AU7180600A - Process for radar measurements of the movement of city areas and landsliding zones - Google Patents

Description

AUSTRALIA

Patents Act 1990 COMPLETE SPECIFICATION STANDARD PATENT Applicant(s): POLITECNICO DI MILANO Invention Title: PROCESS FOR RADAR MEASUREMENTS OF THE MOVEMENT OF CITY AREAS AND LANDSLIDING ZONES The following statement is a full description of this invention, including the best method of performing it known to me/us: 1A, "Process for radar measurements of the movement of city areas and landsliding zones,"

DESCRIPTION

The present invention relates to a process for measuring the movement of city areas and landsliding zones.

As is already known, a synthetic aperture radar or SAR produces a bidimensional image. One dimension of the image is called range and it is a mpasurexnent of the line-of-sight distance from the radar to the object illuminated. The other dimension is called azimuth and is perpendicular to the range, The measuring operation and the rahge accuracy are obtained by means of a synthetic aperture radar determining as precise as possible the time that has passe4 from the transmission of one pulse by the radar to receiving the echo of the illuminated object, The range accuracy is determined by the length of the pulse transmitted. Shorter time pulses ensure a finer resolution, To obtain a fine resolution of the azimuth it is necessary to use a large physical antenna so that the electromagnetic wave transmitted and received:is as similar as possible to a pulse (in the ideal ease the pulse has the shape 20 of a Dirac delta).

Similar to optical systems (such as telescopes), that need large apertures to obtain fine resolutions of the image, also a SAR-type radar, of normal precision, that works at a much lower frequency than those of the optical systems, needs an enormous antenna with enormous apertures (hundreds of metres), that cannot be installed on any platform. Nevertheless a SAR-type radar installed on an aeroplane can collect information during the flight and then elaborate it as if it were an antenna. The distance that the aeroplane covers, simulating the length of the antenna, is called synthetic aperture.

The SAR-type radar consists of a coherent radar, that is a radar which measures both the module and the phase of the electromagnetic wave 2 reflected, operating at a frequency which is usually betwe~n 400 Mh~z and Ghz, and is, as previously said, installed on aetoplanes, and also on orbiting satellites at a height between 250 and 800 Km.

The antenna of the radar is directed towards the earth orthogonally to the direction of the movement of the platform (aeroplane or satellite) with an angle, called "OffnAdir", between 20 and 80 degrees in relation to the direction of Nadi, that is, perpendicularly to the earth.

With said system, resolution cells or grids of the earth surface can be generated with a spatial resolution of a few metres. Said cells present a miimum grid of resolution, that is, they have it spacing within which it is possible to distingu~ish two objects to illiirninate, The most important characteristic of SAR is that it is a coherent image system, It is therefore possible to measure the range difference in two or more SAR images (SAR interferometer) of the same surface with an accuracy of a fraction of the SAR wavelength.

Using focusing techniques that preserve the phase, images are obtained in which every elem~ent of the image (pixel) is associated with a complex o o* number resultin g from the combination of the backseattering of all the objects belonging to the same ground resolution cell and the phase rotation due to the path.

The phase of every pixel is given by the sum of two terms: the first is the phase of the scatterer 4s and the second is given by r 4=5lk where r is the radar resolution cell distance and,% is the radar wavelength (with eooo.: X= c/(21rf), where f is the operating frequency of the radar and c is the speed of the light). The second phase term contains millions of cycles because the wavelengths are a few centimetres and the radar sensor resolution cell o: o.distace is a few hundred kms, while the displacement connected to the 0 scatterers is fundamentally random and therefore the pba~e of a single SAR image is practically unusable. However, if we consider the phase difference between two SA.R images taken from slightly different viewing angles, the Phase term due to the scatterers is cancelled (at least in first 4pproximation if the angle difference is small) and the residual phase term results 47CAr/7. where Ar is the difference of the paths between the sensors and the same ground resolution cell, The phase termi still contains a very high number of cycles, that is kcnown apart from the high integer multiple of 27r, but passing from one resolution cell to an adjacent one, the variation of the phase is usually small enough not to present ambiguity of 2T;, The phase thus deduced is called the interferometric phase and the variation information Ar (which is measured in fractions of wavelength X) between pixel of the SAR image is connected thereto. Knowing the position of the two sensors, the measure of Ar can be used to find the relative elevation between the pixel of the image and therefore generate a digital elevation model ("Digital Elevation Model" or DEWV) that is, an electronic readiing is talen of the topography of the Earth's surface. On the othaer hand, if the topography is knovyn, that is a DEM of the area. of interest is available (there are special data banks fromn which one can take these digital models), its contribution to the intorferornetric phase can be eliminated and possible small surface displacements can be detected. In the case of the satellites ERS-1 and ERS-2 (twin satellites sent into orbit by the European Space Agency, the first, ERS- 1, in 1991, fth secotd, ERS-2, in 1995, operating at a frequency of Gliz, characterised by a 35-day revolution period and by a 20-meter grid resolution), for example, from one passage to the next of the platform (EM- 1 and ERS-2 follow each other at a distance of one day), or of one of the two satellites, several scatterers do not chanige their behaviour, that is, they keep a high coherence and therefore the cancella~tion of their phases is practically perfect. This means that the phase measures obtained by means of this technique can measure movements that are even a few millimetres of the Earth's topography.

Nevertheless, the present techniques of differential interferornetry have some limits. In fact after a few days, in extended zones, the scatterers lose a 4 coherence, that is the scatterers do not remain Similar to themselves after a period of time and therefore coherent zones with dimensions exceeding a few resolution cells cannot be identified. In addition, the wavelength of the incident signal and the displacement of it are function of atmospheric conditions. These cause phase rotations that cannot be distinguished from the movements of the ground that are required to be measured.

Another problem is the physical structure of the single scatterer that influences the phase variation in function of the observation direction and therefore of the baseline, that is of the distance between the two satellites projected orthoganally to the view line. If the stable scatterer is a surface that bacicscatterers and that occupies the entire resolufiqn cell in the range, the phase of the radar echo loses correlation in correspondence with the so called critical baseline (for example in the came of satellites of the ERS type the critical baseline is about 1200 metres). When instead the scatterer is pointwise or is a comer reflector, the phase remains unvaried for much greater baselines.

In view of the state of the art described, the object of the present invention is to identify a measuring process, which resolves the problems of the present techniques so that the movement of city areas and landsliding zones can be measured in a more reliable manner.

According to the present invention, such object is reached through a process for radar measuring of the movement of city areas and landsliding zones which, having available N 20 images taken with a Synthetic Aperture Radar or SAR over a multi-year period, identifies, for every 25 resolution ccU, the scatterers, called permanent scatterers PS, that keep their electromagnetic characteristics unchanged over time, characterized in that said PSs are identified through the following steps: N-1 differential interferograms are formed in relation to the main image, called master, using a digital elevation model or DEM with vertical accuracy better than 50 metres; for every pixel of the image of point selected on the statistical properties of the modulus of the reflectivity, a temporal series of the interferometric phases is generated, and then, spatial differences among temporal series that belong to neighbouring pixels are formed; for every differential temporal series of point the linear phase components are calculated in relation to the baseline and the phase components connected to the displacement model, already known, in relation to the time; the relative error between the precise elevation of the pixel supplied from DEM of point is associated with the linear phase component of point in relation to the baseline; the relative movement of the pixel in the direction of the SAR is associated to the polynomial phase variation in relation to the time of point the phase residuals are formed by subtracting the contributions calculated at points and after a phase unwrapping procedure on the sparse grid of the selected pixels; the spectral power density of the phase residuals is analysed and if the residuals relating to each single image are spatially correlated, 20 attributed to atmospheric artefacts and removed; if the further residual dispersion relating to each single image is too large the pixel is discarded, Said process is characterised in that given a number of PS per surface unit 25 per Km 2 after the elaboration of the phase residuals, the atmospheric artefact of every single image is determined by subtracting said 25 artefact from the vertical precision of the DEM.

Thanks to the present invention, a process can be made for identifying the stable scatterers in time, called PS (regardless of the atmospheric conditions and of the type of platform on which the SAR radar is positioned), which can determine the movement of city areas and landsliding zones.

As well, a process can be provided which makes it possible, from the phase dispersion of the PS, to estimate the dimension and construct a network of natural reflectors suitable for identifying the orbital position of any satellite or aeroplane that illuminates the natural network of said PS, or to mneasure the movements of the PS or of the atmospheric artefact.

The characteristics and advantages of the present invention result as being evident from the following detailed description of an embodiment thereof, illustrated as non-limiting example in the enclosed drawings, in which: Figpre I shows a geometric image of the interferometry SAR in the case of one single cell; Figure 2 illuotrtep some mnterferograms rofenring to a specific area; Figure 3 shows a three-dimensional graph of nine interferograms in fiction of the baseline; Figure 4 shows four examples relative to four different pixels of an interferogram of Figure 3; Figure 5 illustrates a three-dimensional graph of nine interferograms in fanction of the time; Figure 6 shows four examples relative to four different pixels of an interferogram of Figure Figure 7 illustrates the differential contributions of the atmiosphere of the single images compared to the main image ("master"); Figure 8 shows an estimation of the atmospheric contribution present on the master image; Figure 9 illustrates a real example of the lqcalisations and of the spatial densities of the stable 5catterers (called PS) over a three-year time; Figure 10 shows a real example of the present invention made on the Valle del Bove (Etna); Figure 11I is a colour representation that illustrates a real example of the s ubsidence rates of the Valle del Bove (Etna).

In Figure 1 the phase difference between two SAR images taken from slightly different viewing angles is shown.

According to what is illustrated in said Figure, there are noted one axis of the x-co-ordinates, representing sea level or another reference surface.

one axis of the ordinates, representing the height of sea level, or another reference surface; three points 101, 102, 103; 4 horizontal line 108 passing through point 101; a vertical line 104, parallel to the axis of the ordinates, indicating the distance between the axis of the x-co-ordinates and the horizontal line 108; a topographic line 105; an acute angle E; the distance between points 101 and 102, in a normal direction to the view line (called baseline) will be indicated with a segment 111 having length B; the distance 109 between points 101 and 103 is indicated with p; the distance 110 between points 102 and 103 is indicated with p+Ap.

If two receiving and trqnsmitting radar antennae, 101 and 102, which illuminate the same surface zone 103 simultaneously are considered, and point 101 is placed at a distance p from the ground and point 102 at a distance p±Ap from the ground, the displacement of the illumination path is calculated as 4r 4utp/k with k as length of incident and reflected wave. It can be noted that the phase difference depends both on the geometric view and the height of point 103 above the reference surface (axis of the xcoordinates), Therefore, if the geometric view can be controlled or is at least known with sufficient accuracy, the topography 105 in relation to point 103 (called q) can be extrapolated from the measure of the phase difference Oq with a precision of several metres, specifically using the expression 41 1 p sinO Figure 2 shows the interferograms of a specific area generated through the usual computer program using a main image, called "master", and nine secondary images, called "slaves". Each interferogram is characterised in that it has a different baseline, an axis of the x-coordinates indicating the

S

direction of azimrrtb. and an axis of the ordinates, indicating the range direction.

The nine different differential interferogramns are made by subtracting from the phase difference of every pixel the contribution of the topography, and using an existing DEM, that is using digital models which are available on the market, with a better vertical accuracy than 50 m.

The reference DEM can also be generated from the high coherence interferomnetric couples, For example in the case of satellites ERS-1 and ERS-2 the couples of images taken at the distance of a day c=n be used because after a brief period of time from the passage of said satellites, said zones do not modify their stable scatterers. These couples of images generate high coherence interferomotric couples.

In Figure 3, which uses the baseline and distance values of the radar (slanit range), nine interferograms of Figure 2 are show n, generated by the same master image, positioned three-dimenisionally, ordered by increasing According to said Figure it can be noted that each interferogram is referred to the same ground surface area, but has a different baseline.

Four points, called pixels, are identified with 112, 113, 114 and 115, belonging to a specific interferograrn.

Having the nine interferograms; available and taking only one point for example 112, belonging to one of the interferograms, on the basis of the prevous formula of Q~q this has a phase component, relative to a reference pixel, which increases, linearly with the baseline in function of the relative height error, Therefore a mono-dimensional signal is mrade, as hereunder describ~ed with refercrice to Figure 4, which represents a sequence of the interferometric p i e in function of the baseline, The mnethod is the pame for points 113, 114 and 115 frbm which the same number of sequences of the interferornetric phases are extracted in funiction of the baseline.

9 In Figure 4 four examples relative to four different pixels of an interferogram are shown.

According to what is illustrated in said Figure four diagrams of the interferometric phases 127,116,117 and 118 can be noted having as axis of the x-coordinates the baseline variable and as axis of the ordinates the interferometric phase in relation to the master.

Each diagram consists of a multiplicity of points and a straight line which is the result of the interpolation of said points.

The phase linear component is calculated for every temporal series 127, 116, 117 and 118 in relation to the baseline, that is the inclination a of the straight line of equation O=aB+C (where C is a constant) to the squared mwinimum is estimated and which minimises the following expression: q L -aR-C 1: Then the error between the precise elevation of the pixel and that supplied by the reference DEM is associated to the phase linear component n i in relation to the baseline by using the following formula: 'wpsin6 a In this way the relative topography error can be detected, which is connected to the inclination a of the interpolated line, which is more suitable for the data extracted from the interferometric phases, In Figure 5 nine interferograms in function of the time generated by the s same master image are shown.

According to what is illustrated in said Figure it can be noted that every interferogram refers to the same ground surface area, but has a different instant, axis t (time).

Four pixels belonging to a specific interferogram are identified with 119, 120, 121 and 122 as well.

Having the nine interferograms available and taking one single point 119, belonging to one of the interferograms, this has a phase relative to a reference pixel which varies linearly in time (having assumed a constant speed subsidence model) and therefore a signal is made, evidently monodimensiona, as is hereunder described with reference to Figure 6.

The method is the same for pixels 120, 121 and 122 which give rise to the same number of monodimensional signals.

In Figure 6 four examples relating to four different pixels of an interferogram of Figure 5 are shown.

According to what is illustrated in said Figure four diagrams of the interferometric phases 123, 124, 125 and 126 can be noted, having the time variable as axis of the x-coordinates, and the interferometric phase variable in relation to the master as axis of the ordinates.

20 Bach diagram consists of a multiplicity of points and of a straight line which is the result of the interpolation of said points.

~Supposing that we have a subsidence model available, that is a sinking Imovement of the earth's crust at a constant speed which occurs in certain zones called geosynclines, the entity of said movement is estimated by *25 determining to the squared minimum the inclination k of the straight line =kt which minimises the following expression: q j kt) 2 11 In this manner we can find the subsidence speed which is connected to the inclination k of the interpolated straight line which is more suitable for the data extracted from the interferometric phases.

Figure 7 represents differential interferograms having azimuth variable on the x-axis and the range variable on the y-axis, According to what is illustrated in said interferograms, the phase residuals are made after subtracting, by using a known computer program, the contributions given by the error between the precise elevation of the pixel and that supplied by the reference DEM and the movement of the pixels in the direction of the satellite radar.

Figure 8 shows an estimation of the atmospheric contribution present on the master image, obtained by making an arithmetic average of the phase residuals of Fig. 7.

In said Figure it can be noted that the image presents a graduation scale indicating the phase in radians.

The estimation of the contribution present on the master image can be S. subtracted, again by using a known computer program, from the differential *atmospheric contributions seen in Figure 7 giving as result the atmospheric contribution present on every single image, called Atmospheric Phase 20 Screen (APS).

Figure 9 shows a real example of the localisation and the density of the stable scatterers in time, According to what is illustrated in said Figure, an axis of the x-coordinates indicating the azimuth direction and an axis of the ordinates indicating the range direction can be noted. The unit for measuring 25 the axes if the pixel.

A plurality of points that identify the stable pixels in time can be noted as well, In fact the sequence of the operations described in the previous figures cannot be carried out on all the image pixels, but only on those that keep their physical characteristics (PS) during the interval of time in which all the 12 images of the temporal series have been acquired.

This analysis is carried out in two steps: first, PS candidates are selected on the statistical properties of the modulus of the reflectivity, then the spectral power density of the phase residuals is analysed and if the residuals relating to each single image are spatially correlated, attributed to atmospheric artefacts and removed; if the further residual dispersion relating to each single image is too large the pixel is discarded, When the number of stable scatterers per surface unit is sufficient, at least twenty five PS per Km 2 the phase residuals obtained from the subtraction of the phase contribution due to precise elevation of the pixel and movement of the pixel in the direction of the satellite radar, are sufficient for reconstructing the atmospheric artefact of each single image through a low-pass interpolation on the uniform image grid.

This artefact can therefore be removed from each SAR image improving the quality of the DBM and therefore using the interferometric phases, filtered of the atmospheric artefact found with the method previously described, we have an improvement of the degree of correlation of the pixels, classified as PS, Figure 10 shows a real image of the present invention of a temporal 20 series on the Valle del Bove (Etna).

According to what is illustrated in said Figure it can be noted that the axis of the x-coordinates indicates the azimuth direction, while the axis of the ordinates indicates the range direction. Both axes have the pixel as unit of measure.

A grade indicator indicating the phase in radians can also be noted.

The Figure shows the atmospheric outlines relating to an image of the temporal series on the Valle del Bove estimated by interpolating the results obtained in correspondence with the stable scatterers, that is the PS, seen in Figure 9.

Figure 11 shows the subsidence movement in terms of velocity field 13 estimated on the Valle del Bove (Etna) in correspondence with the stable scatterers, that is the PS, of Figure In said Figure an axis of the x-co-ordinates indicating the aianuth direction can be noted and also an axis of the ordinates indicating the range direction. Both axes have pixel 5 as unit of measure.

It cana also be noted that the image is composed of a plurality of points, coloured in different manners. This meqn that thle red ones have the value of a subsidence speed of about four centimetres per year whifle the green ones have the value of zero opeed.

It is to be understood that, if any prior art publication is referred to herein, such reference does not constitute an admission that the publication forms a part of the common general knowledge in the art, in Australia or any other country.

For the purposes of this specification it will be 'a..*clearly understood that the word "comprising" means "including but not limited to", and that the word "comprises" has a corresponding meaning.

Claims (3)

1. Process for radar measurements of movements of city areas and landsliding zones which, having N 20 images made available by a synthetic aperture radar or SAR over a multi-year period, identifies for every resolution cell, the scatterers whose electromagnetic characteristics remain unaltered over time, and which are called Permanent Scatterers or PS, characterized in that said PS are identified through the following steps: N-I differential interfeograms are formned in relation to the main image, called master, using a digital elevation model or DEM with verlical accuracy better than 50 metres; for every pixel of the image of point selected on the statistical properties of the modulus of the reflectivity, a temporal series of the interferometric phases is generated, and then, differences among temporal series that belong to neighbouring pixels are formed; for every differential temporal series of point the linear phase sees.. components are calculated in relation to thec baseline and the phase components connected to the displacement model, already known, in s. 0. relation to the time; the relative error between the precise elevation of the pixel supplied 20 from DEM of point is associated with the linear phase component of S .point in relation to the baseline; the relative movement of the pixel in the direction of the SAR is associated to the polynominal phase variation in relation to the time of point 0 25 the phase residuals are formed by subtracting the contributions calculated at points and after a phase unwrapping procedure on the sparse grid of the previously selected pixels, the spectral power density of the phase residuals is analysed and (gI) if the zesiduals relating to each single image are spatially correlated, attributed to atmospheric artefacts and removed; if the further residual dispersion relating to each single image is too large the pixel is discarded.

2. Process according to claim 1, chuacterised in that: given a number of PS per surface unit 25/Kin after processing the phase residuals, the atmospheric artefact of every single image is determined and from the reference DEMI, improving its ve'rtical precision.

3. Process according to claim 2, characterised in that the process steps and are reiterated, using the interferometric phases filtered of the atmospheric artefact according to step Dated this 24th day of November 2000. POLITECNICO DI MILAO By their Patent Attorneys GRIFFITH RACK Fellows Institute of Patent and Trade mark Attorneys of Australia *soee *see 66 00 0:66