemented through spaceborne, airborne and ground based sensors thus providing relevant information at different spatial scales from the global to the local one. A typical application of the technique is the assessment of ground surface displacement fields over wide areas, whose first successful demonstration, using spaceborne observation dates back to more than 25 years (Gabriel 1989, Massonnet 1993, Massonet 1994, Zebker 1994, Carnec 1995). In fact the technique is extremely powerful in providing information on “changes detection”. Through the comparison between two observations (interferometric pair), of the same scene, made in different moments of time, the portions eventually experiencing modifications in the elapsed time between the observations can be identified and characterised. The nature and the amount of the information that can be retrieved strongly depend on the ‘coherence’ of the observed scene. The coherence has a precise mathematical formulation and it is usually assumed that it measures the changes occurred in the time interval. Often, not enough attention is paid to the fact that the scene may change also during the acquisition of each single observation forming the interferometric pair. Similarly to the exposure time for optical picture the acquisition time for a SAR image plays a fundamental role in governing the quality of the image, what type of phenomenon can be observed and the quantity and quality of the retrieved information. This will in turn impact on the resulting coherence determining the information content about the occurred changes, which may pass from qualitative to quantitative. This may finally result in a precise determination of the contribution to the changes due to the displacement, namely the variation of the distance sensor-‐target along the Line-‐Of-‐Sight (LOS), with a very high accuracy.

Concerning the assessment of the negative effects on the image quality due to displacements of portions of the observed scene during its acquisition it is important to consider the frequency of observation of the sensor and the

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during the acquisition time become comparable with the wavelength the coherence of the portion is severely reduced and will not be correctly imaged. In summary (Prati et al., 1998) the resulting image quality depends on the combination of three factors: i) the entity of the displacement with respect to the wavelength; ii) the time interval necessary for the displacement to reach a value comparable to the wavelength of observation (correlation time); iii) the time to acquire the image (acquisition time).

Consequently changes that develop quickly with a potential severe effect on the coherence may be correctly imaged if the acquisition time is short enough. Shortening the acquisition time of a SAR image allows not only to refine the use of the radar interferometry in traditional fields of application but makes also possible new applications.

Considering the specific context in which the Ground-‐Based Radar Interferometry is used (Tarchi 2003a, Tarchi 2003b, Leva 2003, Monserrat 2014, Caduff 2015) it is now possible to consider a different approach, no longer based on the mechanical movement of the radar sensor, for implementing the SAR principle. A new class of Ground Based radar interferometer can be implemented using the well-‐known concept of antenna array combined with an efficient and switching system able to channel the signal to the different transmitting or receiving elements composing the array. An efficient way to implement this is offered by the Multiple Input Multiple Output (MIMO) technique (Bliss 2006). This approach along with its equivalence to a traditional SAR approach has been demonstrated and experimentally validated (Tarchi 2013). Even though alternative methods to realise an electronically scanned array exist, we will hereinafter use the acronym MIMO-‐SAR to indicate this class of instruments. A fully working prototype has been implemented at the Joint Research Centre of the European Commission and it has been extensively used for the monitoring of the Costa Concordia wreck at the Giglio Island (Broussolle 2014). In operational condition the system has acquired images with an acquisition time of about 0.1 sec but in laboratory test it has been demonstrated the capability to acquire up to 150 frames per second.

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The MIMO-‐SAR it is not originally conceived and designed to be used for GB-‐ InSAR application in a geological context were a traditional approach has demonstrated its capability until the actual level of maturity which makes those systems a standard operational tool to measure ground displacements.

Consequently the work reported here as the main goal to assess in a systematic way whether a similar system, bringing the original capability of an unprecedented short acquisition time may bring advantages in the monitoring of various phenomena of geological interest.

The work analyses the actual validated capabilities of MIMO-‐SAR with respect to other existing approaches/systems currently used analysing a number of real cases, including landslides and various types of slopes instabilities in a volcanic environment, where the monitoring with GB-‐InSAR techniques is being performed. This analysis is then complemented by real tests, executed with the existing prototype that provided evidence of the advantages and limitations of MIMO-‐SAR. By combining the two type of analysis it is finally possible to identify a number of scenarios where the use of MIMO-‐SAR may represent a real advantage. In addition, it has been also possible to suggest further lines of research aiming at improve the MIMO-‐SAR by creating a version tailored for the use in a geological context, which helps, in synergy with other existing system, to further extend and enrich the monitoring capabilities of GB-‐InSAR techniques. The MIMO-‐SAR has new and original capabilities but its optimal use is in combination with a system using a traditional approach since this is still the more efficient solution for a large variety of phenomena.

The outline of the thesis is as follows:

• Chapter 1 – The basic principles of GB-‐InSAR are presented, including a description of the main characteristics of the LISA system, the first example of system based on the mechanical movement of the antenna. The limits, in terms of acquisition time of this approach are analysed and it is presented an example, of geological interest, requiring a much shorter acquisition time to be fully monitored.

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• Chapter 2 – The concept of a Ground Based SAR interferometer with fast acquisition capabilities is presented showing how it can be based on a MIMO approach. The existing MIMO-‐SAR prototype, called MELISSA, is described and results of the validation tests in controlled environment are detailed.

• Chapter 3 – this is devoted first to present a general framework to assess in general terms all the different measurement parameters of a radar interferometer and how they relate and influence each other. The different solutions, including the MIMO-‐SAR are analysed and a diagram, acquisition time vs. maximum distance to summarise the attainable performances is presented. In the second part a number of real cases are analysed and the potential use of a MIMO-‐SAR is evaluated.

• Chapter 4 – This presents the various experiment campaigns performed with the existing MIMO-‐SAR prototype with particular attention on the main elements that have been validated in each case. They include the monitoring of the stability of the Costa Concordia wreck, a test on the Vetto landslides and a test on the Stromboli Volcano.

• Chapter 5 – This is dedicated to summarize the different results obtained through the analysis performed in Chapter 3 and the tests executed and reported in Chapter 4. The reference designed for the MIMO-‐SAR is presented. Different scenarios for a possible operational use of a MIMO-‐ SAR are identified and described. Future activities aiming at further enhancing the system are also discussed.

• Chapter 6 finally contains the conclusions.

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1 Monitoring ground displacement using a

ground-‐based radar system

The Ground Based Interferometric Synthetic Aperture Radar (GBInSAR) (Tarchi 1997, Tarchi 1999) is a radar technique, which allows performing radar measurements installing a system within some distance from the area that is aimed to be monitored. The installation of any other equipment or tool in that area is not necessary to gather reliable and accurate data. This has the advantage not to require in general access to the area under surveillance, which is a key safety feature in critical applications. The technique provides quantitative information of the superficial deformation pattern, along the line-‐of-‐sight (LOS) of the measuring device, of the area under monitoring. The sole requirement is that the radar device is a system installed in a fixed ground position and this bears reasons and consequences that will be described in the following.

However, in general terms, the GBinSAR technique exploits the well-‐known Synthetic Aperture Radar (SAR) principle (Curlander 1992), and the interferometric techniques originally developed for spaceborne earth observation (Zebker 1986). The SAR principle allows increasing the azimuth (or cross-‐) resolution of a radar image by combining a coherent sequence of radar acquisition, using a real antenna of limited size, while it is moving over a known trajectory. Within reasonable limits, the known trajectory can also be reconstructed in post-‐processing with the integration of data from secondary sensors or sources. The data at the end of the entire process result in an image, namely a bidimensional distribution of radar reflectivity of the observed scene, with a spatial resolution approximately equal to that obtainable through a real antenna of an equal dimension to that of the trajectory covered by the sensor (the syhtnetic aperture). This can allow a significant increase of the cross-‐ resolution of the image.

Additional processing can be performed on the collected images. The most applied technique is interferometry. This has had a wide range of theoretical background (Goldstein 1988, Bamler 1998, Fornaro 1996, Rosen 2000, Ferretti 2001, Crosetto 2002, Nico 2004) and operational applications (Gabriel 1989,

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Kimura 2000, Ferretti 2000, Rabus 2003), as it allows retrieving information on the third dimension (i.e. altitude), making it possible to gather a full 3-‐D map. In order to further exploit the SAR technique for the interferometric processing the processed images are requested to be coherent, i.e. they should preserve the phase related to the distance between the sensor and each pixel in the image, as the related information allows to retrieve the third dimension.

The interferometric processing aims at extracting such information by comparing two radar images of the same scene. With reference to a pair of coherent SAR images we term the first master (m) and the latter slave (s). The interferogram I is given, for a generic pixel (k,l), by the following relationship:

𝑰 𝑘, 𝑙 = 𝒎 𝑘, 𝑙 𝒔 ∗ 𝑘, 𝑙 (1) where * indicates the complex conjugate.

In the general case, which is the usual one in case of spaceborne observations the two acquisitions are taken from two slightly different positions and in two different moments of time. The phase of each pixel in the interfegram, termed interferometric phase, varies according to different effects:

i. The topographic effect, due to the different height, with respect to a reference plane, of the portion of terrain corresponding to the pixel in the image. This contribution can be exploited for the generation of Digital Elevation Model of the observed scene. It requires that the two acquisitions are taken from slightly different positions and disappears when the two positions are coincident (zero baseline condition);

ii. The dielectric effect, due to the phase variation induced by the different conditions, in different moments of time, either of the atmospheric layers the signal is propagating through during the acquisition of each image either to the different dielectric properties of the observed scene.

iii. Displacement of the portion of the scene corresponding to each pixel along the line-‐of-‐sight (LOS) of the system. As mentioned above in case of a coherent radar acquisition and SAR signal processing each pixel contains information on the distance between the sensor and the corresponding portion of the scene. If this portion is varying his position

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in the time interval between the two acquisitions the phase of the corresponding pixel in the two images will vary accordingly and the interferometric phase will contain a contribution directly related to the occurred relative displacement.

The optimal condition to use the interferometric phase to measure relative displacement is then minimising or eliminating the contributions i) and ii) mentioned above. It is possible to eliminate completely the contribution i) by repeating the second acquisition exactly from the same position, namely by moving the radar system exactly on the same trajectory in the two passes, while the contribution ii) can be minimised by repeating the second acquisition as close as possible in time or at least in conditions as possible to the previous one. This condition has to be verified case-‐by-‐case and particular techniques can be applied to further minimise any residual effect (Luzi 2004, Pipia 2008)

The use of ground-‐based systems usually allows to control completely the measurement parameters and consequently to fulfil, with affordable operational costs with respect to airborne or spaceborne platforms, both conditions. This capability, in combination with the advantage to adapt in a quite flexible way the acquisition parameters, such as frequency of observation, time interval between acquisitions, duration of the monitoring activities, to the characteristics of the phenomenon of interest, can explain the success of the technique.

In addition, the technique maintains all the usual advantages of a radar system, namely day and night operability and low sensitivity to environmental conditions, and operate from ‘safe ground’, namely from a certain distance from the area of interest. It is not necessary to install reference targets in the monitored area so eliminating the need to access a dangerous area. Today, the technique cannot be longer considered an experimental technique but an operational tool widely used for the monitoring of landslides, ground deformations induced by other phenomena and deformations of large man-‐made structures, such as dams, bridges, buildings and historical monuments (Tarchi 2003a, Tarchi 2003b, Leva 2003, Casagli 2009, Monserrat 2014, Caduff 2015).

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can be used to implement the SAR principle, is a bi-‐dimensional map of the relative displacement along the line-‐of-‐sight (LOS) of the sensor. A similar map is directly retrieved from the phase of the interferogram formed according to (1) as detailed in the following. The two dimensions of the final map are the range, namely the distance sensor/object and the azimuth, namely a direction parallel to the synthetic aperture (trajectory of the sensor). Each pixel of the final map will have a spatial resolution depending in range and azimuth on the extension of radar frequency band and on the length of the synthetic aperture respectively. To be noted that while the range resolution is independent from the range the azimuth resolution decreases as the range increases since the GB-‐InSAR system can only synthetize a sub-‐optimal aperture (Leva 2003):

The fundamental relationships governing the spatial resolution in range (Δr) and azimuth (Δx) are the following:

Δr=c/2B (2)

Δx = (λ/2L)*R (3) where:

ü c = Propagation velocity of the radar signal ü B = Frequency bandwidth of the radar system ü λ = Wavelength of the central frequency ü L = Length of the synthetic aperture

ü R = Distance (range) from the sensor and the portion of the scene corresponding to the pixel

As the resolution and the cross-‐resolution are usually requested to be the same, the two equations above provide a tool for estimating the synthetic aperture. Alternative ratios between the two resolutions can lead to a different dimensioning of the system.

The relative displacement along the LOS (d) of the portion of the scene corresponding to each pixel of the interferogram relates to the interferometric phase according to the following formula:

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d = (λ/4π)* Δϕ (4) where:

ü λ = Waveleght of the central frequency ü Δϕ = Interferometric phase

The GB-‐InSAR technique, in comparison to the other typical platforms for SAR application, allows fulfilling accurately the operational requirements related to the application to the continuous monitoring of slide instabilities and/or other local phenomena. First of all it allows for the necessary persistence of the observations, which is a prerequisite for any operational service. In addition it is possible usually possible to adapt the monitoring capabilities to the specific characteristics of the phenomenon, which may largely vary in terms of size of the affected area, mechanism, entity and rate of displacement, dielectric characteristics of the involved material, spatial distribution of the displacement pattern etc. The technique is suitable for the application on area of limited size, typically of few squared kms. In this respect, in order to cover much larger areas, the use of a spaceborne or airborne platform remains the most effective solution, even though the same flexibility as in case of a ground-‐based system cannot be achieved.

A ground-‐based system maintains all the advantages typical of any other radar system, such as the day and night operability, the robustness against environmental conditions and the capacity to operate from certain distance without the necessity for any reason to directly access the area under monitoring and thus minimising the associated risk for the instrumentation or the personnel. At the same time some typical limitations of the technique are still present. This includes the difficulties to apply it over areas affected by fast de-‐correlation processes, namely where pixels experience fast and randomly distributed phase changes as it might be the case for highly vegetated areas in windy conditions, and the fact that only the displacement component along the LOS can be measured. This latter point has different consequences. The first is that any displacements perpendicular to the LOS cannot be measured. In general terms,

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displacement of the corresponding portion. The use of at least two systems observing from different positions, if applicable, would solve the problem. If this is not possible a single system can be used in a preliminary phase to repeat observations for limited periods of time from different positions in order to retrieve overall information on the direction of displacement. Anyway, this requires assuming that the phenomenon under monitoring is stationary with time, identifying suitable observation sites and to carefully assessing on the feasibility from a logistic point of view of a similar solution. In many cases the problem can be efficiently approached by having a detailed geological analysis of the phenomenon under monitoring in combination with a Digital Elevation Model (DEM) of the affected area. By geolocating the measuring system in the DEM it is possible to calculate the angle between the LOS and the local slope direction in each point of the DEM and finally retrieve a realistic estimate of the total displacement. A further improvement may be represented, in a similar condition, by the existence of total displacement measurements with other devices, even though in few points.

Figure 1 – Detection of displacement along the Line-Of-Sight of the system.

The possibility to retrieve the deformation only along the LOS has the further consequence that different platforms employed, due to their different and peculiar geometries of acquisition, may be suitable for monitoring deformations along different directions. In this sense, even considering some relevant contraints (Ferretti 2014), space-‐borne and GB-‐InSAR platforms can be considered more effective in detectint displacements in a horizontal and vertical plane respectively.

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1.1 The LISA system

The LISA system (Rudolf 1999) (figure 2) is a radar system pioneered by the Joint Research Centre of the European Commission and specifically designed for the application of GB-‐InSAR techniques. It was designed with unique features for monitoring slope instabilities and, after its tests and the validation of its results, has been extensively applied to many measurement campaigns in various sites and a large variety of operational conditions (Tarchi 2003a, Tarchi 2003b, Leva 2003). Figure 3 depicts the working principle for the system. The synthetic aperture is implemented by using a mechanical linear computer controlled rail system. The main characteristic of the movement on the rail is a “stop and go” procedure where the transceiver has been decomposed into a couple of transmitting and receiving module in a ‘quasi-‐monostatic’ arrangement in order to ease its design. The radar system is a Stepped Frequency CW scatterometer

(Robinson 1974) based on a Vector Network Analyser.

The system, during the execution of measurement, needs to be controlled by a computer, which also stores acquired data. Other solutions, in terms of architecture and practical implementation for both the radar and the mechanical components are possible provided that they ensure the necessary stability and accuracy. The "stop and go" movement scheme allows to perform a radar measurement in each selected position along the trajectory, so to reconstruct the movement of the antennas precisely and, consequently, coherently process the received echoes at the end of the scan to obtain the radar image.

On the software side, basic modules for the system include a phase-‐preserving SAR processing algorithm (Fortuny 1994) and a package for interferometric analysis of data in the condition of zero-‐baseline (repeated pass interferometry from exactly the same location). The JRC implemented the original version of the software in the development phase and its core has been kept unchanged throughout the different versions and operational modes of this system.

Another key feature of the developed system was the modularity and the scalability, especially with respect to the transceiver block and the operational

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to Ku (see table 1).

Figure 3 - Schematic of the design of LISA system.

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However the Ku is generally the preferred one on the basis of various reasons. They include:

• Better azimuth resolution with respect to other frequency bands assuming the same length of the rail;

• Cost element taking into account accuracy, reliability and size of both the mechanical and radar components;

• Regulatory aspects, namely the availability of reserved frequency bands for the use of a similar system.

Table 1 - Microwave sub-bands definition (from https://www.ametsoc.org/ams/)

Whilst there are little costs associated to the modularity and scalability of the system, the benefits can be significant and are related to the adaptability of the system to the monitored environment. Whereas objects backscatter a limited amount of energy back to the receiver, it can be convenient to trade some angular resolution, which is achieved using higher frequencies, with additional backscattered power or range coverage, which is typically achieved at lower frequencies. This allows the possibility to tailor the system according to the application.

The equivalent aperture of this system shown in figure 2 is about 3 m but the design is easily scalable and other versions of the system of different size (rail length) can be implemented in order to fulfill specific operational requirements and logistic constraints. In any case, an essential prerequisite for the execution of high precision measurements is the high stability, over the entire duration of the monitoring activities, of the basement the system is installed on.

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system characteristics, such as rail length, frequency band and central frequency of observation as well as on the distance sensor/target area. As a rule of thumb assuming the above-‐mentioned typical characteristics (Ku band, 3m rail length, 100 MHz bandwidth) a spatial resolution of about 3 x 3 m within a range of 1 km and a field of view of about 60 deg can be assumed.

In general terms, the precision of a GB-‐InSAR systems in estimating deformations depends on the Signal-‐to-‐Noise Ratio (SNR) of the measurement, which in turns depends on different factors, such as the characteristics of the target, the distance sensor-‐target and the transmitted power. Usually the precision turns out to be a fraction of the wavelenght of the observation frequency and may range, considering the frequency bands most commonly used (see table 1), from sub-‐millimetres to a few millimetres.

1.2 Limits of an approach based on a mechanical

scanning system

The approach based on the use of a mechanical rail to realize the synthetic aperture or in more general terms on the mechanical movement of the radar sensor or of the antenna system has proven its ability in ensuring an effective tool for the monitoring of deformations until the actual level of maturity that makes it a standard and operational technique. GB-‐InSAR is today routinely used for monitoring activities applied to various phenomena inducing slope instabilities of natural or man-‐made origin, as it is the case in open-‐pit mines. The need to ensure accuracy and repetibility in the movement requires the use of high precision devices and this may have an impact on the cost of the system. This may become even more significant increasing the size of the rail. This will in turn impact also on the necessary maintenance operations, which may become more expansive and/or more frequent in case of monitoring activities to be executed over long period of time and/or in an aggressive environment (volcanic, dusty areas, coastal marine). It is also to consider the impact of the overall size of the system and in particular of the rail, which can make very difficult the operations of installation.

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More importantly, there is a general element concerning the applicability of SAR and InSAR techniques that should be taken carefully into account. This is the assumption that the scene under observation is time-‐invariant, at least in the interval of time necessary to acquire the entire sequence of raw measurements. In fact, it is well known the problem of blurring in the final image that may occur in case of non-‐stationarity of the target (Sullivan 2000). If we assume that the portion of the scene, corresponding to a certain pixel, it is varying its LOS distance to the sensors during the acquisition, this will induce a corresponding phase variation in the acquired sequence of measurement. In order to identify the source of backscattered energy in the bi-‐dimensional image, the SAR processing algorithm processes the phase variation of the scatterers assuming that it is a sole function of the movement of the sensor. The system is actually unable to compensate for significant movements during the acquisition time. In particular, a movement is defined "fast" when the target moves of a distance comparable with the wavelength of observation.

The "fast" movements generate an extra phase shift that will result in a defocus of the target, with at least a part of the backscattered energy that cannot be associated to the right resolution cell but will be spread out over other portion of the image. Depending on the type of motion of the target, and how this combines with the trajectory of the sensor, this may result in an image artefact, i.e. a misplacement/deformation of the target, as in case of moving ships (Tunaley 2003) until a total decorrelation effect, resulting in the entire energy from the corresponding cell randomly distributed over all iso-‐range resolution cells. The final local effect, on the moving area, is a severe loss of coherence, which may prevent to retrieve any quantitative information on the displacement. In addition, the randomly distributed energy will produce a deterioration of the SNR of the image (Prati 99).

Even though the process, from correct focusing to a complete decorrelation is gradual it is possible to identify a value, for the rate of displacement, to be considered as a limit, over which the phenomenon is no longer correctly imaged. We indicate with Δt the time interval necessary to perform an acquisition

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(coherent integration time) and assume a criterion of λ/8, namely only targets eventually moving (along the LOS) less than this value will be correctly imaged. We finally obtain the relationship between Δt and vlim as follows:

𝑣_!"#= (𝜆 /8 𝛥𝑡) (5)

This value is not to be considered a very strict limit since as previously explained the process is gradual and the peculiarity of the displacement may combine in very different way with the synthetic aperture producing a final effect which is quite unpredictable.

It is then more and more relevant that the acquisition time of the system has a severe impact on its performance and application field. For a GB-‐InSAR system exploiting mechanical movements and a stop-‐go acquisition scheme, Δt may be quite long as it depends on both the time for the radar measurement acquisition and the time to move and position the radar system along the rail (or move the antenna pointing in case of real aperture radar system). The latter is certainly the element having the greater impact on Δt. The latter is certainly the element having the greater impact on Δt.

The LISA system was originally designed without consider this as a critical constraint and in the implementation phase no special attention was paid to this aspect. In many applications to the monitoring of landslides typical value for Δt were in the order of several minutes. Today it has been recognized the importance of this element and examples of GB-‐InSAR systems with enhanced capabilities in terms of Δt are available (Roedelsperger 2013). The shortest possible Δt for this class of instruments has to be considered in order of 5-‐10 sec (for a system of about 1 m in length). To be noted that this fast operation mode for system based on a mechanical rail may turn out to be extremely demanding in terms of maintenance when the monitoring has to be performed on very long period of time.

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1.3 The need to extend the applicability field. An

example of geological interest.

An example of the possible advantages deriving from the use of an alternative approach allowing to significantly decrease Δt for a GB-‐InSAR system and to increase the ability to adapt it to the characteristics of the phenomenon to be studied is provided by the explosion that affected the Stromboli Volcano on the 5th_{of
April
2003}_{(Calvari
2006)}_{.
This
event
took
place
when
a
LISA
system
was} continuously monitoring the instabilities of the area of the volcano, termed Sciara del Fuoco, triggered by the landslide occurred few months before.

The selected acquisition time for the LISA system was about 12 minutes, optimised to fulfil this clear and specific operational objective for the monitoring activities (Casagli 2003). However it was beyond the capabilities of the system to decrease significantly this value.

The explosion has triggered deformations of significant portion of the entire volcanic edifice with rates much higher with respect to the selected Δt. It happens while the system is performing a scan and produces the sudden interruption of the measurements for a power shutdown.

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Figure 4 - Optical image of the monitored area of Stromboli Volcano from the position of LISA

and SAR image (power) acquired by LISA and processed over a DEM and displayed using a similar point of view as the optical image. Numbers identify different visible portions of the volcano. With reference to figure 5, showing the power image in its typical radar projection, it is

possible to identify the corresponding areas.

1

2

3

4

5

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Figure 5 - Radar image (power) in range-azimuth projection. Numbers indicates the

correspondence with different visible areas of the volcano (figure 4). 1: Basamento, area where the system is installed; 2,3: different portions of the Sciara del Fuoco; 4,5: Crater areas.

However it was possible to process the portion of scan already completed and generate an interferogram with the corresponding portion in the previous image as displayed in figure 6.

The analysis of the interferogram shows that the area corresponding to the Sciara del Fuoco (2, 3 according to figure 5) is substantially stable (red according to the colour coded scale) while the crater areas (4) and (5) (between 700 and 1100 metres in range) shows a little displacement of about +2 and -‐2 m respectively, namely in opposite directions.

A different kind of elaboration of the existing data has been implemented in order to try to retrieve additional details about the deformation patterns induced by the explosion (Tarchi 2004).

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Figure 6 –Displacement map of the Stromboli volcano just after the explosion of the 5th of April. Since the scan has been interrupted by the power shutdown due to the explosion only the part the

portion already acquired of the whole synthetic aperture has been used.

The technique includes a number of steps as detailed in the following: 1. The following assumptions are made:

i. The fast evolving event is happening in an interval of time belonging to a single scan and it is characterised by a very sudden beginning;

ii. Other phenomena affecting the area and having a different origin are characterised by a very slow deformation rates and do not produce significant displacements in the considered time interval.

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2. In addition to the scan containing the fast event it is selected a reference image that: it is as close as possible in time but fulfilling condition ii) of the previous point, It guarantees the best possible coherence. This usually corresponds to the previous one in the sequence, but a certain number of preceding images should be tested to identify the optimal one. To note that slower is the deformation rate of area further back in time can be identified the optimal reference image.

3. Each of the two acquisitions is divided in ‘sub-‐aperture’, namely a certain set of corresponding portions having a reduced length. They can also be overlapping. Considering for instance a full aperture composed by 300 acquisition points, a single sub-‐aperture of 100 points and an overlapping portion of 50 points we will finally get a set of 5 sub-‐aperture. The choice of the length of the sub aperture and of the overlapping portion depend on the following factors:

i. The length will determine the spatial resolution in azimuth of the ITF formed using corresponding sub-‐apertures. ii. The length, corresponding to a longer acquisition time, will

also determine the level of decorrelation induced by the fast deformation and/or the entity of the low-‐pass filtering effect due to slow acquisition time with respect to a fast deformation rate. Shorter sub-‐aperture will be faster and then more accurate in monitoring the phenomenon.

4. Having produced two sets of sub-‐aperture the entire sequence of ITF is generated using pair of correspondent sub-‐apertures.

If the assumptions at point 1 are satisfied, the obtained sequence will show the evolution of the displacement pattern corresponding to the time of acquisition of each sub-‐aperture with respect to a previous condition of stability. Recalling the step 3 of the procedure there is a resulting space-‐time filtering effect, which can be modulated by varying the length of the sub-‐aperture and the overlapping factor. The temporal averaging will be reduced by making shorter sub-‐apertures