a guide to insar for geophysics - nevada geodetic...

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Contents

1. Introduction to Synthetic Aperture Radar 22. The idea of 'phase' 63. Basic concepts for InSAR over a spherical earth

114. Basic concepts for measuring topography

185. Basic concepts for measuring surface deformation 256. How to make an interferogram - initial steps 307. Baselines and Orbits 348. Phase unwrapping 399. Phase gradients 4310. Quantifying displacement 4511. Atmospheric Effects 5012. Limitations, advantages and resolution 5713. Applications to neotectonics 6114. Obtaining SAR data 67

Emma Hill, Spring 2001, Geol 695

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1. Introduction to Synthetic Aperture Radar

Conventional radar (which itself is an acronym for 'RAdio Detection And Ranging') remote sensing works by illuminating the ground with electromagnetic waves of microwave frequency, and using the amplitude of the signal and the time it takes between transmitting the signal and receiving back the echoes to deduce the distance from the sensor to the image pixel on the ground. These distances are used, along with orbital information, to produce a 2D image of the ground, which looks similar to an aerial photograph.

Figure 1 The electromagnetic spectrum (from the Atlantis Scientific Webpage).).

There are various frequencies of electromagnetic energy in the microwave wavelength range (see Figure 1) that can be used, which correspond to the three commonly used bands L, C and X (see Table 1). There are tradeoffs between using these different frequencies. C band, for example, loses coherence more easily than L band, but is also four times more accurate than L band (which wouldn't be accurate enough to detect small fault displacements) (Massonnet, 1995).

Band

Frequency (GHz)

Wavelength (cm)


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L 1-2 30-15C 4-8 7.5-3.75X 8-12 3.75-2.5

Table 1 Radar band characteristics.

Radar is an 'all weather' system, since the electromagnetic waves can penetrate cloud. Since the energy comes from the system itself (it is an 'active' remote sensing system), rather than the sun (which is where 'passive' systems get their illumination from), it can also be used at night.

The larger the radar antenna, the better the resolution will be. The 'synthetic' part of Synthetic Aperture Radar (SAR) therefore comes from the use of the movement of the satellite (and more complicated processing techniques involving the Doppler history of the radar echoes) to create a 'synthetically' larger antenna and hence improved resolutions. Typical pixel spacing in space-based SAR is 20-100m within a 100km wide swath (see Figure 2 for notation).


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Figure 2 Radar geometry and notation.

References

Burgmann, Roland, Paul A. Rosen and Eric J. Fielding (2000)Synthetic Aperture Radar Interferometry to Measure Earth's Surface Topography and its DeformationAnnu. Rev. Earth Plant. Sci, Vol 28, pp.169-209

Madsen and Zebker (1998)Imaging Radar Interferometry; in Principles and Applications of Imaging Radar, Manual of Remote Sensing; American Society of Photogrammetry and Remote Sensing, Chapter 5, pp.270-358

Massonnet, D. (1995) (check you still need this reference here!)Application of Remote Sensing Data in Earthquake Monitoring.Adv. Space Research, Vol.15, No.11, pp.1137-1144

Atlantis Scientific's Webpage:http://www.atlsci.com/


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2. The idea of 'phase'

The Theory

A processed SAR signal is made up of two things - an amplitude and a phase, which are represented by a complex number. The phase is not used in traditional SAR studies, as it is influenced by so many things that it appears as random over a SAR image and the things that influence it are very difficult to quantify. In fact, the phase information was usually completely destroyed by speckle removal techniques (used to make the radar image look more like an aerial photo), which average the amplitudes of neighboring pixels.

When the radar sensor sends out a pulse of electromagnetic energy, there will be an integer number of complete wavelengths that travel to and from the target, then a final, incomplete wavelength received at the sensor, which is what is termed the 'phase'. Phase is measured as an angle, in radians or degrees. 2 radians of phase make up one phase cycle. The phase is therefore a term that is inadvertently proportional to the range from the satellite to a pixel on the ground.

The most important influences on phase are:Useful:

Topography Geometric displacement of the targets within each pixel (i.e.

surface deformation). Not useful (to us, anyway?!):

Earth curvature


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The reflection of the signal by scatterers in the pixel (rocks, plants, etc).

Change in phase delay caused by differences in the position of these scatterers within each pixel.

Orbit error Atmospheric (ionospheric and tropospheric) delay Phase noise (from the radar system).

This is quite an intimidating list, and we shall see that the focus of anyone trying to use InSAR for research in their field will be to isolate just one of these features, reducing and eliminating the other aspects of phase through mathematical manipulation and calibration. Some of the effects, such as earth curvature, are much easier to deal with than effects such as tropospheric delay, but the closer we get to measuring extremely small effects on phase (for example interseismic strain), to levels smaller than a single fringe, the harder it will become to accurately remove the effects we don't want.

If two images were taken of exactly the same target from exactly the same satellite position, and the ground had not changed, then the phase for each would be the same. This implies that if two images are taken of exactly the same target from slightly different positions and the difference between the phases for each pixel is calculated, the unwanted effects on phase can be removed, leaving only the useful quantities. This combining of images gives us 'Interferometric Synthetic Aperture Radar', otherwise known as the acronym InSAR.

The Math


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Representing Phase as a Complex Number

The radar wave can be viewed as shown in Figure 3. From this we can see that the wave can be defined as , where A is the amplitude and is the number of radians. We get this just from simple trig - remember that you get a similar curve if you plot a graph of .

Figure 3 The electromagnetic wave as a function of amplitude and phase

If we translate these parameters onto real and complex axes, we get Figure 4. In this view, goes round and round the circle with increasing numbers of waves, increasing by 2 each time it completes the loop. If the wave is incomplete, the circle will not be completed and all the preceding full loops of 2 plus the partial value of will be our phase. We can derive the following equations for amplitude by looking at the geometry in the circle:

We can also, most importantly, get an equation for phase, :


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Figure 4 The electromagnetic wave viewed in complex format.

Relating Phase to Range

The total, roundtrip, distance in wavelengths between a radar antenna

and a point on the surface is , where is the range and is the

wavelength of the system. By multiplying this equation by , we get an

equation for the total phase over this distance: . For two-way

travel this is .

We can also translate these equations to find phase difference. The difference in round-trip range distance between two radar antennas to a

point on the surface, in wavelengths, is , where is the difference in


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distance and is the wavelength. This equation multiplied by 2 gives

the phase difference as .

References

Gabriel, Andrew K., Richard M.Goldstein and Howard A.Zebker (1989)Mapping Small Elevation Changes Over Large Areas: Differential Radar InterferometryJournal of Geophysical Research, Vol.94, No.B7, pp.9183-9191

Rosen, Paul A., Scott Hensley, Ian R. Joughin, Fuk Li, Soren N. Madsen, Ernesto Rodriguez and R.M.Goldstein (1999)Synthetic Aperture Radar InterferometryProceedings of the IEEE, Unpublished manuscript


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3. Basic concepts for InSAR over a spherical earth

The Theory

The natural variation of a LOS vector across a scene, caused by the shape of the earth, introduces a gradient of phase across the scene (see Figure 5). The effects of a spherical earth must therefore be removed by 'flattening' the interferogram. We do this by calculating what the gradient of phase change would be assuming that the earth is a sphere, and that there is no topography and has been no surface deformation, and subtracting this from the interferogram. The math behind the removal of phase caused by the shape of the earth is a good introduction to the concepts of interferometry.

Figure 5 Fringes over a spherical earth (exaggerated for effect).


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The Math

What follows are the calculations for obtaining e. They follow the steps of, for example, Zebker et al, 1994, Price and Sandwell, 1998, Price, 2001, Chapter 1, but I have expanded them in tedious detail.

Figure 6 Diagram of geometry for InSAR over a spherical earth. A1 and A2 represent the two sensor positions. is range from A1, + is range from A2. B is the baseline length, with components perpendicular and parallel to the line of flight indicated by and . is the look angle (the angle between the radar ray and the vertical) and is the angle between the baseline and the horizontal.


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For a case with two satellite positions and no topography, the phase difference will only have a contribution from the difference in range over the scene, e, caused by a spherical earth:

Remember the Cosine Rule:

... and set the Cosine Rule up for the geometry in Figure 6

.

Through a collection of trigonometric manipulations (which you could skip reading), we can simplify the right hand side of this equation:

The trig law

means that we can write (**)

This can be simplified further by using the trig laws

to write .

This means that we can write Equation ** as


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Substituted into the original equation, this gives

Expanding the left hand side gives:

Now we start making approximations to simplify things further. e is very small, so e2 is going to be so tiny that we can ignore it. We can also subtract 2 from both sides.

Then, by dividing each side by 2, we get:

(Zebker et al, 1994, swap this around to get , but

how?)

Now we make another assumption - for spaceborne geometries, is going to be very large compared to B (approximately 800km compared to less than several hundred meters), so we can pretty much pretend that the paths from the two antennas are parallel. This idea was introduced by Zebker and Goldstein (1986), and is now termed the 'Parallel Ray Approximation'. This means that B2, in the scale of things, can also be ignored, which gives:


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Now look closely at the diagram again. We can see that Bll, the component of the baseline vector that is parallel to the look direction of the reference satellite, can be described as , which we know from before can be simplified to . For completeness, we can also see that . Combining this range-baseline relationship and the equation for phase difference (

), gives us an equation for range in terms of our observables:

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Since , we can draw the geometry as shown in Figure 7, as many authors do (for example Zebker and Goldstein, 1986). Note that they change the position of to where 90- was before - I guess this is just for convenience. You can see straight away from this that . You can also see that the height of the satellite, H, is . Combining both these equations with the equation for phase difference gives an expression for H in terms of and :


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Figure 7 Alternative notation for geometry over a spherical earth.

References



Price, Evelyn J. and David T.Sandwell (1998)


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Small-scale deformations associated with the 1992 Landers, California, earthquake mapped by synthetic aperture radar interferometry phase gradients.Journal of Geophysical Research, Vol.103, No.B11, pp.27001-27016

Price, Chapter 1 (unpublished, 2001)http://topex.ucsd.edu/insar/


Zebker and Goldstein (1986)Topographic Mapping From Interferometric Synthetic Aperture Radar Observations; JGR, Vol.91, No.B5, pp.4993-4999

Zebker, Howard A., Paul A. Rosen, Richard M. Goldstein, Andrew Gabriel and Charles L. Werner (1994) On the derivation of coseismic displacement fields using differential radar interferometry: The Landers earthquakeJournal of Geophysical Research, Vol.99, No.B10, pp.19617-19634


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4. Basic concepts for measuring topography

The Theory

If the range from two different sensor positions to a single point on the surface of the earth is known, along with the distance between these sensor positions, then it is a relatively simple geometric problem to calculate the position of the point on the surface. If two SAR images are taken from slightly different positions and the backscatter phase does not change between them, then the measured phase difference will be proportional to the difference in range from the sensor positions to each pixel. Simultaneous measurement of range, azimuth angle and elevation angle can therefore provide 3D coordinates for each pixel. Slant range measurements of topography can be converted to ground range to make DEMs in map projection.

The Math


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Figure 8 Diagram of geometry for InSAR over a spherical earth with topography. Notation is the same as for Figure 6 except that o is the look angle from the reference satellite to a spherical earth with no topography and t is the distortion to this angle caused by the presence of topography.

Having been through the derivation of the equations for InSAR geometry on the spherical earth with no topography in Chapter 3, it is now relatively easy to convert these equations into a calculation for topography on a spherical earth.


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The phase is now dependent on contributions from both spherical earth (e) and topography (t):

We must now, therefore, write equation from Chapter 3 as .

Expanding the equation (using the trig laws from Chapter 3) gives,

and.

We can again make approximation here due to the scale of spaceborne geometries, as t is going to be very small. For very small angles (if

they are measured in radians) and , so

and

.

(***CHECK!***) Putting these into the original equation gives

= (except that it doesn't exactly, so I must have missed something here?)

Remembering that and , we can therefore write:


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We can now remove e from these equations using the equation for Bll and the fact that , leaving only a relationship between range and topography; or .

We will actually measure , the phase difference between the two images. We know that is a function of this range difference, .

Combining the equations for range and phase difference ( ) we

get:

We can also use trigonometry to calculate the vertical height of the antennas:

, then use the above equation to calculate an equation for H in terms of our observables:

(CHECK!) Somehow do trig manipulation on to get o+o separate to the rest of the equation, then put this into equation for H.

Combining this equation for H with along-track distance, x, and slant range measurements will give a topographic map in the coordinate system x, and H. [This next bit's from Zebker, 1986, and I'm not quite sure what y is relative to the diagram...??] If we want to transform the coordinate system from slant range to ground range (i.e. x, y and h coordinates (where h is ground elevation)), we can calculate true ground range from the antennas to each pixel using . The image must also be rectified to fit a square grid.


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SAR Systems for measuring topography

There are two different system configurations for measuring topography:

Dual Antenna SystemsIn dual antenna systems, two antennas are mounted on the same platform, so there is a fixed baseline between them and the geometry of the system is well constrained. The Shuttle Radar Topography Mission (SRTM) is the best example of a 'dual antenna system' - see Chapter 14 for more details..

It is worth noting that if the same transmitter is used for both antennas, the phase equation for one-way propagations differences should be used. If each antenna transmits and receives, use the two-way propagation phase equation.

Single Antenna SystemsTopographic mapping using a single antenna is usually called 'repeat-track' or 'dual-pass' interferometry. This is how most space-based systems operate. As the system only has one antenna, the 'slave' image must be obtained in a second orbit following that of the 'master' image. This means that the orbit parameters for the two image takes must be well constrained so that second satellite is in a similar orbital position to the first and so that the baseline between the two satellite positions can be calculated. For repeat track systems you should use the two-way propagation formulae for phase.


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The ERS Tandem mission is a good example of a repeat track system. It was designed to measure topography, so ERS-1 followed ERS-2 in the same orbit, with a one-day separation.

References



Price, Evelyn J. and David T.Sandwell (1998)Small-scale deformations associated with the 1992 Landers, California, earthquake mapped by synthetic aperture radar interferometry phase gradients.Journal of Geophysical Research, Vol.103, No.B11, pp.27001-27016


Toutin, Thierry and Laurence Gray (2000)State-of-the-art of elevation extraction from satellite SAR data.ISPRS Journal of Photogrammetry and Remote Sensing, Vol.55, pp.13-33

Zebker and Goldstein (1986)Topographic Mapping From Interferometric Synthetic Aperture Radar Observations; JGR, Vol.91, No.B5, pp.4993-4999



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SRTM Website:http://www.jpl.nasa.gov/srtm


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5. Basic concepts for measuring surface deformation

The Theory

If two images are taken from exactly the same sensor position of the exactly the same target, at different times, and the returned phases are different, then these different phases relate to a change in the range from the satellite to the target, indicating a change in position of the target. This means that by differencing the phase of images taken before and after the ground has moved, changes towards or away from the satellite can be measured as millimeter level line of site (LOS) (i.e. along the path of the radar signal) displacements.

InSAR can ONLY measure LOS displacements. It can only measure a change in the surface along the look direction of the satellite, not a full, 3D displacement vector. Additional information can be obtained by using images from both ascending and descending orbits (see Chapter 5), but this is at the cost of increased complication in processing and the mercy of data availability.

If the orbits of two satellite passes were repeated perfectly, the phase would only contain a measure of the deformation, but since the two images are unlikely to have been taken from exactly the same position, the phase difference between the two will include both a measure of the deformation and a measure of topography. In order to quantify only surface displacement, therefore, the effects of topography must be removed.


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The Math

Figure 9 Geometry for InSAR over a spherical earth, with topography, that has undergone deformation (d). Notation is the same as for Figure 8, except that d is the change in look angle caused by the surface deformation.

If deformation has taken place, the phase can be written as

, where e represents the range change due to a


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spherical earth, t represents range change due to topography and d represents range change due to surface deformation.

We already know how to remove e (see Chapter 2), which leaves t to be removed in order to isolate d.

Removing Topographic Fringes

Independent DEMs

To use this method, a DEM must be available from external sources. The DEM is used to create a synthetic topographic fringe pattern, which is then subtracted from the interferogram to leave only the fringes caused by surface deformation (Massonnet and Feigl, 1995).

Three-pass, differential InSARThis method is otherwise termed 'double differencing', or, particularly when more than 3 images are used, the 'N-pass' method (see Figure 10). A DEM is created from two SAR images, with at least one unrelated to the pair of interest. This DEM is then subtracted from the interferogram thought to show surface displacement. (Gabriel et al, 1989, Zebker et al, 1994).


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Figure 10 Geometry for the 'N-Pass' method of measuring surface deformation.

References




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Massonnet, D., and K.L.Fiegl (1995)Discrimination of geophysical phenomena in satellite radar interferograms.Geophysical Research Letters, Vol.22, pp.1537-1540

Massonnet, D. and K.L.Feigl (1998)Radar interferometry and its application to changes in the earth's surfaceReviews of Geophysics , Vol.36, pp.441-500



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6. How to make an interferogram - initial steps

Data Processing

Raw data consists of radar echoes collected from the surface. These must first be processed so that each pixel contains amplitude and phase information. Processing algorithms are based on the signal characteristics of the sensor and the satellite orbit. Data that contains amplitude and phase information as an array of complex numbers is called Single Look Complex (SLC). As you can see in Figure 11,complex data looks pretty noisy, and not at all like the amplitude-based radar images we're used to seeing, which have had speckle removed.

Figure 11 An ERS-1 scene over Prudoe Bay, Alaska, in complex format (from the ASF website).


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Corectification

Common pixels between the two images must be mapped, in order that the two images may be overlain exactly. Differences in geometry, and differences caused by inconsistencies in satellite design, must be accounted for; i.e. it may be necessary to warp or stretch one image to fit well over the other. Differences in satellite velocity can cause differences between the two images, giving a systematic along-track distortion. Although the baseline is ideally aligned parallel to the flight track, satellite tracks will usually be divergent, which also introduces a 'linear shear'.

If the pixels are not properly aligned at a sub-pixel level, the random part of the phase caused by scatterers in the image will not cancel out between images. The precision of this alignment must be better than 100s (<1m) along-track and 5ns (<1m) in range for a 5x8m ERS pixel (Burgmann et al, 2000).

bit on how this is automated, and using baselines to do it?

The wavelength scale is of the order of tens of centimeters and the spatial resolution tens of meters, so significant changes to the phase will be insignificant to registration of the images.

Interferogram creation


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To create the interferogram itself, the complex pixels of the 'master' image must be multiplied by the complex conjugates of the same pixels of the 'slave'. This will result in an image in which each cycle of color, or 'fringe', represents a phase change of 2 radians.

A word on complex numbers:If the amplitude and phase of a pixel in the master image is denoted by

, the complex conjugate of the same pixel of the slave will be . and are the real and imaginary parts, respectively. If you

multiply these together, you get . A property of the imaginary unit is that . This means that we can write the previous equation as , which shows that multiplying the complex pixels of the master image by the complex conjugates of the slave actually produces an image that shows the difference in phase between the two images..... not strictly true - go over this.

The phases for each image may not be the true phases corresponding directly to range, since phase errors can result from processing, but as long as the same processing is performed for each image, the phase errors should all the identical, so when images are differenced they should be eliminated (Gabriel et al, 1989).

References


The Alaska SAR Facility:http://www.asf.alaska.edu/


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JPL's ROI-PAC processing software:http://www.seismo.berkeley.edu/~dschmidt/ROI_PAC/

Atlantis Scientific's Webpage:http://www.atlsci.com


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7. Baselines and Orbits

The previous sections have shown the importance of having an accurate knowledge of satellite position and the length of baseline between the satellite position for each image. We saw in Chapter 3, for example, that any ambiguities in baseline calculation will be translated through the flattening operation into a distortion in the interferogram. Errors in the baseline will lead to a nearly constant gradient of deformation across a scene, which can account for up to 6cm ground relative displacement. (Klinger et al, 2000). Adjustment of the baseline length to minimize this distortion, usually carried out by trying to minimize deformation fringes in areas with known zero displacement, is therefore a part of the InSAR processing technique.

The radar satellites currently in use were not designed specifically for InSAR, so their orbits are not as well constrained as we would like. It is now possible to design satellites with orbit accuracies of a few cm (this is a science in itself - see David Sandwell's notes on orbits (2001)), but for now we must make the best of what we have. ERS-1 and -2 have the best orbit control so far.

Optimum baseline length is a function of radar wavelength and the desired result. If the aim is to measure surface deformation, the baseline should be as short as possible, to eliminate the effects of topography. If the aim is to measure topography, the baseline should not be too short, as this will reduce the sensitivity to surface height, but also not too long, as the speckle effects for the images will be too different and the interferogram will suffer incoherence and decorrelation. If terrain is mountainous, smaller baselines are optimal. If terrain is slight, larger baselines are necessary to measure topography.


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The dependence on sensor type and wavelength comes from the fact that both observations should be within the effective beam width of a reradiating resolution element (Gabriel et al, 1989). The use of RADARSAT's fine-beam mode (see Chapter 15) allows for baselines of approximately 1km, which gives greater sensitivity for measuring topography (although is very difficult to use for measuring deformation). Optimal baselines for measuring topography with ERS-1 and -2 usually fall within 300 and 500m.

The importance of which direction the antennas are separated is also a function of the purpose of making the interferogram. If the antennas are separated parallel to the line of flight (in 'azimuth', with no 'cross track' separation) then surface deformations are more easily measured as topographic effects are minimized. Processing must remove the effects of pitch, yaw and roll of the platform. Antennas separated perpendicular to the line of flight (in 'range') will measure topography, after the component of the baseline that is not perpendicular to the line of flight is estimated and geometric rectification applied (Gabriel et al (1989).

The orbit information that comes in the header files of the image data is not usually accurate enough for the purposes of InSAR. Precise orbits can be computed by locating ground control points on the image, or, in the case of ERS, download from Delft University (see Chapter 15). A good illustration of how important it is to use precise orbits, when available, is in a paper about creating an interferogram over the 1999 Hector Mine earthquake, by Sandwell et al (2000): "The first interferogram, formed 19 hours after the download, had an artificial cross-track slope of 20 fringes (560mm) caused by errors in the predicted orbit. The interferogram was re-computed 5 days later using


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the more accurate 'fast-delivery' orbit and no slope corrections were needed."

Sun et al (2000) discuss the merits of using large numbers of ground control points (GCPs) to improve baseline estimates by calculating the precise 3D position of the satellite. Since the baselines are rarely parallel, it is often necessary to compute a number of baselines at several points along the flight lines. They don't mention how they obtain these GCPs, but I guess they identify bright reflectors in the image and then survey these using either traditional surveying techniques or GPS.

An interesting proposal by the people at UCSD is to place radar reflectors at GPS stations (or place them nearby and tie them precisely to the GPS stations using ground survey methods). It should then be possible to precisely locate these SAR pixels to precisions of less than 1mm. I'm not sure if anyone else has tried this yet (CHECK).

Computing baselines, from Price and Sandwell (1998):If s(t1) is the position of the satellite at time t1, and time s(t2) is the position at the time of closest approach (where and

), then the baseline length is .

The baseline elevation angle, , is , where Bv and BH are the

local vertical and horizontal components of the baseline; ,

(this is positive in the radar look direction).


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Figure 12 Baseline geometry.

Satellites can usually view a scene from the different directions (which is useful for measuring deformation in more dimensions that just LOS). Ascending orbits fly south to north. Descending orbits fly north to south.

References

Klinger, Yann, Reni Michel and Jean-Phillipe Avouac (2000)Co-seismic defomation during the Mw 7.3 Aqaba earthquake (1995) from ERS-SAR interferometryGeophysical Research Letters, Vol.27, No.22, pp.3651-3654


Sandwell's notes on orbits:http://topex.ucsd.edu/insar/orbits.pdf

Scharoo, R and P.N.A.M. Visser (1998)Precise orbit determination and gravity field improvement for the ERS satellitesJournal of Geophysical Research, Vol.103, pp.8113-8127

Guoquing Sun, K.Jon Ranson, Jack Bufton and Micheal Roth (2000)Requirement of Ground Tie Points for InSAR DEM Generation


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Photogrammetric Engineering and Remote Sensing, Vol.66, No.1, pp.81-85

InSAR/GPS Integration:http://topex.ucsd.edu/SAR/proposals/sar_gps.html


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8. Phase Unwrapping

Although the final fraction of a wave that was received at the satellite is known, the integer number of complete wavelengths that came before this is not. Referring to Figure 4 this means that we do not know how many times looped round the circle before it was finally measured at the sensor as as a fraction of 2). There is therefore an integer number, which must be calculated and then multiplied by 2(people call this 'knowing the phase modulo 2') in order to obtain the total distance between the sensor and each pixel. This is very similar to ambiguity resolution for very precise, carrier-wave GPS surveying. In other words, a phase measurement of x radians cannot be distinguished from a phase measurement of x+2n radians, where n is any integer (Zebker and Goldstein, 1986), so targets at different heights can still appear at the same phase.

As an example, if a phase change of 2 is equal to 11.8cm of displacement along the LOS for JERS-1 data (Kimura and Yamaguchi, 2000), for 20cm of displacement the phase change is 3.4. Because the phase can only be modulo 2, though, only 1.4 will be recorded by the satellite.

For DEMs of areas with very slight relief, or differential interferograms of areas that have undergone very little deformation, it is not always necessary to unwrap. It may also be easy in some cases to interpret the image without the hassle of unwrapping. If an image of surface displacement is to be unwrapped, it is usually easier to unwrap the image containing the deformation phase, rather than the images containing topographic phase, as this is likely, although not always, in the case of


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large earthquakes, to be a smaller phase change than that for topography.

Although there have been many attempts made at developing an automated unwrapping technique, this step still requires user input and a certain level of artistic license. Whilst fringes may be visible to the naked eye, computer algorithms often find them harder to distinguish, particularly if the noise level is high. This is something to bear in mind when deciding whether to unwrap or leave wrapped, as unwrapping can lead to loss of signal over areas that had fringes that were visually interpretable.

The general method for phase unwrapping is to choose a starting location, where there is little noise and the phases are bright and clear, then unwrap its neighbors in expanding contours by adding the multiple of 2 to them which minimizes the phase change between adjacent points. This still leaves a global 2m ambiguity, where m is an underdetermined integer constant. This ambiguity can only be removed using ground control points (Zebker and Goldstein, 1986, Gabriel et al, 1989).

Problems arise when the algorithm encounters a sharp jump in phase, or when the phase is very noisy. This is where the user's understanding of the image comes into play, as they must delimit phase breaks, over which the algorithm will not integrate. For example, in interferograms over an earthquake rupture, incoherence is likely to be a serious problem close to the fault, causing difficulties in phase unwrapping. A previous geological map of the fault can be useful for defining a discontinuity in along the fault, over which the phase may not be directly unwrapped.


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Common phase unwrapping techniques

Iterative Disk MaskingA number of seeds are placed over the image and each seed acts as a new starting point for phase unwrapping, as phase differences are integrated in expanding contours. These seeds are placed in areas with good coherence and where phases have little noise. This is the method that the Atlantis Scientific EarthView InSAR software uses.

The Goldstein, Hartle and Nearest Neighbor MethodsAll these techniques are fairly similar. They calculate the gradient from one point to the next and integrate this to form a smoother path (Goldstein, 1998). Phase along a closed path should return to the starting value.

Least SquaresThis usually minimizes the function that describes the difference between wrapped phases of adjacent rows and columns. It is more effective than some other methods as it can work for corrupt data and poor geometry, but it has the disadvantage that it will not just calculate integer numbers of cycles (Zebker and Lu, 1997).

References


Goldstein, R.M., H.A.Zebker and C.L.Werner (1988)


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Satellite radar interferometry: Two-dimensional phase unwrappingRadio Science, Vol.23, pp.713-720

Kimura, Hiroshi and Yasushi Yamaguchi (2000)Detection of Landslide Areas Using Satellite Radar Interferometry.Photogrammetric Engineering and Remote Sensing, Vol.66, No.3, pp.337-344


Zebker, H.A. and R.M.Goldstein (1986)Topographic Mapping From Interferometric Synthetic Aperture Radar Observations; JGR, Vol.91, No.B5, pp.4993-4999

Zebker, Howard A. and Yanping Lu (1997)Phase Unwrapping Algorithms for Radar Interferometry: Residue-Cut, Least Squares and Synthesis AlgorithmsSubmitted to JOSA-A (on Howard Zebker's webpage)


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9. Phase Gradients

The use of phase gradients can eliminate the need for phase unwrapping.Like phase differences, phase gradient is a function of topography and surface deformation. Phase gradient caused by topography can be eliminated from interferograms using the same technique as that for phase difference. Phase gradient is computed from the real and imaginary parts of the interferogram (hence it is unique and there are no 2 ambiguities). The phase gradient can also be scaled by any real number (unlike phase difference, which can only be scaled by an integer number).

Large scale deformations don't show up that well on phase gradient images - they appear as more of a regional shift than local displacements. The big advantage of using a phase gradient approach, however, is that it is very sensitive to small displacements, that otherwise may not be identified.

"Small scale deformations are associated with secondary fractures, preexisting faults, dry lake beds, and mountainous regions; they provide insight into the formation of such geomorphic features and help define the role of these features in fault interactions" (Price and Sandwell, 1998).

Price and Sandwell, 1998, use phase gradients to examine short-wavelength features of the 1992 Landers Earthquake, which reveal previously unresolved strain patterns.

The Math


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The phase gradient (note the symbol - don't confuse this with phase difference, - the indicates that it is a gradient operator), can be

expressed as , where R and I are the real and

imaginary parts of the complex SAR signal (from Price and Sandwell, 1998).

more on this - how did they get this expression?see Price and Sandwell, p27006

References

(CHECK!) Peltzer, G., K.W.Hudnut and K.L.Feigl (1994)Analysis of coseismic surface displacement gradients using radar interferometry: new insights into the Landers earthquakeJournal of Geophysical Research, Vol.99, No.B11, pp.21971-21981



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10. Quantifying displacement

Reading the interferogram

The basic information that you need to know to interpret an interferogram is the wavelength of the sensor, as this will tell you what change in range to the satellite each fringe (a whole cycle of color) represents. Each fringe represents one half of the wavelength, which is equal to a 2 increment of phase. For example, this number is 28mm for ERS satellites, which have a full wavelength of 56mm.

To calculate the total amount of displacement at a point in an unwrapped interferogram, it is usual to estimate where the fringe of zero displacement is, which is far from the earthquake, and then count back from there. Alternatively, you can take a point with a known displacement (from a survey point or GPS station, for example), translate this displacement into LOS displacement, and count from there. It is important to look at the key and see which order of fringes represents movement towards the satellite. The opposite order will represent movement away from it (like in Figure 13).


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Figure 13 Interpreting interferogram fringes.

Some computer algorithms have been created to automatically create a grid over the area and calculate height or displacement at each point (for example Beauducel et al, 2000). This allows for calculation of standard deviations.

InSAR only measures 1D changes along the LOS. If you only have orbits flown in one direction, therefore, only 1D displacements can be resolved. The addition of data from other, non-parallel, orbits will allow for resolution of the displacement vectors in their 3D entirety. In practice, we can only resolve a maximum of two components of displacement from satellite measurements, from ascending and descending orbits, and


48

this depend on whether data from both directions is available. Problems can occur where displacement is close to perpendicular to the LOS.

Inverse Methods

Displacements taken from differential interferograms can be used in conjunction with inverse mathematics (simulated annealing seems to be a particularly popular method, since it explores the whole model space and does not allow for local minima) to estimate fault parameters such as location, length, strike, dip and width, along with variable slip distributions along the length of the rupture. The derived fault parameters and equations for displacement in a layered elastic space (such as those of Okada, 1985) can be used to form synthetic interferograms (by calculating ground displacements over a grid and converting these to LOS displacements), which when differenced with true interferograms can outline InSAR noise and deficiencies in the slip distribution, along with artifacts that cannot be explained by simple models of deformation (eg. Delouis et al, 2000).

Studies such as that by Hurst et al (2000) have also investigated comparisons between SAR interferograms and synthetic interferograms derived from the inversion of GPS data. These also have the potential for outlining atmospheric noise, problems in phase unwrapping and features in InSAR images that could not have been identified with GPS alone.

References

Beauducel, Francois, Pierre Briole and Jean-Luc Froger (2000)


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Volcano-wide fringes in ERS synthetic aperture radar interferograms of Etna (1992-1998): Deformation or tropospheric effect?Journal of Geophysical Research, Vol.105, No.B7, pp.16391-16402

Delouis B., P.Lundgren, J.Salichon and D.Giardini (2000)Joint inversion of InSAR and teleseismic data for the slip history of the 1999 Izmit (Turkey) earthquakeGeophysical Research Letters, Vol.27, No.20, pp.3389-3392

Hurst, Kenneth J., Donald F.Argus, Andrea Donnellan, Michael B.Heflin, David C.Jefferson, Gregory A.Lyzenga, Jay W.Parker, Mark Smith, Frank H.Webb and James F.Zumberge (2000)The coseismic geodetic signature of the 1999 Hector Mine EarthquakeGeophysical Research Letters, Vol.27, No.17, pp.2733-2736

Okada, Yoshimitsu (1985)Surface Deformation due to Shear and Tensile Faults in a Half-spaceBSSA, Vol.75, No.4, pp.1135-1154


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11. Atmospheric Effects

The Theory

Since InSAR is based on converting precise time delays and phase shifts into range distances, a propagation speed must be assumed. This is normally taken to be constant, as if the wave was passing through a homogeneous medium. ERS satellites, as an example, orbit at approximately 790km. This means that the electromagnetic wave must pass through the ionosphere, stratosphere and troposphere, and it must do this twice. The signal will therefore travel through several changes in the index of refraction (as a result of changes in pressure, temperature and water content) before returning to the sensor. The refractive indices of the atmosphere are higher than that of free space, which lowers the velocity of the radar wave, lowers the propagation time and therefore contaminates the distance measurement.

Atmospheric effects are spatially variable and can produce up to 80 to 290m of topographic error for baselines between 400 and 100m (Zebker et al, 1997) and up to 10cm error in displacement in repeat pass differential interferograms for humidity variations of 20% (Lu et al, 2000). The greatest problem with atmospheric noise is that it can contaminate the deformation signal, leaving interpretation open to debate. Larger baselines have smaller propagation effects (why?) and, sadly, smaller baselines, which we need to get the most accurate measurements of deformation, are affected the most.


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The troposphere is the worst offender, due to its unstable nature and variable humidity. Ionospheric effects can also, however, lead to signals in interferograms, and are important in the auroral zone of polar regions.

Areas of high humidity, particularly at lower elevations and higher temperatures, will suffer the most from atmospheric effects, whereas high, dry areas will suffer the least. The atmosphere is generally more stable at night.

Longer wavelengths are affected less than shorter wavelengths. Would it be possible to remove ionospheric effects if you have two wavelengths, like you can for dual-frequency GPS?

Recognizing atmospheric effects

Short wavelength artifacts are the most easily confused with tectonic deformations. They typically have length scales of 5-10km, causing as much as 10cm excess two-way range (Price and Sandwell, 1998). This means that atmospheric effects can account for up to 3 fringes in an ERS interferogram (each fringe usually represents 2.8cm displacement).

Long wavelength artifacts are most likely to cause a planar phase gradient over the interferogram, which looks similar to the effect of miscomputing the baseline length. In fact, one of the easiest ways to reduce the effect of long wavelength atmospheric artifacts is to adjust the baseline length until fringes are not seen in areas with known minimal displacement.


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Removing atmospheric effects

If there are multiple scenes over the area (and you have the money to obtain them) then stacking is an effective technique for removing atmospheric effects. It basically just averages all the interferograms to create one image with a noise level of , where N is the number of interferograms used. It doesn't actually eliminate atmospheric features, but it will reduce their amplitude. The reduction of noise not only helps reduce atmospheric effects, but also aids in phase unwrapping.

Alternatively, an independent source such as GPS (see below) or meteorological measurements of pressure and humidity can be used to calibrate the image, by using measurements of atmospheric delay at a few points to build a model over the whole area.

If the position of a continuously monitoring GPS receiver is well constrained, then any delays in the signal from the GPS satellite to the receiver can be calculated. These delays can then be used to calculate atmospheric delay. It is, in fact, usual practice to estimate tropospheric delay when processing highly accurate GPS, with the intention of removing it from the signal. Inversion of the atmospheric delay at GPS points, to solve for atmospheric delay over the entire region, can then aid in the correction of interferograms (Williams et al, 1998), although the fact that the troposphere is so variable over small distances can cause problems.

Sandwell and Sichoix (2000) suggest a method of using a low resolution DEM (up to 1km spacing) to constrain the long-wavelength phase errors. A similar technique to this would be to compare GPS heights with heights obtained through InSAR as a means of calibration.


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As a last resort it is possible to use external information such as geological measurements, to remove atmospheric effects by reducing the number of fringes in areas that should show little deformation. This method is to be avoided if possible, as it introduces scope for purposely fitting the results to an alternative dataset.

The Math

The following is taken mainly from Zebker(1997):

The complex amplitude of a unit intensity plane wave at position x in a medium is , where n(x) is the variable refractive index, is

wavelength and k is the wavenumber ( ).

If we differentiate this, we get a relation between incremental path

length dx and incremental signal phase d in the form .

Integrating along the propagation path then gives

If the wave is propagating through a vacuum, then n(x)=1, so we get the

familiar equation . In the previous chapters, therefore, we only

considered the phase to be dependent on wavelength and range x.

For the earth's atmosphere n(x) is not a constant (but always real and just a little greater than 1), which makes things more complicated by introducing an additional phase shift. We model n(x) for the earth's


54

atmosphere as 1 + 10-6N(x), where N(x) is the refractive index. The 10-6 shows how small the change from our value of n(x)=1 really is.

We can therefore write the previous equations as ,

or , where . (x)dry represents hydrostatic

delay and (x)wet represents delay due to water vapor.

References

Beauducel, Francois, Pierre Briole and Jean-Luc Froger (2000)Volcano-wide fringes in ERS synthetic aperture radar interferograms of Etna (1992-1998): Deformation or tropospheric effect?Journal of Geophysical Research, Vol.105, No.B7, pp.16391-16402

Goldstein, R.M. (1995)Atmospheric Limitations to repeat-track radar interferometryGeophysical Research Letters, Vol.22, pp.2517-2520

Hanssen, Ramon F., Tammy M.Weckwerth, Howard A.Zebker and Roland Klees (1999)High-resolution Water Vapor Mapping from Interferometric Radar Measurements.Science, Vol.283, pp.1297-1299

Lu, Zhong, Dorte Mann, Jeffrey T.Freymueller and David J.Meyer (2000)Synthetic aperture radar interferometry of Okmok volcano, Alaska: Radar observationsJournal of Geophysical Research, Vol.105, No.B5, pp.10791-10806


Sandwell, David T and Lydie Sichoix (in press, 2000)


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Topographic Phase Recovery from Stacked ERS Interferometry and a Low Resolution DEMSubmitted to Journal of Geophysical Research

Tarayre, J. and D. Massonnet (1996)Atmospheric propagation heterogeneities revealed by ERS-1 interferometryGeophysical Research Letters, Vol.23, pp.989-992

Williams, Simon, Yehuda Bock and Peng Fang (1998)Integrated satellite interferometry: Tropospheric noise, GPS estimates and implications for Interferometric synthetic radar products.Journal of Geophysical Research, Vol.103, No.B11, pp.27051-27067

Zebker, Howard A., Paul A. Rosen and Scott Hensley (1997)Atmospheric effects in interferometric synthetic aperture radar surface deformation and topographic maps.Journal of Geophysical Research, Vol.102, pp.7547-7563


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12. Limitations, Advantages and Resolution

Resolution

Figure 14 shows the factors that limit the spatial dimensions of detectable signals. These include the sensor parameters of pixel size, signal noise and swath width (see Table 2, p. 65, for these parameters for various sensors), the upper and lower limits of the amount of deformation and atmospheric noise effects. Deformation signals which are spatially smaller than a pixel or larger than a scene cannot be detected by InSAR alone. These limits on spatial resolution of deformation can be changed by processing techniques such as stacking and filtering.

Figure 14 Spatial limitations of measuring deformation for the ERS satellites. Taken from Price (2001), Chapter 1.


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Phase noise can prevent measurements of deformation signals that are smaller than a few mm. Massonnet (1995) suggests measurements of the Landers earthquake with a typical precision of 2 to 10 mm over a 35000km2 area. To measure deformation to a greater precision than this, we must better understand all the effects on phase, particularly the atmosphere.

Limitations

Spatial Decorrelation

Larger baselines mean better resolution of topography and decreased levels of atmospheric noise, but they also mean that the reflection from scatters in each pixel can change. Even if we were measuring deformation and had a way to remove atmospheric effects, it is still not always possible to get short baselines, since orbit control of the SAR satellites is not very precise. This prevents successful coregistration and phase unwrapping of images, leaving areas of gray where phase cannot be interpreted.

Layover is also a problem, with gray areas caused by blocking of the surface from the view of the satellite by relief. This is particularly a problem in mountainous areas, and for systems with steep look angles.

Temporal Decorrelation

If there is a long time between data takes, the interferogram can suffer decorrelation as the scatterers in each pixel change over time. This is particularly a problem in vegetated areas, and areas of heavy


58

agriculture, where the scatterers change every time a field is ploughed or a new crop grown.

The problem is not so bad in the desert, and interferograms spanning as much as 7 years have been made over very dry regions, although even changes in the surface caused by sand blowing can cause decorrelation.

Advantages

Don’t need line of sight between stations. All-weather Can be done at night. High spatial resolution (approx 20m pixel spacing) compared to

other geodetic techniques. No need for instrumentation on the ground. Particularly sensitive to vertical displacements, unlike GPS Worldwide coverage

References


Massonnet, D. (1995) Application of Remote Sensing Data in Earthquake Monitoring.Adv. Space Research, Vol.15, No.11, pp.1137-1144


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13. Applications in neotectonics

The first study to introduce the idea of double differencing to measure surface deformation was published by Gabriel et al (1989). The study uses Seasat data over Imperial Valley, California, to measure ground swelling caused by water-absorbing clays. Massonnet (1995) then used space-based InSAR, with ERS data, to dramatic effect over the 1992 Landers earthquake (see Figure 15) and Goldstein (1993) demonstrated the utility of InSAR for measuring glacial ice flow in Antarctica. Since these studies, there have been increasing numbers of studies using InSAR to monitor neotectonics, with increasingly imaginative uses for the technique. What follows is just a few examples of interesting studies.

Near real-time studies

Sandwell et al, 2000, have illustrated the utility of InSAR for near real-time mapping of the 1999 Hector Mine earthquake. The ability to produce interferograms within days after an event will be a huge help to geologists, since the interferograms will illuminate areas of rupture for mapping, and ensure that smaller ruptures are discovered and mapped before the surface traces have been destroyed.

Near real-time InSAR can only be achieved with efficient ground stations for SAR data download, reliable processing software and precise, real-time orbits. The timing also depends on the timing of an overflight of a SAR satellite after the event. Sandwell et al, 2000, produced an interferogram 20 hours after the first orbit of the area after the earthquake, and this was 4 days after the earthquake.


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Figure 15 Interferogram of deformation caused by the 1992 Landers Earthquake. One fringe represents 2.8cm of motion. Image was taken from http://www-ee.Stanford.edu/~zebker/stanfordreport/landersigramcolor.gif.

Studies of dynamic processes

Delouis et al, 2000, use a combined inversion of InSAR and teleseimic data to study the distribution of slip with respect to both space and time, at the time of an earthquake. The use of both data sets limits tradeoffs between rupture timing and slip location, in that InSAR provides a


10km

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detailed slip distribution upon which to base teleseismic measurements. Previous studies of this nature, without geodetic constraints on slip, could not determine if changes in rupture velocity were real, or a function of the tradeoff. The study showed that for stretches of the fault with high coseismic displacements, rupture velocities were high, whereas stretches of the fault with low coseismic displacements saw lower rupture velocities. The slower patches correspond with geological barriers, i.e. stronger patches of ground.

Postseismic Deformation

"Postseismic deformation includes aftershocks, afterslip on and surrounding the coseismic rupture, transient slip on nearby faults, and viscous relaxation of the mid- to lower- crust and upper mantle" (Burgmann et al, 2000).

By characterizing post-seismic deformation after an earthquake using geodetic measurements, it is possible to quantify ductility of the upper mantle and thus characterize the strength of the lithosphere. Previous studies have been hampered by the problems of separating broadscale, deep relaxation and localized crustal afterslip, which can give similar deformation patterns. A combination of horizontal measurements from GPS and vertical measurements from InSAR can help to avoid this problem. Pollitz et al (2000) use such a combination to characterize mantle viscosity after the 1992 Landers Earthquake.

References

Burgmann, R., E. Fielding and J. Sukhatme (1998)


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Slip along the Hayward fault, California, estimated from space-based SAR interferometryGeophysical Research Letters, Vol.24, pp.37-40

Delouis B., P.Lundgren, J.Salichon and D.Giardini (2000)Joint inversion of InSAR and teleseismic data for the slip history of the 1999 Izmit (Turkey) earthquakeGeophysical Research Letters, Vol.27, No.20, pp.3389-3392

Gabriel, A.K., R.M.Goldstein and H.A.Zebker (1989)Mapping small elevation changes over large areas; differential radar interferometry.Journal of Geophysical Research, Vol.94, No.7, pp.9183-9191

Goldstein, R.M., H.Engelhardt, B.Kamb and R.M.Frolich (1993)Satellite radar interferometry for monitoring ice sheet motion: Application to an Antarctic ice streamScience, 262, pp.1525-1530

Klinger, Yann, Reni Michel and Jean-Phillipe Avouac (2000)Co-seismic defomation during the Mw 7.3 Aqaba earthquake (1995) from ERS-SAR interferometryGeophysical Research Letters, Vol.27, No.22, pp.3651-3654

Massonnet, D. (1995) Application of Remote Sensing Data in Earthquake Monitoring.Adv. Space Research, Vol.15, No.11, pp.1137-1144

Massonnet, D., M.Rossi, C.Carmona, F.Adragna, G.Peltzer, K.Feigl and T.Rabaute (1993)The displacement field of the Landers earthquake mapped by radar interferometryNature, Vol.364, pp.138-142

Massonnet, D., K.Feigl, M.Rossi and F.Adragna (1994)Radar interferometric mapping of deformation in the year after the Landers earthquakeNature, Vol.369, pp.227-230

Peltzer, G., K.W.Hudnut and K.L.Feigl (1994)Analysis of coseismic surface displacement gradients using radar interferometry: new insights into the Landers earthquakeJournal of Geophysical Research, Vol.99, No.B11, pp.21971-21981


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Peltzer, G., and P.Rosen (1995)Surface displacement of the 17 May 1993 Eureka Valley, California earthquake observed by SAR interferometryScience, Vol.286, pp.1333-1336

Pollitz, Fred F., Gilles Peltzer, Roland Burgmann (2000)Mobility of continental mantle: Evidence from postseismic geodetic measurements following the 1992 Landers earthquakeJournal of Geophysical Research, Vol.105, No.B4, pp.8035-8054


Sandwell, David T., Lydie Sichoix, Duncan Agnew, Yehunda Bock and Jean-Bernard Minster (2000)Near real-time radar interferometry of the Mw 7.1 Hector Mine EarthquakeGeophysical Research Letters, in press.



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14. Finding SAR data

There is a good amount of SAR data available (see Table 2 for common SAR sensors), but none of the SAR sensors were designed with InSAR in mind, so it can sometimes be difficult to find the scenes you want with the desired lengths of temporal and spatial baselines. ERS satellites currently have the best orbit control (and you can download the Delft University precise orbits for free). ESA also flew the 'Tandem Mission' from May 1995 to June 1999, in which ERS-1 and ERS-2 flew the same flight path with a one-day separation. This means that it is easier to produce topographic interferograms. With the advent of STRM this may not be such a consideration.

Satellite

Agency/country

LaunchYear

Band/Frequency (GHz)

Altitude (km)

Repetition Period (days)

Incidence Angle

Swath Width (km)

Resolution (m)

Seasat NASA/USA 1978 L (1.3) 800 3 23o 100 23ERS-1 ESA 1991 C (5.3) 785 3, 35,

16823o 100 25

JERS-1 NASDA/Japan 1992 L (1.2) 565 44 35o 75 30SIR-C NASA/USA

DASA/GermanyASI/Italy

1994 X (9.7), C (5.2), L (1.3)

225 variable 15-55o 15-90 10-200

ERS-2 ESA 1995 C (5.3) 785 35 23o 100 25Radarsat

Canada 1995 C (5.3) 792 24 20-50o 50-500

28

Table 2 SAR sensor characteristics, taken from Price (2001), Chapter 1


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SRTM

The Shuttle Radar Topography Mission (SRTM) was launched on February 11th 2000 (check?), and the mission lasted for 11 days. The aim of the mission was to map over 80% of the earth's land coverage using a dual frequency (C and X band) fixed antenna SAR system. The aim was to create a DEM of the world with 30x30m spatial sampling, <16m absolute vertical height accuracy, <10m relative vertical height accuracy and <20m horizontal accuracy. The mission was a success, but it will take them 2 years to process the data, which will probably come available in 2002. You can see the SRTM website for more details, but they have been teasing us with sample images prior to the data release, such as in Figure 16.

Figure 16 SRTM perspective view, with a LandSat overlay, of the Caliente Range and Cuyama Valley in California (from the SRTM website).

ERS data


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To decide which Track and Frame numbers you need to order:

1. Go to the European Space Agency Earthnet On-Line Interactive (EOLI) Query site - http://odisseo.esrin.esa.it/eoli/eoli.html2. Download Swing if you don't have it - you need this plug-in to run the EOLI applet. The EOLI page should prompt you to do this. Install Swing in the C directory. Restart computer after installation.3. Reload the EOLI webpage. This can take a while as it starts the applet and loads a map.4. Choose 'ERS/SAR' collection and 'Interferometry' query mode.5. Navigate and zoom in to the area you want on the map.6. Enter the start and end dates for your search.7. Click on the 'Set Area' button and draw a box around the area you are interested in on the map (you can also enter coordinates or track and frame numbers here instead).8. Click on 'Submit Query.'9. Write down the track, frame and orbit numbers for the scenes you want. .......what about baselines - check this - do you still have to go through the baseline checker:?

The data must be ordered in SLC format, or raw if you have a SAR processor available. Processing the raw data to SLC yourself allows for greater control of phase and geometry, and may make input of the data into the InSAR processor easier if the SAR processor is designed by the same manufacturers of the software.

WinSAR


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UNR is a member of the WinSAR consortium, a group of Western US universities and research groups that have formed to distribute ERS SAR data. If they have the data you need in their archive (there is a list of Tracks/Scenes on http://topex.ucsd.edu/winsar, which are shown in Figure 17 of this paper), you can ftp the scenes for free (in RAW data format, so you need a SAR processor to convert the radar echoes to Single Look Complex format for input to an InSAR software) from http://www.winsar.scec.org. You need a password to do this, which must be obtained through the university representative (at present John Bell).

Figure 17 ERS scenes currently available through WinSAR for the Western USA (maps taken from the SDSU website).


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Orbits

ERS precise orbits can be downloaded from the Delft University website. Precise orbits are available for ERS-1 and -2 satellites 4-6 months after a data take. Fast delivery orbits, which are not as accurate, are available approximately 1 week after the data take and preliminary precise orbits are available for ERS-2 approximately 1 month after the orbit has been flown.

1. First check the arclist, which can be found on their websites, to decide which 'ODR' files you need. The ODR files contain the orbital position of the ERS satellites as a function of time.

For ERS-1 orbits go to http://www.deos.tudelft.nl/ers/precorbits/orbits/ers_1dgm.shtmlFor ERS-2 orbits go tohttp://www.does.tudelf.nl.ers/precorbits/orbits/ers_2dgm.shtml

NB: 'Arc' stands for 'orbit generation run'. There are often two possible orbits for a single ERS image. The

recommended 'begin' of the precise part of the arc is in the middle, which is always over the Antarctic, so choose the orbit that best matches this - check on this.....

It is useful to write down the ancillary data for your selected orbits, especially the residuals.

2.


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ftp (in BINARY mode) the precise orbits from; falcon.grdl.noaa.gov/pub/delft/ODR.ERS-1/dgm-e04 falcon.grdl.noaa.gov/pub/delft/ODR.ERS-2/dgm-e04 (Fast delivery orbits are stored in ~/dgm-e04.fdPreliminary precise orbits are stored in ~/dgm-e04.prelim)

You will need to download both the arclist and the ODR files into the same directory. The dgm-e04 directory is named so as the orbits are based on the DGM-E04 gravity field.

If you don't know how to ftp:1. Go to the C: prompt.2. Change to the local directory you want to download orbits to by typing cd .. to move back a directory and cd dir to change to a new directory.3. Type ftp falcon.grdl.noaa.gov4. For the username, type anonymous.5. Type your email address as the password.6. Type cd pub/delft to change to the Delft directory.7. Type cd ODR.ERS-1/dgm-e04 or cd OCR.ERS-2/dgm-e04 to change to the right directory for ERS-1 or ERS-2 orbits.8. Type bin to make sure that you're going to get the ODR files in binary format.9. Type get arclist, to ftp the arclist to your local directory.10. Type get ODR.*** (where *** is the number of the ODR file that you need) (NB. To see a list of files in this directory type ls).11. Type Bye to exit ftp.

Section on finding other types of SAR data....??


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References


Scharroo, R. and P.N.A.M.Visser (1998)Precise orbit determination and gravity field improvement for the ERS satellitesJournal of Geophysical Research, Vol.103, No.C4, pp.8113-8127

Toutin, Thierry and Laurence Gray (2000)State-of-the-art of elevation extraction from satellite SAR data.ISPRS Journal of Photogrammetry and Remote Sensing, Vol.55, pp.13-33

ESA EOLI Website:http://odisseo.esrin.esa.it/eoli/eoli.html

Delft University Website:http://www.deos.tudelft.nl/ers/precorbs/orbits

WinSAR websites:http://topex.ucsd.edu/winsarhttp://www.winsar.scec.org

Sources of SAR data:http://www/atlsci.com/library/sar_sources.html

JPL Radar Page:http://www.jpl.nasa.gov/radar/

SDSU Website:http://www.ssi.sdsu.edu/class/geo647/geol600/insar/winsar.htm

ESA Baseline page:http://odisseo.esrin.esa.it/baseline/baseline.html

SRTM website:http://www.jpl.nasa.gov/srtm


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a guide to insar for geophysics - nevada geodetic...

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