# EE/Ae 157 b Week 4b Interferometric Synthetic Aperture Radar: Differential Inter

## EE/Ae 157 b Week 4b Interferometric Synthetic Aperture Radar: Differential Inter

Ascencio, Fernando, News Director & President has reference to this Academic Journal, PHwiki organized this Journal EE/Ae 157 b Week 4b Interferometric Synthetic Aperture Radar: Differential Interferometry Three-pass repeat track interferometry uses two baselines to acquire interferograms at different times. Despite exaggeration in picture on the right, the incidence angles in addition to absolute ranges are nearly the same. Now suppose that the surface de as long as med slightly between the second in addition to 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 in addition to receiver are in the same place. There as long as e, the interferometric phase is DIFFERENTIAL INTERFEROMETRY HOW DOES IT WORK DIFFERENTIAL INTERFEROMETRY HOW DOES IT WORK (continued) As shown be as long as e, the interferometric phase between the first in addition to second acquisition can be written as Similarly, we can write the interferometric phase between the first in addition to third acquisition as Subtracting the flat earth components, leaves us with the two flattened interferograms:

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DIFFERENTIAL INTERFEROMETRY HOW DOES IT WORK (continued) 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 as long as the third acquisition The topography has to change by an amount equal to the ambiguity height as long as 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 DIFFERENTIAL INTERFEROMETRY HOW DOES IT WORK (continued) 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 there as long as e is related to a change in the range (or path length) to the surface DIFFERENTIAL INTERFEROMETRY What can cause the range to change There could be several causes as long as 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. Vertical Movement Horizontal Movement

DIFFERENTIAL INTERFEROMETRY Typical Applications Tectonic de as long as mations (pre-, co- in addition to post-seismic de as long as mations) Ground subsidence due to oil or groundwater extraction Volcanic inflation in addition to deflation due to magma movement Glacier movement, both regular ice stream movement in addition to 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. DIFFERENTIAL INTERFEROMETRY Provides Dense Spatial Sampling DIFFERENTIAL INTERFEROMETRY Example of Co-Seismic De as long as mation  Eureka Valley On 17 May, 1993, a M6.1 earthquake occurred in the Eureka on the border between Cali as long as nia in addition to 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.

DIFFERENTIAL INTERFEROMETRY Example of Co-Seismic De as long as mation  Eureka Valley The aftershocks define a north-northwest trend, in addition to include two shocks of M~5 in addition to several of M>4. Small surface ruptures as long as med 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, in addition to circles smaller aftershocks Dashed line delineates area shown in radar interferograms DIFFERENTIAL INTERFEROMETRY Example of Co-Seismic De as long as mation  Eureka Valley 14 Sep. 1992 – 23 Nov. 1992 23 Nov. 1992 – 8 Nov. 1993 Difference DIFFERENTIAL INTERFEROMETRY Example of Co-Seismic De as long as mation  Eureka Valley 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 in addition to propagated diagonally upward in addition to southward on a west dipping, north-northeast fault plane, reactivating the largest escarpment in the Saline Range

DIFFERENTIAL INTERFEROMETRY Example of Co-Seismic De as long as mation  Eureka Valley 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 in addition to Rosen, Surface displacement of the 17 May 1993 Eureka Valley earthquake observed by SAR interferometry, Science, 268, 1333-1336, 1995. DIFFERENTIAL INTERFEROMETRY June 28, 1992, M 7.3, L in addition to ers, Cali as long as nia Earthquake DIFFERENTIAL INTERFEROMETRY Example: 1995 North Sakhalin Earthquake (M 7.6) Reference: Tobita, et al., Earth Planets Space, 50, 1998 Radar Differential Interferogram De as long as mation Model Predictions

DIFFERENTIAL INTERFEROMETRY Example of Post-Seismic De as long as mation  L in addition to ers GPS, trilateration, strainmeter, in addition to SAR interferometry (InSAR) data revealed patterns of various scales in the surface de as long as mation field associated with post-seismic processes after the 1992 L in addition to ers 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 DIFFERENTIAL INTERFEROMETRY Example of Post-Seismic De as long as mation  L in addition to ers DIFFERENTIAL INTERFEROMETRY Example of Strain Accumulation  Cali as long as nia

DIFFERENTIAL INTERFEROMETRY Example of Ground Subsidence  LA Basin Regions of ground subsidence include the Pomona (P) area (water), the Beverly Hills (BH) oil field (oil) in addition to localized spots in the San Pedro in addition to Long Beach airport (LBA) area (probably oil industry activity). Noticeable surface uplift is observed in Santa Fe Springs oil field (SFS) in addition to 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. DIFFERENTIAL INTERFEROMETRY Example of Magma Movement  Darwin Volcano, Galapagos Interferogram 1992-1998 Predicted de as long as mation The best fitting point source is 3 km deep DIFFERENTIAL INTERFEROMETRY Example of Magma Movement  Sierra Negra Volcano, Galapagos

DIFFERENTIAL INTERFEROMETRY Example of Magma Movement  Sierra Negra Volcano, Galapagos Point source Magma sill Reference: Amelung, F., S. Jonsson, H. A. Zebker, in addition to P. Segall,, Nature, 407, No.6807, 993-996, 2000. DIFFERENTIAL INTERFEROMETRY Example of Glacier Movement: Ryder Glacier, Greenl in addition to Reference:Joughin et al., Science, 1996 21-22 September 1995 26-27 October 1995 DIFFERENTIAL INTERFEROMETRY Measuring 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 in addition to 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

DIFFERENTIAL INTERFEROMETRY Example of Glacier Tidal Flexing: Nioghalvfjerdsbrae Glacier, Greenl in addition to Reference: Rignot, ESA SP-414, 1997 DIFFERENTIAL INTERFEROMETRY Example of Glacier Recession, Pine Isl in addition to Glacier, Antarctica Reference: Rignot, Science, 1998 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 underst in addition to flow dynamics of the potentially unstable marine ice sheet. Joughin et al , 1999

Temporal Decorrelation from R in addition to om Disturbance Assuming that temporal correlation primarily results from r in addition to om movement of scatterers between observations in addition to that L-b in addition to in addition to P-b in addition to 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.

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