introduction to interferometric synthetic aperture radar - insar there are several applications to...

Introduction to Interferometric Synthetic Aperture Radar - InSAR

There are several applications to InSAR. We shall focus on the mapping of surface deformation.

Principals of InSAR (based largely on: epsilon.nought.de/tutorials/insar_tmr/img0.htm)

Case studies and applications

Change in LOS

1 2

First Acquisition (Master)Second Acquisition (Slave)

5.56 mmMaster

Slave

If:

Earth was flat.The satellite orbit was fixed.

No atmosphere.

Then:

Things were simple, and the calculation of ground deformation would have

been indeed an easy task.

In practice, however, in order to obtain the deformation field, it is necessary to perform quite a few corrections.

Viewing Position Spherical Earth Topography

Atmosphere Deformation

SAR is an active sensor

Unlike passive sensors, the SAR transmits a signal and measures the reflected wave. So the SAR can “see” day-and-night.

The signal wave length was selected such that its absorption by atmospheric molecules is minimal.

ERS

SAR geometry

azimuth

rangeERS1/2

Launch date: ERS1 July 1991 ERS2 April 1995Altitude: 780 kmIncidence angle: 23 degreesPeriod: 100 minutesRepeat time: 35 days

Orbit geometry

Polar (almost) orbit Ascending and descendingGround tracks

Descendingtrack

Ascendingtrack

The (SAR) data

The SAR records the amplitude and the phase of the returned signal

amplitude phase

Note that while the amplitude image shows recognizable topographic pattern, the phase image looks random.

Image from http://epsilon.nought.de/tutorials/insar_tmr/img35.htm

Mt. Etna

The phase

Figure from Rosen et al., 2000

The phase is mostly due to the propagation delay, but also due to coherent sum of contributions from scatters within the resolution element.

The phase

The phase is proportional to the two-way travel distance divided by the transmitted wavelength.

InSAR geometry

Baselines should be less than 200 meters, and the shorter the better!

The baseline, B, is the orbit separation vector.

InSAR processing:amplitude coregistration

The two images, i.e. the “slave” and the “master”, do not overlap. So we need to figure out which group of pixels in the “slave” corresponds to which group of pixels in the “master”. This is done through cross-correlating sub-areas in the two images.


This step requires a huge number of operations, and is by far the most time consuming step in the process.

InSAR processing:phase interferogram

Calculate phase interferogram, i.e. subtract the phase of of the “slave” from that of the “master”.

- =

phase “master” phase “slave” phase interferogram

Note that while both the master and slave appear random, the interferogram does not.

InSAR processing:flat-earth removal

Next, we need to remove the phase interferogram that would result from a flat-earth.

- =

After removing the flat-earth effect we are left with an interferogram that contains topography+deformation between the two acquisitions and atmospheric effect.

InSAR processing:Remove topographic phase

Height of ambiguity: the amount of height change that leads to a 2 change in interferometric change:

€

ha = 2π∂z

∂φ=

rλ sinγ

2B⊥

InSAR processing:Remove topographic phase (cont.)

The longer the baseline, the smaller the topographic height needed to produce a fringe of phase change (or, the longer the baseline is the stronger the topographic imprint).


InSAR processing:unwrapping

The interferogram is a map of an ambiguous phase offset between - and +. In order to recover the absolute unambiguous phase offset, one needs to unwrap the data.

Phase unwrapping is a tricky business, here’s one algorithm:


While the wrapped phase looks like this:

The unwrapped phase looks like this:

* Note that in this specific example the topographic effect has not been removed, thus the unwrapped phase map correspond mainly to topographic height.

InSAR processing:geocoding

This final step amounts to mapping the phase from satellite to geographic coordinates.

Figure from: http://earth.esa.int/applications/data_util/SARDOCS/_icons/c2_SAR_geo2.jpg

latit

ude

longitude

azim

uth

range

The seismic cycle:

Figure from: Wright, 2002.

Seismic displacement:

The utilization of SAR data to map surface deformation started with the ground-breaking study of the 1992 Landers earthquake in California [Massonnet et al., 1993].

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

Seismic displacement (cont.):

It is hard to unwrap the interferogram, if the deformation is discontinuous. In such cases, it is convenient to present the results in wrapped form.

Yellow-red-blue : target moved a way from the satellite.

Red-yellow-blue : target moved towards the satelite.

Figure from: http://www.eorc.jaxa.jp/ALOS/gallery/images/5-disaster/obs-geometry5.gif


It turned out that the crust is an elastic half-space!

4 Dec. 1992, Magnitude 5.1, near Landers - CA


Magnitude 5.6 from Western Iran. Processed and calculated by Maytal Sade


The 1999 Izmit earthquake in Turkey [Wright et al., 2001]


Modeling the data helps to:

Constrain the rupture geometry and co-seismic slip distribution.

Identify triggered slip.



The displacement field projected onto a map view may be obtained by using both the ascending and the descending tracks. In order to go beyond the 2D displacement field, an additional information should be incorporated - the azimuth offset.

The 3-D displacement field in the area of 1999 Hector Mine in California (Fialko et al., 2001):

The 3 equations:

The 3 unknowns:

Inter-seismic displacement:

Obviously, resolving co-seismic (large) deformation is easier than resolving inter-seismic (small) deformation. The signal to noise ratio may be amplified by stacking multiple interferograms (the more the better).

Application of the stacking approach to NAF (Wright et al., 2001):

Because inter-seismic strain accumulates steadily with time, the contribution of each pair is scaled proportionally to the interval between acquisitions.

Inter-seismic displacement (cont.):

Figure from Wright et al., [2001, GRL]

It is useful to form interferogram chains in such a way that each date is used as a master the same number of times it is used as a slave. The atmospheric effect of these acquisitions is exactly canceled out, and we are left only with the atmospheric contribution from the start and the end of the chain (see Holley, 2004, M.Sc. thesis, Oxford).

A recipe for reducing atmospheric contribution:

Earthquake location:

Locating small-moderate quakes in southern Iran (Lohman and Simons, 2005):

Figure from Pritchard, 2006, Physics Today

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