IEEE Geoscience and Remote Sensing Magazine - March 2020 - 73

area. For a repeat-pass SAR paradigm, the interferometric
phase z int (generated by complex multiplication of the
complex signals carried by the two registered SAR images) mainly consists of the flat-Earth phase z flat, topographic phase z topo, orbital error phase z orbit, atmospheric
phase screen (APS) z atm, decorrelation noise phase z noise,
and integer phase cycles 2kr [9], i.e.,
	 z int . z flat + z topo + z atm + z noise + z orbit + z defo + 2kr. (1)
If all of the phase components except z defo in (1) can
be resolved and/or removed, the ground surface deformation along the radar LOS, i.e., d los, can be isolated
from the remaining deformation phase component, i.e.,
d los = m /4r $ z defo; this is the core idea of DInSAR for ground
surface deformation detection.
To this end, z flat and z topo in (1) can first be removed
using accurate error vectors and topography. z noise is then
mitigated by interferometric-phase filtering [10], [11]. Finally,
2kr is determined by phase unwrapping [12]. The z atm can
be mitigated by external data (e.g., GPS, a medium-resolution imaging spectrometer, and a moderate-resolution
imaging spectroradiometer data) or models [13], and z orbit
can be avoided if accurate orbit data are available or can be
reduced (if existing) using polynomial fitting [14]. We refer
interested readers to [4] and [9] for more details about the
DInSAR technique.
The DInSAR technique does have some inherent limitations. First, it can detect only a 1D surface displacement
along the radar LOS direction from a single InSAR pair
[15]. Second, the APS in the interferometric phase is difficult to remove perfectly, which can reduce the accuracy
of LOS deformation observation and may even dominate
the deformation map, even though external data have been
used [16]-[18]. Third, the residual orbital and decorrelation noise phases can further reduce the accuracy of LOS
deformation estimation. Finally, DInSAR cannot work in
those areas where deformation gradients exceed the detectable gradient of InSAR pairs [19]. To reduce the effects of
the aforementioned limitations as much as possible, SAR
images with long wavelengths (e.g., L band), high spatial
resolution, and short time separation are preferable for
DInSAR-based mining deformation monitoring.
MULTIPLE-APERTURE INTERFEROMETRY
Multiple-aperture interferometry (MAI) is a common technique used for detecting ground surface along-track (or
azimuth) deformation, rather than the LOS direction for
DInSAR, from the phase information of SAR images [20].
This technique first creates four subaperture SAR images
from two coregistered SAR images over the same area using split-beam InSAR processing [20], [21]. Forward- and
backward-looking interferograms are then generated from
these four created subaperture images. For an azimuth
displacement d azi, the forward- and backward-looking interferometric phases, i.e., z forward and z backward, can be expressed as [20]
MARCH 2020

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

	

4r
a
$ d azi $ sin` i SQ + 4 j
m
*
4r
a , (2)
z backward = $ d azi $ sin` i SQ - 4 j
m
z forward = -

where i SQ and a denote the radar nominal "squint" angle
and antenna angular beamwidth, respectively. Differentiating the forward- and backward-looking interferometric
phases obtains
	

z MAI = z forward - z backward

a
2r
4r
=$ d azi $ 2 $ sin 4 $ cos i SQ . l $ d azi,
m

(3)

where a . m /l, with l being the antenna length. Finally,
the azimuth deformation can be estimated from the MAI
phases by d azi = l/2r $ z MAI, based on (3).
It is noted that a minor difference between the perpendicular baselines of the created forward- and backwardlooking interferograms may cause a disturbance in MAI
measurements. Generally, this disturbance can be fitted
and further removed by a second-order polynomial model
[22]. Furthermore, ionospheric electron concentration is
likely to cause significant errors in MAI measurements,
especially for SAR images with long wavelengths; this can
be minimized by a directional filtering and interpolation
procedure [23]. It should also be pointed out that the MAI
technique is very sensitive to interferometric coherence and
that the accuracy of MAI measurements will be poor for
those mining areas with low coherence [20].
PIXEL-OFFSET TRACKING
Unlike the phase-based DInSAR and MAI techniques, pixel
offset tracking (OT) can measure ground surface deformation along both the LOS and azimuth directions, based on
either the amplitude or phase information of two coregistered SAR images [24], [25]. This technique first obtains the
range (i.e., LOS) and azimuth offsets of two SAR images over
the same area using the cross-correlation algorithm based
on amplitude images [26] or the fringe visibility algorithm
based on complex images [27]. The range and azimuth offsets, i.e., R OT and A OT, respectively, can be approximated by
	

'

R OT . R orbit + R stero + R defor + R noise
, (4)
A OT . A orbit + A stero + A defor + A noise

where R orbit, R stero, R defor, and R noise denote the offsets
due to orbit separation, stereoscopic effects, the surface
deformation component, and noise in the range direction, respectively; and A orbit, A stero, A defor, and A noise, respectively, represent the offsets due to the same factors,
but in the azimuth direction. The offset contributions of
the orbit separation and stereoscopic effects (in both the
range and azimuth directions) can be removed using accurate orbit and topography data [28]. The noise offsets
R noise and A noise can be mitigated using filtering. Finally,
the ground surface displacements along the LOS and azimuth directions can be retrieved from the remaining offset measurements [24].
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IEEE Geoscience and Remote Sensing Magazine - March 2020

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