ee/ae 157 b week 4b interferometric synthetic aperture radar: differential interferometry

EE/Ge 157 b, Week 4 4 - 1

EE/Ae 157 bWeek 4b

Interferometric Synthetic Aperture Radar:Differential Interferometry

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• Three-pass “repeat track” interferometry uses two baselines to acquire interferograms at different times.

• Despite exaggeration in picture on the right, the incidence angles and absolute ranges are nearly the same.

• Now suppose that the surface deformed slightly between the second and third acquisitions in such a way that the range changed by an amount

• In the repeat-track implementation of interferometry, the signal travels each path twice, since the transmitter and receiver are in the same place. Therefore, the interferometric phase is

(B1,1); (B2 , 2 )

DIFFERENTIAL INTERFEROMETRYHOW DOES IT WORK?

B2B1

1 2

range4

range22

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DIFFERENTIAL INTERFEROMETRYHOW DOES IT WORK? (continued)

• As shown before, the interferometric phase between the first and second acquisition can be written as

• Similarly, we can write the interferometric phase between the first and third acquisition as

• Subtracting the “flat earth” components, leaves us with the two flattened interferograms:

B2B1

1 2

1011011 cos

4sin

4 BB

4cos

4sin

42022022 BB

1011 cos

4 Bflat

4cos

42022 Bflat

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• Let us look at the flattened phase of the second interferogram in more detail

• The first term is the phase due to the presence of topography

• The second term is related to the change in the range for the third acquisition

• The topography has to change by an amount equal to the ambiguity height for the first term to change by a cycle, whereas only a range change equal to half the wavelength is required to produce the same amount of phase change in the second term

B2B1

1 2

4cos

42022 Bflat

2022 cos

4 Btopo

42change

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• Now, let us rescale the phase of the first interferogram as if it was acquired with the same baseline as the second one:

• Next, we subtract this rescaled interferogram from the second interferogram

• This is the so-called differential interferogram.

• Any residual phase in the differential interferogram therefore is related to a change in the range (or path length) to the surface

B2B1

1 2

)cos(

)cos(

11

2211

B

Bflatflat

412 flatflat

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DIFFERENTIAL INTERFEROMETRYWhat can cause the range to change?

• There could be several causes for a change in range.

• Suppose the surface actually changed in the vertical direction due to subsidence or inflation. The change in range is then

• Or, say the surface moved in the horizontal direction, such as in the case of a glacier. The change in range is then

• Surfaces can move in both directions at the same time, also. In that case, we need more than one measurement looking in different directions to completely measure the movement of the surface.

h cosh

y

Vertical Movement

Horizontal Movement

siny

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DIFFERENTIAL INTERFEROMETRYTypical Applications

• Tectonic deformations (pre-, co- and post-seismic deformations)

• Ground subsidence due to oil or groundwater extraction

• Volcanic inflation and deflation due to magma movement

• Glacier movement, both regular ice stream movement and tidal flexing of glaciers

The major advantage of differential interferometry is the spatial patterns that are measured, as opposed to single point measurements that are typically measured

with GPS receivers.

The major advantage of differential interferometry is the spatial patterns that are measured, as opposed to single point measurements that are typically measured

with GPS receivers.

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DIFFERENTIAL INTERFEROMETRYProvides Dense Spatial Sampling

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DIFFERENTIAL INTERFEROMETRYExample of Co-Seismic Deformation – Eureka Valley

• On 17 May, 1993, a M6.1 earthquake occurred in the Eureka on the border between California and Nevada.

• This earthquake occurred at a depth of 13 km along the west side of the Eureka Valley.

• The focal mechanism of the main shock indicates that the earthquake ruptured a north-northeast-striking fault, steeply dipping to the west.

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DIFFERENTIAL INTERFEROMETRY Example of Co-Seismic Deformation – Eureka Valley

• The aftershocks define a north-northwest trend, and include two shocks of M~5 and several of M>4.

• Small surface ruptures formed in the central part of the Eureka valley (arrow A1 on right).

• Arrow A1 shows location of surface breaks recognized in the field after the earthquake

• Arrow A2 points to fault segment where seismic rupture reached the surface, as inferred from the radar data.

• Large star indicates location of main shock, small stars, locations of aftershocks of magnitude greater than 4.5, and circles smaller aftershocks

• Dashed line delineates area shown in radar interferograms

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14 Sep. 1992 - 23 Nov. 1992 23 Nov. 1992 - 8 Nov. 1993 Difference

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• ERS-1, 3-pass interferograms show that the Eureka Valley earthquake produced an elongated subsidence basin oriented north-northwest, parallel to the trend defined by the aftershock distribution, whereas the source mechanism of the earthquake implies a north-northeast striking normal fault.

• These observations suggest that the rupture initiated at depth and propagated diagonally upward and southward on a west dipping, north-northeast fault plane, reactivating the largest escarpment in the Saline Range

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• The ±3 mm accuracy of the radar observed displacement map over short spatial scales, allowed identification of the main surface rupture associated with the event.

Reference: Peltzer and Rosen, Surface displacement of the 17 May 1993 Eureka Valley earthquake observed by SAR interferometry, Science, 268, 1333-1336, 1995.

Reference: Peltzer and Rosen, Surface displacement of the 17 May 1993 Eureka Valley earthquake observed by SAR interferometry, Science, 268, 1333-1336, 1995.

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DIFFERENTIAL INTERFEROMETRY June 28, 1992, M 7.3, Landers, California Earthquake

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DIFFERENTIAL INTERFEROMETRYExample: 1995 North Sakhalin Earthquake (M 7.6)

Reference: Tobita, et al., Earth Planets Space, 50, 1998

RadarDifferential

Interferogram

Deformation ModelPredictions

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DIFFERENTIAL INTERFEROMETRYExample of Post-Seismic Deformation – Landers

• GPS, trilateration, strainmeter, and SAR interferometry (InSAR) data revealed patterns of various scales in the surface deformation field associated with post-seismic processes after the 1992 Landers earthquake.

• A large scale pattern consistent with after-slip on deep sections of the fault was observed in all data sets

– After-slip models imply vertical movements of up to 4 cm in the 10-20 km range from the fault, which are inconsistent with the range change observed in the InSAR data spanning 1-4 years after the earthquake.

• InSAR data revealed several centimeters of post-seismic rebound in step-overs of the 1992 break with a characteristic decay time of 0.7 years.

– Such a rebound can be explained by shallow crustal fluid flow associated with the dissipation of pore pressure gradients caused by co-seismic stress changes

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DIFFERENTIAL INTERFEROMETRYExample of Post-Seismic Deformation – Landers

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DIFFERENTIAL INTERFEROMETRYExample of Strain Accumulation – California

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Satellite synthetic aperture radar interferometry revealed an undiscovered transient strain pattern along the Blackwater-Little Lake fault system within the Eastern California Shear Zone (See map). The surface strain map obtained by averaging eight years (1992-2000) of ERS (1) radar data shows a 120 km-long, ~20 km-wide zone of concentrated shear between the southern end of the 1872 Owens Valley earthquake surface break and the northern end of the 1992 Landers earthquake surface break. The observed shear zone is continuous through the Garlock fault, which does not show any evidence of localized left-lateral slip during the same time period. A dislocation model of the observed shear indicates that the Blackwater-Little Lake fault is currently creeping below the depth of ~5 km at a rate of 7±3 mm/yr in a right-lateral direction. This rate is about 3 times larger than the long-term geological rate estimated for the Blackwater fault(2) and takes up more than 50% of the entire right-lateral shear distributed across the Eastern California Shear Zone.

This transient slip rate observed in the 1992-2000 ERS radar data and the absence of resolvable slip on the Garlock fault during the same time period may be the manifestation of an oscillatory strain pattern between interacting, conjugate fault systems. Such a cycle provides a possible explanation for the observed clustering of large earthquakes in the ECSZ and on the Garlock fault. In this interpretation, the recent seismicity in the ECSZ (Owens Valley 1872, Landers 1992) may have been triggered by accelerated, localized strain accumulation within the shear zone in the last several hundred years as it is now observed along the Blackwater-Little Lake fault system.

Alternatively the fast, localized shear observed along the Blackwater-Little Lake fault system may have been triggered by the recent large earthquakes at both ends (Owens Valley, 1872 and Landers, 1992) but the mechanism by which these earthquakes may have triggered the observed shallow creep is not understood.

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DIFFERENTIAL INTERFEROMETRYExample of Ground Subsidence – LA Basin

• Regions of ground subsidence include the Pomona (P) area (water), the Beverly Hills (BH) oil field (oil) and localized spots in the San Pedro and Long Beach airport (LBA) area (probably oil industry activity).

• Noticeable surface uplift is observed in Santa Fe Springs oil field (SFS) and east of Santa Ana (SA). Surface uplift in these areas may result from the recharge of aquifers or oil fields with water, or from the poro-elastic response of the ground subsequent to water or oil withdrawal.

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DIFFERENTIAL INTERFEROMETRYExample of Magma Movement – Darwin Volcano, Galapagos

Interferogram 1992-1998 Predicted deformation

The best fitting point source is 3 km deep

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DIFFERENTIAL INTERFEROMETRYExample of Magma Movement – Sierra Negra Volcano, Galapagos

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DIFFERENTIAL INTERFEROMETRYExample of Magma Movement – Sierra Negra Volcano, Galapagos

Point source

Magma sill

Reference:Amelung, F., S. Jonsson, H. A. Zebker, and P. Segall,, Nature, 407, No.6807, 993-996, 2000.

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DIFFERENTIAL INTERFEROMETRYExample of Glacier Movement: Ryder Glacier, Greenland

Reference:Joughin et al., Science, 1996

21-22 September 1995 26-27 October 1995

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DIFFERENTIAL INTERFEROMETRYMeasuring Tidal Displacements on Glaciers

• For most glaciers, the underlying movement of the glacier can be considered constant over extended periods of time.

– The exceptions are mini surges of glaciers as illustrated on the previous page

• The floating “tongue” of the glacier moves up and down because of sea-level changes associated with tides

• If two different velocity maps are constructed as shown in the previous slide, changes between the two differential interferograms are associated with tidal flexture of the glacier

• The position of the grounding (or hinge) line is a sensitive indicator of the mass of the glacier tongue

Glacier

Bedrock

Ocean

Glacier Movement

Tongue MovementTidal

Movement

Grounding Line

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DIFFERENTIAL INTERFEROMETRYExample of Glacier Tidal Flexing: Nioghalvfjerdsbrae Glacier,

Greenland

Reference: Rignot, ESA SP-414, 1997

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DIFFERENTIAL INTERFEROMETRYExample of Glacier Recession, Pine Island Glacier, Antarctica

Reference: Rignot, Science, 1998

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West Antarctic Ice Streams from InSAR

The time evolution of ice stream flow variability is uniquely imaged by

InSAR. Complete coverage by InSAR is needed to understand flow dynamics of the potentially unstable

marine ice sheet.

Joughin et al , 1999

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DIFFERENTIAL INTERFEROMETRYERROR SOURCES

• Uncompensated differential motion– Any residual error in position of the radar will appear as surface deformations

• Atmospheric effects– The expressions derived earlier assumes that the radar signal propagates through a

medium with index of refraction equal to 1. Water vapor in the atmosphere, for example, could modify the index of refraction slightly, leading to an observed differential phase. These artifacts change on relatively small time and spatial scales.

• Temporal decorrelation– If objects move too much, the phase becomes random, and we cannot generate an

interferogram to begin with. This happens in vegetated areas, especially for shorter wavelengths, but could also occur as a result of changing surface conditions (freezing, snow, etc). Also happened for glaciers that move too far between observations.

• Layover– Cannot unwrap the phase to begin with

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Atmospheric Effects

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Atmospheric Effects

Reference: Hansen et al., 1999, Science

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Atmospheric Effects


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Atmospheric Effects


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Temporal Decorrelation

L-band (left) and C-band absolute phase (modulo 2 pi) assuming scattering centers are at the center of each pixel. Pixel size is 10m

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L-band (left) and C-band absolute phase (modulo 2 pi) assuming scattering centers are distributed uniformly randomly within each pixel. Pixel size is 10m

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L-band (left) and C-band interferometric phase (modulo 2 pi) assuming scattering centers are distributed uniformly randomly within each pixel. Pixel size is 10m, baseline is 5 m

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L-band (left) and C-band interferometric phase (modulo 2 pi) assuming scattering centers are distributed uniformly randomly within each pixel. Pixel size is 10m, baseline is 5 m. We further assume a uniformly random movement of 5 mm of the scattering centers between acquisitions.

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L-band (left) and C-band interferometric phase (modulo 2 pi) assuming scattering centers are distributed uniformly randomly within each pixel. Pixel size is 10m, baseline is 5 m. We further assume a uniformly random movement of 5 cm of the scattering centers between acquisitions.

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Scatterer Motion - Temporal Decorrelation

• Motion of scatterers within the resolution cell from one observation to the next will lead to randomly different coherent backscatterphase from one image to another, i.e. “temporal” decorrelation.

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Form of Motion Correlation Function

• The Fourier Transform relation can be evaluated if Gaussian probability distributions for the motions are assumed

where y,z is the standard deviation of the scatterer displacements cross-

track and vertically

Note correlation goes to 50% at about 1/4 wavelength displacements

†

† The is valid if the x and y motions are uncorrelated.

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Temporal Decorrelation from Random Disturbance

• Assuming that temporal correlation primarily results from random movement of scatterers between observations and that L-band and P-band backscatter results from scattering off the same objects then we would expect the temporal correlations to scale by the square of the ratio of wavelengths.

ee/ae 157 b week 4b interferometric synthetic aperture radar: differential interferometry

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